30625 Volume 15 2001 Number 2 ' XI- vg / sv4t'x'4.;. 7; -l *- ,.-~ 7,- OXF;ORD I SSN 02s S 6 ()7 THE WORLD BANK ECONOMIC REVIEW EDITOR FranSois Bourguignon, World Bank EDITORIAL BOARD Abhijit Banerjee, MassachusettsInstitute of Justin Yifil Lin, China CenterforEconomic Technology, USA Research, Peking University, China Kaushik Basu, CornellUniversity, USA Mustapha Kamel Nabli, WorldBank Tim Besley,London SchoolofEconomics,UK Juan Pablo Nicolini, Universidaddi Tella, Anne Case, PrincetonUniversity, USA Argentina Stijn A. Claessens, UniversityofAmsterdam, Howard Pack, UniversityofPennsylvania,USA TheNetherlands Jean-Philippe Platteau, Facult/s Universitaires Paul Collier, WorldBank Notre-Dame de laPaix, Belgium David R. Dollar, World Bank Boris Pleskovic, World Bank Antonio Estache, WorldBank Martin Ravallion, WorldBank Augustin Kwasi Fosu,African Economic Carmen Reinhart, UniversityofMaryland, USA Research Council, Kenya Mark R. Rosenzweig, University of Mark Gersovitz, TheJohns Hopkins Pennsylvania, USA University, USA Joseph E. Stiglitz, Stanford University, USA Jeffrey S. Hammer, WorldBank Moshe Syrquin, UniversityofMiami, USA Karla Hoff, WorldBank Vinod Thomas, WorldBank Gregory K. Ingram, WorldBank Jan Willem, FreeUniversity,Amsterdam, The Ravi Kanbur, Cornell University, USA Netherlands Elizabeth M. King, WorldBank L. Alan Winters, UniversityofSussex,UK TheWorldBankEconomicReview is aprofessionaljournal for the dissemination of World Bank-sponsored and outside research that may inform policy analyses and choices. It is directed to an international readership among economists and social scientists in government, business, and international agencies, as well as in universities and development researchinstitutions. The Review emphasizes policyrelevanceand operational aspects of economics,rather than primarily theoretical and methodological issues.It isintended for readers familiar with economic theory and analysis but not necessarilyproficient in advanced mathematical or econometric techniques. Articles will illustrate how professional research can shed light on policy choices. Inconsistency with Bank policy will not be grounds for rejection of an article. Articles willbe drawn from work conductedby World Bank staffand consultants and from papers submitted by outside researchers. Before being accepted for publication, all articles will bereviewed by two referees who are not members of the Bank's staffand oneWorld Bank staffmember. Articles must alsobe recommended by a member of the Editorial Board. Non-Bank contributors are requested to submit a proposal of not more than two pages in length to the Editor or a member of the Editorial Board before sending in their paper. Comments or brief notes responding to Review articles are welcome and will be considered for publication to the extent that spacepermits. Please direct alleditorial correspondence to the Editor, The WorldBank Economic Review, The World Bank, 1818 H Street, Washington, DC 20433, USA, or wber@worldbank.org. For more information, please visit the Web sites of the EconomicReview at www.wber.oupjournals.org, the World Bank at www.worldbank.org, and Oxford University Press at www.oup-usa.org. THE WORLD BANK ECONOMIC REVIEW Volume 15 - 2001 * Number 2 WHAT HAVE WE LEARNED FROM A DECADE OF EMPIRICAL RESEARCH ON GROWTH? It's Not Factor Accumulation: Stylized Facts and Growth Models 177 William Easterlyand RossLevine Comment on "It's Not Factor Accumulation: Stylized Facts and Growth Models" 221 Pete Klenow Comment on "It's Not Factor Accumulation: Stylized Facts and Growth Models" 225 Paul Romer Growth Empirics and Reality 229 WilliamA. Brockand Steven N. Durlauf Comment on "Growth Empirics and Reality" 273 Lant Pritchett Comment on "Growth Empirics and Reality" 277 Xavier Sala-i-Martin Applying Growth Theory across Countries 283 RobertM. Solow Crisis Transmission: Evidence from the Debt, Tequila, and Asian Flu Crises 289 Jose'De Gregorioand Rodrigo0. Valde's Mutual Fund Investment in Emerging Markets: An Overview 315 GracielaL. Kaminsky,Richard K Lyons, and Sergio L. Schmukler The World Bank Economic Review (ISSN 0258-6770) is published three times ayear by Oxford University Press, 2001 Evans Road, Cary, NC 27513-2009 for The International Bank for Reconstruction and Development / THE WORLD BANK. Communications regarding original artides and editorial management should be addressed to The Editor, The World BankEconomicReview, 66, avenue d'1ena, 75116 Paris, France. E-mail: wber@worldbank.org. Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide. SUBSCRIPTIONS: Subscription is on a yearly basis.The annual rates are US$40 (£30 in UK and Europe) for individuals; US$90 (£63 in UK and Europe) for academic libraries; US$110 (£75 in UK and Europe) for corporations. Single issues are available for US$17 (£13 in UK and Europe) for individuals; US$38 (£26 in UK and Europe) for academic libraries; US$46 (£31 in UK and Europe) for corporations. All prices in- clude postage. Individual rates are applicable only when a subscription is for individual use and are not available if delivery ismade to a corporate address. Subscriptions are providedfree of charge to non-OECD countries. All subscription requests, single issue and back issue orders, changes of address, and claims for missing issues should be sent to: NorthAmerica: Oxford University Press, Journals Customer Service, 2001 Evans Road, Cary, NC 27513- 2009, USA. Toll-free in the USA and Canada: 800-852-7323, or 919-677-0977. Fax:919-677-1714. E-mail: jnlorders@oup-usa.org. Elsewhere: Oxford University Press, Journals Customer Service, Great Clarendon Street, Oxford OX2 6DP, UK. Tel: +44 1865 267907. Fax: +44 1865 267485. E-mail: jnl.orders@oup.co.uk. ADVERTISING: Helen Pearson, Oxford Journals Advertising, P.O. Box 347, Abingdon SO, OX14 1GJ, UK. Tel/Fax: +44 1235 201904. E-mail: helen@oxfordads.com. REQUESTS FOR PERMISSIONS, REPRINTS, AND PHOTOCOPIES: Allrightsreserved;nopart of this publica- tion may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, elec- tronic, mechanical, photocopying, recording, or otherwise, without either prior written permission of the publisher (Oxford UniversityPress,Journals Rights and Permissions,Great Clarendon Street, Oxford OX2 6DP, UK; tel: +44 1865 267561; fax: +44 1865 267485) or a license permitting restricted copying issued in the USA by the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923 (fax: 978- 750-4470), or in the UK by the Copyright Licensing Agency Ltd., 90 Tottenham Court Road, London WlP 9HE, UK. Reprints of individual articles are available only from the authors. COPYRIGHT: Copyright (C)2001 The International Bank for Reconstruction and Development / THE WORLD BANK. It is acondition of publication in thejournal that authors assign copyright to The International Bank for Reconstruction and Development / THE WORLD BANK. However, requests for permission to reprint material found in the journal should come to Oxford University Press. This ensures that requests from third parties to reproduce articles are handled efficiently and consistently and will also allow the article to be disseminated as widely as possible. Authors may use their own material in other publications provided that the journal is acknowledged as the original place of publication and Oxford University Press is noti- fied in writing and in advance. INDEXING AND ABSTRACTING: The WorldBank EconomicReview is indexed and/or abstracted by CAB Abstracts, Current Contents/Socialand Behavioral Sciences,Journal of EconomicLiterature/EconLit, PAIS International, RePEc (Research in Economic Papers), and Social Sciences Citation Index. The microform edi- tion is available through UMI, 300 North Zeeb Road, Ann Arbor, MI 48106, USA. PAPER USED: The WorldBank EconomicReview is printed on acid-free paper that meets the minimum requirements of ANSI Standard Z39.48-1984 (Permanence of Paper). POSTAL INFORMATION: The WorldBank EconomicReview (ISSN 0258-6770) is published three times a year by Oxford University Press, 2001 Evans Road, Cary, NC 27513-2009. Send address changes to The WorldBankEconomicReview, Journals Customer ServiceDepartment, Oxford University Press,2001 Evans Road, Cary, NC 27513-2009. THE WORLD BANK ECONOMIC REVIEW, VOL. 15, NO. Z I77-219 What have we learnedfrom a decade of empiricalresearchon growth? It's Not Factor Accumulation: Stylized Facts and Growth Models William Easterlyand Ross Levine The article documents five stylized facts of economic growth. (1) The "residual" (total factor productivity, accounts for most of the in- TFP) rather than factor accumulation come and growth differences across countries. (2) Income diverges over the long run. (3) Factor accumulation is persistent while growth is not, and the growth path of coun- tries exhibits remarkable variation. (4) Economic activity is highly concentrated, with all factors of production flowing to the richest areas. (5) National policies are closely associated with long-run economic growth rates. These facts do not support models with diminishing returns, constant returns to scale, some fixed factor of production, or an emphasis on factor accumulation. However, empirical work does not yet deci- sively distinguish among the different theoretical conceptions of TFP growth. Econo- mists should devote more effort toward modeling and quantifying TFP. The central problem in understanding economic development and growth is not understanding the process by which an economy raises its savings rate and in- creases the rate of physical capital accumulation.1 Although many development practitioners and researchers continue to target capital accumulation as the driv- William Easterly is senior advisor, Development Research Group, at the World Bank. His e-mail address is weasterly@worldbank.org. Ross Levine is with the University of Minnesota. His e-mail ad- dress is rlet'ine@csonm.wn.edu. The authors are grateful to Lant Pritchett, who shaped the paper, gave comments, and provided many of the "stylized facts." They also thank Francois Bourguignon, Ashok Dhareshwar, Robert G. King, Michael Kremer, Peter Klenow, Paul Romer, Xavier Sala-i-Martin, Roh- ert Solow, Albert Zeufack, two anonymous referees, and students and faculty at the Economics Educa- tion Research Consortium program in Kiev, Ukraine, Harvard University's Kennedy School of Govern- ment, and Johns Hopkins School of Advanced International Studies for useful comments. An earlier version of this article was presented at the World Bank conference "What Have We Learned from a Decade of Empirical Research on Growth?" held on 26 February 2001. 1. This is a reversal and slight rewording of Arthur Lewis's (1954, p. 155) famous quote, "The central problem in the theory of economic development is to understand the process by which a com- munity which was previously saving and investing 4 or 5 percent of its national income or less, con- verts itself into an economy where voluntary saving is running at about 12 to 15 percent of national income or more. This is the central problem because the central fact of development is rapid capital accumulation (including knowledge and skills with capital)." Though Lewis recognizes the impor- many tance of knowledge and skills and later in his book highlights the importance of institutions, development economists who followed Lewis adopted the more limited focus on savings and physi- cal capital accumulation. (C2001 The International Bank for Reconstruction and Development / TH- WORI) BANK 177 178 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. Z ing force in economic growth,2 "something else" besides capital accumulation is critical for understanding differences in economic growth and income across countries. This conclusion is based on evidence on the sources of economic growth, the patterns of economic growth, the patterns of factor flows, and the impact of national policies on economic growth. This study does not argue that factor accumulation is unimportant in general or deny that it is critically important for some countries at specific junctures. As Robert Solow noted in 1956, economists construct models to reproduce crucial empirical regularities and then use these models to interpret economic events and make policy recommendations. Thisarticle documents important empirical regu- larities about economic growth with the hope of highlighting productive direc- tions for future research and improving public policy. I. SOMETHING ELSE A growing body of research suggests that, even after physical and human capi- tal accumulation are accounted for, something else accounts for the bulk of cross- country differences in the leveland growth rate of gross domestic product (GDP) per capita. Economists typically refer to the something else as total factor pro- ductivity (TFP). This article follows that convention. Different theories offer very different conceptions of TFP. These range from changes in technology (the instructions for producing goods and services)to the role of externalities, changes in the sector composition of production, and the adoption of lower-cost production methods. Evidence that confidently assesses how well these conceptions of TFP explain economic growth is lacking. Econo- mists need to provide much more shape and substance to the amorphous term TFP, distinguishing empirically among these different theories. This article examines five stylized facts that illuminate TFP and its determi- nants to enable more precise modeling of long-run economic growth and the design of appropriate policies. 2. Academic researchers in the 1990s started a "neoclassical revival" (in the words of Klenow and Rodriguez-Clare 1997b). The classic works in the academic literature's stress on factor accumulation were Mankiw, Romer, and Weil (1992); Barro and others (1995); Mankiw (1995); and Young (1995). The summary of the Global Development Network conference in Prague in June 2000, representing many international organizations and development research institutes, says "physical capital accumu- lation was found to be the dominant source of growth both within and across regions. Total factor productivity growth (TFPG) was not as important as was previously believed" (u'ww.gdnet.org/pdfs/ GRPPragueMtgReport.pdfl. A leading development textbook (Todaro 2000) says that an increase in investment is "a necessary condition" for economic takeoff. The development textbook of Ray (1998, p. 54) refers to investment and saving as "the foundations of all models of economic growth." Many development practitioners also stress investment. For example, the International Monetary Fund (Hadjimichael and others 1996, p. 1) argues, "The adjustment experience of sub-Saharan Africa has demonstrated that to achieve gains in real per capitaGDP an expansion in private saving and investment is key." The Bank for International Settlements (1996, p. 50) concludes, "Recent experience has under- lined the central importance of national saving and investment rates in promoting growth." And the International Labor Organization (1995, p. 12) argues that "policies to raise the rate of investment ... I Easterly and Levine 179 * Stylized fact 1. Factor accumulation does not account for the bulk of cross- country differences in the levelor growth rate of GDP per capital;something else-TFP-does. In the search for the secrets of long-run economic growth, a high priority should go to rigorously defining TFP, empirically dissecting it, and identifying the policiesand institutions most conducive to its growth. * Stylized fact 2. There are huge and growing differences in GDI' per capita; divergence-not conditionalconvergence-is the bigstory. An emphasis on TFP growth with increasing returns to technology is more consistent with divergence than are models of factor accumulation with decreasing returns, no scale economies, and some fixed factor of production. Over the past two centuries, the big story has been the widening difference between the richest and the poorest countries. Moreover, the growth rates of the rich are not slowing, and returns to capital are not falling.Just as business cycles look like little wiggles around the big story when viewed over a long hori- zon, understanding slow, intermittent conditional convergence seems less intriguing than uncovering why the United States has enjoyed steady growth for 200 years while much of world still lives in poverty. * Stylized fact 3. Growth is not persistent over time, but capitalaccumulation is. Some countries take off, others experience peaks and valleys, a few grow steadily, and some have never grown. Changes in factor accumulation do not closelytrack changesineconomicgrowth. This findingisconsistent across very different frequencies of data. Tangentially, but critically, this stylized fact also suggests that models of steady-state growth, whether based on capital externalities or technological spillovers,will not capture the experiences of many countries. While steady-state growth models may fit U.S. experience over the past 200 years, these models will not fit the experiences of Argen- tina, the Republic of Korea, Thailand, or Venezuela very well. In contrast, models of multiple equilibria do not fit the U.S.data verywell. Thus models tend to be country-specificrather than general theories. Meanwhile, empiri- cal work is still going on to explain why the United States is different, how are critical for raisingthe rate of growth and employment in an economy." Finally "additional invest- social arena" ment is the answer-or part of the answer-to most policy problems in the economic and (United Nations 1996, p. 8). Similarly, the World Bank (1993, p. 191) states that inEast Asia, "accu- p. 10, 23) mulation of productive assets is the foundation of economic growth." World Bank (1995, promises that in Latin America "enhancing saving and investment by 8 percentage points of GDP would raise the annual growth figure by around 2 percentage points." The World Bank (2000a, p. 10) says the saving rate of the typical African country "is far below what is needed to sustain a long-term boost in economic performance." The World Bank (2000c, p. 1) says that southeastern Europe can seize trade opportunities only if "domestic and foreign entrepreneurs increase their investment dramatically." For more citations, see Easterly (I 999a) and King and Levine (I1994).Although common, the stress on capital accumulation is far from universal among development practitioners and researchers. For example, the World Bank (2000b, p. 4) report on East Asia's recovery suggests that "future growth hinges less on increasing physical capital accumulation and more on raising the productivity growth of all factors." Collier, Dollar, and Stern (2000) stress policies, incentives, institutions, and exogenous factors as the main drivers in growth with little mention of investment, as does World DeVelopment Report 2000/ 2001 (World Bank 2000/2001, pp. 49-52). 180 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. 2 Argentina can go from being like the United States early in this century to the struggling middle-income country it is today, and how Korea or Thai- land can go from being like Somalia to having thriving economies. * Stylized fact 4. All factors of production flow to the same places, suggesting important externalities.Although this has been noted and modeled by Lucas (1988), Kremer (1993), and others, this article further demonstrates the per- vasive tendency for all factors of production, including physical and human capital, to bunch together. As a consequence, economic activity is highly concentrated. This tendency holds whether consideringthe world, countries, regions, states, ethnic groups, or cities. Thus the something else that accounts for the bulk of differences in growth across these units needs to be fleshed out and givena prominent position in theories and policyrecommendations. * Stylized fact 5. National policies influence long-run growth. In models with zero productivity growth, diminishing returns to factors of production, and some fixed factor, national policies that boost physical or human capital accumulation have only a transitional effect on growth. In models that emphasizeTFP growth, national policies that enhance the efficiencyof capital and labor or alter the endogenous rate of technological change can boost productivity growth and accelerate long-run economic growth. Thus the finding that policy influences growth is consistent with theories that em- phasize productivity growth and technological externalities and cast increas- ing doubt on theories that focus excessively on factor accumulation. Although many economists have examined TFP growth and assessed growth models, this article makes several new contributions. Besides conducting tradi- tional growth accounting with new Penn-World Table 5.6 capital stock data, this article fully exploits the panel nature of the data. Using an international cross- section of countries, it addresses two questions: * What accounts for cross-country growth differences? * What accounts for growth differences over time? Overwhelmingly the answer isTFP, not factor accumulation. The article also examines differences in the level of GDP per worker across countries. It updates Denison's (1962) original level accounting study and ex- tends Mankiw, Romer, and Weil's (1992) study by allowing technology to dif- fer across countries and by assessing the importance of country-specific effects. Unlike Mankiw, Romer, and Weil (1992), it finds that large differences in TFP account for the bulk of cross-country differences in income per capita, even controlling for country-specific effects. The article also compiles new information documenting massive divergence in the levelof income per capita across countries. Although many studies base their modeling strategies on the U.S. experience of steady long-run growth (see, for ex- ample, Jones 1995a, 1995b; and Rebelo and Stokey 1995), the U.S. experience is the exception. In much of the world miracles and disasters and changing long-run Easterly and Levine 181 growth rates are the rule, not stable long-run growth rates. Finally, the article pre- sents abundant new evidenceon the concentration of economic activity, drawing on cross-country information, county-leveldata for the United States, developing country studies, and information on the international flow of capital, labor, and human capital to demonstrate the geographic concentration of activity and relate this to models of economic growth. The overwhelming concentration of economic activity isconsistent with some theories of economic growth and inconsistentwith others. Though individual countries at specificpoints in their development fit dif- ferent models of growth, the big picture emergingfrom cross-country growth com- parisons is that creating the incentivesfor productive factor accumulation is more important for growth than factor accumulation itself. II. STYLIZED FACT I. IT'S NOT FACTOR ACCUMULATION, IT'S TFP Although physical and human capital accumulation may play key roles in igniting and accounting for economic progress in some countries, something else-TFP- accounts for the bulk of cross-country differencesin the leveland growth of GDP per capita in a broad cross-section of countries. The empirical importance of TFP has motivated economists to develop models of TFP. These focus variously on tech- nologicalchange (Aghionand Howitt 1998; Grossman and Helpman 1991; Romer 1990); impediments to adopting new technologies (Parente and Prescott 1996); externalities (Romer 1986; Lucas 1988); sectoral development (Kongsamut, Rebelo, and Xie 1997); or cost reductions (Harberger 1998). This section briefly presents evidence on factor accumulation and growth and discusses the implications for models and policy. It considers three questions. First, what part of a country's growth rate is accounted for by factor accumula- tion and TFP growth? Looking at the sources of growth in individual countries over time helps answer this question. Second, what part of cross-ccuntry differ- ences in economic growth rates is accounted for by cross-country differences in growth rates of factor accumulation and TFP? Third, what part of the inter- temporal difference in economic growth rates is accounted for by time-series differences in growth rates of factor accumulation and TFP? Traditional growth accounting forms the basis for answering these questions. Growth Accounting The organizing principle of growth accounting is the Cobb-Douglas aggregate production function: (1) y = Ako(nla), where y is national output per person, 3 A is technological progress, k is the physi- cal capital stock per person, n is the number of units of labor input per person 3. We switch between output per worker andoutput per person depending on data availability and what's appropriate foreach usage. 182 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. 2 (reflecting work patterns, human capital, and the like), and a is a production function parameter (equal to the share of capital income in national output under perfect competition). Output growth isthen divided into components attributable to changes in the factors of production. Rewriting equation 1 in growth rates: (2) (Ay / y) = (AA I A) + a(Ak / k) + (1 - a)(An / n). Consider a hypothetical country with a growth rate of output per person of 2 percent, growth in capital per capita of 3 percent, growth in human capital of 0, and capital's share of national income of 40 percent (a = 0.4). In this example, TFPgrowth is 0.8 percent, and therefore, TFP-growth accounts for 40 percent (0.8/2) of output growth in this country. DETAILEDGROWTH ACCOUNTING. Many researchers conduct detailed growth ac- counting exercises of one or a few countries, using disaggregated data on capi- tal, labor, human capital, and capital shares of income. Early, detailed growth accounting exercises of a few countries by Solow (1957) and Denison (1962, 1967) found that the rate of capital accumulation per person accounted for be- tween one-eighth and one-fourth of GDPgrowth rates in the United States and other industrialized countries, whereas TFP-growthaccounted for more than half of GDPgrowth in many countries. Subsequent studies showed that it is important to account for changes in the quality of labor and capital (see papers in Jorgenson 1995). For example, if growth accountants fail to consider improvements in the quality of labor inputs due to improved education and health, they would assign these improvements to TFPgrowth. Unmeasured improvements in physical capital would similarly be inappropriately assigned to TFP. Nonetheless, to the extent that TFPincludes quality improvements in capital, a finding that TFP explains a substantial amount of economic growth will properly focus attention on productivity rather than on factor accumulation itself. Later detailed growth accounting exercises for a few countries incorporated estimates of such changes in the quality of human and physical capital (table 1).4 These studies also find that TFP growth tends to account for a large component of the growth of output. Christenson, Cummings, and Jorgenson (1980) do this for a few Organisation for Economic Co-operation and Development (OECD) countries, albeit prior to the productivity growth slowdown. Dougherty (1991) does the exercise for some OECDcountries including the slow productivity growth period. Elias (1990) conducts a rigorous growth accounting study for seven Latin American countries. Young (1995) focuses on fast growing East Asian countries. Although there are large cross-country variations in the fraction of growth ac- counted for by TFP growth, some general patterns emerge. TFP growth accounts 4. We use the summary in Barro and Sala-i-Martin (1995, pp. 380-81). Easterly and Levine 183 for about half of output growth in OECD countries. Variation is greater among Latin American countries, with an average of 30 percent. Young (1995) argues that factor accumulation was a key component of the growth miracle in some East Asian economies. These detailed growth accounting exercises may seriously underestimate the influenceof TFP growth on growth in output per worker as emphasized by Kienow and Rodriguez-Clare (1997a). The studies summarized in table 1 examine out- put growth. If the analysis is adjusted to focus on output per worker, TFP growth accounts for a much larger share of output per worker growth than for the out- put growth figures in table 1. In an extension of Young (1995), Klenow and Rodriguez-Clare (1997a) show that factor accumulation plays the crucial role Results for Individual Countries TABLE 1. Selected Growth Accounting (percent) Share of capital Share contributed by innational TFP Economy output GDPgrowth Capital Labor OECD 1947-73 41 4 55 France .40 5.40 41 3 56 Germany .39 6.61 34 2 64 Italy .39 5.30 35 23 42 Japan .39 9.50 1 52 United Kingdom .38 3.70 47 24 33 United States .40 4.00 43 OECD 1960-90 58 1 41 France .42 3.50 59 -8 49 Germany .40 3.20 49 3 48 Italy .38 4.10 57 14 29 Japan .42 6.81 -4 52 United Kingdom .39 2.49 52 42 13 United States .41 3.10 45 Latin America 1940-80 43 26 31 Argentina .54 3.60 51 20 29 Brazil .45 6.40 34 26 40 Chile .52 3.80 40 23 37 Mexico .69 6.30 57 34 9 Venezuela .55 5.20 East Asia 1966-90 28 30 Hong Kong, China .37 7.30 42 32 -5 Singapore .53 8.50 73 42 12 Korea, Rep. of .32 10.32 46 40 20 Taiwan, China 0.29 9.10 40 (1991); Source: For OECD,Christenson, Cummings, and Jorgenson (1980)and Dougherty for Latin America, Elias (1990);for East Asia,Young (1995). 184 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. Z only in Singapore (a small city-state) but in none of the other East Asian miracle economies. In addition, the share attributed to capital accumulation may be exaggerated because it does not take into account how much TFPgrowth induces capital accumulation (Barro and Sala-i-Martin 1995, p. 352.) In sum, although there are cases in which factor accumulation is closely tied to economic success, detailed growth accounting examinations suggest that TFP growth frequently accounts for the bulk of growth in output per worker. AGGREGATE GROWTH ACCOUNTING. There are also aggregate growth account- ing exercises of a large cross-section of countries that use a conglomerate measure of capital and an average value of the capital share parameter from microeconomic studies. King and Levine (1994) and Nehru and Dhareshwar (1994) make some initial estimates of the capital stocks of countries in 1950. They then use aggre- gate investment data and assumptions about depreciation rates to compute capi- tal stocks in later years for over 100 countries. The importance of the estimate of the initial capital stock diminishes over time due to depreciation. This study uses the new Penn-World Table (PWT) 5.6 capital stock data, based on disaggregated investment and depreciation statistics for 64 countries. Though these data exist for a smaller number of countries, they suffer from fewer aggre- gation and measurement problems than the aggregate growth accounting exer- cises using less precise data. 5 5. The Penn World Tables document the construction of these data. Capital stock figures were also constructed for more countries using aggregate investment figures. For some countries, the data start in 1951. These data use real investment in 1985 prices and real GDP per capita (chain index) in constant 1985 prices. A perpetual inventory method was used to compute capital stocks. Specifically, let K(t) equal the real capital stock in period t. Let I(t) equal the real investment rate in period t. Let d equal the depreciation rate, assumed to be .07. Thus, the capital accumulation equation states that K(t+l) = (1 -d) K(t) +I(t). To compute the capital per worker ratio, divide K(t) by L(t), where L(t) is the working age population in period t as defined in the Penn World Tables. To compute the capital-output ratio, divide K(t) by Y(t), where Y(t) is real GDP per capita in period t. To make an initial estimate of the capital stock, we make the assume that the country is at its steady-state capital-output ratio. Thus in terms of steady-state value, let k = K/Y, let g = the growth rate of real output, let i = IIY. Then, from the capital accumulation equation plus the assumption that the country is at its steady-state, k = i/(g + d). Thus, with reasonable estimates of the steady-state values of i, g, and d, a reasonable estimate of k can be computed. The Penn World Tables have data on output back to 1950. Thus, the initial capital stock estimate can be computed as kY(initial). To make the initial estimate of k, the steady state capital out- put ratio, set d = .07. The steady-state growth rate g is computed as a weighted average of the countries average growth rate during the first ten years for which we have output and investment data and the world growth rate , computed as 0.0423. Based on Easterly and others (1993), the world growth rate is given a weight of 0.75 and the country growth rate 0.25 in computing an estimate of the steady-state growth rate for each country. Then i can be computed as the average investment rate during the first ten years for which there are data. Thus, with values for d, g, and i for each country, k can be estimated for each country. Average real output value between 1950-52 is used as an estimate of initial output, Y(initial), toreduce the influence of business cycles in estimating Y(initial). Thus the capital stock in 1951 is given as Y(initial)k. If output and investment data do not start until 1960, everything is moved up one decade for that country. Given depreciation, the guess at the initial capital stock becomes rela- tively unimportant decades later. Easterly and Levine 185 The aggregate growth accounting results for a broad selection of countries also emphasize growth. There is enormous cross-country TFP'S role in economic growth. In variation in the fraction of growth accounted for by capital and TFI' the average country, considering only physical capital accumulation, TFP growth accounts for about 60 percent of growth in output per worker using the PWT 5.6 capital data and setting the share of capital in national output (a) at .4, which is consistent with individual country studies. Other measures of the capital stock from King and Levine (1994) and Nehru and Dhareshwar (1993) yield similar results. Aggregate growth accounting results are illustrated in figure 1usinlgdata from PWT 5.6 for 1980-92. Countries aregrouped by decilebased on output per capita growth, from the slowest growing (group 1) to the fastest. Capital growth gen- erally accounts for less than half of output growth, and the share of growth ac- countries. counted for by larger in the faster growing TFP growth is frequently capital There are large differences across countries in the relationship between accumulation and growth. For example, Costa Rica, Ecuador, Peru, and Syria all saw real per capita 1 percent a year, while real per GDP fall by more than capita capital stocks grew by more than 1 percent a year and educational attain- ment was rising. Clearly, these factor injections were not being used productiv- ity. Albeit unrepresentative, these cases illustrate the shortcoming of focusing too heavily on factor accumulation.6 Incorporating estimates of human capital accumulation into these aggregate growth accounting exercises does not materially alter the findings. In the aver- age country, for more than half of growth in output TFP growth still accounts per worker. Moreover, the data suggest a weak-and sometimes inverse-rela- tionship between improvements in educational attainment of the labor force and and Pritchett growth of output per worker growth. Benhabib and Spiegel(1994) (2001), using cross-country data on economic growth rates, show that increases in human capital resulting from improvements in educational attainment have not positively affected the growth in output per worker (perhaps because of a mismatch between education and the skills needed for activities that generate social returns). There is disagreement, however. Krueger and Lindahl (1999) argue that mea- surement error accounts for the failure to find a relationship between growth find per capita and human capital accumulation. Hanushek and Kimko (2000) that the quality of education is strongly linked with economic growth. Klenow (1998) demonstrates that models that highlight the role of ideas and productiv- ity growth do a much better job of matching the data than models that focus on the accumulation of human capital. More work is needed on the relationship between education and economic development. 6. It may be that the conventional measure of investment effort is a cost-based measure that does makes this point, not translate necessarilyinto increasingthe value of thecapital stock.Pritchett (1999) especially-but not only-with regard to public investment. 186 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. Z FIGURE 1. Growth Accounting: Growth Rates by Decile 7% 6% ~J4% E Residual 3% E CapitalShare El 2% 1% -e -1% 2 -2% -3% _ . _ J -4% I 1 2 3 4 5 6 7 Poor 8 9 10 Rich Income Decile (CapitalStock EstirnatesfromPWT 5.6) VarianceDecomposition Although traditional growth accounting measures that part of a country's growth rate that may be attributable to factor accumulation, this study uses variance decomposition to construct indicators of that part of cross-country differences in economic growth rates accounted for by cross-country differences in TFP and factor growth (Jones 1997). Assuming that ox= .4, the following holds for the cross-section of countries: (3) VAR(Ay/y) = VAR(ATFP/TFP) + (0.4)2fVAR(Ak/k)} + 2(0.4)fcov(ATFP/TFP, Aklk)). Decomposing the sources of growth across countries using different data sets shows that cross-country variations in TFP growth account for more that 60 percent of output growth using alternative data sets (table 2). The cross-country variation in physical capital alone-excluding the covariance with TFP growth- never accounts for more than 25 percent of the cross-country variation in per capita GDP growth. Researchers also incorporate human capital accumulation into decomposi- tion exercises, rewriting the variance-decomposition equations as: (4) VAR(Ay/y) = VAR(ATFP/TFP) + (0.7)2{VAR(Af/f)l + 2(0.7){cov(ATFP/TFP, Aff)}, where Af/fisfactor accumulation per worker, defined as the average growth rate of physical capital per worker and educational attainment per worker. Specifi- cally, Af/f = (Ak/k + Ah/h)12, where h is educational attainment per worker. 7 7. Again, differentauthors use differentweights, thoughthis tends not to change the basic findings. Easterly and Levine 187 TABLE 2. Variance Decomposition Contribution of Covariance of capital growth and TFP growth Capital growth TFP growth Without human capitala 0.01 1960-92 0.58 0.41 0.13 1980-92 0.65 0.21 With human capital -0.45 1960-92b 0.94 0.52 0.12 1980-87' 0.68 0.20 'Sixty non-oil-exporting countries. bForty-four countries. CFiftycountries. Source: Authors's calculations based on the PWT 5.6 capital stock series and Benhabib and Spiegel's (1994) estimates of human capital growth. Incorporating human capital does not alter the basic result. TFP growth dif- Klenow and ferentials account for the bulk of cross-country growth differences. account for Rodriguez-Clare (1997b) estimate that differences in TFP growth worker for a about 90 percent of the variation in growth rates of output per sample of 98 countries during 1960-95 after accounting for human capital ac- cumulation (based on schooling and job experience). The use of the PWT 5.6 capi- tal stock series and estimates of the growth rate of human capital from Benhabib for about and Spiegel(1994) also shows that differences in TFP growth account 90 percent of cross-country differences in real per capita GDP growth during 1960-92. Thus differences in TFP growth-rather than in factor accumulation rates-seem likethe natural place to start in explaining cross-country differences in long-run growth rates. Growth accounting has several limitations. It isa mechanical procedure, and using it to elucidate a causal story is dangerous. For example, in Solow's (1956) model, if technological progress (A) grows at the exogenously given steady- account- state rate x, then y and k grow at the steady-state rate x, too. Growth ing will, therefore, attribute ax of output growth to capital growth, yielding the conclusion that a times 100 percent of growth is due to physical capital statistical significance accumulation. Also, growth accounting does not test the of the relationship between output growth and capital accumulaltion. (The tem- and savings, investment, poral-Granger-causal-relationships between growth and education are discussed later.) and Jones (1999) recently reex- LEVEL ACCOUNTING AND THE K/Y RATIO. Hall amined the level accounting question, asking what part of cross-country differ- ences in income per capita is accounted for by differences in physical capital per capita. They find that productivity differences across countries account for the bulk of cross-country differences in output per worker. This study addresses this 188 THE WORLD BANK ECONOMIC REVIEW,VOL. 15, NO. 2 question usingthe traditional Denison (1962)approach and a modified Mankiw, Romer, and Weil (1992) approach. To conduct Denison-level accounting, take the ratio of two national incomes of output per person from equation 1: (5) [y, / yi] = [A, / A,j[ki / k,]"[ni / ni]l Given data on the factors of production, cross-country differences in TFP can be measured by: (6) [Ai / Aj] = [yi I yj]/{[k, / kj]ol[ni / n,]j"-}. The fraction of differences in national output levels due to capital equals the ratio, 'ki- (7) Oki = alog(ki / k,) / log(yi / yj). Equation 7 can be rewritten as: (8) Pk,= a + alog(k, I k,) / log(y, / y,), because log(k,/k;) = log(Ki/Kj) - log(yyi/y 1 ), letting K=k/y. This allows measurement of the contribution of capital due to capital share (a) and that due to differences in the capital-output ratios. If capital-output ratios are constant across coun- tries i and j, then the contribution of capital due to differencesin output per capita in countries i and j simply equals a. To conduct levelaccounting, first calculate the percentage shortfall in output of country i relative to the reference country j. Pi = 1OO(yi- y)/y,. Then construct the contribution of capital due to the output difference as, Pi kv. As in 4 King and Levine (1994), the levelaccounting uses figures on aggregate capital stocks (but from PWT 5.6). Countries are classified into fivegroups, from poorest to richest. The richest group is the reference group. Figure 2 summarizes the level accounting results. Group 1, the poorest, has more than a 90 percent shortfall in GDP per capita relative to the reference group. TFP accounts for the bulk of cross-country differences in levels of income per capita. The rest is due to capital share of output, assuming constant capital-out- put ratios, and to the tendency for capital-output ratios to rise with income per capita. Even accounting for systematic cross-country differences in capital-out- put ratios, the data indicate that capital differences account for less than 40 percent of the cross-group differences in income per capita. 8 8. Though not directly related to growth accounting, note that the K/Y ratio systematically varies with income per capita. Capital-output ratios are systematically larger in richer countries; and, capital- output ratios tend to rise as countriesgrow, which are inconsistent with Kaldor's stylized fact on capital- output ratios. Consider the regression of the capital-output ratio (ici) on a measure of income per capita relative to thatin the United States in the 1980s (yi/yusA).The regression yields the following result: Ki = 0.76+ 0.59[yi/yUSA], (0.10) (0.18) Easterly and' Levine 189 FIGURE 2. Development Accounting by Income Quintiles (57 Non-Oil-Exporting Countries) 1 . Residual 90 80 Differencesin: 70 | -z 60KY 50 40o-1 Capital Share L 30 20 10> 0> 1 2 3 4 Quiintile Note: Data cover 57 non-oil-exporting countries. stock estimates. Source: Authors' calculations based on Penn World Table 5.6 for capital MANKIW, ROMER, AND WEIL (MRW) LEVELACCOUNTING. A second approach to level accounting is suggested by Mankiw, Romer, and Weil (1992), who argue that the Solow model does a good job of accounting for cross-country differ- ences in the level of income per capita. In the steady-state of the Solow model, output per person is given by: (9) Y/L = A [s/(x+6+n)]all-), where Y/L is output per person, A isthe level of labor-augmenting productivity, s is the ratio of investment to GDP,x is the rate of labor-augmenting productiv- ity growth, 6 isdepreciation, n is population growth, and a isthe share of capi- tal income in GDP.A 2 percent productivity growth rate and a 7 percent depre- ciation rate are assumed. Logs are taken of both sides, and the log of output per person is regressed on a constant (InA) and on the log of the second multiplica- tive term in equation 9: are in parentheses, and the regression where ratio in country i, standard errors Ki is the capital-output output per person includes 57 non-oil-exporting countries. Thereis a strong positive relationship between to rise in relative to the United States and the KIY ratio. Also, figure 3 shows that the K/Y ratio tends with fast growing countries. Here, the average value of KIY ratios are plotted year by year for countries per capita growth rates higher than 3.5 percent a year over the period 1960-92. The K/Y ratio rises dynamics, rapidly over this fast growth period. Though these differences might be due to transitional explain past works suggests that physical capital accumulation along the transition path is unlikely to fully level and growth differences (King and Rebelo 1993). 190 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. Z (10) ln(Y/L) = In A + a/(l-a) [In s - ln(x+6+n)]. This second term will be called MRW. The MRW approach is then extended by allowing A to differ across regions, oil-producing and non-oil-producing countries, and OECD and non-OECD coun- tries. (The regions are all-inclusive; the OECD and OIL dummy variables measure shifts relative to their respective regions.) Though there is a significant correlation of income with the MRW investment term (consistent with the Solow model), the results in table 3 refute the original MRW idea that productivity levels are the same across countries. South Asia and Sub-Saharan Africa have significantly lower productivity than other regions (in- come differences that are not explained by the MRW term). The OECD has higher productivity than the rest of the world by a factor of 3 (el087). Once the produc- tivity level is allowed to vary, the coefficient on MRW implies a capital share of .31-which is in line with most estimates from national income accounting. Mankiw, Romer, and Weil report that they are even more successful at ex- plaining cross-country income differenceswhen they include a measure of human capital investment, which they define as [In Sh - ln(x + 5 + n)]. They define the flow of investment in human capital s, as the secondary enrollment ratio times the proportion of the labor force of secondary school age. Klenow and Rodriguez- Clare (1997b) and Romer (1995) criticize this measure as overestimating the cross-country variation in human capital by ignoring primary enrollment, which varies much less across countries than secondary enrollment. The results for this TABLE 3. MRW Least Squares Regression with Regional, Oil, and OECD Dummy Variables Variable Coefficient Standard error t-statistic Probability OECD 1.087817 0.107084 10.15857 0.0000 East Asia 7.559995 0.176696 42.78525 0.0000 South Asia 7.065895 0.139239 50.74634 0.0000 Sub-Saharan Africa 6.946945 0.090968 76.36658 0.0000 Western Hemisphere 7.838313 0.102363 76.57349 0.0000 Middle East and North Africa 7.777138 0.143632 54.14642 0.0000 Europe 7.717543 0.133190 57.94384 0.0000 OIL 0.691058 0.157605 4.384760 0.0000 MRW 0.442301 0.096847 4.567031 0.0000 R2 0.752210 Mean dependent variable Adjusted R2 7.79 0.738969 Standard error of dependent 0.994 variable Standard error of regression 0.508076 Akaike information criterion 1.539 Sum of squared residual 33.81651 Schwarz criterion 1.708 Log likelihood -98.99247 F-statistic 56.810 Probability (F-statistic) 0.000 Note: Average logincome per capita in 1960-95 is thedependent variable. Number of observations = 139. Standarderrors and covariance are White heteroskedasticity-consistent. Source: Authors' calculations basedon World Bank data. Easterly and Levinte 191 new regression show that although the human capital investment term is highly significant, the original physical capital investment term is only marginally sig- nificant (table 4). The OECD productivity advantage and the regional differences in productivity are of the same magnitude as before. When equation 10 is estimated in first differencesfrom the first half of the pe- riod to the second to eliminate country fixed effects, the MRW variable isnot sta- tistically significantwhile TFP growth-the constant in the equation in first differ- ences-varies significantlyacross regions.This isconsistent with the earlier finding that most of the cross-country variation in growth rates per capita is do to differ- ences in TFP growth and not to transitional dynamics between steady states. Causality Growth accounting is different from causality. Factor accumulation could ig- nite productivity growth and overall economic growth. Thus factDr accumula- tion could cause growth even though it does not account for much the cross- country differences in growth rates in the levelof GDP per capita. If this were the case, it would be both analytically appropriate and policy wise to focus on fac- between tor accumulation. There is alsothe well-known cross-sectioncorrelation investment share and growth (see Levine and Renelt 1992). Evidence suggests, however, that physical and human capital accumulation do not cause faster growth. For instance, Blomstrom, Lipsey, and Zejan (1996) show that output growth Granger-causes investment. Injections of capital do not seemto be the driving force of future growth. Similarly, Carroll and Weil (1993) TABLE 4. MRW Least Squares Regression Including Human Capital, with Regional, Oil, and OECD Dummy Variables t-statistic Probability Variable Coefficient Standard error 0.126361 7.907255 0.0000 OECD 0.999172 37.89818 0.0000 East Asia 8.040507 0.212161 41.06093 0.0000 South Asia 7.593671 0.184937 0.0000 Sub-Saharan Africa 7.636055 0.207923 36.72545 0.0000 Western Hemisphere 8.285468 0.136361 60.76117 0.0000 Middle East and North Africa 8.345100 0.192838 43.27516 50.86290 0.0000 Europe 8.222288 0.161656 3.449517 0.0008 OIL 0.618785 0.179383 1.768343 0.0796 MRW 0.168531 0.095305 4.862086 0.0000 MRWH 0.433868 0.089235 R2 0.812286 Mean dependent variable 7.779659 Adjusted R2 0.797722 Standard error of dependent variable 1.024315 1.363849 Standard error of regression 0.460689 Akaike information criterion 1.588951 Sum of squared residual 24.61913 Schwarz criterion 55.77363 Log likelihood -75.92250 F-statistic Probability (F-statistic) 0.000000 of observations Note: Average log income per capita in 1960-95 is the dependent variable. Number = 126. Standard errors and covariance are White heteroskedasticity-consistent. Source: Authors' calculations based on World Bank data. 192 THE WORLD BANK ECONOMIC REVIEW, VOL. 15, NO. Z show that causality tends to run from output growth to savings, not the other way around. Evidence on human capital tells a similar story. Bils and Klenow (1996) argue that the direction of causality runs from growth to human capital, not from human capital to growth. Thus in terms of both physical and human capital, the data do not provide strong support for the contention that factor accumulation ignites faster growth in output per worker. Summary Although there are important exceptions, as Young (1995) makes clear, "some- thing else" besides factor inputs accounts for the bulk of cross-country differ- ences in income per capita and growth rates. Furthermore, although growth ac- counting does not show causality, research suggests that increases in factor accumulation do not ignite faster output growth in the future. While more work is needed, the evidence does not suggest that causality runs from physical or human capital accumulation to economic growth in the broad cross-section of countries. Finally, measurement error may reduceconfidence in growth and level accounting. However, the residual is large in both level and growth accounting. Also, level and growth accounting for the 1950s and 1960s produce similar es- timates as those for the 1990s. This implies that measurement error would have to have two systematic components. Both the growth rate of measurement error and the level component of measurement error would have to be positive and large in rich, fast-growing countries. Measurement problems may play a role, but a considerable body of evidence suggests that something else-TFP-besides factor accumulation iscritical for understanding cross-country differences in the leveland growth of GDP per capita. In giving theoretical content to this residual, Grossman and Helpman (1991), Romer (1990) and Aghion and Howitt (1998) focus on technology, on better instructions for combining raw materials into useful products and services.Romer (1986), Lucas (1988), and others focus on externalities, including spillovers, economies of scale, and various complementarities in explaining the large role played by 9 TFP. Harberger (1998) views TFP as real cost reductions and urges economists not to focus on one underlying cause of TFP because several factors may produce real costs reductions in different sectors of the economy at differ- ent times.i0 This is consistent with industry studies that reveal considerable cross- sector variation in TFP growth (Kendrick and Grossman 1980). Prescott (1998) also focuses on technology. He suggests that cross-country differences in resis- tance to the adoption of better technologies-arising from politics and policies- help explain cross-country differences in TFP (see Holmes and Schmitz 1995; Parente 1994; Parente and Prescott 1996; and Shleiferand Vishny 1993). It would 9. Yet, Burnside (1996) presentsevidence suggesting that physical capital externalities are relatively unimportant. Klenow (1998) presents evidence that is consistentwith technological change-based model of growth. 10. Costello (1993) shows that TFP has a strong country component and is not specific to particular industries. Easterly and Levine 193 be useful in designing models and policies to determine empirically the relative importance of each of these conceptions of TFP. III. STYLIZED FACT z. DIVERGENCE, NOT CONVERGENCE, Is THE BIG STORY of Over the very long run, there has been "divergence, big time," in the words Pritchett (1997). The richest countries in 1820 subsequently grew faster than the 1 in 1820 poorest countries in 1820. The ratio of richest to poorest went from 6to to 70 to 1 in 1992 (figure 3). Prior to the Industrial Revolution (1700-50), the about 2 difference between the richest and poorest countries was probably only to 1 (Bairoch 1993, pp. 102-6). Thus, the big story over the past 200-300 years is one of massive divergence in the levels of income per capita between the rich and the poor."I The poor are not getting poorer, but the rich are getting richer a lot faster than the poor. Absolute divergence has continued over the past 30 years, though not as dramatically as in earlier periods (see table 5). And while China and India- countries with very large populations-have performed well recently, growth has diverged significantly even using recent data.12 Moreover, the data presented in table 5 understate absolute divergence over 1960-92 because data were lacking for many low- and middle-income countries for the 1990s but not for any high-income countries. This imparts a bias toward convergence in the data similar to that pointed out by De Long (1988) regard- ing Baumol's (1986) finding of convergence among industrial cotntries. When sample the countries that are rich at the end are overrepresented in the sample, the of the is biased toward convergence. The growth rates of the lower three-fifths per- sample would be even lower if data were available for some of the poorly forming low- and middle-income economies in the 1990s. Within the postwar period, this tendency toward divergence has become more pronounced with time. Easterly (2001) found that the bottom half of countries ordered by per capita income in 1980 registered zero per capita growth over 1980-98, while the top half continued to register positive growth. The reason was not a divergence in policies; policies in poor countries were converging to- ward those of rich countries over 1980-98. Although many cross-economydata setsexhibitconditional convergence(Barro and Sala-i-Martin 1992), it is difficult to look at the growing differences between the rich and poor and not focus on divergence. Conditional convergencefindings hold onlyafter conditioningon an important mechanism for divergence-spillovers he interprets asreflecting lt. See Lucas (1998) for an extensive discussion of this divergence, which new countries different takeoff times for various economies, and which he predicts will decrease as take off. relied on dataothat went through 12. The usual finding that initialincome and growth are uncorrelated recent data (through 1981 or 1985, using a linearregression of growth on initial income. The use of more 1992) and the analysis of quintiles account for this finding of absolute divergence. ,N 194 THE WORLDBANK EcoMICV Groth F E RatesDivergebetween Rich d Netherlands Auistralia -Austna 64 Belgium -USA Denmarkd, France NSleden Italy = - Spain -Norway frelanid G Canada 4' 16 _-Meaico l iFwland Brazil = = tfMdone1sia -Tnai E= C2hs0ai -Nigeiia -- Barglade5 ~h - Infdia " -~Pakistan _~China Egypt Ghana -- Tanzania 2 - Buni, _~Zaire Ethiopia -- - Fesotho ~Togo I ~~~1820 Malawi Note: Orderinl1820 fro riche,, (top) to Poorest (bottom). Sot"rce: Maddison 199s5m19 fro mnth e 'ntiallevelof knowledge (for which condi ti n l c n e g f~ e r s i~ mo uld og efol wle vel o ol g Con da from mneanreversIongQua 1993)ina B (vreneas mnodels are closed icnrYTndl,1t s wors'n(Qa a93wecatsemotgowt j:X~~In foundabsoutediveres.e Kreer (1993) and Ades and 'Glaeser(19)hv gsIng an "extent Ofthe market" effect ongo g e s t , er e n~ n th e mnaj or ity o f c os d e v l p n e o o m s, ncosedngeconomies s g These findings fats.Romr izeizedRo.fact er(on686)sho o iegnesolshudbenWithin ( 9dsvrho~s that the growth ratesofthe riches ong,ot Icoe cnmofoterssyl thecontextco unt hres thave Easterly ana' Levine 195 TABLE 5. Rich Countries Grew Rapidly, Poor Countries Slowly in 1960-92 Average growth of income Income quintile per person, 1960-92 (%) Poorest fifth of countries 1.4 Second poorest fifth of countries 1.2 Middle fifth of countries 1.8 Second richest fifth of countries 2.6 Richest fifth of countries 2.2 Note: Countries are classified by income per person in 1960. Sotirce: Authors' calculations based on Summers-Heston 1991 data with subsequent on-line updates. not slowed over the last century. King and Rebelo (1993) show that returns to capital in the United States have not been falling over the last century. Together, these observations do not naturally suggest a model that emphasizes capital ac- cumulation and that has diminishing returns to factors, some fixed factor of production, and constant returns to scale. Neither do they providleunequivocal support for any particular conception of what best explains the something else behind these stylized facts. IV. STYLIZED FACT 3. GROWTH Is NOT PERSISTENT, BUT FACTOR ACCUMULATION Is Growth is remarkably unstable over time. The correlation of per capita growth in 1977-92 with per capita growth in 1960-76 across 135 countries isonly .08.13 This low persistence is not just a characteristic of the postwar era. For the 25 countries for which there are data (Maddison 1995), the correlation between 1820-70 and 1870-1929 is only .097. In contrast, the cross-period correlation of growth in capital per capita is0.41. For models that postulate a linear relationship between growth and the share of investment in GDP (using investment share in GDP as an alternative measure of capital accumulation), the mismatch in persistence is even worse.14 The correla- tion of investment share in GDP in 1977-92 with investment share in 1960-76 is .85. Nor do models that postulate growth per capita as a function of human capital accumulation do better. The correlation across 1960-76 and 1977-92 for primary enrollment is .82, while the cross-period correlation for secondary enrollment is .91. This suggests that much of the large variation of growth over 13. Data on per capita growth are from the PWT 5.6. The low persistence of growth rates, andthe high persistence of investment and education, was previously noted in Easterly and others (1993). 14. Models supposing a linear relationship between growth and investment have a long history in economics. See Easterly (1999b) for a review of the Harrod-Domar tradition that continues down to the present. For a new growth theory justification of this relationship, see McGrattan (1998). 196 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. Z time is not explained by the much smaller variation in physical and human capi- tal accumulation. Takeoff into Steady-State Growth Is Rare The typical model of growth, in both the old and new growth literatures, fea- tures a steady-state growth rate. Historically, this was probably inspired by the U.S.experience of remarkably steady growth of about 2 percent per capita over nearly two centuries (Jones 1995a, 1995b; Rebelo and Stokey 1995). Becauseall countries must have had prior histories of stagnation, another char- acterization of the typical growth path isthe "takeoff into self-sustained growth" (the phrase is from Rostow 1960; more recent theoretical modeling of takeoff includes Baldwin 1998, Krugman and Venables 1995, Jones 1999, Lucas 1998, and Hansen and Prescott 1998). The prevailing image is a smooth acceleration from stagnation into steady-state growth. Developing countries are supposed to have taken off beginning in the 1960s, when their growth was rapid and exceeded expectations. Experience did not bear out the idea of steady growth beginning in the 1960s. Many countries experienced booms and crashes (Pritchett 2000, Rodrik 1998). Even when ten-year average growth rates are used, which should belong enough to iron out cyclical swings, the cross-section standard deviation is about 2.5 percentage points and the variation over time swamps the cross-section varia- tion. In 48 of 119 countries with 20 years or more of data over 1960-97, a breakpoint can be found in which the subsequent decade's per capita growth is more than 5 percentage points-two cross-section standard deviations- above or below the previous decade's growth.1 SA11of the countries with growth booms or crashes were developing countries, except for Greece and Portugal. Figure 4 illustrates the rollercoaster ride of C6te d'Ivoire, Guyana, Jamaica, and Nigeria. Stable growth may be a better description of industrial than developing coun- tries. Of 88 industrial and developing countries with complete data for 1960- 97, only 12 had growth above 2 percent per capita in every decade. Half were in East Asia. Variance Decomposition over Time This supposition of unstable growth is further confirmed by variance decom- position exercises, with decomposition over time rather than across countries. In conjunction with the cross-country variance decomposition presented above, this analysis represents a full exploration of the panel data on growth and its factors. A panel of seven five-year time periods was constructed for each country for per capita growth and growth in physical capital per capita. Country means are 15. Thirty-seven countries had a growth drop of S percentage pointsor more, 19 countriesof 5 percentage pointsor more, and 8 countrieswere included inboth groups. Easterly anarLevine 197 FIGURE 4. Examples of Variable Per Capita Income over Time: 1960-96 0.8 Coted'tvoire -s1-- - Jamaica 0.7 Nigeria G 0.6 / \ ------ ~Guyana 0.5 0 5/ 0.4/ 2( 0.3 /I ~)0.2 C) 0.1 01O.I , -.--- -0.1I -0.2 1993 1996 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 Source: WorldBank data. then subtracted and the variance is analyzed using the same formula as before (see equation 3). For the same sample of countries, TFP accounts for 86 percent of the intertemporal variation in overall growth and 61 percent of the cross- sectional variation. Thus, growth is much more unstable over time than physi- cal capital growth. Besidesemphasizing the importance of TFP in explaining long-run development patterns, the findings that growth is not persistent and that growth patterns are very different across countries complicate the challenge for economic theorists. 198 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. 2 Existing models miss important development experiences. Some countries grow steadily (the United States). Some grow steadily and then stop for long periods (Argentina). Some do not grow for long periods and then suddenly take off (Re- public of Korea, Thailand). Others have never grown (Somalia). Accounting for these very different growth experiences will be very difficult with sole reliance on either steady-state models or standard multiple-equilibria models. Differentmod- els may be needed for different patterns of growth across countries. Steady-state models fit the U.S.type experience.Multiple equilibria models are a better fit for unstable growth cases because countries' long-run fundamentals are stable.16 V. STYLIZEDFACT 4. WHEN IT RAINS, IT POURS: ALL FACTORS FLOW IN THE SAME DIRECTION This section presents new information on the concentration of economic activity, using cross-country data, data from counties in the United States, information on developing countries, and data on international flows of capi- tal, labor, and human capital. This concentration has a fractal-like quality. It recurs at all levels of analysis, from the global to the urban. It suggests that some regions have "something" that attracts all factors of production, whereas others do not. Better policies (legal systems, property rights, political stability, public edu- cation, infrastructure, taxes, regulations, macroeconomic stability) in one area than in another could explain these factor flows. But such policies are national; they cannot explain findings of within-country concentration (discussed below). Externalities may lead to factor congregation. Critically, policy differences, or externalities, or differences in something else do not have to be large. Small dif- ferences can have dramatic long-run implications. So, although no specific ex- planation is offered, the results of this analysis suggest a need for more work on economic geography as a vehicle for understanding economic growth. Concentration An obvious observation at the global level is that high income is concentrated among a small number of countries (see map 1). The top 20 countries have only 15 percent of world population but produce 50 percent of world GDP. The poorest 16. The nonpersistence of growth rates does not inherently contradict the stylized fact of diver- gence or the stylized fact that national policies influence long-run growth rates. While policies are per- sistent and significantly associated with long-run growth (which is not persistent), the R2 of the growth regression is generally smaller than 0.50. Thus, something else (besides national policies) is very impor- tant for explaining cross-country differences in long-run growth rates. In terms of divergence, the styl- ized fact of the nonpersistence of growth rates emphasizes that growth follows very different paths across countries and that there is a high degreeof volatility. Nevertheless,there are countries that have achieved comparatively greater success over the long run. While France, Germany, and the United Kingdom have experienced growth fluctuations, they have enjoyed a steeper-and less volatile-growth path than Argentina and Venezuela, for example, whose growth paths have not only been more volatile but ex- hibited dramatic changes in trends. Easterly and Levine 199 MAP 1. The Rich and the Poor v v0 ,- -,1 .w~' '' ._. - percent of world GDP. The countries in black contain 15 percent of world population but produce 50 14 percent of world GDP. The countries in gray contain 50 percent of world population but produce 17 half of the world's population accounts for only 14 percent of its GDP. These concentrations of wealth and poverty have an ethnic and geographic dimen- sion: 18 of the top 20 countries are in Western Europe or were settled primarily by Western Europeans; 17 of the poorest 20 countries are in tropiLcalAfrica. The richest country in 1985 (the United States) had an income 55 timnesthat of the in- poorest country (Ethiopia). When inequality within countries is considered, ternational income differences are even starker. The income of the richest quintile in the United States was 528 times that of the poorest quintile in Guinea-Bissau. Income is highly concentrated by area as well, as shown by data on GDP per square kilometer. The densest 10 percent of world land area accounts for 54 percent of global GDP; the least dense for only I1 percent.'" These calculations understate the degreeof concentration becausethey assume that income is evenly spread among people and land area within countries. A of wealth more detailed look within countries also shows high concentrations and poverty. measured be- 17. These calculations omit the oil-exporting countries, in which GDP is not properly cause all of oil extraction istreated as current income rather than asset depletion. of the 18. An alternative explanation would be that some land areas, accounting for a small share (1999) argue that earth's surface, have a large productivity advantage. Mellinger, Sachs, and Gallup activity would temperate coastal zones have a large productivity advantage. If thiswere true, economic intrinsic differences be distributed fairly evenly along temperate coastal zones (adjusting for any small casual observations would suggest among such zones). However, even along temperate coastal zones, high bunching of activitv. 200 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. Z MAP 2. Densely Populated U.S. Counties Counties shown in black take up 2 percent ofU.S. land area but account forhalf of U.S. GDP. Consider the United States. Data on GDP per square mile for 3,141 counties show that counties accounting for only 2 percent of the land produce 50 percent of GDP, while the least dense counties that account for 50 percent of the land produce only 2 percent of GDP (map 2). Nor isthis finding a consequence merely of the large unsettled areas of the West and Alaska. The same calculation for land east of the Mississippi River yields similarly extreme concentration: 50 percent of GDP is produced on 4 percent of the land. The densest county isNew York, New York, with a GDP per square mileof $1.5 billion.This is about 55,000 times more than the least dense county east of the Mississippi ($27,000 per square mile in Keweenaw, Michigan). Even this understates the degree of concentra- tion because even the most casual empiricism will detect rich and poor areas within a given county (New York county contains Harlem as well as Wall Street). The concentration of counties accounting for half of U.S. GDP is explained by the fact that these are metropolitan counties and most economic activity takes place in denselypopulated metropolitan areas. Metropolitan counties are $3,300 richer per person than rural counties (the difference is statistically significant, with a t-statistic of 29). More generally, there is a strong correlation between per capita income of U.S. counties and their population density (correlation coefficient of .48 for the log of both concepts, with a t-statistic of 30 on the bi- variate association). But concentration is high even within metropolitan coun- ties: 50 percent of metropolitan GDP is produced in counties accounting for only 6 percent of metropolitan land area.19 There are also regional income differences between metropolitan areas. Metropolitan areas in the Boston-Washington corridor have a per capita in- 19. Metropolitan counties arethose that belong to a PMSA or MSA in the census classificationof counties. Easterly ana' Levine 201 come $5,874 higher on average than other metropolitan areas. This is a huge difference: It isequal to 2.4 standard deviations inthe metropolitan area sample. unlikely to be Although there may be differences in the cost of living, they are living so large as to explain this difference. (The rent component of the cost of seems may reflect the productivity or the amenity advantages of the area-it unlikely that amenities are different enough among areas to explain these differences.) There are other possible explanations of geographic concentration, such as inherent geographic advantages. Like Mellinger, Sachs, and Gallup (1999), Rappaport and Sachs (1999) argue that spatial concentration of activity in the United States has much to do with accessto the coast. However, casual observa- tion suggests high concentration even within coastal areas (there are sections along the Boston-Washington corridor with no radio reception). Some studies suggest that hightransport costs and lowcongestion costs could also play a role (Krugman 1991, 1995, 1998; Fujita, Krugman, and Venables 1999). However, these stud- ies also point to locations of particular industries (the Silicon Valley phenom- enon) as evidence of other types of geographic spillover, including technology spillovers and specialized producer serviceswith high fixed costs. And the high rents in downtown metropolitan areas suggest that congestion costs are signifi- cant. As Lucas (1988, p. 39) says, "What can people be paying Manhattan or downtown Chicago rents for, if not for being near other people'" Poor Areas Like wealth, poverty is also concentrated. In the United States, poverty isregion- ally concentrated. These concentrations have an ethnic dimension as well (see map 3). Four ethnogeographic clusters of counties have poverty rates above 35 percent: * Counties in the West with large proportions (> 35 percent) of Native Americans. * Counties along the Mexican border with large proportions (> 35 percent) of Hispanics. * Counties along the lower Mississippi River in Arkansas, Mississippi, and Louisiana and in the "black belt" of Alabama, all of which have large pro- portions of blacks (> 35 percent). * Virtually all-white counties in the mountains of eastern Kentucky. The county data did not pick up the well-known phenomenon of inner-city poverty, mainly among blacks, because counties that include inner cities also include rich suburbs. (An isolated example of an all-black city is East St. Louis, Illinois,which is98 percent black and has a poverty rateof 44 percent.) Of course, poverty is concentrated in the inner city as well. An inner city zII' code in Wash- ington, D.C., College Heights in Anacostia, has only one-fifth of the income of a rich ziP code in Bethesda, Maryland. This has an ethnic dimension again be- cause College Heights is 96 percent black and the rich ziP code in Bethesda is 96 percent white. The Washington, D.C., metropolitan area as a whole shows 202 THE WORLD BANK ECONOMIC REVIEW,VOL. I5, NO. Z MAP3. Poverty Traps in the U.S. County Data Counties in black have more than 35 percent poverty tate. the striking East-West divide between poor and rich zIP codes, which again roughly corresponds to the black-white ethnic divide (see map 4).20 Borjas (1995, 1999) suggests that strong neighborhood and ethnic externali- ties may help explain poverty and ethnic clusters within cities. The 1990 census tracts with the highest shares of blacks have 50 percent of the black population but only 1 percent of the white population.2 1 Although this segregation by race and class could simply reflect the preferences of rich white people to livenext to each other, economists usually prefer to offer economic motivations rather than exogenous preferences as explanations of economic phenomena. Benabou (1993, 1996) stresses the endogenous sorting between rich and poor, so the rich can take advantage of such externalities as locally funded schools. Poverty areas exist within many countries: northeast Brazil, southern Italy, Chiapas in Mexico, Balochistanin Pakistan, and the AtlanticProvincesin Canada. Researchers have found that externalities explain part of these poverty clusters. Bouillon, Legovini, and Lustig (1999) find a negative Chiapas effect in Mexican household income data, an effect that has worsened over time. Households in the poor region of Tangail-Jamalpur in Bangladeshearned lessthan households with similar characteristics in the better-off region of Dhaka (Ravallion and Wodon 1998). Ravallion and Jalan (1996) and Jalan and Ravallion (1997) likewisefound that households in poor counties in southwest China earned lessthan households with identical human capital and other characteristics in rich Guangdong Prov- ince. Rauch (1993) found that individuals with identical characteristics earn less in low human capital cities in the United States than in high human capital cities. 20. Brookings Institution (1999)notes that this East-West geographic divide of the Washington, D.C., area shows up in many socioeconomic variables (poverty rates, free and reduced price school lunches, road spending). 21. From the Urban Institute's Underclass Database, which contains data on white, black, and "other" population numbers for 43,052 census tracts in the United States. Easterly and Levine 203 MAP4. Rich and Poor ziP Codes in the Washington, D.C., Metropolitan Area $ MontgomeryCounty MD > $ $ / PrinceGeorge'sCountyMD NorthernVA a, $At $ DC #<# # # $ indicates richest fourth of zip codes in metropolitan area; # indicates poorest fourth. Ethnic and RelatedDifferentials Some theories stress in-group externalities (Borjas 1992, 1995, 1999; Benabou 1993, 1996). Poverty and riches are also concentrated in certain ethnic groups. Exogenous savings preferences are not an appealing explanation. Discrimina- tion and intergenerational transmission could explain ethnic differences, but for growth models the differencesseemmore consistent with in-group spilloversthan with individual factor accumulation. Asians The purely ethnic differentials in the United States are well known. earn 16 percent more than whites, and blacks earn 41 percent less,Native Ameri- subtle cans 36 percent less, and Hispanics 31 percent less.22 There are also more Austrian grand- ethnic earnings differentials. Third-generation immigrants with immigrants parents had 20 percent higher wages in 1980 than third-generation with Belgiangrandparents (Borjas 1992). Among Native Americans, the Iroquois earn almost twice the median household income of the Sioux. Other ethnic differentials appear by religion. Episcopalians earn 31 percent Forbes 400 more than Methodists (Kosmin and Lachman 1993, p. 260). Of the of the U.S. richest Americans, 23 percent are Jewish, although only 2 percent population is Jewish (Lipset 1997).23 States (United States Government 22. Tables 52 and 724, 1995 Statistical Abstract of the United 1996). dimension of rich trading 23. Ethnic differentials are also common in other countries. The ethnic Chinese elites is well known-the Lebanese in West Africa, the Indians inEast Africa, and the overseas for-their success.For in Southeast Asia. Virtually every country has its own ethnographic group noted 204 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. 2 In Latin America, the main ethnic divide is between indigenous and nonin- digenous populations (table 6). But even within indigenous groups, there are ethnic differentials. For example, there are four main language groups among Guatemala's indigenous population. Patrinos (1997) shows that the Quiche- speaking indigenous groups earn 22 percent less on average than Kekchi- speaking groups. For Africa, there are numerous anecdotes about income differentials between ethnic groups, but little hard data. An exception is South Africa, where whites have 9.5 times the income of blacks. More surprisingly, among all-black tradi- tional authorities (an administrative unit something like a village)in the state of KwaZulu-Natal, the richest traditional authority has 54 times the income of the poorest (Klitgaard and Fitschen 1997). FactorMovement Factor movement toward the richest areas reinforces the concentration of eco- nomic activity. Each factor of production flows to where it is already abundant. Labor migration is overwhelmingly toward the richest countries. The three richest countries alone (the United States, Canada, and Switzerland) receive half the net immigration of all countries reporting net immigration. Countries in the richest quintile are all net recipients of migrants. Only 8 of the 90 countries in the bottom four-fifths of the sample are net recipients of migrants. Barro and Sala-i-Martin (1995, pp. 403-10) find that migration goes from poorer to richer regions in samples of U.S. states, Japanese prefectures, and European regions. Migration alsogoes from sparsely populated to denselypopulated areas. There is a statistically significant correlation of .20 between the immigration rate of U.S. counties from 1980 to 1990 and population density in 1980. Labor flowed to areas where it was already abundant. Migration goes from poor to rich coun- ties, with a statistically significant correlation of .21 between initial income and immigration rate (confirming the Barro and Sala-i-Martin 1995 finding for U.S. states). These two findings are related, as there is a significant positive correla- tion between population density and per capita income across counties.24 A re- gression of the immigration rate for 1980-90 by county on population density in 1980 and income per capita in 1980 finds both to be highly significant.2 5 Embodied in this flow of labor are flows of human capital toward rich coun- tries, the famous "brain drain." In the poorest fifth of countries, the probability of emigrating to the United States is3.4 times higher for an educated person than example, in The Gambia a tiny indigenous ethnic group called the Serahule is reported to dominate business out of all proportion to their numbers. In Zaire, Kasaians have been dominant in managerial and technical jobs since the days of colonial rule (New York Times, 9/18/1996). 24. Ciccone and Hall (1996) have a related finding for U.S. states. 25. The t-statistics are 8.2 for thelog of population density in 1980 and 8.9 for thelog of per capita income in 1979. The equation has an R2 of .065 and has 3,133 observations. The county data are from Alesina, Baqir, and Easterly (1999). Easterly and Levine 205 TABLE 6. Poverty Rate Differential among Indigenous and Nonindigenous Groups in Selected Latin American Countries Country Indigenous groups Nonindigenous groups Bolivia 64.3 48.1 Guatemala 86.6 53.9 Mexico 80.6 17.9 Peru 79.0 49.7 Source: Psacharopoulos and Patrinos 1994 (p. 6). for an uneducated person (based on data from Grubel and Scott 1977). Because education and income are strongly and positively correlated, human capital is flowing to where it is already abundant-the rich countries. Carrington and Detragiache (1998) found that in 51 of 61 developing coun- tries in their sample, people with a university education were more likely to emi- grate to the United States than people with a secondary education. In,all 61 coun- tries, migration rates to the United States were lower for people with a primary education or lessthan for people with a secondary or universityeducation. Lower bound estimates for the highest rates of emigration by those with university edu- cation range as high as 77 percent (Guyana), with rates of 59 percent for The Gambia, 67 percent for Jamaica, and 57 percent for Trinidad and Tobago.26 None of the emigration rates for the primary or less educated exceeds 2 percent. may The disproportionate weight of the skilledpopulation in U.S.immigration reflect U.S. policy. However, Borjas (1999) notes that U.S. immigration policy has tended to favor unskilledlabor with familyconnections in the United States rather than skilled labor. In the richest fifth of countries, moreover, the lprobabilityis roughly the same that educated and uneducated will emigrate to the United States. Borjas,Bronars, and Trejo (1992)also find that the more highly educated aremore likely to migrate within the United States than the less educated.27 Capital also flows mainly to areas that are already rich, as Lucas (1990) fa- mously pointed out. In 1990, the richest 20 percent of world population received 92 percent of gross portfolio capital inflows, whereas the poorest 20 percent re- ceived 0.1 percent. The richest 20 percent of the world population received 79 percent of foreign direct investment, and the poorest 20 percent received 0.7 per- cent. Altogether, the richest 20 percent of the world population received 88 per- cent of gross private capital gross inflows, and the poorest 20 percent received 1 percent. 26. Note these are all small countries. Carrington and Detragiache (1998) point out that U.S. im- immigra- migration quotas are less binding for small countries, because with some exceptions the legal tion quota is 20,000 per country regardless of population size. and doctors con- 27. Casual observation suggests "brain drain" within countries. The best lawyers gregate within a few metropolitan areas like New York, where skilled doctors and lawyers are abun- dant, while poorer areas have difficulty attracting the top-drawer professionals. 206 THE WORLDBANKECONOMICREVIEW,VOL. I5, NO. Z SkillPremiaand Human Capital Skilled workers earn less, rather than more, in poor countries. This seems in- consistent with the open economy version of the neoclassical factor accumula- tion model by Barro and others (1995). In the Barro and others model, capital flows equalize the rate of return to physical capital across countries, while human capital isimmobile. Immobile human capital explainsthe differencein per worker income across countries. As Romer (1995) points out, this implies that both the skilledwage and the skillpremium should bemuch higher in poor countries than in rich countries. To illustrate, specifya standard production function for coun- try i: (1) Y, = AK"L'H'--P. Assuming that technology (A) is the same across countries and that rates of re- turn to physical capital are equated across countries, the ratio of the skilled wage in country i to that in country j is a function of their per capita incomes: 0Y __ (12) AH ____ OH, On the basis of the physical (.3) and human capital shares (.5) suggested by Mankiw (1995), skilled wages should be five times greater in India than in the United States (to correspond to a 14-fold difference in per capita income). In general, equation 12 shows that skilledwages differences across countries should be inversely related to per capita income if human capital abundance explains income differences across countries, as in the Barro and others model. The skill premium should be 70 times higher in India than in the United States. If the ratio of skilled tounskilled wages is about 2 in the United States, the ratio should be 140 in India. This would imply an astonishing rate of return to education- 70 times larger than in the United States. The facts do not support these predictions. Skilled workers earn more in rich countries. Fragmentary data from wage surveys show that engineers average $55,000 inNew York and $2,300 in Bombay (Union Bank of Switzerland 1994). Far from being 5 times higher in India than in the United States, skilled wages are 24 times higher in the United States than in India. The higher wages across all occupational groups are consistent with greater technological progress (A) in the United States than in India. The skilled wage (proxied by salaries of engi- neers, adjusted for purchasing power) is positively associated with per capita income across countries, as a productivity explanation of income differences would imply (figure5), and not negativelycorrelated, as a Barro and others model of human capitalexplanation would imply.The correlation between skilledwages and per capita income across 44 countries is .8 1. Easterly and Levine 207 Within India, engineers earn onlyabout three times what building laborers earn. Rates of return to education arealso onlyabout twice as high in low-incomecoun- tries (11 percent) as in high-income countries (6 percent; Psacharopolous 1994, p. 1332)-not 42 times higher. Consistent with this evidence, the flow of human capital is toward rich countries, despite barriers to immigration. EvaluatingGrowth Modelsin Light of Income Concentration The high concentration of income, reinforced by the flow of all factors toward the richest areas, is inconsistent with the neoclassical growth model. The distri- bution of income across space and across people at all levels ishighly skewed to the right (skewness coefficient of 2.58 across countries in 1980, 2.2 across U.S. cities, and 1.6 across U.S. counties in 1990, where 0 is symmetry). There is no reason to think that the determinants of income in the neoclassical model (sav- ing, population growth) are skewed to the right, but models of technological complementarities (see, for example, Kremer 1993) can explain the skewness. Moreover, the concentration of factors in rich, densely populated areas even within countries is incompatible with a version of the neoclassical model that FIGURE 5. Skilled Real Wage and Per Capita Income across Countries 41.4 4 e~~~~~~~~~~~~~~~~~~~~ 0 8 4 4 o Log per capita income (1985 Sununers-Heston) 7~~~~~~~~~~~~~~~~~~~~~~ 710 Bank Source: Authors'calculations based on Summers and Heston for per capita income and Union of Switzerland for engineering sataries. 208 THEWORLDBANKECONOMICREVIEW,VOL. 15, NO.Z includes land as a factor of production. With land in fixed supply, physical and human capital and labor should all flow to areas abundant in land (adjusting for land quality) but scarce in other factors. Furthermore, in the neoclassical model of Mankiw, Romer, and Weil (1992), physicaland human capitalshould also flow from rich to poor areas, and unskilled labor from poor to rich. But as this study shows, physical and human capital flow toward rich areas, as does unskilled labor, though it is less mobile. Stylized fact 4 isin harmony with Klenow and Rodriguez-Clare (1997b), who complain that the "neoclassicalrevival in growth economics" has "gone too far." The neoclassical model does not explain why wealth and poverty are concen- trated in certain regions within countries or why there are such pronounced in- come differences between ethnic groups. Stylized fact 4 is consistent with pov- erty trap models (Azariadis and Drazen 1990, Becker, Murphy, and Tamura 1990, Kremer 1993, Murphy, Shleifer, and Vishny 1989); with models of in- group ethnic and neighborhood externalities (Borjas1992, 1995, 1999, Benabou 1993, 1996), and with models of geographic externalities (Krugman 1991, 1995, 1998, Fujita, Krugman, and Venables 1999). Stylizedfact 4 also seems to be more consistent with a productivity explana- tion of income differences than with a factor accumulation story. If a rich area is rich because technology (A) is more advanced, then all factors of production will tend to flow toward this rich area, reinforcing the concentration. Spillovers between agents also seem more natural with technological models of growth, as technological knowledge is inherently more nonrival and nonexcludable than factor accumulation. Technological spillovers between agents will lead to en- dogenous matching of rich agents with each other, and those matches will rein- force the matching of poor people with other poor people (as in the 0-ring story of Kremer [1993] or the inequality model of Benabou [1996]). A better under- standing of economic geography and externalities would help shape more real- istic models of economic growth. VI. STYLIZED FACT 5. POLICY MATTERS The empirical literature on national policies and economic growth is huge. There is considerable disagreement about which policies are most strongly linked with economic growth. Some analysts focus on openness to international trade (Frankel and Romer 1999), some on fiscal policy (Easterly and Rebelo 1993), some on fi- nancial development (Levine,Loayza, and Beck 2000), and some on macroeco- nomic policies (Fischer 1993). All these studies have at least one feature in com- mon: They all find that some indicator of national policy is strongly linked with economic growth, confirming the argument made by Levine and Renelt (1992). Most empirical assessments of the growth-policy relationship are plagued by three shortcomings. First, most do not confront endogeneity. Even when instru- mental variables are used, studies frequently assume that many of the regressors are exogenous and focus only on the potential endogeneity of one variable of Easterly and Levine 209 interest. This failure to fully confront causality may produce biased assessments. Second, traditional cross-country regressions may suffer from omitted variable bias. That is, cross-country growth regressions may omit an important country- specific effect and thereby produce biased coefficient estimates. IThird, almost all cross-country regressions included lagged real per capita GDP as a regressor. Because the dependent variable is the growth rate of real per capita GDP, this specification may produce biased coefficient estimates. This study uses recent econometric techniques to examine the links between economic growth and a range of national policies. These new techniques ame- liorate these potential biases sothat more accurate inferences can be drawn about the impact of national policies on economic growth. The goal is not to identify the most important policies influencing growth; it isto compile key stylized facts associated with long-run growth. Use of the latest econometric techniques (see appendix) confirms earlier find- ings that national policies are strongly linked with economic growth. The re- gression results are consistent with policies having significant long-run effects on national growth rates or on steady-state levels of national output. The re- gression results also show that national policies are strongly linked with TFP growth (Beck, Levine, and Loayza 2000). The relationship between the exogenous component of national policies and economic growth is assessed using a set of conditioning information and policy indicators suggested by theory and past empirical work. Specifically, the initial level of real income per capita is included to control for convergence. The stan- dard neoclassical growth model predicts convergence to the steady-state output per person ratio (Barro and Sala-i-Martin 1995). The coefficient on initial income does not necessarily capture only neoclassical transitional dynamics. In technol- ogy diffusion models, initial income may proxy for the initial gap inTFP between economies. In these models, therefore, catch-up can be in TFP as well as in tradi- tional factors of production. Average years of schooling was included as an indi- cator of the human capital stock in the economy. Its inclusioncan help incontrol- ling for differences in steady-state levelsof human capital (Barro and Sala-i-Martin 1992). Also, schooling may directly influence economic growth (Lucas 1988). Fivepolicyindicators were used. The inflation rate and the ratio ofgovernment expenditures to GDPwere included as indicators of macroeconomic stability (East- erly and Rebelo 1993, Fischer 1993). Exports plus imports as a share of GDP and the black market exchangerate premium were included to capture clegreeof open- ness (Frankel and Romer 1999). Financial intermediary credit to the private sec- tor as a share of GDP was included as a measure of financial intermediary develop- ment (Levine,Loayza, and Beck2000). There is no attempt to suggest that these are the most important policy indicators. They are used only to assess whether economic growth is strongly linked with these national policy indicators after controlling for endogeneity and other biases in existing empirical work. As in much of the cross-country literature, the regression results show evi- dence of conditional convergence (table 7). Specifically, contingent of the level 210 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. 2 of human capital, poorer countries tend to grow faster than richer countries as each country converges toward its steady-state. This finding is consistent with a major implication of the textbook neoclassical growth model. The regression also shows that greater human capital-as measured by average years of schooling of the working age population-is associated with faster economic growth. Moreover, since the GMM panel estimator controls for endogeneity, this finding suggests that the exogenous component of schooling exerts a positive impact on economic growth. These results are consistent with models that focus on factor accumulation or on TFP growth. The results are consistent with-but not proof of-long-run growth effects of national policies, which isconsistent with an endogenous productivity growth model. In contrast, models that feature only transitional factor accumulation dynamics usually predict weaker policy effectson growth than endogenous pro- ductivity growth models. Furthermore, complementary work in Beck, Levine, and Loayza (2000) suggests a powerful connection between national policies and TFP growth. The exogenous components of international openness-as measured TABLE 7. Economic Growth and National Policies Variable Result Constant 0.082 (0.875) Initial income per capitaa -0.496 (0.00 1) Average years of schooling" 0.950 (0.001) Openness to tradea 1.311 (0.001) Inflation6 0.181 (0.475) Government size, -1.445 (0.001) Black market premiumb -1.192 (0.001) Private credita 1.443 (0.001) Sargan test, (p-value) 0.506 Serial correlation testd (p-value) 0.803 Note: Numbers in parentheses are p-values. The dependent variable is real per capita GDP growth. aIncluded as log(variable). bIncluded as log(1 + variable). cThe null hypothesis is that the instruments used are not cor- related with the residuals. dThe null hypothesis is that the errors in the first-difference regression exhibit no second-order serial correlation. Souirce:Authors's calculations based on analyses in Beck, Levine, and Loayza (2000). Easterly and Levine 211 by the ratio of trade to GDP and by black market exchange rate premia-are significantly correlated with economic growth. Macroeconomic policy is also important. Large government tends to hurt economic growth, although inflation does not enter significantly. A higher black market exchange rate premium exerts a negative impact on growth. More inter- national trade tends to boost economic growth. While consideralble research suggests a negative link between inflation and economic performance (Bruno and Easterly 1998), recent research suggests that inflation is strongly linked with fi- nancial development (Boyd, Levine, and Smith 2001). Thus, it may not enjoy an independent link with growth when financial development is controlled for. Fi- nally, a higher level of financial development boosts economic growxth.In sum, national policies are strongly linked with economic growth. VII. CONCLUSION The major empiricalregularities of economic growth emphasizethe role of some- thing else besidesfactor accumulation. The TFP residual accounts for most of the cross-country and cross-timevariation in growth. Income acrosscountries diverges over the long run, while the growth rates of the rich are not slowing and returns to capital are not falling.This observation is lessconsistent with simple models that feature diminishingreturns, factor accumulation, some fixed factor of production, and constant returns to scale and more consistent with the observation that some- thing else is important for explaining long-run economic success. Growth is highly unstable over time, whereas factor accumulation is more stable, which certainly emphasizes the role of something else in explaining variations in economic growth. All factors of production flow to the richest areas, suggesting that they are rich because of high A rather than high K. Divergence of per capita incomes and the concentration of economic activity suggestthat technology has increasing returns. Finally, national policiesare strongly linkedwith long-run economicgrowth rates. Nothing in this study argues that factor accumulation is unimportant in gen- eral or denies that it is critically important for some countries at specific junc- tures. TFP does not explain everything, everywhere, always. Rather, the study shows that something else-besides factor accumulation-plays a pirominentrole in explaining differences in economic performance across countries. More research is needed on the "residual" determinants of growth and in- come, such as technology and externalities. There is little doubt that technology is a formidable force. Nordhaus (1994) estimates that 1 Btu of fuel consump- tion today buys 900 times more lighting (measured in lumen hours) than it did in 1800. Over the past two decades, computing power per dollar invested has risen by a factor of 10,000, and the cost of sending information over optical fiber has fallen by a factor of 1,000 (World Bank 1999, pp. 5 and 57).Just from 1991 to 1998, the price of a megabyte of hard disk storage fell from $5 to $0.03.28 28. uwww.duke.edul-mccannlq-tech.htm#Deathof Distance. 212 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. Z Not every technology has improved at this speed of course. But Mokyr (1992) was right to call technology "the lever of riches." APPENDIX: ECONOMETRIC METHODOLOGY A generalized method of moments (GMM)dynamic panel estimator was used to assess the relationship between policy and economic growth. Panel data for 73 countries over the period 1960-95 were averaged over seven nonoverlapping five-year periods. Consider the following equation: (13) Yu - = (a - 1)yt-i + 1P'Xit+ Ili+£t where y is the logarithm of real per capita GDP,X is the set of explanatory vari- ables (other than lagged per capita GDP), Tj is an unobserved country-specific effect, Eis the error term, and the subscripts i and t represent country and time period. Time dummy variables were also included to account for time-specificeffects. Equation 13 can be rewritten as: (14) y,t = ayZt,l + 13Xit + ili +s,it. First differences of equation 14 are taken to eliminate the country-specific effect: (15) Y*,t- Yit-l = C(Yit-I - Yit-2) + W(Xij + Xz,t-1) + (it - Ci,t-1)- The useof instruments isrequired to dealwith the correlation, by construction, of the new error term eit- eit,j with the lagged dependent variable Yit1 - Yit2 and with the likely endogeneityof the explanatory variables. Under the tested as- sumptions that the error term (£) is not serially correlated and the explanatory variables (X) are weakly exogenous (the explanatory variables are assumed to be uncorrelated with future realizations of the error term), appropriately laggedval- ues of the regressors can be used as instruments, as specified in the following moment conditions: (16) E| (£i,,-t Fi, 1)] = 0 for s > 2; t =3, . . ., T (17) E[X,-s (et - Eit- )] = 0 1 1 for s 2 2;t =3, . . ., T. The GMMestimator based on these conditions is referred to as the difference estimator. There are, however, conceptual and statistical shortcomings with this differ- ence estimator. It eliminates the cross-country relationship between national poli- cies and per capita GDPgrowth, which isof conceptual interest. Statistically,when the regressors in equation 15 are persistent, lagged levels of X and y are weak in- struments. Instrument weakness influences the asymptotic and small-sample per- formance of the difference estimator. Asymptotically, the variance of the coefficients rises. In small samples, weak instruments can produce biased coefficients. To reduce the potential biases and imprecision associated with the usual dif- ference estimator, Arellano and Bover (1995) and Blundell and Bond (1997) Easterly and Levine 213 for develop a system of regressions in differences and levels. The instruments for the regression in differences are the same as those above. The instruments the regression in levels are the lagged differences of the corresponding variables. These are appropriate instruments under the following additional assumption: although there may be correlation between the levels of the right-hand-side vari- ables and the country-specific effect in equation 14, there is no correlation be- tween the differences of these variables and the country-specific effect. This as- sumption results from the following stationarity property: (18) E[yi.,, * ,] = E[yit+q rTl] 1 and E[Xit+p * ,] = EXi,t+q *Ili] for all p and q. The additional moment conditions are. s = 1 (19) E[(y,,,, - yj,,Q(r,l + _,)] = 0 for (20) E[(Xi,-S - Xi,--) (Tk+ ei,)]= 0 1 for s = 1. Thus the moment conditions presented in equations 16, 17, 19, ancl20 are used with a GMM estimator to generate consistent and efficient parameter estimates. Consistency of the GMMestimator depends on the validity of the instruments. To address this issue two specification tests were considered, as suggested by Arellano and Bond (1991), Arellano and Bover (1995), and Blundell and Bond (1997). The first isa Sargan test of overidentifying restrictions to test the overall con- validity of the instruments by analyzing the sample analog of the rnoment ditions used in the estimation. The second test examines the hypothesis that the error term -itis not serially correlated. In both the difference regression and the system regression the differenced error term is tested for second-order serial correlation (by construction, the differenced error term is probably first- order serially correlated even if the original error term is not). This system es- timator is used to assess the impact of policies on economic growvth.In addi- tion to the system estimator, the analyses use purely cross-section, ordinary least squares regressions with one observation per country, the pure different estimator described above, and the panel estimator with only the level compo- values nent of the system estimator. All yield similar results and parameter (Levine, Loayza, and Beck 2000). REFERENCES Ades, Alberto, and Edward Glaeser. 1999. "Evidence on Growth, Increasing Returns, and the Extent of the Market." Quarterly Journal of Economics 114(3):1025-46. Aghion, P., and P. Howitt. 1998. Endogenous Grotvth Theory. Cambriclge,Mass.: MIT Press. Alesina, Alberto,Reza Baqir, and William Easterly. 1999. "Public Goods and Ethnic Divisions."QuarterlyJournalof Economics114(4):1243-84. 214 THEWORLDBANKECONOMICREVIEW,VOL. I5, NO. Z Arellano,Manuel, and Bond, Stephen."SomeTests of Specificationfor Panel Data. Monte Carlo Evidence and an Application to Employment Equations." Review of Economic Studies 58(2):277-97. Arellano, Manuel, and Bover, Olympia. 1995. "Another Look at the Instrumental-Vari- able Estimation of Error-Components Models." Journal of Econometrics 68(1):29-52. Azariadis, Costas, and Allan Drazen. 1990. "Threshold Externalities in Economic De- velopment,"QuarterlyJournalof Economics105:501-26. Bairoch,Paul. 1993. Economics and World History: Myths and Paradoxes. Chicago: University of Chicago Press. Baldwin, Richard E. 1998. "Global Income Divergence,Trade and Industrialization.The Geography of Growth Take-offs." NBER WorkingPaper SeriesNo. 6458.1. NBER, Wash- ington, D.C. Bank for International Settlements. 1996. 66th Annual Report. BIS,Basel. Barro, Robert, and Xavier Sala-i-Martin. 1992. "Convergence." Journal of Political Economy 100(2):223-51. . 1995. Economic Growth. New York: McGraw-Hill. Barro, Robert, J. Mankiw, N. Gregory, and X. Sala-i-Martin. 1995. "Capital Mobility in Neoclassical Models of Growth." American Economic Review 85:103-15. Baumol, William J. 1986. "Productivity Growth, Convergence, and Welfare. What the Long Run Data Show." American Economic Review 76(5):1072-85. Beck, Thorsten. Ross Levine, and Norman Loayza. 2000. "Finance and the Sources of Growth." Journal of Financial Economics 58(1-2):261-300. Becker, Gary S., Kevin M. Murphy, and Robert Tamura. 1990. "Human Capital, Fertil- ity, and Economic Growth." Journal of Political Economy 98(5):S12-S37. Benabou, Roland. 1993. "Workings of a City. Location, Education, and Production." QuarterlyJournalof Economics108:619-52. .1996. "Heterogeneity, Stratification, and Growth. Macroeconomic Implications of Community Structure and SchoolFinance." American Economic Review 86(3):584- 609. Benhabib.J., and M. Spiegel.1994. "Role of Human Capital in Economic Development. Evidence from Aggregate Cross-Country Data." Journal of Monetary Economics 34:143-73. Bils,Mark, and P. Klenow. 1996. "Does SchoolingCause Growth?" American Economic Review 90(5.):1160-83. Blomstrom, Magnus, R. Lipsey, and M. Zejan. 1996. "Is Fixed Investment the Key to Economic Growth?" Quarterly Journal of Economics 111(1):269-76. Blundell,Richard, and Bond, Stephen. 1997. "Initial Conditions and Moment Restrictions in Dynamic Panel Data Models." University College London Discussion Paper 97-07. Borjas, George J. 1992. "Ethnic Capital and Intergenerational Mobility." Quarterly Journal of Economics107:123-50. . 1995. "Ethnicity, Neighborhoods, and Human Capital Externalities." Ameri- can Economic Review 85(3):365-90. .1999. Heaven's Door. Immigration Policyand the American Economy. Princeton, N.J.: Princeton University Press. Borjas, George J.,Stephen G. Bronars, and Stephen J. Trejo. 1992. "Self Selection and Internal Migration in the United States." Journal of Urban Economics 32:159-85. Easterly and lIevine 215 Bouillon, Cesar,Arianna Legovini,and Nora Lustig. 1999. "Rising Inequality inMexico, Returns to Household Characteristics and the 'Chiappas' Effect." Inter-American Development Bank, mimeo. Finan- Boyd, John H., Ross Levine, Bruce D. Smith. 2001. "The Impact of Inflation on cial Sector Performance." Journal of Monetary Economics. Forthcoming. Brookings Institution Center on Urban and Metropolitan Policy. 1999. A Region Di- vided. The State of Growth in Greater Washington. Washington, D.C.: Brookings Institution. Growth." Bruno, Michael, and Easterly, William. 1998. "Inflation Crisesand Long-run Journal of MonetaryEconomics41:3-26. Burnside, Craig. 1996. "Production Function Regressions, Returns to Scale and Exter- nalities."Journal of MonetaryEconomics37:177-200. Drain?" Carrington, William J., and Enrica Detragiache. 1998. "How Big Is the Brain International Monetary Fund Working Paper 98/102. Carnegie- Carroll, C. D.,and D. N. Weil. 1993. "Saving and Growth. A Reinterpretation." Rochester Series on Public Policy. of Economic Ciccone, Antonio, and Robert E. Hall. 1996. "Productivity and the Density Activity." American Economic Review 86(1):54-70. of Development." Collier, Paul, David Dollar, and Nicholas Stern. 2000. "Fifty Years World Bank, mimeo. of Productivity Costello, Donna M. 1993. "Cross-Country, Cross-Industry Comparison Growth." Journal of Political Economy 101:207-22. Christiansen, L. R. D. Cummings, and D. Jorgenson. 1980. "Economic Growth, 1947- 1973: An International Comparison." In J. W. Kendrick and B. Vaccara (eds.), New and Developments in Productivity Measurement and Analysis. Studies in Income Wealth, Vol. 41, Chicago: University of Chicago Press. and Welfare. Com- De Long, J. Bradford. 1988. "Productivity Growth, Convergence, ment." American Economic Review 78(5):1138-54. United States and the Denison, Edward F. 1962. Sources of Economic Growth in the Development. Alternatives Before Us. New York. Committee for Economic . 1967. Why Growth Rates Differ. Washington, D.C. Brookings Institution. Dougherty,Christopher. 1991.A Comparisonof Productivityand EconomicGrowth in the G-7 Countries. Ph.D. dissertation, Harvard University. Model Easterly, William. 1999a. "The Ghost of Financing Gap. Evaluating the Growth of the International Financial Institutions." Journal of Development Economics, December. 1999b. "Life During Growth." Journal of Economic Growth 4(3):239-76. 2001. "The Lost Decades. Developing Countries' Stagnation in Spite of Policy Reform1980-98." Journalof EconomicGrowth 6(2):135-57. Growth. An Easterly, William, and Sergio Rebelo. 1993. "Fiscal Policy and Economic Empirical Investigation." Journal of Monetary Economics 32:417-58. "Good Easterly, William, Michael Kremer, Lant Pritchett, and Lawrence Summers. 1993. Policy or Good Luck? Country Growth Performance and Temporary Shocks." Jour- nal of MonetaryEconomics32:459-83. Elias, Victor J. 1990. Sources of Growth. A Study of Seven Latin American Economies. International Center for Economic Growth. 216 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. 2 Fischer, Stanley. 1993. "The Role of Macroeconomic Factors in Growth." Journal of Monetary Economics 32:485-512. Frarikel, J. A., and David Romer. 1999. "Does Trade Cause Growth?" American Eco- nomic Review 89:379-99. Fujita, Masahisa, Paul Krugman, and Anthony Venables. 1999. The Spatial Economy: Cities, Regions, and International Trade. Cambridge, Mass.: MIT Press. Grossman, G., and E. Helpman. 1991. "Quality Ladders in the Theory of Economic Growth." Review of Economic Studies 58:43-61. Grubel, Herbert G., and Anthony Scott. 1977. The Brain Drain. Determinants, Mea- surement and Welfare Effects. Waterloo, Ontario: Wilfrid Laurier University Press. Hadjmichael, Michael T., Michael Nowak, Robert Sharer, and Amor Tahari. 1996. Adjustment for Growth. The African Experience. Washington, D.C.: IMF. Hall, Robert E., and Charles Jones. 1999. "Why Do Some Countries Produce SoMuch More Output per Worker than Others?" Quarterly Journal of Economics 114(1):83- 116. Hansen, Gary D., and Edward Prescott. 1998. "Malthus to Solow." NBER Working Paper Series No. 6858.1-24. Hanushek, Eric A., and Dennis D. Kimko. 2000. "Schooling, Labor-Force Quality, and the Growth of Nations." American Economic Review 90(5):1184-1208. Harberger, Arnold C. 1998. "A Vision of the Growth Process." American Economic Review 88(1):1-32. Holmes, T., and J. A. Schmitz Jr. 1995. "Resistance to New Technologies and Trade between Areas." Federal Reserve Bank of Minneapolis Quarterly Review 19:2-18. International Labor Organization. 1995. World Employment. Geneva. Jalan, Jyotsna, and Martin Ravallion. 1997. "Spatial Poverty Traps?" World Bank Policy Research Working Paper No. 1862. Jones, Charles. 1995a. "R&D-Based Models of Economic Growth." Journal of Political Economy 103:759-84. . 1995b. "Time SeriesTests ofEndogenous Growth Models." Quarterly Journal of Economics 105(2):495-526. . 1997. "Comment on Peter Kienow and Andres Rodriguez-Clare, 'The Neoclas- sical Revival in Growth Economics. Has It Gone Too Far?"'NBER Macroeconomics Annual 12:73-103. . 1999. "Was an Industrial Revolution Inevitable? Economic Growth Over the Very Long Run." Stanford University, mimeo. Jorgenson, Dale W. 1995. Productivity. Cambridge, Mass.: MIT Press. Kendrick, John W., and Elliot S. Grossman. 1980. Productivity in the United States: Trends and Cycles. Baltimore, Md.: Johns Hopkins University Press. King, Robert G., and Ross Levine. 1994. "Capital Fundamentalism, Economic Develop- ment and Economic Growth." Carnegie-Rochester Conference Serieson Public Policy 40:259-92. King, Robert G., and Sergio Rebelo. 1993. "Transitional Dynamics and Economic Growth in the Neoclassical Model." American Economic Review 83:908-31. Klenow, Peter. 1998. "Ideas versus RivalHuman Capital. Industry Evidence on Growth Models." Journal of Monetary Economics 42:2-23. I Easterly and Levine 217 Klenow. Peter, and Andres Rodriguez-Clare. 1997a. "Economic Growth. A Review Es- say." Journal of Monetary Economics 40:597-617. .1997b. "The Neoclassical Revivalin Growth Economics. Has It Gone Too Far?" NBER Macroeconomics Annual 12:73-103. Klitgaard, Robert, and Amand Fitschen. 1997. "Exploring Income Variations across Traditional Authorities in KwaZulu-Natal, South Africa." Development Southern Africa 14(3). Kongsamut, Piyabha, SergioRebelo,and Danyang Xie. 1997. "BeyondBalanced Growth." University of Rochester Working Paper. God. Religion in Kosmin, Barry A., and Seymour P. Lachman. 1993. One Nation under Contemporary American Society. New York: Harmony Books. Kremer, Michael. 1993. "O-ring Theory of Economic Development." Quarterly Jour- nal of Economics108:551-75. Krueger, Alan B., and Mikael Lindahl. 1999. "Education for Growth in Sweden and the World." NBER Working Paper Series No. 7190.1-54. Krugman, Paul R. 1991. Geography and Trade. Cambridge, Mass.: MIT Press. 1995. Development, Geography, and Economic Theory. Cambridge, Mass.: MIT Press. .1998. "Space.The FinalFrontier." Journal of Economic Perspectives12:161-74. Krugman, Paul R., and Anthony J. Venables. 1995. "Globalization and the Inequality of Nations." Quarterly Journal of Economics 110(4):857-80. Lipset, Seymour Martin. 1997. American Exceptionalism. A Double Edged Sword. New York: Norton. Levine, Ross, and David Renelt. 1992. "A SensitivityAnalysis of Cross-Country Growth Regressions." American Economic Review 82(4):942-63. Levine, Ross, Norman Loayza, and Thorsten Beck. 2000. "Financial Intermediation and Growth. Causality and Causes." Journal of Monetary Economics 46:31-77. Lewis, W. A. 1954. "Economic Development with Unlimited Supplies of Labor." Manchester School of Economic and Social Studies 22(2):139-91. Lucas, Robert E., Jr. 1988. "On the Mechanics of Economic Development." Journal of Monetary Economics 22:3-42. . 1990. "Why Doesn't Capital Flow from Rich to Poor Countries?" American Economic Review, Papers and Proceedings 80:92-96. .1998. "The Industrial Revolution.Pastand Future." Mimeo, Universityof Chicago. Maddison. Angus. 1995. Monitoring the World Economy, 1820-1992. I'aris: Develop- ment Centre of the Organisation for Economic Co-operation and Development. Mankiw, N. Gregory. 1995. "The Growth of Nations." Brookings Papers on Economic Activity 1:275-326. to the Mankiw, N. Gregory, David Romer, and David N. Weil. 1992. "Contribution Empirics of Economic Growth." Quarterly Journal of Economics 107:407-37. McGrattan, Ellen R. 1998. "A Defense of Fed- AK Growth Models." Quarterly Review, eral Reserve Bank of Minneapolis 22:13-27. Water Mellinger, Andrew D., Jeffrey D. Sachs,and John L. Gallup. 1999. "Climate, Devel- Navigability, and Economic Development." Harvard Center for International opment Working Paper No. 24. 218 THEWORLD BANKECONOMICREVIEW,VOL. I5, NO. Z Mokyr, Joel. 1992. The Leverof Riches. Technological Creativityand Economic Progress. New York: Oxford University Press. Murphy, Kevin M., Andrei Shleifer, and Robert Vishny. 1989. "Industrialization and the Big Push." Journal of Political Economy 97:1003-26. Nehru, Vikram, and A. Dhareshwar. 1993. "A New Database on PhysicalCapital Stocks. Sources, Methodology, and Results." Revista de Andlisis Econ6mico 8(1):37-60. Nordhaus, William. 1994. "Do Real Output and Real Wage Measures Capture Reality? The History of Lighting SuggestsNot." YaleCowlesFoundation DiscussionPaper 1078. Parente, Stephen. 1994. "Technology Adoption, Learning-by-Doing, and Economic Growth." Journalof EconomicTheory 63:346-69. Parente, S. L., and E. C. Prescott. 1996. "Barriers to Technology Adoption and Devel- opment."Journalof PoliticalEconomy 102(2):298-321. Patrinos, Harry Anthony. 1997. "Differences in Education and Earnings across Ethnic Groups in Guatemala." Quarterly Review of Economics and Finance 37(4):807-21. Prescott, Edward. 1998. "Needed. A Theory of Total Factor Productivity." International Economic Review 39(3):525-32. Pritchett, Lant. 1997."Divergence, BigTime." Journal of Economic Perspectives 11(3): 3-17. .1999. "The Tyranny of Concepts. CUDIE (Cumulated, Depreciated, Investment Effort) Is Not Capital." World Bank, mimeo. . 2000. "Patterns of Economic Growth. Hills, Plateaus, and Mountains." World Bank Economic Review 14(2):221-49. . 2001. "Where Has All the Education Gone?" World Bank Economic Review. Forthcoming. Psacharopoulos, George. 1994. "Returns to Investment in Education. A Global Update." World Development 22:1325-1343. Quah, Danny. 1993. "Galton's Fallacy and Tests of the ConvergenceHypothesis." Scan- dinavianJournal of Economics95(4):427-43. Rappaport, Jordan, and Jeffrey Sachs. 1999. "The United States as a CoastalNation." Harvard Center for International Development, mimeo. Rauch, James E. 1993. "Productivity Gains from Geographic Concentration of Human Capital. Evidence from the Cities." Journal of Urban Economics 34:380-400. Ravallion, Martin, and Jyotsna Jalan. 1996. "Growth Divergence Due to Spatial Exter- nalities." Economics Letters 53:227-32. Ravallion, Martin,and Quentin Wodon. 1998. "Poor Areas or Only Poor People?" World Bank, mimeo. Ray, Debraj. 1998. Development Economics. Princeton, N.J.: Princeton University Press. Rebelo, Sergio,and Nancy L. Stokey. 1995. "Growth Effects of Flat-Rate Taxes." Jour- nal of PoliticalEconomy 103:519-50. Rodrik, Dani. 1998. "Where Did all the Growth Go? External Shocks, Social Conflict and Growth Collapses." NBER Working Paper Series No. 6350. Romer, Paul. 1986. "Increasing Returns and Long-Run Growth." Journal of Political Economy 94:1002-37. . 1990. "Endogenous TechnologicalChange." Journal of PoliticalEconomy 98:S71-S102. Easterly andLevine 219 Brookings 1995. "Comment on N. Gregory Mankiw, 'The Growth of Nations"' Papers on Economic Activity 1:313-20. Rostow, W. W. 1960. The Stages of Economic Growth. A Non-Communist Manifesto. Cambridge: Cambridge University Press. Econom- Shleifer, Andrei,and Robert Vishny. 1993. "Corruption." Quarterly Journal of ics 108(3):599-667. Solow, R. 1956. "A Contribution to the Theory of Economic Growth." Quarterly Jour- nal of Economics 70:65-94. . 1957. "Technical Change and the Aggregate Production Function." Review of Economics and Statistics 39:312-20. Mass.: Addison- Todaro, Michael P. 2000. Economic Development, 7th ed. Reading, Wesley. Union Bank of Switzerland. 1994. Pricesand Earnings around the Globe. Zurich: United Bank of Switzerland. United Nations. 1996. World Economic and Social Survey. United States Government. 1996. 1995 Statistical Abstract of US. Washington, D.C. D.C.: World Bank. World Bank. 1993. The East Asian Miracle. Washington, . 1995. Latin America after Mexico. Quickening the Pace. Washington, D.C.: World Bank. Press. 1999. World Development Report. Oxford: Oxford University Bank. 2000a. Can Africa Claim the 21st Century? Washington, D.C.: World Bank. 2000b. East Asia. Recovery and Beyond. Washington, D.C.: World 2000c. The Road to Stability and Prosperity in South Eastern Europe. Europe and Central Asia Region, Washington, D.C.: World Bank. .2000/2001. World Development Report. Attacking Poverty. Washington, D.C.: World Bank. Realities Young, Alwyn. 1995. "The Tyranny of Numbers: Confronting the Statistical of the East AsianGrowth Experience." Quarterly journal of Economics 110:641-80. i i I I I THE WORLD BANK ECONOMIC REVIEW, VOL. 15, NO. 2 ZI-Z2.4 What have we learnedfrom a decade of empirical researchon growth? Comment on "It's Not Factor Accumulation: Stylized Facts and Growth Models," by William Easterly and Ross Levine PeteKlenow William Easterly and Ross Levinedocument five stylized facts about growth and argue that they imply a bigger role for total factor productivity (TFP)and tech- nology than for physical and human capital. I agree with the first four of their facts and believe facts 1 and 3 provide strong support for their conclusion that TFP should be the focus of growth research. FACT I: TFP ACCOUNTS FOR MOST INCOME AND GROWTH DIFFERENCES I would add another piece of evidence pointing to the same conclusion. Jasso, Rosenzweig, and Smith (2000) compare earnings of U.S. immigrants with their earnings in their country of origin. With adjustments for local purchasing States as power, the average immigrant earns 2.2 times as much in the United in their country of origin. That is 75 percent as big as the earnings gap be- tween the average U.S. worker and the average worker in source countries, suggesting that 75 percent of the gap between U.S. and source country earn- ings cannot be explained by general human capital. Easterly and Levine at- tribute about 25 percent of the gap to physical capital per worker. That leaves about 50 percent accounted for by TFP. capital exter- TFP differences could reflect disembodied technology, human nalities, access to specialized or high-quality capital or intermediate goods, the degreeof competition, or measurement error. Research has barely begun to quan- tify the contributions of each of these. As important as TFP is for country differences, it seems less important for the overall upward trend in GDP per capita. Averaging across 98 countries, Klenow and Rodriguez-Clare (1997) attributed 70 percent of growth to physical and human capital. Pete Klenow isa senior economistat the Federal ReserveBank of Minneapolis. C 2001 The International Bank for Reconstruction and Development / THE WORLD BANK 221 222 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. Z FACT 2.: INCOME DIVERGES OVER THE LONG RUN Whether income diverges over the long run is not so clear for more recent peri- ods. Parente and Prescott (2000) find that the "East" grew much faster than the "West" during 1960-95. Using Summersand Heston data for 102 countries over 1960-90, I find a 2 percent decline in the population-weighted standard devia- tion of log per capita income. Easterly and Levine argue that divergence is inconsistent with growth being driven by factor accumulation; because of diminishing returns, factors should tend to equalize rather than diverge. But differences in institutions can work against factor convergence. Certain policies (high tax rates, protectionism, weak property rights) can reduce accumulation of physical and human capital. Diver- gence in policies can therefore lead to divergence of factors. The West's institu- tions may have improved in the 19th century, producing a century of divergence. The East may have adopted better policies since 1960, leading to factor conver- gence since then. This is not to say that divergence-even if traced to policy divergence-re- quires a factor interpretation. Policies can affect TFP, too. Similarly, one can offer TFP explanations for convergenceepisodes. Parente and Prescott (2000) note that all 20th-century growth miracles have occurred in countries starting far behind the richest countries, consistent with technology catch-up. And the later they take off, the fasterthey catch up. Factors can diverge or converge, and so can TFP. Episodes of divergence and convergence need to be examined more closely to determine the roles of physi- cal capital, human capital, and TFP. For the five Asian miracle economies, Young (1995, 2000) points to factor accumulation. FACT 3: FACTOR ACCUMULATION Is PERSISTENT, GROWTH Is NOT The corollary to fact 3 is that TFP growth is not very persistent. Related, East- erly and others (1993) show that country policy differences are much more per- sistent than country growth rate differences. Why would policies be more per- sistent than TFP growth? The answer may be that policies affect the level of a country's TFP, not its growth rate. And changes in policies may only temporarily affect a country's growth rate. Picture countries trending together, linked by technology diffusion. Countries with higher levelsof income are the ones with better policies. Growth miracles are produced by dramatic improvements in policies, and growth disas- ters by deteriorating policies. China is a fast grower not because its institutions are among the best but because it has improved its institutions so much in the last two decades. If it does not reform further, its per capita income might level out at, say, 30th percentile in the world distribution. In this view, TFP growth is not persistent because changes in policies are not persistent. Some countries follow up reforms with more reforms, but others go IlKlenow 223 back on their reforms. This conjecture could be investigated by looking at the persistence of policy changes and how policy changes correlate with TFP growth. If policy changes are not persistent, however, why is factor accumulation persistent? Schooling yields returns for decades. Schooling may respond not to current policies but to the much smoother "average" policy expected over fu- ture working life. Physical capital investments are shorter lived, but still last a decade or more on average. In contrast, private returns to raising TFP may be shorter-lived and more sen- sitive to current policy. A firm improving its efficiency may gain for only a few years, until competitors imitate it. Changes in market share between efficient and less efficient firmsmay be reversed when policies are reversed. FACT 4: EcONOMIc ACTIVITY Is HIGHLY CONCENTRATED GEOGRAPHICALLY As Easterly and Levine document, economic activity is highly concentrated even within countries. They argue that, without differences in TFP, factors should spread out evenly because of diminishing returns. That factors do not spread out evenly suggests differences in and TFP, perhaps owing to technology externalities. But just as policy divergence could lead to factor divergence, policy differ- ences can lead to geographic concentration within countries. Take the coastal areas of China. These areas were opened to foreign trade much earlier and more extensively than the rest of China, attracting huge inflows of labor and capital. For another example, Holmes (1998) documents heavy concentration of manu- facturing in right-to-work states within the United States. If land is not a very important factor, then lots of concentration can result from modest differences in policy or geography or technology. Suppose land's share is 5 percent, as in Lucas (forthcoming). If TFP differs across locations by a factor of 1.4 (compared to say 5 or 6 across countries), then output per unit of land will differ by a factor of 1,000 to equate returns to physical and human capital. If TFP differsby a factor of 1.6, output per unit of land will differ by a factor of 10,000. FACT 5: NATIONAL POLICIEs AFFECT LONG-RuN NATIONAL GROWTH RATES Easterly and Levineshow that country growth rates are correlated with country policy variables such as schooling, openness to trade, the size of government, the black market premium, and private credit. They are keenly aware that some of these variables may result from growth rather than cause it, so they are care- ful to instrument with lags. But even lagged variables can be subject to reverse causality. For example, increases in private credit could result from higher ex- pected future growth. 224 THE WORLD BANKECONOMICREVIEW,VOL. 15, NO. Z If establishing any causal effect is difficult, establishing a long-run effect on the growth rate is harder still. The data could berevealing temporary rather than permanent growth effects. Consistent with this, many policies are correlated with growth only when simultaneously controlling for initial income. Openness to trade, for example, might have a positive coefficient because it facilitates tech- nology diffusion. But once a country closes in on the technology frontier, open- ness will not continue to keep the growth rate high, only the levelof incomehigh. The fact that policies are more persistent than growth rates is consistent with policies affecting long-run levelsmore than long run growth rates. REFERENCES Easterly, William, Michael Kremer, Lant Pritchett, and Lawrence H. Summers. 1993. "Good Policyor Good Luck? Country Growth Performance and Temporary Shocks." Journal of Monetary Economics 32(3):459-83. Holmes, Thomas J. 1998. "The Effect of State Policies on the Location of Manufactur- ing: Evidence from State Borders." Journal of Political Economy 106(4):667-705. Jasso, Guillermina, Mark R. Rosenzweig, and James P. Smith. 2000. "The Earnings of U.S.Immigrants: SkillTransferabilityand Selectivity."Department of Economics, New York University, New York, N.Y. Klenow, Peter J., and Andres Rodriguez-Clare. 1997. "The Neoclassical Revival in Growth Economics: Has It Gone Too Far?" Macroeconomics Annual 1. Cambridge, Mass.: National Bureau of Economic Research. Lucas, Robert E.Forthcoming.. "Externalitiesand Cities." Review of Economic Dynamics. Parente, Stephen L., and Edward C. Prescott. 2000. Barriersto Riches. Cambridge, Mass.: MIT Presss. Young, Alwyn. 1995. "The Tyranny of Numbers: Confronting the Statistical Realityof the East Asian Growth Experience." Quarterly Journal of Economics 110(3):641-80. .2000. "Gold into Base Metals: Productivity Growth in the People's Republic of China during the Reform Period." NBER Working Paper 7856. National Bureau of Economic Research, Cambridge, Mass. THE WORLD BANKECONOMIC REVIEW, VOL. 15, NO. Z 225-ZZ7 What have we learnedfrom a decade of empirical researchon growth? Comment on "It's Not Factor Accumulation: Stylized Facts and Growth Models," by William Easterly and Ross Levine PaulRomer When economists in the 1950s and 1960s used growth models to understand the experience of developing countries, they allowed for the possibility oftechnology differences between developing countries and the United States. But because they did not have a good theory for talking about the forces that determined the level of the technology-in the United States any more than in developing countries- technology factors tended to be pushed into the background in policy discussions. MODELING THE TECHNOLOGY FACTOR In the 1980s, several economists began to develop formal models of this tech- nology factor, which has conventionally beendesignated A.We used those models to think about the behavior of A in the United States and in other countries. These "new growth" models had striking implications. Output per capita could diverge. Capital and skilledworkers might flow from poor to rich countries. Trade in goods or investment decisions by firms could influence the diffusion of A between developed and developing countries. All this meant that government policies that affect incentives for firms could have big effects on economic outcomes. The new growth theory of the 1980s generated a counterreaction in the 1990s that Pete Klenow and Andres Rodriguez-Clare have called the "neoclassical re- vival." Proponents of the neoclassical view argued that for purposes of explain- ing cross-country variation in levels of income or rates of growth, economists could return to the framework of the 1960s and append the strong assumption that A is the same in all countries. In this approach, the cross-country variation in the level and rate of economic development could be understood entirely in terms of differences in the level and rate of accumulation of traditional inputs: physical capital, human capital, and unskilled labor. Paul Romer isprofessor of economicsat Stanford University. © 2001 The International Bank for Reconstruction and Development / THE WORLDBANK 225 226 THE WORLD BANK ECONOMIC REVIEW,VOL. I5, NO. 2 ATTACKING BUSINESS AS USUAL IN EMPIRICAL GROWTH THEORY The article by William Easterly and Ross Levineis part of the next swing in the scholarly pendulum. It moves away from the critical assumption in the neoclas- sical revival that the level of technology is the same in all countries. Equally important (if not more so), it makes an implicit case for moving away from a narrow focus on testing models. In its place, the authors challenge economists to understand what happens in the countries that they study. At a substantive level, they suggest that there is abundant evidence that some- thing such as the levelof the technology does vary across countries. That much is clear. But at a methodological level, they are doing more. They attack business as usual in empirical growth theory. To avoid the threat that a wide variety of evi- dence would pose to the neoclassical revival, economists who supported this pro- gram advocated a narrow methodology based on model testing. Pick a few sum- mary statistics generated from a specially selected data source. (Typically they are partial correlations generated by running a regression on a cross-country data set.) Use strong theoretical priors to restrict attention to a very small subset of all pos- sible models. Then show that one of the models from within this narrow set fits the data and, if possible, show that there are other models that do not. Having tested and rejected some models so that the exercise looks like it has some statis- tical power, accept the model that fits the data as a "good model." The obvious problem with this approach is that many models are consistent with the few correlations that emerge from a single data set. Many alternative models are never considered in the standard model testing exercise, so it has no power against these alternatives, no ability to weigh their plausibility relative to that of the "good model." Suppose an economist runs a regression conditioned on other variables and finds that countries with lower initial income grow more rapidly. Within a neoclassical model with an exogenously determined level of A, this finding can be interpreted as evidence of diminishing returns to physical capital or human capital because of exogenous variation in rates of investment in physical or human capital. But it is also possible that the technology is lower in the country that starts at a lower level of development and grows faster as better technology diffuses there. Ifthe economist looks only at the cross-country regression evidence, there isnothing that would raise questions about the initial assumption of identical technologies in all countries. But as Easterly and Levine point out, if you bring other evidence, such as the pattern of flows of people between countries, the identical technologies model no longer fits. For someone who wants to maintain an unreasonable prior as- sumption, the advantage of a narrow focus on one piece of data is that it does not threaten the convenient theoretical framework built on this prior. It is pos- sible to go through the motions of doing science, testing various theories and rejecting some in favor of others. But far from advancing the science, this ap- proach is a dead end. It does not allow for rejecting or modifying prior beliefs that simply turn out to be wrong. Romer 227 Of course, economists who would like to stay in the business of doing these narrow, model-testing exerciseshave a response. They say that one model should be used to explain cross-country regressions and another to explain factor flows between countries. If they were defense attorneys in a criminal case, they could provide a different theory to explain every specificpiece of evidence at the crime scene. But they would not be able to tella consistent story about what actually happened. No amount of methodological obfuscation about "as-if" modeling, "parsi- mony," "pushing the limits of benchmark models," and the like should be al- lowed to hide the fact that, like judgesand jurors, policymakers and economists have to make judgments about what actually happened. Otherwise, they have no basis for making well-informed decisions about what to do next. Easterly and Levine show economists how they can best contribute in this effort-assemble as much evidence as possible and search for a consistent theoretical explanation that fits it all. At a substantive level, the authors suggest that there isabundant evidence that something like the level of technology does vary between countries. Admitting this possibility could have important implications for policy. If economists take the classical model seriously as a description of the development process-that is, if they acceptthat an economy is well described as a competitive equilibrium with an exogenously given level of technology-then Harberger's pioneering analysis of the welfare costs of distortionstells us that bad government policies imply tiny welfare losses. Economists would then be left with a st.rikingconclu- sion, one that few practitioners would take seriously: Countries are poor not becauseof bad policies but because of exogenous preference differencesthat cause them to accumulate less physical and human capital. The risk is not that practi- tioners will take this conclusion seriously, but that they will dismiss formal eco- nomic theory and empirical work as flawed beyond repair. THEWORLD BANKECONOMICREVIEW,VOL. I 5, NO. 2 ZZ9-2'72 What have we learnedfrom a decade of empirical researchon growth? Growth Empirics and Reality William A. Brock and StevenN. Durlauf This article questions current empirical practice in the study of growth. It argues that regres- much of the modern empirical growth literature is based on assumptions about sors, residuals, and parameters that are implausible from the perspective of both eco- nomic theory and the historical experiences of the countries under study. Many of these problems, it argues, are forms of violations of an exchangeability assumption that implicitly underlies standard growth exercises. The article shows that these implausible assumptions can be relaxed by allowing for uncertainty in model specification. Model uncertainty consists of two types: theory uncertainty, which relates to which growth re- determinants should be included in a model; and heterogeneity uncertairity, which lates to which observations in a data set constitute draw from the same statistical model. The article proposes ways to account for both theory and heterogeneity uncertainty. Finally, using an explicit decision-theoretic framework, the authors describe how one can engage in policy-relevant empirical analysis. There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy. -William Shakespeare Hamlet, act 1, scene 5 The objective of this article is ambitious-to outline a perspective on empirical growth research that will both address some of the major criticisms to which this research has been subjected and facilitate policy-relevant empirics. It is no exaggeration to say that the endogenous growth models pioneered in Romer (1986, 1990) and Lucas (1988) have produced a sea change in the sorts of ques- tions around which macroeconomic research is focused. In empirical macroeco- nomics, efforts to explain cross-country differences in growth behavior since World War II have become a predominant area of research. The implications of this work for policymakers are immense. For example, strong links exist between national growth performance and international poverty and inequality. Differ- University of William A. Brock and Steven N. Durlauf are with the Department of Economics, Wisconsin. Their e-mail addresses are wbrock@ssc.wisc.edu and sdurlauf@ssc.wisc.edu. The authors Foundation, Vilas Trust, thank the National Science Foundation, John D. and Catherine T. MacArthur for initiating thisre- and Romnes Trust for financial support. They thank Francois Bourguignon both search and for helpful suggestions, as well as Gernot Doppelhofer, Paul Evans, Cullen Goenner, Andros Kourtellos,Artur Minkin, Eldar Nigmatullin, Xavier Sala-i-Martin, Robert Solow, seminar participants Ming at Carnegie-Mellon and Pittsburgh, and three anonymous referees for helpful cornments. Chih Easterly and Ross Levine Tan has provided superb research assistance. Special thanks go to William for sharing data and helping with replication of their results. An earlier version of this article was pre- of Empirical Research sented at the World Bank conference "What Have We Learned from a Decade on Growth?" held on 26 February 2001. 0 2001 The International Bank for Reconstruction and Development / THE WORLD BANK 229 230 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. 2 ences in per capita income across countries are substantially larger than those within countries; Schultz (1998) concludes that two-thirds of (conventionally measured) inequality across individuals internationally is due to intercountry differences, so that efforts to reduce international inequality naturally focus on cross-country growth differences. In turn, the academic community has used this new empirical work as the basis for strong policy recommendations. A good example is Barro (1996). Based on a linear cross-country growth regression of the type so standard in this literature, Barro (1996, p. 24) concludes that The analysis has implications for the desirability of exporting democratic institutions from the advanced western economies to developing nations. The first lesson isthat more democracy isnot the key to economic growth. ... The more general conclusion isthat advanced western countries would contribute more to the welfare of poor nations by exporting their eco- nomic systems, notably property rights and free markets, rather than their political systems. Yet there is widespread dissatisfaction with conventional empirical methods of growth analysis. Many critiques of growth econometrics have appeared in recent years. Typical examples include Pack (1994, pp. 68-69) who described a litany of problems with cross-country growth regressions: Once both random shocks and macroeconomic policy variables are recog- nized as important, it is no longer clear how to interpret many of the expla- nations of cross-country growth.... Many of the right hand side variables are endogenous.... The production function interpretation is further muddled by the assumption that all countries are on the same international production frontier . . . regression equations that attempt to sort out the sourcesof growth alsogenerallyignoreinteraction effects.... The recent spate of cross-country growth regressions also obscures some of the lessons that have been learned from the analysis of policy in individual countries. Another is Schultz (1999, p. 71): "Macroeconomic studies of growth often seek to explain differences in economic growth rates across countries in terms of lev- els and changes in education and health human capital, among other variables. However, these estimates are plagued by measurement error and specification problems." In fact, it seems no exaggeration to say that the growth literature in economics is notable for the large gaps that persist between theory and empirics. A recent (and critical) surveyof the empiricalliterature, Durlauf and Quah (1999, p. 295), concludes that the new empirical growth literature remains in its infancy. While the litera- ture has shown that the Solow model has substantial statistical power in explaining cross-country growth variation, sufficientlymany problems exist with this work that the causal significance of the model is not clear. Fur- Brock and Dur/auf 231 ther, the new stylized facts of growth, as embodied in nonlinearities and distributional dynamics have yetto be integrated into full structuralecono- metric analysis. Our purposes in this article are threefold. First, we attempt to identify some general methodological problems that we believe explain the widespread mis- trust of growth regressions. Although the factors we identify are not exhaustive, they do represent many of the most serious criticisms of conventional growth econometrics of which we are aware. These problems are important enough to at best seriouslyqualify and at worst invalidate many of the standard claimsmade in the new growth literature concerning the identification of economic structure. In particular, we argue that causal inferences as conventionally drawn in the empirical growth literature require certain statistical assumptions that may eas- ily be argued to beimplausible. This assertion holds from the perspective of both economic theory and the historical experiences of the countries under study. We further argue that a major source of skepticism about the empirical growth lit- erature, and one that incorporates many of the usual criticisms, is,the failure of certain statisticalconditions representing forms of a property known as exchange- ability to hold in conventional empirical growth exercises. Second, we argue that the exchangeability failures underlying many criticisms of growth models may be constructively dealt with through explicit attention to model uncertainty in the formulation of growth regressions; see Temple (2000) for a complementary analysis. What we mean is the following: In estimating a particular regression, the inferences are made conditional both on the data and on the specification of the regression. The exchangeability objection to a regres- sion amounts to questioning whether the specification of the regression is cor- rect. The assumption that a particular specification is correct can be relaxed by treating model specification as an additional unknown feature of the data, that is, by explicitly incorporating model uncertainty in the statistical analysis. In taking this approach, we follow some important recent developments in the empirical growth literature-Fernandez, Ley, and Steel (1999) and Doppelhofer, Miller, and Sala-i-Martin (2000)-in endorsing the use of Bayesian methods to address explicitly the model uncertainty that we believe underlies the mistrust of conventional growth regressions. This analysis does not address all the criti- cisms we describe in the first part of the article. In particular, we argue that questions of causality versus correlation, which are of first-order importance in interpreting growth regressions, may only be addressed using substantive infor- mation that originates outside the models under analysis. Nevertheless, account- ing for exchangeability can strengthen the confidence that may be attached to causal interpretations of regression exercises. Third, we argue that the appropriate use of empirical growth analyses for policy analysis requires an explicit decision-theoretic formulation. Current em- pirical practice in growth is therefore not "policy-relevant" in the sense that the 232 THE WORLD BANK ECONOMIC REVIEW, VOL. 15, NO. z policy inferences of a given data analysis are decoupled from the analysis itself. For example, one often sees a statistically insignificant coefficient used as evi- dence that some policy is not important for growth or, conversely, the assertion that statistical significance establishes the importance of some policy. We argue that these types of claims are not appropriate. Ideally, empirical growth exer- cises should employ cross-country growth data to compute predictive distribu- tions for the consequences of policy outcomes, distributions that can then be combined with a policymaker's welfare function to assess alternative policy sce- narios. A decision-theoretic approach to evaluating growth regressions can pro- vide a better measure of the levelof the evidence inherent in the available data, especially for the construction of policy-relevant predictive structures through empirical growth analyses. The title of this article intentionally echoes the classic Sims (1980) critique of macroeconometric models. The growth literature does not suffer from the exact type of "incredible" assumptions (Sims 1980) that were required to identify eco- nomic structure through 1960s-style simultaneous equation models and whose interpretation Sims was attacking. Yet this literature does rely on assumptions that may be argued to be equally dubious and whose implausibility renders the inferences typically claimed by empirical workers to be equally suspect.' As will be clear from our discussion, this article only begins to scratch the surface of a policy-relevant growth econometrics. Our hope isthat the ideas herein will fa- cilitate new directions in growth research. At the same time, our purpose is not to argue that statistical analyses of cross- country growth data are incapable of providing insights. Regression and other forms of statistical analysis have several critical roles in the study of growth. One role isthe identification of interesting data patterns, patterns that can both stimu- late economic theory and suggest directions along which to engage in country- specific studies. Quah's work (1996a, 1996b, 1997) is exemplary in this regard. However, we focus explicitly on the role of empirical work in formulating policy recommendations. In particular, a second goal of this article is to explore how one can, by casting empirical analysis in an explicitly decision-theoretic frame- work, develop firmer insights into the growth process. Throughout we will take an eclectic stance on how one should go about data analysis. Many of our ideas are derived from the Bayesian statistics literature. Yet the basic arguments we make are relevant to frequentist analyses. Our view of data analysis is essentially pragmatic. Data analyses of the sort that are con- ventional in economics should be thought of as evidence-gathering exercises aimed at facilitating the evaluation of hypotheses and the development of policy- relevant predictions for future trajectories of variables of interest. For example, one starts with a proposition such as "the level of democracy in a country caus- ally influences the levelof economic growth." Once this statement is mathemati- 1. A number of the issues we raise echo, at least inspirit, Freedman (1991, 1997), who has made serious criticismsof the use of regressions to uncover causal structure in the socialsciences. Brock and Durlauf 233 cally instantiated (which means that ceteris paribusconditions are formalized, a more or lessconvincing theoretical model or set of models of causal influence is formulated in a form suitable for econometric implementation, etc.), the pur- pose of an empirical exercise isto see whether the statement ismore or lessplau- sible once the analysis has been conducted. The success or failure of an empiri- cal exercise rests on whether one's prior views of the proposition have been altered by the analysis and on whether the level of uncertainty around a conclusion is low enough for the conclusion to be of policy relevance. Our position is that one should evaluate statistical procedures on the basis of whether they success- fully answer the questions for which they are employed; we are unconcerned, at least in this article, with abstract issues that distinguish frequentist and Bayesian approaches, for example. Many of our criticisms of the empirical growth literature apply in principle to other empirical contexts. They take on particular force in the growth context because of the complexity of the objects under study, the poor data available for empirical growth work, and the qualitative nature of the theories that drive the new growth literature. I. A BASELINE REGRESSION The bulk of modern empirical work on growth has focused on cross-country growth regressions of the type pioneered by Barro (1991) and Mankiw, Romer, and Weil (1992). Although recent work has extended growth analysis to con- sider panels (Evans 1998; Islam 1995; Lee, Pesaran, and Smith 1997), the argu- ments we make relating to conventional empirical growth practice as well as our proposed alternative approach are generally relevant to that context too, so long as cross-section variation is needed for parameter identification. I lence we focus on cross-sections. A generic form for various cross-country growth regressions is (1) gi= Xyir + Z,7 + £i where g, is real per capita growth in economy i over a given period (typically measured as the change in per capita income between the beginning and end of the sample divided by the number of years that have elapsed). We have divided the regressors into two types. Xi represents variables whose presence issuggested by the Solow growth model: a constant, initial income and a set of country-specific savings and population growth rate controls. The Solow model isoften treated as a baseline from which to build up more elaborate growth models, hence these variables tend to be common across studies. Z1, in contrast, consists of variables chosen to capture additional causal growth determinants that a researcher be- lieves are important and so generally differs across analyses.2 2. See Galor (1996)for a discussionof the implications of different growth theories for convergence and Bernard and Durlauf(1996) for an analysis of the economic and statistical meanings of convergence. 234 THE WORLD BANK ECONOMIC REVIEW, VOL. 15, NO. 2 Though this regression is typically applied to national aggregates, it can in principle be applied to regions or sectors once giis reinterpreted as a vector of growth rates within a country. This isparticularly important for policy analysis when a given policy may affect different regions or population groups differ- ently. Our conjecture is that such decompositions are important when evaluat- ing growth policies with significant distributional consequences. In our discussion we assume that the motivation for the estimation of a re- gression of the type givenin equation 1 is policy driven. Specifically,we assume that a policymaker is interested in using this equation to advise some country i on whether it should change some policy instrument z. If the policymaker's ob- jectivefunction depends on the growth rate in country i, he will presumably need to understand the country's overall growth process and hence to make inferences about a number of aspects of equation 1 in addition to ir;,the coefficient on the policy instrument. We return to this issue in section VI. II. ECONOMETRIC ISSUES In this section we discuss three problems with the use of the baseline equation 1 in policymaking or other exercisesin which one wishes to give a structural inter- pretation to this regression. These problems all, at one level, occur because of violations of the assumptions necessary to estimate equation 1 using ordinary least squares (OLS) and interpret the estimated equation as the structural model of growth dynamics implied by the augmented Solow model. Each of these criti- cisms ultimately reduces to questioning whether growth regressions as conven- tionally analyzed can provide the causal inferences that motivate such analyses. As discussed in the introduction, growth regressions have been subjected to a wide range of criticisms from many authors. We do not claim that any of the criticisms are necessarily original to us; instead, we believe our contribution in this section lies inthe way we organize and unify these criticisms. Open-Endednessof Theories A fundamental problem with growth regressions isdetermining what variables to include in the analysis. This problem occurs because growth theories are open- ended. By open-endedness, we refer to the idea that the validity of one causal theory of growth does not imply the falsity of another. So, for example, a causal relation- ship between inequality and growth has no implications for whether a causal re- lationship exists between trade policy and growth. As a result, well over 90 differ- ent variables have been proposed as potential growth determinants (Durlauf and Quah 1999), each of which has some ex ante plausibility. As there are at best about 120 countries available for analysis in cross-sections (the number may be far smaller as a result of missing observations on some covariates), it is far from obvious how to formulate firm inferences about any particular explanation of growth. This issue of open-endedness has not been directly dealt with in the literature. Instead, a number of researchers have proposed ways to deal with the robust- Brockand l)urlauf 235 ness of variables in growth regressions. The basic idea of this approach is to identify a set of potential control variables for inclusion in equation 1 as ele- ments of Z,. Inclusion of a variable in the final choice of Zi requires that its as- sociated coefficient prove to be robust with respect to the inclusion of other variables. Levine and Renelt (1992) introduced this idea to the growth litera- ture, employing Edward Leamer's ideas on extreme bounds analysis (seeLeamer 1983 and Leamer and Leonard 1983). In extreme bounds analysis, a coefficient is robust if the sign of its OLS estimate stays constant across a set of regressions representing different possible combinations of other variables. Sala-i-Martin (1997), arguing that extreme bounds analysis islikely to lead to the rejection of variables that do influence growth, proposes computing likelihood-weighted significance levels of coefficients across alternative regressions. These proposals for dealing with the plethora of growth theories are useful, but neither is definitive as a way to evaluate model robustness.3 The reason is simple. In these approaches a given coefficient will prove not to be robust if its associated variable is highly collinear with variables suggested by other candi- date growth theories. This is obvious for the Sala-i-Martin approach, because collinearity affects significance levels. It is also true for extreme bounds analy- sis, in the sense that a given coefficient is likely to be highly unstable when alter- native collinear regressors are included alongside its corresponding regressor. Hence these procedures will give sensible answers only if lack of collinearity is a "natural" property for a regressor that causally influences growth. Yetwhen one thinks about theories of how various causal determinants of growth are them- selvesdetermined, it is clear that collinearity isa property that one might expect to hold for important causal determinants of growth.4 This is easiest to see by considering a recursive model for growth. Suppose that growth is causally de- termined by a single regressor, di, and that this regressor in turn depends caus- ally on a third regressor, ci, so that (2) gi = diyd+ F1 di =circ + r,- It is easy to construct cases (which will depend on the covariance structure of c,, F, and q1) in which adding cito the growth equation will render di fragile. Important recent papers by Doppelhofer, Miller, and Sala-i-Martin (2000) and Fernandez, Ley, and Steel (2001) have proposed ways to deal with regressor 3. Leamer's work on model uncertainty falls into two parts: a powerful demonstration of the im- suggestion, extreme portance of accounting for such uncertaintyin making empirical claims, and a specific of hounds analysis, for determining when regressors are fragile. The first constitutes a fundamental set ideas. The second is a particular way of instantiating Leamer's deep ideas of accounting for model uncertainty and is more easily subjected to criticism. By analogy, Rawl's controversial use of minimax arguments to infer what rules are just in a society does not diminish the importance of his idea of the veil of ignorance. Economists have inappropriately used criticisms of extreme bounds analysis to ig- nore the conceptual issues raised by Leamer's work. 4. Leamer is quite clear on this point. See Leamer (1978, p. 172) for further discussion. 236 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. 2 choice and hence at least indirectly with model open-endedness through the use of Bayesianmodel averaging techniques. We exploit the approach used in those papers and therefore defer discussion of them until section V. ParameterHeterogeneity A second problem with conventional growth analyses is the assumption of pa- rameter homogeneity. The vast majority of empirical growth studies assume that the parameters that describe growth are identical across countries. This assump- tion is surely implausible. Does it really make sense to believethat a change in the level of a civil liberties index has the same effect on growth in the United States as in the Russian Federation? Although the use of panel data approaches to growth has addressed one aspect of this problem by allowing for fixed effects (Evans [1998] isparticularly clear on this point), it has not addressed this more general question. In some sense this criticism might seem unfair, as it presumably applies to any socioeconomic data set. After all,economic theory does not imply that individual units ought to be characterized by the same behavioral functions. That said, any empirical analysis necessarily will require a set of interpretable statistical prop- erties that are common across observations; when homogeneity assumptions are or are not to be made is a matter of judgment. Our contention isthat the assump- tion of parameter homogeneity is particularly inappropriate in studying com- plex heterogeneous objects, such as countries. See Draper (1997) for a general discussion of these issues. Evidenceof parameter heterogeneity has been developed in different contexts, such as in Canova (1999); Desdoigts (1999); Durlauf andJohnson (1995); Durlauf, Kourtellos, and Minkin (2000); Kourtellos (2000); and Pritchett (2000). These studies use very different statistical methods, but each suggests that the assump- tion of a single linear statistical growth model that applies to all countries is incorrect.5 Put differently, the reporting of conditional predictive densities based on the assumption that all countries obey a common linear model may under- state the uncertainty present when the data are generated by a family of models; Draper (1997) provides further analysis of this idea. There has been substantial interest in the empirical growth literature in in- corporating forms of parameter heterogeneity when panel data are available. Islam(1995) isan early analysisthat allows constant terms to differacross country growth processes for a panel in which growth ismeasured in five-year intervals. In what appears to be the richest analysis of parameter heterogeneity to date, Lee, Pesaran, and Smith (1997) show how to allow for parameter heterogeneity for regressor slope parameters for a growth model employing annual data. 5. Conventional growth analyses give some attention to parameter heterogeneity between rich and poor countries: Barro(1996), for example,allows the effectsof democracy on growth to differ between rich and poor countries. Brock and Durlauf 237 The idea that panel data may be used to model rich forms of parameter het- erogeneity is of course important; a comprehensive analysis isPesaran and Smith (1995). However, this approach is of limited use in empirical growth contexts, because variation in the time dimension is typically small. This occurs for two reasons. First, many of the variables used as proxies for new growth theories do not vary over high frequencies. For some variables, such as political regime, this is true by their nature; for others, this is due to measurement. In any event, this means that cross-section variation must be used to uncover parameters. Second, there is a conceptual question of the appropriate time horizon over which to employ a growth model. High-frequency data will contain business cycle fac- tors that are presumably irrelevant for long-run output movements. Hence it is difficult to see how annual or biannual data, for example, can be interpreted in terms of growth theories. In our view the use of long run averages has a power- ful justification for identifying growth as opposed to cyclical factors. CausalityversusCorrelation A final source of skepticism about conventional growth empirics relates to a problem endemic to all structural inference in social science-the question of causality versus correlation. Many of the standard variables used to explain growth patterns-democracy, trade openness, rule of law, social capital, and the like-are as much outcomes of socioeconomic decisions and interrelationships as growth itself is. Hence there is an a priori case that the use of OLs estimates of the relationship between growth and such variables cannot be treated as struc- tural any more than coefficients produced by OLS regressions of price on quan- tity can be. Yet the majority of empirical growth studies treat the various growth controls as exogenous variables and so rely on ordinary or heteroskedasticity- corrected least squares estimation. What is particularly ironic about the lack of attention to endogeneity is that it was precisely this lack of attention in early business cyclemodels that helped drive the development of rational expectations econometrics. Recent econometric practice in growth has begun to employ instrumental variables to control for regressor endogeneity. This is particularly common for panel data sets where temporally lagged variables are treated as legitimate in- struments. However, this trend toward using instrumental variables estimation has not satisfactorily addressed this problem. The reason is that the failure to account properly for the open-endedness of growth theories has important im- plications for the validity of instrumental variables methods. What we mean by this is the following. For a regression of the form (3) Yi = R,y + £- the use of some set of instrumental variables 1,as instruments for R, requires, of course, that each element of Ii be uncorrelated with Ei.In the growth litera- ture this is not a condition typically employed to motivate the choice of instru- ments. Instead, instruments are typically chosen exclusively because they are 238 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO.Z in some sense exogenous, which operationally means that they are predeter- mined with respect to eg.Predetermined variables, however, are not necessar- ily valid instruments. As discussed in Durlauf (2000), a good example of this pitfall can be found in Frankel and Romer (1996), which studies the relationship between trade and growth. Frankel and Romer argue that because trade openness is clearly endog- enous, it isnecessary to instrument the trade openness variable in a cross-country regression to consistently estimate the trade opennesscoefficient. To do this, they usea geographic variable, area, as an instrument and argue in favor of itsvalidity that area is predetermined with respect to growth. Their argument that the in- strument ispredetermined iscertainly persuasive. Nevertheless, it ishard to make an argument that it isa valid instrument. Is it plausible that country land size is uncorrelated with the omitted growth factors in their regression? The history and geography literatures are replete with theories of how geography affects political regime, development, and so on. For example, larger countries may be more likelyto be ethnically heterogeneous, leading to attendant social problems. Alternatively, larger countries may have higher per capita military expenditures, which means relatively greater shares of unproductive government investment, higher distortionary taxes, or both. Our argument is not that any one of these links isnecessarily empirically salient, but that the use of land area as an instru- ment presupposes the assumption that the correlations between land size and all omitted growth determinants are in total negligible.It isdifficult to see how such an assumption can be defended when these omitted growth determinants are neither specified nor evaluated. It is interesting to contrast the difficulties of identifying valid instruments in growth contexts with the relative ease with which this is done in rational expec- tations contexts. The reason for this differenceisthat rational expectations models are typically closed in the sense that a particular theory will imply that some combination of variables isa martingale differencewith respect to some sequence of information sets. For the purposes of data analysis, rational expectations models therefore generate instrumental variables, that is, any variables observ- able at the time expectations are formed, whose orthogonality to expectation errors may be exploited to achieve parameter identification. Of course, rational expectation models can be faulted for imposing sufficientlywide-ranging restric- tions on the economic behavior under study that some of the assumptions nec- essary for identification are not plausible; that is, for being insufficiently open- ended in the sense we have described. So the problems associated with theory open-endedness in growth are hardly nonexistent in other contexts. III. EXCHANGEABILITY Inferences from any statistical model can only be made, of course, conditional on various prior assumptions that translate the data under study into a particu- Brock and Durlauf 239 lar mathematical structure. One way to evaluate the plausibility of inferences drawn from empirical growth regressions is by assessing the plausibility of the assumptions made in making this translation. In the empirical growth literature it iseasyto find examples where the assumptions employed to construct statistical models are clearly untenable. For example, researchers typically assume that the errors in a cross-section regression are jointly uncorrelated and orthogonal to the model's regressors.6 Do they really wish to argue that no omitted factors exist that induce correlation acrossthe innovations in the growth regressionsassociated with the model? More generally, it is easy to see that parameter heterogeneity and omitted variables,which, we argued in the previoussection, are endemic to growth regressions, can each lead to a violation of the error uncorrelatedness assumption, the regressor orthogonality assumption, or both. On the other hand, econometrics has a long tradition of identifying mini- mal sets of conditions under which coefficients and standard errors may be consistently estimated. Examples include the emphasis on orthogonality con- ditions between regressors and errors as the basis for OLS consistency (rather than the interpretation of the OLS estimators as the maximum likelihood esti- mates for a linear model with nonstochastic regressors and i.i.d. normal errors) or the use of mixing conditions to characterize when central limit theorems apply to dependent data (rather than the modeling of the series as a known autoregressive moving average process). Hence any critique of cross-country growth analyses that isbased on the plausibility of particular statistical assump- tions needs to argue that the violations of the assumptions invalidate the ob- jectives of a given exercise. In this section we argue that of the three econometric issueswe have raised, the first two may be interpreted as examples of deviations of empirical growth mod- els from a statistical "ideal" that allows for the sorts of inferencesresearchers wish to make in growth contexts. Our purpose is to establish a baseline for statistical growth models suchthat if a model does not meetthis standard, a researcher needs to determine whether the reasons for this invalidate the goal of the ernpiricalexer- cise. Hence the baseline does not describe a necessary requirement for empirical work, but instead helps define a strategy that we think empirical workers should follow in formulating growth models. When a model does not meet this standard, researchers should be prepared to argue that the violations of the standard do not invalidate the empirical claims they wish to make. This standard is based on a concept in probability known as exchangeability.7 6. In the subsequent discussion, we focus on OLS estimation of growth regressions. In the empirical growth literature examples can be found of heteroskedasticity corrections to relax assumptions of iden- tical residual variances and instrumental variables to deal with violations of error/regressor orthogo- nality. Our discussion is qualitatively unaffected by either of these alternatives to OLs. 7. Bernardo and Smith (1994) provide a complete introduction to exchangeability. )raper and others (1993) develop a detailed argument on the importance of exchangeability to statistical inference. Our analysis is much indebted to their perspective. 240 THE WORLDBANKECONOMICREVIEW,VOL. I5, NO. 2 Basic Ideas A formal definition of exchangeability is as follows. DEFINITION: EXCHANGEABILITY. A sequence of random variables 71;is exchange- able if, for every finite collection ill ... rIKof elements of the sequence, (4) p(r1l al . . . t1K = aK) = (rlpj)= a,, **. 7p(K)= aK)8 where p( . ) is any operator that permutes the K indices. Exchangeability is typically treated as a property of the unconditional prob- abilities of random variables. In regression contexts, however, it is often more natural to think in terms of the properties of random variables conditional on some information set. For example, in a regression, one is interested in the prop- erties of the errors conditional on the regressors. We therefore introduce a sec- ond concept, F-conditional exchangeability.9 DEFINITION: F-CONDITIONAL EXCHANGEABILITY.For a sequence of random vari- ables q, and a collection of associated random vectors Fi, 1iis F-conditionally exchangeable if, for every finite collection 1m. ... K of elements of the sequence, ,u(711= al***, 71K = aK IF ) = Yu(77p(i)= a, *1p(K-) rl = aK IF ) where p( ) is any operator that permutes the K indices and F = (F1 . . . FK}. If F, = o V i, the empty set, F-conditional exchangeability reduces to exchangeability. Associated with exchangeability and F-conditional exchangeability isthe idea of partial exchangeability. DEFINITION: PARTIAL EXCHANGEABILITY. A sequence of random variables 71iis partially exchangeable with respect to a sequence of random vectors Yiif, for every finite collection 77m .. . .nK of elements of the sequence, (6) p(17= a, ... , K = aKIYi =Y iE 1 ... K)= p(ilp(l) = a, * 17p(Kfi- = aKlYi = Y V i E_ (1 . .. K}) where p( *) is any operator that permutes the K indices. The key difference between exchangeability and partial exchangeability isthe 8. Throughout, p( . ) is used to denote probability measures. 9. F-conditional exchangeability was originally defined in Kallenberg (1982). Ivanoff and Weber (1996) provide additional discussion. The notion of F-conditional exchangeability is rarely employed in the statistics literature and isnot mentioned in standard textbooks such as Bernardo and Smith (1994). We believe the reason for this is that exchangeability analyses in the statisticsliterature generally focus on whether the units under study are exchangeable, rather than whether they are conditional on certain characteristics, the more natural notion in economic contexts. Brockand Durlauf 241 conditioning on common values of some random vectors Yisassociated with the q,sinthe partial exchangeability case. If Yiisa discrete variable, partial exchange- ability implies that a sequence may be decomposed into a finite or countable number of exchangeable subsequences. Even though F-conditional exchangeability of model errors constitutes a stron- ger assumption than is needed for many of the interpretations of OLS, this ex- changeability condition is nevertheless useful as a benchmark in the construc- tion and assessment of statistical models. We make this claim for two reasons. First, this exchangeability concept helps organize discussions of the plausibility of the invariance of conditional moments that lie at the heart of policy relevant predictive exercises. Draper (1987, p. 458 ) describes the critical role of exchange- ability in any predictive exercise: Predictive modeling is the process of expressing one's beliefs about how the past and future are connected. These connections are established through exchangeabilityjudgments:with what aspects of past experience will the future be more or less interchangeable, after conditioning on relevant fac- tors? It is not possible to avoid making such judgments; the only issue is whether to make them explicitly or implicitly. Put in the context of growth analysis, the use of cross-country data to predict the behavior of individual countries presupposes certain symmetry judgments about the countries, judgments that are made precise by forms of exchangeability. Second, exchangeability is separately important because of its implications for the appropriate statistical theory to apply in growth contexts. The reason for this relates to a deep result in probability theory known as de Finetti's Rep- resentation Theorem.10 This theorem, formally stated in the technical appendix, establishes that the sample path of a sequence of exchangeable random variables behaves as if the random variables were generated by a mixture of i.i.d. pro- cesses. For empirical practice, de Finetti's Representation Theorem is important because it creates a link between a researcher's prior beliefs about the nature of the data under analysis (specifically, the properties of regressiornerrors) that permits the researcher to interpret OLS estimates and associated test statistics in the usual way.11 10. See Bernardo and Smith (1994, chs. 4 and 6) for an insightful discussion of thienature and im- plications of the theorem and Aldous (1983) for a comprehensive mathematical development of vari- ous forms of the theorem. I1. Caution is needed in using de Finetti'stheorem to calculate the distributions of regression esti- mators. For linear regression models of the form of equation 1, with normally distributed errors and for the model nonstochastic regressors, Arnold (1979, p. 194) shows that "many optimal procedures with i.i.d. errors arealso optimal procedures for the model with exchangeably distributed errors . .. in the univariate case the best linear unbiased estimator and the ordinary least squares estimator are equal . . . as long as the experimenter is only interested in hypotheses about (the slope coefficients of the de Finetti's regression) he may act as though the errors were i.i.d." Further, if the errors are non-normal, theorem leads one to expect analogous asymptotic equivalences. Similarly, we believe that analogies to exchangeability, al- de Finetti's theorem can be developed for stochastic regressors and F-conditional though as far as we know no such results have been established. 242 THE WORLDBANKECONOMICREVIEW,VOL. I5, NO. 2 Exchangeabilityand Growth How does exchangeability relate to the assumptions underlying cross-country growth regressions?These models typically assumethat oncethe included growth variables in the model are realized, no basis exists for distinguishing the prob- abilities of various permutations of residual components in country-level growth rates, that is, these residuals are F-conditionally exchangeable, where F is the modeler's information set. Notice that F may include variables beyond those included in a growth regression as well as knowledge about nonlinearities or parameter heterogeneity in the growth process. Various forms of exchangeability appear, in our reading of the empirical growth literature, to implicitly underlie many of the regression specifications. An implicit (F-conditional) exchangeability assumption is made whenever the empirical implementation of the growth trajectory for a single country from a given theoretical model is turned into a cross-country regression (typically af- ter linearizing) by allowing the trajectory's state variables to differ across coun- tries and appending an error term. Such an assumption of exchangeability has substantive implications for how a researcher thinks about the relationship be- tween a given observation and others in a data set. Suppose that a researcher is considering the effect of a change in trade openness on a country, for ex- ample, Tanzania, in Sub-Saharan Africa. How does the researcher employ es- timates of the effects of trade on growth in other countries to make this assess- ment? The answer depends on the extent to which the causal relationship between trade and growth in Tanzania can be uncovered using data from other countries. More generally, notice how a number of modeling assumptions that are stan- dard in conventional growth exercises are conceptually related to the assump- tions that the model errors £, are F-conditionally exchangeable and that the growth rates g, are partially exchangeable with respect to available information. Specifically, 1. The assumption that a given regression embodies all of a researcher's knowledge of thegrowth process isrelated tothe assumption that the errors in a growth regression are F-conditionally exchangeable. 2. The assumption that the parameters in a growth regression are constant is related to the assumption that country-level growth rates are partially exchangeable. 3. The justification for the use of ordinary (or heteroskedasticity-corrected) least squares, as is standard in the empirical growth literature, isrelated to the assumption that the errors in a growth regression are exchangeable (or are exchangeable after a heteroskedasticity correction). Our general claim is that exchangeability, in particular, F-conditional ex- changeability of model errors, is an "incredible" (Sims1980) assumption in the context of the standard cross-country regressions of the growth literature. (Bya Brock and Durlauf 243 standard regression, we refer to equation 1, in which a small number of regres- sors are assumed to explain cross-country growth patterns.12 ) For exchangeability to hold for a givenregression and information set, the likelihood of a positive error for a givencountry-say, Japan-would need to be the sameas that for any other country in the sample. In turn, for this to betrue, no prior information could exist about the countries under study that would render the distribution of the asso- ciated growth residuals for these countries sensitiveto permutations. To repeat, exchangeability is not necessary to justify the estimation methods and structural interpretations conventionally given to cross-country growth re- gressions."3 Hence our use of the term relatedin the three points above. What exchangeability does is provide a baseline, based on economic theory and a researcher's prior knowledge of the growth process, by which to assess cross- country regressions. Exchangeability isa valuable baseline for two reasons. First, the conditions under which various types of exchangeability do or do not hold for growth rates or model residuals can be linked to a researcher's substantive understanding of the growth process in ways that alternative sets of (purely sta- tistical) assumptions on errors usually cannot be. In turn, once exchangeability is believed to be violated, a researcher can naturally link the reasons that ex- changeability fails to hold to the question of whether the estimation methods used in the growth literature nevertheless can be expected to yield consistent parameter estimates and standard errors. Second, exchangeability is important because it shifts the focus of specifica- tion analysis away from the question of theory inclusion (determining which variables need to be included in a growth regression to cover relevant structural growth determinants) to the identification of groups of countries that obey a common regression surface and hence can provide information on the growth process. This shift of emphasis is important for two reasons. First, for many growth determinants, the variables used to proxy for theories are very poor measures. For example, in the standard Gastil index of political rights, often used to measure levelsof democracy, South Africa is ranked as high as or even higher than (depending on the period) the Republic of Korea for the period 1972-84. It is difficult to know what this means (political rights for whom?) and in what sense this rank ordering is relevant for the aspects of democracy conducive to growth. A more fruitful exercise is to identify groups of countries that obey a common, parsimonious growth model. Put differently, if, as seems plausible, many growth determinants such as political regime are common background variables for subsets of countries, a more productive empirical strategy may be to identify these subsets rather than to use crude empirical proxies for regime. Second, to the extent that nonquantifiable factors, such as "culture" (seeLandes 12. To be fair, empiricalgrowth papers often check the robustness of variables relative to a small number of alternative controls, but such robustness checks do not address exchangeability per se. is useful for 13. In section VIwe return to the question of when the fullforce of exchangeability policy analysis. 244 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. Z 2000), matter for growth, the identification of partially exchangeable subsets may be necessary for any sort of growth inferences. To see how exchangeability plays a role in the leap from the identification of statistical patterns to structural inference, suppose that one runs the baseline Solow regression and observes that regression errors for the countries in Sub- Saharan Africa are predominately negative (as is the case). How does one inter- pret this finding? One can either attribute the finding to chance (the errors are, after all, zero mean with nonnegligiblevariance) or conclude that there was some- thing about those countries that was not captured by the model. Easterly and Levine (1997), for example, develop a comprehensive argument on the role of ethnic divisions as a causal determinant of growth working from this initial fact. Or, put differently, Easterly and Levine (1997), from prior knowledge about the politics and cultures of thesecountries, developed their analysison the basis that the Solow errors were not exchangeable, that is, that there was something about Sub-Saharan African countries that should have been incorporated into the Solow model. Does the requirement of exchangeability imply the impossibility of structural inference whenever observational data are being studied? This would grossly exaggerate the import of our critique. Exchangeability of errors is conceivable for a wide range of models with observational data sets. For example, exchange- ability seems to be a plausible assumption for statistical models based on the use of individual-level data sets, such as the Panel Study of Income Dynamics (PSID), once relevant information about the individuals under study is controlled for. One reason for this relates to the units of analysis. A basic difference between microeconomic data sets of this type and macroeconomic data sets of the type used in growth analysis is that macroeconomic observations pertain to large heterogeneous aggregates for which a great deal of information is known; infor- mation that can imply that exchangeability does not hold. In addition, the large size of individual-level data sets such as the PSID means that the range of pos- sible control variables is much greater than that for growth. By this we mean something deeper than "the more data points, the more regressors may be included." Instead, we argue that large data sets of the type found in micro- economics will contain observations on groups of individuals who are sufficiently similar with respect to observables that they may beplausibly regarded as repre- senting exchangeable observations. That said, we fully accept that exchangeability for observations on objects as complicated as countries may well be problematic. Will our knowledge of the histories and cultures of the countries in cross-country regressions ever be em- bedded in the regressions to such an extent that the exchangeability requirement is met? This question is at the heart of many of the controversies about the em- pirical growth literature. To summarize, conventional growth econometrics has failed to consider the ways in which appropriate exchangeability concepts may or may not hold for Brock and Durlauf 245 the specific models analyzed. This failure in turn renders these studies difficult if not impossible to interpret, because one must know whether any exchangeabil- ity violations that are present invalidate the statistical exercise being conducted. We therefore concur with Draper and others (1993, p. 1), who argue that statistical methods are concerned with combining information from differ- ent observational units and with making inferences from the resulting sum- maries to prospective measurements on the same or other units. These operations will be useful only when the units to be combined are judged to be similar (comparable or homogeneous) . . . judgments of similarity in- volve concepts more primitive than probability, and these judgments are central to preliminary activities that all statisticians must perform, even though probability specifications are absent or contrived at such1a prelimi- nary stage. Exchangeabilityand Causality Though exchangeability is a useful benchmark for understanding some of the major sources of skepticism about growth regressions, it does not bear in any obvious way on the third of our general criticisms, the lack of attention to cau- sality versus correlation in growth analysis. For example, following a nice ex- ample due to Goldberger (1991), a regression of parental height on daughter height can have a perfectly well-defined set of exchangeable errors, so that pa- rental heights are partially exchangeable, yet the interpretation of the associated regression coefficient is obviously noncausal. More generally, causality is a dif- ferent sort of question than the other issues we have addressed, in that it cannot be reduced to a question of whether the data fulfill a genericstatisticalproperty. As Heckman (2000, p. 89) notes, "causality is a property of a model. .. many models may explain the same data and . .. assumptions must be made to iden- tify causal or structural models." And (2000, p. 91): Some of the disagreement that arises in interpreting a given body of data is intrinsic to the field of economics because of the conditional nature of causal knowledge. The information in any body of data is usually too weak to eliminate competing causal explanations of the same phenomenon. There is no mechanical algorithm for producing a set of "assumption free" facts or causal estimates based on those facts. In our subsequent discussion we do not address strategies for dealing with questions of causality. Instead, we focus on model uncertainty, which presup- poses that causality uncertainty within a given model has been addressed by suitable assumptions by the analyst. In doing this, we are not dliminishingthe importance of thinking about causal inference; instead, we believe that causal arguments require judgments about economic theory and qualitative informa- tion about the problem at hand that represent issues separate from those we address. 246 THE WORLDBANKECONOMICREVIEW,VOL. I5, NO. Z IV. A DIGRESSION ON NONECONOMETRIC EVIDENCE Regression analyses of the type conventionally done are useful mechanisms for summarizing data and uncovering patterns. These techniques are not, as cur- rently employed, particularly credible ways to engage in causal inference. Be- fore proceeding to econometric alternatives, we wish to point out the importance of integrating different sources of information in the assessment of growth theo- ries. These sources are often the basis on which exchangeability can be ques- tioned in a particular context. The economic history literature is replete with studies that are of enormous importance in adjudicating different growth explanations, yet this literature usually receives only lip service in the growth literature.1 4 An exemplar of his- torical studies that can speak to growth debates is Clark (1987), which explores the sources of productivity differences between cotton textile workers in New England and those workers in other countries in 1910. These differences were immense-a typical New England textile worker was about six times as produc- tive as his counterpart in China or India and more than twice as productive as his counterpart in Germany. Clark painstakingly shows that these differences cannot be attributed to differences in technology, education, or management.15 Instead, they seemto reflect cultural differences in work and effort norms. Such studies have important implications for understanding why technology may not diffuse internationally and how poverty traps may emerge, and should play a far greater role in the empirical growth literature. Historical and qualitative studies also play a crucial role in the development of credible statistical analyses. One reason for this is that these sorts of studies provide information on the plausibility of identifying assumptions that are made to establish causality. Further, our discussion on exchangeability and growth analysis may be interpreted as arguing that a researcher needs to do one of two things to claimthat a regression provides causal information. The researcher must make a plausible argument that, given the many plausible growth theories and plausible heterogeneity in the way different causal growth factors affect differ- ent countries, the errors in a particular growth regression are nevertheless ex- changeable. Or, the researcher can make the argument that the violations of exchangeability in the regression occur in ways that do not affect the interpreta- tion of the coefficients and standard errors from those that are employed. To some extent exchangeability judgments must be made prior to a statistical exer- cise, as Draper and others (1993) note above. Where does information of this type come from? Often from qualitative and historical work. Hence, the detailed study of individual countries that is a hallmark of work by the World Bank, for example, plays an invaluable role in allowing credible statistical analysis. 14. There are notable exceptions, suchas Easterly and Levine (1997) and Prescott(1998). 15. See also Wolcott and Clark (1999), which provides detailed evidence that managerialdiffer- ences cannot explainthe low productivity in Indian textiles. Brock and D)urlauf 247 V. MODELING MODEL UNCERTAINTY The main themes of our criticisms of current econometric practice may be sum- marized as two claims: 1. The observations in cross-country growth regressions do not obey vari- ous exchangeability assumptions given the information available on the countries under study. This implies that: 2. Model uncertainty isnot appropriately incorporated into empirical growth analyses. There are no panaceas for the interpretation problems we have described for growth regressions. Although our formulation of model uncertainty can reduce the dependence of empirical growth studies on untenable exchangea1 bilityor other assumptions, growth regressions will always rely on untestable and possibly controversial assumptions if causal or structural inferences are to be made. It may be impossible, for example, to place everypossible growth theory in a com- mon statistical analysis, so critiques based on theory open-endedness will apply, at some level, to our own suggestions. Further, we will not be able to model all aspects of uncertainty about partial exchangeability of growth rates. However, we do not regard this as a damning defect. Empirical work always r elieson judg- ment as well as formal procedures, what Draper and others (1993, p. 16) refer to as "the role of leaps of faith" in constructing statistical models. What we wish to do is reduce the number and magnitude of such leaps. GeneralFramework We assume that the structural growth process for country i obeys a linear struc- ture that applies to all countries j that are members of classJ(i). Suppose that this model is described by a set of regressors S that we partition into a subset X and a scalar z. Our analysis focuses on how to employ data to uncover f3z,the coefficient that determines the effect of z, on country i's growth. We work with models of the form: (7) gj = Sj; + E,= X,ir + Z,P + , jEJ(i). When a given model represents the "true" or correct specification of the growth process for countries inJ, the sequence of residuals £, will be F-exchangeable. The information set F comprises the total available information to a researcher about the countries. For our purposes, F will consist of a collection of regressors available to a researcher; S is a subset of these. The idea that a model consists of the specification of a set of growth determinants, (S,),and the specification of a set of countries with common parameters, J(i), that together render the associ- ated model errors F-conditionally exchangeable, will, as we shall see, parallel our earlier discussion of the first two sources of criticisms of growth regressions. 248 THE WORLDBANKECONOMICREVIEW,VOL. I5, NO. 2 It is skepticism about the claim that a particular model is correctly specified in the sense we have described that renders many of the empirical claims in the growth literature not credible. The standard approach to statistical analysis in the growth literature can be thought of as using a single model M and given data set D to analyze model parameters. Suppose that the goal of the exercise isto uncover information about a particular parameter fi. From a frequentist perspective, this involves calculat- ing an estimate of the parameter f3zalong with an associated standard error for the estimate. From a Bayesian perspective, this involves calculating the poste- rior density pu(pID,M). We will employ the Bayesian framework in our subse- quent discussion. That said, we will be interested in relating our analysis to frequentist analyses of growth. For this reason we shall often employ a "leading case" in the analysis. As described in the technical appendix, under some condi- tions the posterior mean of the set of regression coefficients in equation 7 equals the OLS estimates of the parameters and the posterior variance/covariance ma- trix equals the variance/covariance matrix of the OLS estimates. We will use this equivalence repeatedly in the next section. FormulatingTypes of Model Uncertainty Suppose that there exists a universe of models, M with typical element M,,, that arepossible candidates for the "true" growth model that generated the data under study; the true model is assumed to lie in this set.'6 This universe is generated from two types of uncertainty. First, there is theory uncertainty. In particular, we assume that there is a set X of possible regressors to include in a growth re- gression whose elements correspond to alternative causal growth mechanisms. In our framework a theory is defined as a particular choice of regressors for a model of the form of equation 7. Second, there is heterogeneity uncertainty. By this we mean that there isuncertainty as to which countries make upJ(i), that is are partially exchangeable with country i.17 In the presence of these types of uncertainty a researcher will be interested not in pu(f I D,M,0) for a particular Mm but in p(f,3ID); the exception, of course, is when the correct growth theory and the set of countries that are partially exchangeable with country i are known with certainty to the modeler. This dichotomy of model uncertainty can, at least in principle, incorporate other forms of uncertainty as well. Consider the question of nonlinearities in the growth process. One could attempt to deal with functional form uncertainty through the addition of regressors. Examples would include adding regressors that are nonlinear functions of the initial set of theory-based regressors (appeal- ing to Taylor series-type or other approximations) or adding regressors whose 16. It is possible toconsider contexts where no model in M is correct, as discussed in Bernardo and Smith (1994), but that is beyond the scope of this paper. 17. These two types of uncertainty arenot independent; for example, theory uncertainty may in- duce heterogeneity uncertainty. Brock and I)urlauf 249 values are zero below some threshold and equal to a theory-based regressor above that threshold (as suggested by such models as Azariadis and Drazen [1990]. In this sense heterogeneity uncertainty is no different from theory uncertainty. It is possible to integrate theory uncertainty and some forms of lheterogeneity uncertainty into a common variable selection framework. Doing so has the im- portant advantage that it allows us to draw on new developments in the statis- tics literature stemming from an important paper by Raftery, Madigan, and Hoeting (1997). By definition, theory uncertainty is a question of variable inclu- sion. To see how to interpret heterogeneity uncertainty in a similar way, we proceed as follows. For a given regressor set S, suppose that one believes that the countries under study may be divided into two subsets with associated sub- scripts Al and A2 such that the countries within each subset arepartially exchange- able, but that countries in one subset may not be partially exchangeable with countries in the other because of parameter heterogeneity. Each of these subsets is characterized by a linear equation so that (8) gj=X1iT+zPz,f+IifjE Al and (9) g =Xj7r' + z 3'4+ E1 if j e A2. This last equation can be rewritten as ifjE . (10) g, = Xjt +zfz3 + Xi (T' -i) + Zj(P -fz) + £j A2 Therefore, the two equations can be combined into a single growArth regression of the form: ( 1) gi = Xpt+ z,fz+ Xi 61,A(7c'- t) + jEcA u A2 1 2 Zj31,A2 ('zz-iz) + £, if where The additional regressors X,I',A 2 and Z,6jA, 3jA2 = 1 if j c A2, 0 otherwise. therefore produce a common regression for all observations.1S Of course, this type of procedure is often done in empirical work; our purpose in this develop- ment here isto emphasize how heterogeneity uncertainty may be explicitly mod- eled in terms of variable inclusion. Notice that it is straightforward to generalize this procedure to multiple groups of partially exchangeable countries. This pro- cedure isnot completely general in that it restricts the sort of possible parameter heterogeneity allowed; for example, each country is not allowed a separate set of coefficients. To allow for this more general type of heterogeneity would re- quire moving to an alternative structure, such as a hierarchical linear model (see Schervish 1995, ch. 8); we plan to pursue this in subsequent work. 18. When heterogeneity uncertainty is introduced, the variable z will be associated with different parameters for different countries. For ease of exposition we let J3 refer to therelevant parameter for the country i that isof interest. 250 THEWORLDBANKECONOMICREVIEW,VOL. 15, NO. Z PosteriorProbabilities Once a researcher has formulated a space of possible models, it is relatively straightforward to calculate posterior probabilities that do not rely on the as- sumption that one model istrue. In the presence of model uncertainty the calcu- lation of ,u(I,3I D) requires integrating out the dependence of the probability measure ,u(p,ID,Mm)on the model Mm.By Bayes's rule, the posterior density of a given coefficient conditional only on the observed data is (12) i'(p ID) = Yi(p3 I D,Mm)Ju(Mm I D), which can be rewritten as (13) u(f, I D) -p(,fi 1 I D,Mm),u(D I Mm)u(Mm), where ocmeans "is proportional to," p(D IMm)is the likelihood of the data given model Mm, and II(Mm) is the prior probability of model Mm. This formulation gives a way of eliminating the conditioning of the posterior density of a given parameter on a particular model choice. Calculations of this type originally appeared in Leamer (1978) and are reported in Draper (1995). Leamer (1978, p. 118) gives the following derivations of the conditional mean and variance of f,3given the data D: (14) E(J31 I D) = Y 4u(Mm I D)E(P3 I D,M,m) and (15) var(f,3 I D) = E(2,f I D) - (E(/3 I D)) 2 = Y4 I(Mm I D)(var(p, IMm,D) + (E(flz M I D,Mm))2 ) - (E(fozI D))2 = Y41(Mm I D)var(p,BIMm,D) + YX/(Mm I D)(E(f3l I D,Mm) - (E(/3zI D))2. As discussed in Leamer (1978) and Draper (1995), the overall variance of the parameter estimate I,3depends on the variance of the within-model estimates (the first term in equation 15) and the variance of the estimates across models (the second term in equation 15). Equation 12 and the related expressions are all examples of Bayesian model averages. The methodology surrounding Bayesianmodel averaging isspecifically developed for linear models with uncertainty about variable inclusion in Raftery, Madigan, and Hoeting (1997).19Doppelhofer, Miller, and Sala-i-Martin (2000), focusing on theory uncertainty only, compute a number of measures of variable robustness based on the application of this formula to growth regressions and conclude that initial income isthe "most robust" regressor. Fernandez, Ley, and Steel (1999) also employ Bayesian model averaging for theory uncertainty, fo- cusing on the explicit computation of posterior coefficientdistributions. Our own development should be read as an endorsement and extension of the analyses in 19. The survey by Hoeting and others(1999) provides a nice introduction to model averagingtech- niques. See also Wasserman (2000). Brock and D)urlauf 251 these articles. Our formulation differs in two respects from previous work. First, we treat heterogeneity uncertainty as well as theory uncertainty as part of over- all model uncertainty. Draper and others (1993) provide a general overview of the importance of accounting for heterogeneity uncertainty in constructing credible empirical exercises. As our discussion illustrates, heterogeneity uncer- tainty can be treated as a question of variable inclusion, so the ideas in Doppelhofer, Miller, and Sala-i-Martin (2000) and Fernandez, Ley, and Steel (1999) can be extended to this domain in a straightforward fashion. Second, we develop an explicit decision-theoretic approach to interpreting growth regres- sions. As far as we are aware, this analysis is new. Outliers One important concern in the empirical growth literature has revolved around the role of outliers in determining various empirical claims. A famous example is the role of the Botswana observation in determining the estimated magnitude of social returns to equipment investment (DeLong and Summers 1991, 1994; and Auerbach, Hassett, and Oliner 1994).20 Outliers can be dealt with in a straightforward fashion. There are three strat- egies one can pursue. First, one can always employ a within-model estimator that is designed to be robust to outliers. As Temple (2000) points out, one can employ a trimmed least square estimator (one that drops or downweights ob- servations whose associated OLS residuals are large) in estimating each model's parameters and stillemploy whatever posterior analysis one wishes. Second, one can explicitly allow the density for model errors to accommodate outliers. For example, one can model errors as drawn from a mixture distribution. Third, and most promising in our view, one can employ a Bayesian bagging procedure due to Clyde and Lee (2000). Bayesian bagging ("bagging" is an abbreviation for bootstrap aggregating) was introduced by Breiman (1996) to improve the per- formance of what he called "unstable" prediction and modeling methods. A method is "unstable" when small changes in the data set lead to large changes in the method's output. Intuitively, the Clyde and Lee procedure constructs boot- strap data sets from the empirical distribution function of a data set, computes a model average for each sample, and then averages these results. (Seetheir ar- ticle for details.) Clyde and Lee provide reasons to think that this modification of model averaging will be robust to outliers. That said, the ex post analysis of outliers, as was carried out in the Botswana case we described, is often problematic; as Leamer (1978, p. 265) remarks, the mechanical and typically ad hoc dropping of outliers both leads to invalid sta- tistical conclusions and ignores valuable information. 20. The role of outliers in growth regressionshas been somewhat overstated; for example, the DeLong and Summers results are far more robust to the inclusion or exclusion of Botswana than is often as- serted, as a carefulreading of DeLong and Summers (1991, 1994) and Auerbach, Flassett, and Offner (1994) clearly reveals. Temple (1998) is a more persuasive example of the importance of dealing with outliers. 252 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. 2 Priors on the Space of Possible Models An important issue in the implementation of the model averaging approach that we describe is the choice of the prior distribution on the space of models. For the problem of variable inclusion, this is typically handled by assuming that all 2k possible models (where k isthe number of regressors that may be placed in a given model) have equal probability; Fernandez, Ley, and Steel (1999) follow this procedure in their analysis. The procedure in essence assumes that the prior probability that a given regressor is in a model is 1/2. Doppelhofer, Miller, and Sala-i-Martin (2000) make the alternative assumption that for a regression whose expected number of included regressors is k, the probability of inclusion of a given regressor is k I k. They make this assumption to avoid "a very strong prior belief that the number of included variables should be large" (2000, pp. 15-16). These alternative approaches to setting model priors are not very appealing from the perspective of economic theory. Clearly, the addition of a given regres- sor to the set of possible regressors should affect the probabilities with which other variables are included. It isunclear, for example, why the effect of ethnicity on growth should be independent of the effect of democracy, as it can easily be imagined that one will affect growth only if the other does as well. The conven- tional approaches to modeling the space of priors ignore this fact. This problem is closelyassociated with a standard criticismof the "irrelevance of independent alternatives" assumption in choice theory, originally due to Debreu (1960) and later instantiated in the choice literature as the "red bus/blue bus problem" (see Ben-Akiva and Lerman 1985, sec. 3.7). In discrete choice theory irrelevance of independent alternatives means that the ratio of choice probabilities between any two alternatives should be unaffected by the presence of a third. As pointed out by Debreu, this assumption is untenable if the third choice is a close substitute for one of the other two. For the analysis of growth regressions, the priors we have discussed suffer from a similar problem, although the reasons aremore complicated. As noted above, the likelihood that one growth theory matters may covary positively with whether another one matters. Fur- ther, because the variables employed to capture growth theories are often crude proxies for underlying theories, their inclusion probabilities could covary posi- tively, as each helps measure some common growth determinants. For example, contra Doppelhofer, Miller, and Sala-i-Martin (2000, n. 15), the likelihood that political assassinations predict growth differences could be positively associated with the likelihood that revolutions predict growth differences, as each helps instrument the unobservable variable "political instability." We have no advice to offeron how to deal with this problem, becauseits reso- lution will depend on one's priors on the space of underlying growth models, as determined by the interconnections between particular growth theories. In our view, it makes more sense at this stage of development to treat the prior distri- bution over models as a benchmark for reporting posterior statistics. (Anumber of Bayesians have developed a similar view of priors; see, for example, the dis- Brock and Durlauf 253 cussion of "robust" priors in Berger 1987, p. 111.) Because the complexity of the growth process speaks to the strong likelihood that a large number of growth factors substantively matter, the uniform prior of Fernandez, Ley,and Steel(1999) makes the most sense at this stage in providing a benchmark. That said, there isnothing theoretically compelling about the assumption that the inclusion probability of each regressor is 1/2. We therefore believe that it might make sense in future work to report values for some benchmark alterna- tive probabilities, inorder to help evaluate the robustness of results. By choos- ing inclusion probabilities lower than 1/2, it is possible to incorporate the spirit of the Doppelhofer, Miller, and Sala-i-Martin concerns without having to form prior beliefs on the expected number of regressors in a model, which seems ex- tremely problematic. VI. TOWARD A POLICY-RELEVANT GROWTH EcONOMETRICS The framework developed in the previous section provides a general way of describing model uncertainty in growth regressions. It does not, however, pro- vide any guidance on how to determine what variables should be included in a regression, or on when to regard the sign or magnitude of a regression coeffi- cient as robust. The reason is that the posterior densities embodied in equations 12 to 15 are nothing more than data summaries. As such, they can inform policy analysis only to the extent that they are integrated with a specific formulation of the decision problem of a policymaker. Hence it is necessary to develop an ex- plicit decision-theoretic basis for assessing growth data. The decision-theoretic framework we describe explicitly incorporates the various forms of model un- certainty associated with possible violations of exchangeability, as discussed in the previous section. In this section we discuss the use of growth regressions to inform empirical analysis when one of the growth controls is under the control of a policymaker. Many of the purported policy variables included in growth regressions-for example, indices of political stability-are not necessarilytightly linked to the variables over which a policymaker has control. The framework we describe can be generalized to incorporate a more complicated relationship between growth determinants and policy than the one we analyze here. The decision-theoretic perspective involves moving away from a specific con- cern with a particular hypothesis to an evaluation of the implications of a given set of data for a particular course of action. Kadane and Dickey (1980, p. 247) argue The important question in practice is not whether a true effect is zero,for it isalready known not to do exactlyzero, but rather, How large isthe effect? But then this question is only relevant in terms of How large is important? This question in turn depends on the use to which the inference will be put, namely, the utility function of the concerned scientist. Approaches which attempt to explain model specification from the viewpoint of the inappro- 254 THE WORLDBANKECONOMICREVIEW,VOL. I5, NO. 2 priate question, Is it true that. .. ? have a common thread in that they all proceed without reference to the utility function of the scientist. And there- fore, from the decision theory point of view, they all impose normative conditions on the utility function which are seldom explicit and often far from the case. Substituting policymakerfor scientist inthis quotation makes it clearwhy policy- relevant growth econometrics needs to explicitly integrate policy objectives and empirical practice. Our approach iswell summarized by Kass and Raftery (1994, p. 784): "The decision making problem is solved by maximizing the posterior expected utility of each course of action considered. The latter is equal to a weighted average of the posterior expected utilities conditional on each of the models, with the weights equal to the posterior model probabilities." In other words, we argue that policy-relevant econometrics needs explicitly to identify the objectives of the policymaker and then calculate the expected consequences of a policy change. Policy Assessment: Basic Ideas The basic posterior coefficient density described by equation 12 and the associ- ated first and second moments described by equations 14 and 15 represent data summaries and as such have no implications for either inference or policy as- sessment. The goal of a policy analysis isnot to construct such summaries but to assess the consequences of changes in a policy. Similarly, such data summaries do not imply the validity of particular rules for data evaluation or inference. For example, the assessment of whether regressors are robust, such as is in extreme bounds analysis or the comparison of models using Bayes factors, ' 2 may not be appropriate for certain policy exercises. Put differently, decisions on whether to treat regressors as robust and the like should, for the purposes of policy analy- sis, be derived from the policymaker's assessment of the expected payoffs asso- ciated with alternative policies. In this section we explore policy assessment when model uncertainty has been explicitly accounted for. The purpose of this exercise is twofold. First, it cap- tures what we believe is the appropriate way for policymakers to draw infer- ences from data. Second, it shows that various rules for the assessment of re- gressor fragility, such as extreme bounds analysis, will arise in such exercises. A critical feature of this approach to model assessment is it illustrates that the evaluation of regressor robustness can be derived from particular aspects of the policymaker's objective function. For expositional purposes we initially suppose that the goal of an empirical exercise is to evaluate the effect of a change dz 22 in some scalar variable that is 21. For any two models M, and M., the Bayes factor B,. is defined as p(D I M.) / p(D I Mm). Kass and Raftery (1994)provide an extensive overview of the use of Bayes factors in model evaluation. 22. Without loss of generality, we generallyassume that dz, > 0. Brock and iDurlauf 255 under the control of a policymaker and believed to have some effect on growth. Therefore, the decisionmaker's set of actions A is {0,dzj.This decision rule is based on a vector observable data D. This means that a decisionmrakerchooses a rule o(.) that maps D to A so that (16) h(D) =dz, if D E D qp(D)= 0 otherwise. D, is therefore the acceptance region for the policy change. We assume that the "true" linear growth model is a causal relationship that will allow evaluation of the effect of this change. Because we restrict ourselves to linear models, the analysis of the policy deci- sion is particularly straightforward, as p(12 ID) will describe the 3 posterior distri- bution of the effect of a marginal change in z on growth in a given country. A marginal policy intervention in country i can be evaluated as follows. Let zi de- note the level of a policy instrument in country i. This instrument appears as one of the regressors in the linear model that describes cross-country growth. Sup- pose one has the option of either keeping the policy instrument at its current value or changing it by a fixed amount dz,. Let g, denote the growth rate in the country in the absence of the policy change, and g, + Izdzithe growth rate with the change. Finally, let V(gi,Oi)denote the utility value of the growth rate to the policymaker. O, is a placeholder vector that contains any factors relating to country i that affect the policymaker's utility. An expected utility assessment of the policy change can be based on the comparison (17) E(V(g, + O3zdzi,O,) I D) - E(V(g,, Oj) I D). Calculations of the expected utility differential in equation 17 implicitly contain all information relevant to a policy assessment. From the perspective of policy evaluation, the various rules that have been proposed for the assessment of re- gressor robustness should be an implication of this calculation. Notice that this calculation requires explicitly accounting for model uncertainty, because the conditioning is always done solely with respect to the data. Policy Assessment under Alternative Utility Functions In this section we consider the implications of some alternative utility functions for the analysis of growth regressions. Our goal is to show how particular utility functions will lead a policymaker to decide whether or not to implement a policy on the basis of aspects of the posterior distribution of f,3.We do not claim that the utility functions we examine are particularly compelling. We have chosen them to illustrate what sort of utility functions can justify some of the standard ways of interpreting growth regressions. RISKNEUTRALITY. Suppose that Vis linear and increasing in the levelof growth, that is, 256 THE WORLD BANK ECONOMIC REVIEW, VOL. 15, NO. 2 (18) V(gi,O,) = aO + algi,al > 0. For this policymaker the relevant statistic is the posterior mean of the regressor coefficient. In this case it is straightforward to see that the policy change is justi- fied if the expected value of the change in the growth rate is positive, that is, (19) YXp(M1n I D)E(p, I D,M,..) > 0. When the prior model probabilities are equal, this is equivalent to the condition (20) Yp(D IM..)E(/3 I D,M,,,) > 0 "I so the likelihoods p(D IMJ1) determine the relative model weights. MEAN/VARIANCE UTILITY OVER CHANGES IN THE GROWTH RATE. Suppose that a policymaker has preferences that relate solely to changes in the growth rate, as opposed to its level. The idea here is that a policymaker assesses a policy relative to the baseline g,. Operationally, we assume that one chooses the elements of O, and the functional form of V( , .) so that (21) E(V(gi +/dz,,Oi) ID) - E(V(g,, 0,) ID) = aoE(fzdzi ID) + alvar(/zdzi ID)"/2, ao > 0, a, < 0. When lao/aII=1/2, this utility specification implies that the policymaker will act only if the t-statistic (the posterior expected value of P. divided by its posterior standard deviation) is greater than 2. Hence this specification, at least qualita- tively, corresponds to the standard econometric practice of ignoring regressors whose associated t-statistics are less than 2. From a decision-theoretic perspective, the conventional practice of ignoring "statistically insignificant" coefficients (by which we mean coefficients whose posterior standard errors are more than twice their posterior expected values) can be justified only in very special cases. First, it isnecessary to assume that the form of risk aversion of the policymaker applies to the standard deviation rather than to the variance of the change in growth. Otherwise, the desirability of the policy will depend on the magnitude of dzi. For example, if the utility function is (22) E(V(g, + izdzi,Oi)I D) - E(V(gi, O,) I D) = ccOE(Pzdzi I D) + alvar(fdz, I D), aO > 0, a, < 0 with lao/a1 I= 1/2, there will be a threshold level T such that for all 0 < dzi < T a policy change increases the policymaker's utility.23 Therefore, the rule of ignor- ing regressors with t-statistics less than 2 presupposes a very specific assump- tion about how risk affects the policymaker's utility. Second, if equation 22 is the correct utility function, the policymaker may stillchoose to act with the fixed dz, level we started with under (conventionally defined) statistical insignificance 23. This is an example of the famous result of Pratt that one will always accept a small amount of a fair bet. We plan to addressthe question of the optimal choice of dz, in future work. Brock and Durlauif 257 or, alternatively, may decline to act when the coefficient is statistically signifi- cant. These possibilities can be generated through appropriate choices of lac/all. have KNIGHTIAN UNCERTAINTY AND MAXIMIN PREFERENCES. In the examples we studied thus far we have allowed all uncertainty about the correct model Mm to be reflected in the posterior model probabilities p(M,, I D). An alternative ap- proach to model uncertainty, one in the tradition of Knightian uncertainty, as- sumes that an additional layer of uncertainty exists in the environment under study that may be interpreted as a distinct type of risk, sometimes called ambi- guity aversion, as will be seen below. As before, let M denote the universe of possible growth models. A risk sensi- tive utility function for the policymaker can be defined as (23) (1- e)E(V(g,,Oi) I D) + e(infM, E ME(V(g1,O) I D,Mn,)) In this equation e denotes the degree of ambiguity. This equation ismotivated by recent efforts to reconceptualize utility theory in light of results such as the classic Ellsberg paradoxes. For examrple,if experi- mental subjects are given a choice between (1) receiving $1 if they draw a red ball at random from an urn that they know contains 50 red balls and 50 black balls and (2)receiving $1 ifthey draw a red ball when the only infoirmation avail- able isthat the urn contains 100 red and black balls, the subjects typicallychoose the first, "unambiguous" urn (Camerer 1995, p. 646). Clearly, if subjects were Bayesians who placed a flat prior on the distribution of the balls in case 2, they would be indifferent between the two options.24 Experimental evidence of ambiguity aversion has led researchers-including Anderson, Hansen, and Sargent (1999); Epstein and Wang (1994); and Gilboa and Schmeidler (1989)-to consider formal representations of preferences that exhibit ambiguity aversion. One popular representation, studied in Epstein and Wang (1994), replaces expected utility calculations of the form fu(m)dP(o) with infp C I Su(eo)dP(o),where P is a space of possible probability measures. When this space contains a single element, this second expression reduces to the first, which is the standard expected utility formulation. A variant of this formula- tion isto assume that P consists of a set of mixture distributions (1 - e)PO+eP1 , where POis a baseline probability measure that a policymaker believesto betrue, PI isthe least favorable of all possible probability measures for the policymaker, and e represents the strength of the possibility that this measure applies. When the universe of alternative processes for growth isthe space of linear models that we have described, one can replace P with M,nand P with M and obtain the sec- ond part of equation 23. In using this specification, we do not claim that it isthe only sensible way to model ambiguity aversion by policymakers. We introduce 24. See Camerer (1995) for additional examples of ambiguity aversion as well as a surveyof the implications of differentresults in the experimentaleconomics literature forutility theory. 258 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. 2 it to illustrate how recent developments in decision theory may belinked to econo- metric practice. We can explore the effects of this additional uncertainty on our analysis by considering the two specifications of V studied above. First, assume that V is linear and increasing, while equation 23 characterizes the ambiguity aversion we have described. In this case the policy change dz is justified if (24) (1 - e)E(/,3ID) + e(infM E ME(pz I D,Mm)) > 0. When e = 1, the policy action will be taken only when E(I3l I D,Mm) > 0 for all MmE M. This has an interestinglink to OLS coefficientsfor different models in M. In the leading case described in the technical appendix, the posterior expectation E(oz ID,Mm) equals z the OLS coefficient associated with the regressor z for model Mm. If e = 1, this utility function would then mean that a policymaker will choose to implement dzi if the OLS coefficient estimate of f,3 is positive for every model in M. Alternatively, assume that the policymaker is risk-averse in the sense that equation 21 describes his utility function. In this case the policy change should be implemented if (25) (1 - e)(aoE(Iz I D) + alvar(, I D)½2)+ e(infM, E M (a0E(Iz ID,Mm) + alvar(Iz ID,Mm)J)) > 0. Again, this rule has an interesting link to OLS parameter estimates. If e = 1 and Ia0/ac I= 1/2,then for the leading case in the technical appendix, the policymaker will not act unless the OLS regression coefficient ilzm is positive and statistically significant (in the sense that the t-statistic is at least 2) for each model in M. (Here, we rely on the additional fact that for the leading case, var(/3z ID,Mm) equals the OLS variance of Az,m-) The policy rules that hold for e = 1 are closely related to the recommenda- tions made by Leamer for assessing coefficient fragility through extreme bounds analysis (see Leamer 1983 and Leamer and Leonard 1983). In extreme bounds analysis, recall that when a regressor "flips signs" across specifications, this is argued to imply that the regressor is fragile. From the perspective of policy rec- ommendations, we interpret this notion of fragility to mean that no policy change should bemade when there isa model of the world under which the policy change can be expected to make things worse off. This suggests that extreme bounds analysis is based on a maximin assumption of some type. Our derivations show that this intuition can be formalized. This derivation of extreme value analysis appears to complement a number of the objections raised against it by Granger and Uhlig (1990) and McAleer, Pagan, and Volker (1985). Both these articles argue that extreme bounds analy- sis can lead to spurious rejections of regressors as a result of changes in sign in- duced by regressions that are, by standard tests, misspecified. In our view these criticisms need to be developed from the perspective of the objectives of the empirical exercise. Put differently, the salience of these critiques of extreme Brock and Durlauf 259 bounds analysis requires that one reject the utility functions we have described as supporting extreme bounds analysis. Further, we believethat our derivations provide an appropriate way of modi- fying extreme bounds analysis-through the use of utility functions, such as equation 23 for 0 < e < 1. For such cases the relative goodness of fit of different models will be relevant to the empirical exercise. As is well known (see Wasserman 2000, p. 94 for a nice exposition), when Bayesianmodel selection between two models is based on posterior odds ratios and the prior odds on the models are equal, the posterior odds ratios will equal the ratio of their likelihoods, that is, the posterior odds will reflect the relative likelihoods of the data under the alter- native models. Further, as the amount of data becomes large enough, for this special case of equal prior odds, the model with the minimum Kullback-Leibler Information Criterion (KLIC) distance to the "truth" will be revealed. If the set of models under scrutiny includes the true model, the true model will berevealed in large samples.25 Thus in our context, under our assumption of equal prior odds across models, we may expect the data in large samples to ultimately place greater weight on models whose KLIC distance is closer to the true model.26 Bychoosing 0 0, yr(-)bounded otherwise. One will then have the implied de- cision rule that a single sign change in the OLS coefficient estimate /zm as one moves across models is sufficient to imply that the policymaker should not act to either increase or decrease z, by dz. This type of utility function induces be- havior mimicking that found under Knightian uncertainty. At first glance this might appear to be an unreasonable utility function for a policymaker. This conclusion is at least partially incorrect. Suppose that each state of the world is indexed by the growth process that is "true" under it. The utility of the policymaker will then depend on both the growth rate that is ex- pected to prevail and the state of the world under which it transpires. For ex- ample, suppose that there is a model of the world in which the expected effect of democracy on growth is negative. Such a model could be one whose features imply that a policymaker is particularly wary of reducing growth by changing a given policy instrument. For example, if there is a (positive probability) model of the world inwhich democracy isespeciallyfragileand may not survivea growth reduction, a policymaker might be especially wary of the policy change for fear this would prove to be the correct model of the world. This type of argument can be formalized by considering model-dependent utility specifications. Suppose that conditional on model Mm, the utility from a policy change is equal to (28) U(E(f31 I D,Mm)dzi,M?n) = U(f&mdZi,,Mm) so that the posterior expected utility of the policy change is (29) E(U(lizmdz,,Mm) I D) = Xpu(M0 , I D)U(&zmdZi,Mnm) m Manipulating U(.,-), one can produce (under the leading case) a result that is consistent with refusing to act whenever the posterior mean /3zm is negative for at least one Mm, thereby producing extreme bounds-like behavior in the sense that one would not choose dzi >0, even though for all other models /9z.mis positive. Policy Analysis and Exchangeability A decision-theoretic approach of the type we have advocated makes clear the importance of a growth model being rich enough for a researcher to plausibly Brock and Duirlauf 261 regard the observations as F-conditionally exchangeable. Suppose that a re- searcher is using data from I countries to provide a recommendation for the optimal choice of zisubject to some constraint set Z, for country i. In other words, a researcher is attempting to solve the problem (30) maxz,e z,E(V(g,,z,)) where information in computing this expression is taken from the regression described by equation 1. What information in equation 1 is relevant to this calculation? The answer depends on the shape of V. Suppose that V islinear in growth rates, as in equa- tion 18 above. The only information needed about the growth process as de- scribed by equation 1 is the posterior expected value of o3z.In our leading case, the OLScoefficient in a growth regression will be sufficient for policy analysis as long as all countries are described by a common linear model. Growth rates need not be partially exchangeable, because partial exchangeability rec[uiressymme- try with respect to all moments of the growth process. Similarly, suppose that V is quadratic. In this case one will need only the second moments from the poste- rior densities generated by equation 1 to apply to country i; partial exchange- ability is still not necessary. However, if V is arbitrary, one will need to employ equation 1 to obtain in- formation on the full conditional distribution F(EcIX,,Z,). To reveal this type of statistic from cross-country data, one will require full F-conditional exchange- ability of the type we have discussed. VII. AN EMPIRICAL EXAMPLE In this section we reconsider an important growth study, Easterly and Levine (1997), which examines the role of ethnic conflict in growth.27 We chose to re- examine this study for three reasons. The study is widely regarded as quite im- portant in the growth literature. It has important implications for policy and the sorts of advice and advocacy an international organization would engage in. And the authors of the study have done an admirable job of making their data and programs publicly available. Easterly and Levine's analysis is designed to explain why in standard cross- country growth regressions the performance of Sub-Saharan Africa28 is so much worse than that of the rest of the world. Rather than remain content with mod- eling this phenomenon as a fixed effect (a dummy variable) for these countries, Easterly and Levineargue that a major cause of the poor growth performance is the presence of ethnic conflict in these countries. They construct a measure of ethnic diversity to proxy for this conflict. This variable is substantially larger for 27. We thank Duncan Thomas for suggesting to us that the findings in Easterly and Levine (1997) warrant reexamination. 28. See the data appendix for the list of the countries in Sub-Saharan Africa. 262 THE WORLD BANK ECONOMIC REVIEW,VOL. 15, NO. 2 Sub-Saharan Africa than for the rest of the world. Inclusion of the variable in a cross-country growth regression reduces the size of the African fixed effect and isitself statistically significant. Easterly and Levine(1997, p. 1241) conclude that "the results lend support to the theories that interest group polarization leads to rent-seeking behavior and reduces the consensus for public goods, creating long- run growth tragedies." Our reexamination of this study has an explicitly narrow focus. In our view it is important to see whether and how the influence of ethnolinguistic heteroge- neity on growth depends on what other variables are included in the regression. Further, a natural alternative to the claim that the African growth experience is different because of an omitted variable, ethnolinguistic heterogeneity, is that other growth determinants influence Africa differently than they do the rest of the world. Put differently, parameter heterogeneity is a natural alternative ex- planation. We therefore conduct the following analysis to account for the effect of model uncertainty on Easterly and Levine's results. A data appendix describes the vari- ables we employ; these are identical to those used in Easterly and Levine(1997). The data are based on decade-long average observations for the 1960s, 1970s, and 1980s, except where indicated in the appendix. We focus on a reexamina- tion of Easterly and Levine's equation 3, table IV, which by conventional mea- sures (such as the statistical significance of all included variables) is arguably their strongest regression in support of the role of ethnic diversity in growth. Our results using this regression are reported in column 1of our table 1. The key variable of interest is ELF60, a measure of ethnic diversity in each country in 1960. We explore the role of model uncertainty in two ways. We first consider the impact of theory uncertainty on inferences about the determinants of growth. We do this by constructing a universe of models that consists of all possible com- binations of the variables in Easterly and Levine's baseline regression. This ex- ercise should be interpreted as a robustness check for Easterly and Levine's re- sults. To perform this exercise, we employ an approximation algorithm whereby posterior model probabilities are replaced with their maximum likelihood esti- mates. We perform the subsequent calculation of the posterior mean and stan- dard deviation of each regression coefficient using formulas 14 and 15.29 Our results incorporating theory uncertainty are reported in column 2 of table 1. Interestingly, we find that the evidence of a role for ethnic diversity in the growth process is slightly strengthened through the model averaging technique. Specifically, the posterior mean of ELF60 is -0.02 under model averaging, com- pared with the -0.017 estimate reported by Easterly and Levine. Our primary conclusion from this exercise is that Easterly and Levine's main result is robust to theory uncertainty as we have characterized it. 29. See the computational appendix for details on the calculation of thesequantities. Ethnolinguistic heterogeneity is not, of course, directly subject to a policymaker's control, so we do not explore the issues raised in section VI. The policy importance of the variable stems from the implications of its importance to questions of institutional design. Brock and Durlauf 263 TABLE 1. OLS and Bayesian Model Averaging Coefficient Estimates and Standard Errors Using Data from Easterly and Levine (1997) [6] [1] [2] [3] [4] [5] Interceptterm 0.1382 - - - - 0.4013 - - - - (0.3985) (0.0336) - Dummy for Sub- -0.0113 -0.0031 0.9558 0.0761 - Saharan Africa (0.0048) (0.0053) (0.3704) (0.0302) - - Dummyfor Latin -0.0191 -0.0197 -0.0197 -0.0184 - - America and the (0.0036) (0.0042) (0.0035) (0.0037) - - Caribbean Dummy for 1960s -0.2657 -0.2200 -0.3643 -0.0028 - - (0.0998) (0.1765) (0.1328) (0.0326) - - 0.0050 Dummy for 1970s -0.2609 -0,2154 -0.3520 0.0009 0.0080 (0.0997) (0.1745) (0.1332) (0.0325) (0.0134) (0.0079) -0.0024 Dummy for 1980s -0.2761 -0.2298 -0.3650 -0.0143 -0.0038 (0.0996) (0.1751) (0.1336) (0.0325) (0.0132) (0.0058) -0.0004 Log of initial 0.0870 0.0756 -0.1090 0.0218 -0.0696 (0.0027) income (0.0254) (0.0444) (0.0986) (0.0088) (0.11,71) -0.0000 Log of initial -0.0063 -0.0056 0.0070 -0.0022 0.0044 (0.0002) income squared (0.0016) (0.0029) (0.0067) (0.0006) (0.0088) -0.0017 Log of schooling 0.0117 0.0130 -0.0220 0.0130 -0.0131 (0.0042) (0.0056) (0.0216) (0.0045) (0.0194) (0.0077) -306.4870 -343.4434 Assassinations -12.8169 -3.3629 -377.3810 -30.6120 (9.2709) (7.8137) (165.5661) (86.9027) (158.4484) (181.6948) 0.0104 Financial depth 0.0162 0.0111 0.1010 0.0129 0.0774 (0.0058) (0.0083) (0.0497) (0.0075) (0.0483) (0.0278) -0.0039 Blackmarket -0.0188 -0.0219 -0.0130 -0.0207 -0.0171 (0.0081) premium (0.0045) (0.0053) (0.0098) (0.0043) (0.0107) 0.0948 Fiscal surplus/GDP 0.1210 0.1717 0.1200 0.1382 0.1654 (0.0314) (0.0411) (0.0874) (0.0357) (0.0986) (0.1071) -0.1595 Ethnicdiversity -0.0169 -0.0222 -0.2020 -0.1437 -0.1516 (0.0353) (0.0327) (ELF60) (0.0060) (0.0066) (0.0376) (0.0279) [11 Ordinary least squares estimates for model "ALL". [2] Bayesian model averaging estimates for model "ALL". [31 Ordinary least squares estimates for model "ALI. +A I.*I(AFRICA)";composite coefficient estimates set of regres- and standard errors reported. AFRICA, LATINCA, and DUAM6O dropped from AFRICA-specific sors. [41 Bayesian model averaging estimates for model "ALL + ALL*I(AFRICA)"; composite coefficient es- timates and standard errors reported. AFRICA, LATINCA, and DUM6O dropped from AFRICA-specific set of regressors. [5] Ordinary least squares on AFRICA subsample. [6] Bayesian model averaging on AFRICA subsample. Note: Standard errors are in parentheses. As we have emphasized, theory uncertainty is not the only form of model uncertainty that needs to be accounted for in cross-country analysis. We there- fore next incorporate heterogeneity uncertainty. Following equation 11, we do this by constructing for each regressor x, in the baseline regressorsa corresponding variable Sub-Saharan Africa and 0 other- Xij 1 if country j isin 1A where jiA = 6 , wise. This allows for the p1ossibilitythat the Sub-Saharan African countries have different growth parameters than the rest of the world. Column 3 in table 1 re- 264 THE WORLD BANKECONOMICREVIEW,VOL. 15, NO. 2 ports the OLS values and standard errors of the regressor coefficients for the African countries; column 4 reports the same statistics when model averaging is done over the augmented variable set. Column 5 reports OLS estimates of the growth regression coefficients and standard errors when the African sub- sample is analyzed in isolation; column 6 reports the corresponding model average results. Our explorations of the role of heterogeneity uncertainty provide a rather different picture of the role of ethnicity in African growth than of its role in the rest of the world. The coefficientestimates for Africa are about 7-10 timesgreater than the corresponding estimates for the world.30 This result is extremely strik- ing and makes clear that the operation of ethnic heterogeneity on growth is dif- ferent in Africa, not just the levels of ethnic heterogeneity. Further, a compari- son of the other regressorcoefficientsfor Africawith those of the rest of the world makes clear that the growth observations for African countries should not be treated as partially exchangeable with the growth rates of the rest of the world. These results in no way diminish the importance of Easterly and Levine's find- ings. In fact, our exercises show that their basic claims are robust to a limited variable uncertainty exercise. Our finding of parameter heterogeneity with re- spect to ethnolinguistic heterogeneity suggests a direction along which to extend their research. Our results illustrate how additional insights can be obtained by explicitly controlling for model uncertainty. Finally, we again note that this reexamination is quite narrow. A full-scale study should at a minimum include explicit calculations and presentation of the predictive distribution of the effects of the policy change on growth. Fernandez, Ley, and Steel (1999) provide a good illustration of how to present results of this type. More generally, the reporting of results should always include the in- formation necessary to calculate the posterior expected utility changes of the policymaker. Our own reporting is useful for mean/variance utility functions, but not for the others we have discussed. In addition, we have not allowed for parameter heterogeneity for countries outside Sub-Saharan Africa; doing so is a natural extension of this exercise. The results we report should be treated as suggestive, in this sense, of more elaborate examinations of the role of ethnic heterogeneity in the growth process. VIII. CONCLUSIONS This paper has had two basic aims. First, we attempted to delineate the major criticisms of cross-country growth regressions and to show how to interpret two 30. Similar results are obtained when one compares Sub-Saharan Africa with the rest of the world. When the Sub-Saharan African countries are dropped from the data set, the OLS estimate for the FLF60 regressor is -0.0115 with an associated standard error of 0.006. The associated values when model averaging is done across different regressor combinations (to check for robustness to theory uncertainty) are -0.013 and 0.009. By conventional levels, one would conclude that ethnicity is marginally statisti- cally significantoutside Sub-Saharan Africa. Brock and Durlauf 265 of these criticisms, theory uncertainty and parameter uncertainty, as violations of a particular assumption-F-conditional exchangeability-in the residual com- ponents of growth models. Second, we outlined a framework for conducting and interpreting growth regressions. For conducting regressions, we aLdvocatedan explicit modeling of theory and heterogeneity uncertainty and the use of model averaging to condition out strong assumptions. For interpreting re!gressions,we argued that the policy objectives associated with a given exercise must be made explicit in the analysis. We outlined a decision-theoretic approach to growth regressions and explored its relationship to conventional approaches to assess- ing model robustness. Finally, in an empirical application we showed how at- tention to model uncertainty can provide new insights into the relationship be- tween ethnicity and growth. To amplify some earlier remarks, we do not believethat there is a single privi- legedway to conduct statistical or, forthat matter, empirical analysis in the social sciences.Persuasive empirical work always requires judgments anclassumptions that cannot be falsified or confirmed within the statistical procedure being em- ployed.31 Indeed, this isthe reason that we have not included a treatment of how we to provide more robust arguments in favor of causality in this article. What hope is that this article has provided some initial steps toward the development of a language in which policy-relevant empirical growth research may be better expressed. COMPUTATIONAL APPENDIX All model averaging calculations were done using the program bicreg, which was written in SPLUSby Adrian Raftery and is available at www.research.att.com/ -volinsky/bma.html. Given the large number of possible models, this program, as is standard in the model averaging literature, uses a search algorithm that explores only a subset of the model space; the key feature of the design of the algorithm isthat it ensures that the search proceeds along directions such that it is likely to cover models that are relatively strongly supported by the data. We follow the procedure suggested by Madigan and Raftery (1994); see Raftery, Madigan, and Hoeting (1997); and Hoeting and others (1999) for additional discussion. Though the reader should see those papers for a full description of the search algorithm, Hoeting and others (1999, p. 385) provide sanice intuitive description: First, when the algorithm compares two nested models and decisivelyre- jects the simpler model, then all submodels of the simpler model arerejected. The second idea, "Occam's window," concerns the interpretation of the ratio of posterior model probabilities pr(MO/D)/pr(M1 /D). Here Mo is "smaller" than Ml.... If there is evidence for Mothen MSis rejected,but rejecting Morequires strong evidence for the larger model Ml. such issues. 31. See Draperand others (1993) and Mallows (1998) for valuable discussions of 266 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. 2 In implementing the model averaging procedure, the algorithm we em- ploy uses an approximation, due to Raftery (1995), based on the idea that, be- cause for a large enough number of observations, the posterior coefficient dis- tribution will be close to themaximum likelihood estimator, and so one can use the maximum likelihood estimates to avoid the need to specify a particular prior. We refer the reader to Raftery (1994) as well as to Tierney and Kadane (1986) for technical details. While some evidence exists that this approximation works well in practice, more research is needed on the specification of priors for model averaging; an important recent contribution is Fernandez, Ley, and Steel (2001). DATA APPENDIX: VARIABLE DEFINITIONS All data are the same as those used in Easterly and Levine (1997). * AFRICA: Dummy variable for Sub-Saharan African countries, as defined by the World Bank. These countries are Angola, Benin, Botswana, Burkina Faso, Burundi, Cameroon, Cape Verde, the Central African Republic, Chad, Comoros, Democratic Republic of Congo, Republic of Congo, C6te d'Ivoire, Djibouti, Equatorial Guinea, Ethiopia, Gabon, The Gambia, Ghana, Guinea, Guinea-Bissau, Kenya, Lesotho, Liberia, Madagascar, Malawi, Mali, Mauritania, Mauritius, Mozambique, Namibia, Niger, Nigeria, Rwanda, Sao Tome and Principe, Senegal, Seychelles, Sierre Leone, Somalia, South Africa, Sudan, Swaziland, Tanzania, Togo, Uganda, Zambia, and Zimbabwe. * ASSASS: Number of assassinations per 1,000 population. * BLCK: Black market premium, defined as log of 1 + decade average of black market premium. * DUM6o: Dummy variable for 1960s. * DUM7o: Dummy variable for 1970s. * DUM8O: Dummy variable for 1980s. * ELF60: A measure of ethnic diversity, equalling an index of ethnolinguistic fractionalization in 1960. This variable measures the probability that two randomly selected individuals from a given country will not belong to the same ethnolinguistic group. * GYP: Growth rate of real per capita GDP. * LATINCA: Dummy variable for countries in Latin America and the Carib- bean. * LLY: Financial depth, measured as the ratio of liquid liabilitiesof the finan- cial system to GDP, decade average. Liquid liabilities consist of currency held outside the banking system plus demand and interest-bearing liabili- ties of banks and nonbank financial intermediaries. * LRGDP: Log of real per capita GDP measured at the start of each decade. * LRGDPSQ: Squareof LRGDP. Brock and D)urlauf 267 * LSCHOOL: Log of 1 + average years of school attainment, quinquennial val- ues (1960-65, 1970-75, 1980-85). * SURP: Fiscal surplus/GDP: Decade average of ratio of central government sur- plus to GDP, both in local currency, local prices. TECHNICAL APPENDIX 1. De Finetti'sRepresentationTheorem De Finetti's theorem establishes that the symmetry inherent in thleconcept of the exchangeability of errors leads to a representation of the joint: distribution of the errors in terms of an integral of the joint product of identlicalmarginal distributions against some conditional distribution function. The theorem is as follows. If mli isan infinite exchangeable sequence with associated probability measure P, there exists a probability measure Q over F, the space of all distribution func- tions on R, such that the joint distribution function F( i. . .. li+k)for any finite collection nl,i may be written as -7i li ... + k k (A-1) F(r7, . . . ii . . . li+k) =J nlF(ni7±)dQ(F) SeeBernardo and Smith (1994, p. 177), for this formulation of de Finetti's theo- rem as well as a proof. 2. Some RelationsbetweenOLS Estimatesand BayesianPosteriors For the linear model (A-2) gj =S'Z+£i i= ... suppose that (1) conditional on 1 S . . . SI,the Eisare independent and identically distributed and jointly normal; the marginal distribution of the typical element is N(0,ca), (2) d is known, and (3) prior information on ; is characterized by the noninformative (improper) prior (A-3) M(O gc where c is a constant. Denote the OLS estimate (as well as the classical maximum likelihood estimate) of ; as 4,and denote the data matrix of regressors in equa- tion A-2 as S. As shown for example in Box and Tiao (1973, p. 115), the posterior density of the parameter vector ; given the available data D, p(; ID,M), is, under our assumptions, multivariate normal. Specifically, (A-4) y(; I D) - N(4, (S'S) -lo) The posterior density of any particular coefficient can of course be calculated from this vector density. Under the assumptions justifying A-4, the posterior 268 THEWORLDBANKECONOMICREVIEW,VOL. 15, NO. Z mean and variance of g therefore correspond to the standard OLSestimates of the parameter vector and its associated covariance matrix. When i~ is unknown, the posterior density of ;can also be characterized and related to OLS estimates. Formally, if Oc2is unknown and has a noninformative prior (A-5) p(a') oc -2, then it can be shown (Box and Tiao 1973, p. 117) that (A-6) (4ID,o*)- N(4I(S'S)-SIa2). For reasonably large samples, i can bereplaced with the OLSestimate 2 so that, approximately, (A-7) p(; ID)- N(S,(S'S)-] 2) and again the posterior mean and variance of ; may be equated with the corre- sponding OLSestimates. We refer to this as the "leading case" in the text. In our evaluation of growth models, we have emphasized the role of F- exchangeable, as opposed to independent and identically distributed errors. De Finetti's theorem provides a link between exchangeability and independence and so motivates our use of this leading case. REFERENCES The word "processed" describes informally reproduced works that may not be commonly available through library systems. Aldous, D. 1983. "Exchangeability and Related Topics." In Pcole d'te de Probabilites de Saint Flour XIII. Lecture Notes in Mathematics Series, no. 1117. New York: Springer-Verlag. Anderson, E., L. Hansen, and T. Sargent. 1999. "Risk and Robustness inEquilibrium." Department of Economics, Stanford University. Processed. Arnold, S. 1979. "Linear Models with Exchangeably Distributed Errors." Journal of the American Statistical Association 74:194-99. Auerbach, A., K. Hassett, and S.Oliner. 1994. "Reassessing the Social Returns to Equip- ment Investment." Quarterly Journal of Economics 109:789-802. Azariadis, C.,and A. Drazen. 1990. "Threshold Externalitiesin EconomicDevelopment." QuarterlyJournalof Economics105:501-26. Barro, R. 1991. "Economic Growth in a Cross-Section of Countries." Quarterly Jour- nal of Economics 106:407-43. . 1996. "Democracy and Growth." Journal of Economic Growth 1:1-27. Ben-Akiva, M., and S. Lerman. 1985. Discrete Choice Analysis: Theory and Applica- tion to Travel Demand. Cambridge, Mass.: MIT Press. Berger,J. 1987. Statistical DecisionTheory and BayesianAnalysis. New York: Springer- Verlag. Bernard, A., and S. Durlauf. 1996. "Interpreting Tests of theConvergence Hypothesis." Journalof Econometrics71:161-72. Brock and L)urlauf 269 Bernardo, J., and A. Smith. 1994. Bayesian Theory. New York: John Wiey and Sons. Box, G., and G. Tiao. 1973. Bayesian Inference in Statistical Analysis. New York: John Wiley and Sons. Reprinted 2000. Breiman, L. 1996. "Bagging Predictors." Machine Learning 26:123-40. Camerer, C. 1995. "Individual Decision Making." In J. Kagel and A. Roth, eds., Hand- bookof Experimental Economics. Princeton, N.J.: Princeton University Press. Canova, F. 1999. "Testing for Convergence Clubs in Income Per-Capita: A Predictive Density Approach." Department of Economics, University of Pompeu Fabra, Spain. Processed. Clark, G. 1987. "Why Isn't the Whole World Developed? Lessonsfrom the Cotton Mills." Journalof EconomicHistory 47:141-73. Clyde, M., and H. Lee. 2000. "Bagging and the Bayesian Bootstrap." Duke University, Department of Statistics, Durham, N.C. Processed. Debreu, G. 1960. "Review of R. D. Luce, Individual Choice Behavior: A Theoretical Analysis." American Economic Review 50:186-88. DeLong, J. B., and L. Summers. 1991. "Equipment Investment and Economic Growth." Quarterly Joumral of Economics 106:445-502. . 1994. "Equipment Investment and Economic Growth: Reply." Quarterly Jour- nal of Economics 109:803-7. Desdoigts, A. 1999. "Patterns of Economic Development and the Formation of Clubs." Journalof EconomicGrowth4:305-30. Doppelhofer, G., R. Miller, and X. Sala-i-Martin. 2000. "Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (BACE) Approach." Working Paper no. 7750, National Bureau of Economic Research, Cambridge, Mass. Draper, D. 1987. "Comment: On the Exchangeability Judgments in Predictive Model- ing and the Role of Data in Statistical Research."Statistical Science 2:454-61. .1995. "Assessment and Propagation of Model Uncertainty." Journal of the Royal Statistical Society, Series B 57:45-70. . 1997. "On the Relationship between Model Uncertainty and Inferential/Predic- tive Uncertainty." School of Mathematical Sciences, University of Bath. Processed. Draper, D., J. Hodges, C. Mallows, and D. Pregibon. 1993. "Exchangeability and Data Analysis." Journal of the Royal Statistical Society, Series A 156:9-28. Durlauf, S. 2000. "Econometric Analysis and the Study of Economic Growth: A Skepti- cal Perspective." In R. Backhouse and A. Salanti, eds., Macroeconomics and the Real World. Oxford: Oxford University Press. Durlauf, S., and P. Johnson. 1995. "Multiple Regimes and Cross-Country Growth Be- havior." Jouirnalof Applied Econometrics 10:365-84. Durlauf, S.,and D. Quah. 1999. "The New Empirics of Economic Growth." In J. Tay- lor and M. Woodford, eds., Handbook of Macroeconomics. Amsterdam: North Holland. Durlauf, S., A. Kourtellos, and A. Minkin. 2000. "The Local Solow Growth Model." Forthcoming in the EuropeantEconomic Review, Papers and Proceedinlgs. Easterly, W., and R. Levine. 1997. "Africa's Growth Tragedy: Policies and Ethnic Divi- sions." QuarterlyJournalof Economics 112:1203-50. Epstein, L., and T. Wang. 1994. "Intertemporal Asset Pricing Behavior LinderKnightian Uncertainty." Econometrica 62:283-322. 270 THE WORLD BANK ECONOMIC REVIEW, VOL. 15, NO. I Evans, P. 1998. "Using Panel Data to Evaluate Growth Theories." International Eco- nomic Review 39:295-306. Fernandez, C., E. Ley, and M. Steel. 1999. "Model Uncertainty in Cross-Country Growth Regressions." Department of Economics, University of Edinburgh (also forthcoming, Journalof AppliedEconometrics). . 2001. "Benchmark Priors for Bayesian Model Averaging." Journal of Econo- metrics 100:381-427. Frankel, J., and D. Romer. 1996. "Trade and Growth: An Empirical Investigation." Working Paper 5476, National Bureau of Economic Research. Cambridge, Mass. Freedman, D. 1991. "Statistical Models and Shoe Leather." In P. Marsden, ed., Socio- logical Methodology 1991. Cambridge: BasilBlackwell. . 1997. "From Association to Causation via Regression." In V. McKim and S. Turner, eds., Causality in Crisis. South Bend, Ind.: University of Notre Dame Press. Galor, 0. 1996. "Convergence? Inferences from Theoretical Models." Economic Jour- nal 106:1056-69. Gilboa, I., and David Schmeidler. 1989. "Maximin Expected Utility with Nonunique Prior." Journalof MathematicalEconomics18:141-53. Goldberger, A. 1991. A Course in Econometrics. Cambridge, Mass.: Harvard Univer- sity Press. Granger, C., and H. Uhlig. 1990. "Reasonable Extreme-Bounds Analysis." Journal of Econometrics44:159-70. Heckman, J. 2000. "Causal Parameters and Policy Analysis in Economics: A Twentieth Century Retrospective." Quarterly Journal of Economics 115:45-97. Hoeting, J., D. Madigan, A. Raftery, and C. Volinsky. 1999. "Bayesian Model Averag- ing: A Tutorial." Statistical Science 14:382-401. Islam, N. 1995. "Growth Empirics: A Panel Data Approach." Quarterly Journal of Eco- nomics 110:1127-70. Ivanoff, B., and N. Weber. 1996. "Some Characterizations of Partial Exchangeability." Journal of the AustralianMathematicalSociety,SeriesA 61:345-59. Kadane, J., and J. Dickey. 1980. "Bayesian Decision Theory and the Simplification of Models." In J. Kmenta and J. Ramsey, eds., Evaluation of Econometric Models. New York: Academic Press. Kallenberg, 0. 1982. "Characterizations and Embedding Properties in Exchangeability." Zeitschrift fiir Wahrscheinlichkeitstheorie und verwandte Gebiete 60:249-81. Kass, R., and A. Raftery. 1994. "Bayes Factors." Journal of the American Statistical Association90:773-95. Kourtellos, A. 2000. "A Projection Pursuit Approach to Cross-Country Growth Data." Department of Economics, University of Wisconsin. Processed. Landes, D. 2000. "Culture Makes Almost All the Difference." In L. Harrison and S. Huntington, eds., Culture Matters. New York: Basic Books. Leamer, E. 1978. Specification Searches. New York: John Wiley. . 1983. "Let's Take the Con Out of Econometrics." American Economic Review 73:31-43. Leamer, E., and H. Leonard. 1983. "Reporting the Fragility of Regression Estimates." Review of Economics and Statistics 65:306-17. Brock and l)urlauf 271 Lee, K., M. H. Pesaran, and R. Smith. 1997. "Growth and Convergence in a Multi- Country Stochastic Solow Model." Journal of Applied Econometrics 12:357-92. Levine, R., and D. Renelt.1992. "A Sensitivity Analysis of Cross-Country Growth Re- gressions." American Economic Review 82:942-63. Lucas, R. 1988. "On the Mechanics of Economic Development." Journal of Monetary Economics22:3-42. Madigan, D., and A. Raftery. 1994. "Model Selection and Accounting for Model Un- certainty in GraphicalModels Using Occam's Window." Journal of the Anierican Sta- tisticalAssociation89:1535-46. Mallows, C. 1998. "The Zeroth Problem." American Statistician 52:1-9. Mankiw, N. G., D. Romer, and D. Weil. 1992. "A Contribution to the Empirics of Eco- nomic Growth." Quarterly Journal of Economics 107:407-37. McAleer, M., A. Pagan, and P. Volker. 1985. "What Will Take the Con Out of Econo- metrics?" American Economic Review 75:293-307. Pack, H. 1994. "Endogenous Growth Theory: Intellectual Appeal and Ernpirical Short- comings."Journalof EconomicPerspectives8:55-72. Pesaran, M. H., andR. Smith. 1995. "Estimating Long-Run Relationships from Dynamic Heterogeneous Panels." Journialof Econonmetrics68:79-113. Prescott, E. 1998. "Needed: A Theory of Total Factor Productivity." International Economic Review 39:525-52. Pritchett, L. 2000. "Patterns of Economic Growth: Hills, Plateaus, Mountains, and Plains." World Bank Economic Review 14:221-50. Quah, D. 1996a. "Convergence Empirics across Economies with Some Capital Mobil- ity." Journalof EconomicGrowth 1:95-124. .1996b. "Empirics for Growth and Economic Convergence." European Economic Review 40:1353-75. 1997. "Empirics for Growth and Distribution: Polarization, Stratification, and ConvergenceClubs."Journalof EconomicGrowth2:27-59. Raftery, A. 1995. "Bayesian Model Selection in Social Research." In P. Marsden, ed., Sociological Methodology 1995. Cambridge: Blackwell. Raftery, A., D. Madigan, and J. Hoeting. 1997. "Bayesian Model Averaging for Linear Regression Models." Journal of the American Statistical Association 92:179-91. Raiffa, H., and R. Schlaifer. 1961. AppliedStatistical Decision Theory. New York: John Wiley. Romer, P. 1986. "Increasing Returns and Long Run Growth." Journlal of Political Economy 94:1002-37. Romer, P. 1990. "Endogenous Technical Change." Journal of Political Economy 98:S71- S102. Sala-i-Martin, X. 1997. "I Just Ran Two Million Regressions." American Economic Review, Papers and Proceedings 87:178-83. Schervish, M. 1995. Theory of Statistics.New York: Springer-Verlag. Schultz, T. P. 1998. "Inequality in the Distribution of Personal Income in the World: How It Is Changing and Why." Journal of Population Economics 11]:307-44. . 1999. "Health and Schooling Investments in Africa." Journal of Economic Growth 13:67-88. Sims, C. 1980. "Macroeconomics and Reality." Econometrica 48:1-48. 272 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. Z Temple, J. 1998. "Robustness Tests of the Augmented Solow Growth Model." Journal of Applied Econometrics 13:361-75. .2000. "Growth Regressions and What the Textbooks Don't Tell You."Bulletin of Economic Research 52:181-205. Tierney, L., andJ. Kadane. 1986. "Accurate Approximations for Posterior Moments and MarginalDensities."Journalof theAmericanStatisticalAssociation81:82-6. Wasserman, L. 2000. "Bayesian Model Selection and Model Averaging." Journal of Mathematical Psychology 44:97-102. White, H. 1994. Estimation, Inferenceand SpecificationAnalysis.Cambridge: Cambridge University Press. Wolcott, S., andG. Clark. 1999. "Why Nations Fail: Managerial Decisions and Perfor- mance in Indian Cotton Textiles, 1890-1938." Journal of Economic History 59:397- 423. THE WORLD BANK ECONOMIC REVIEW, VOL. 15, NO. 2 173-275 What have we learnedfrom a decade of enipiricalresearchonigrowth? Comment on "Growth Empirics and Reality," by William A. Brock and Steven N. Durlauf Lant Pritchett World Bank economists are mostly practical people-people who try to answer the question, "What exactly should this particular country do right now?" But ifthey had hoped that the growth regression lessonssummarized in William Brock and Steven Durlauf's article would enhance their practical advice giving, they might feel some dissatisfaction. How would they change their advice to, say, Brazil? But that iswhy this article is important conceptually. It goes to the heart of the matter by proposing a change in the empirical growth literature's funda- mental methodology-from model testing to decision theoretic. The article's valiant but flawed attempt reveals the difficulties in making this shift, however. I'd like to make three points: There is a tension between the interests of academics and practitioners in growth regressions. Output response heterogeneity is a huge practical problem. And policy decisions can be guided only in broad outlines by growth regressions. THE TENSIONS BETWEEN ACADEMIC AND PRACTICAL INIERESTS What Paul Romer said about the intellectual history is on point: First there was this received model, the Solow model, and then along came others-but nearly all were essentially models of Organisation of Economic Co-operation and De- velopment (OECD) countries. The interest in empirically testing these competing models of the evolution of GDP in technologically advanced countries led in two directions, reflecting two sources of pressure. The first source of pressure is that even though a model may be about Ger- many or the United States (technological leaders), data from Guyana and Papua New Guinea and Senegal get recruited into increasing the degrees of freedom for the statistical tests among models. But that should not lead anyone to be- lievethat the model is about Guyana. The second isthat the model testing perspective focuses attention on hypoth- esesthat present a clean separation between alternative models-but not neces- sarily on what is empirically or practically most important. This may account for the seemingly casual approach to the specification of "policy." Robert Hall, Lant Pritchett is economiston leave from the World Bank at the KennedySchool of Government. 0 2001 The International Bank for Reconstruction and Development / THE WORID BANK 273 274 THE WORLD BANK ECONOMIC REVIEW, VOL. 15, NO. 2 in a nice paper in honor of Professor Solow's birthday, (Hall 1990) basically points out that if we take Solow's "toy" model literally, everything should be orthogonal to total factor productivity (TFP). The reason isthat giventhe model's assumptions, there cannot be incentives to augment TFP because factor payments to labor and capital exhaust product. From the narrow perspective of model testing, proving that any policy affected steady-state or TFP growth by altering incentivesprovides a clean separation of the models. Empiricalwork that couldn't possibly contribute to the practical advice but provided a clean separation be- tween competing models became academically important. THE PROBLEM OF OUTPUT RESPONSE HETEROGENEITY Assume that we are considering a permanent shift in the value of policy P from level P to P' at time t. A key question is, "What is the difference between prop- erly measured GDP with policy P' and that with policy P at time t, t + 1, t + 2, out to t + N?" A huge problem with empirical estimation of an output response function, however, is that there is no reason to believe that it looks the same- across countries or over time. Brock and Durlauf's article does a good job of emphasizing this problem by focusing on parameter heterogeneity. But even characterizing the problem as parameter heterogeneity-and, especially,limiting heterogeneity to a small num- ber of linear interactions-artificially narrows the problem, as output response function could vary in many ways for many reasons. It could depend on struc- tural differences across economies, on economic structure, on institutional dif- ferences that would mediate the policy change, or on complementary policies that could affect the output response of a given policy. This proliferation of parameters for characterizing output response makes the empirical situation seem bad-but it is much worse than that. Even for coun- tries observationally equivalent in terms of structure, output response dynamics could depend on timing, expectations, and history. Soa policy that may be perfect for bringing a country out of a recession might be neutral, or even counter- productive, at the peak of the cycle. Expectations play a huge role in output re- sponse-observationally equivalent policy changes can potentially have enor- mously different impacts depending on whether all people believethat the policy change will persist or all believe that it will not persist. Finally, there may be output response function hysteresis, in which the output response function depends not just on conditions today but on an economy's entire history of policy changes and their impacts. THE LIMITS OF GROWTH REGRESSIONS AS A SOURCE OF POLICY ADVICE The policy variables that go into growth regressions are at a levelof abstraction far greater than that at which policy recommendations and decisions are made Pritchett 275 and implemented in the real world. So although it is possible to come up with a growth regression that says that, on average, countries that are more open tend to grow faster, that leaves a million questions about trade policy reform unan- swered: Should the tariff be lowered on this good or that set of goods? Should tariff reductions be concertina or from the top down? Should changes becarried out in one stroke or phased in? Suppose we take the decision-theoretic approach to empirics seriously. The inevitable problem is that the level of specificity at which most growth econo- mists need to work isfar greater than can ever be adequately informed by growth regressions. Some people act disappointed that we haven't learned more from growth regressions-but we have to live with the fact that growtlh regressions are not going to tell us w"hatthe tariff on capital goods in Brazil should be in 2001. Growth regressions are incredibly useful in providing a general empirical background of stylized facts about the world. The partial associations of policy variables with growth provide a grounding in reality from which policy discus- sions can build. But none of us is in any danger in the near term of being re- placed by an automaton based on growth regressions that takes in country con- ditions, searches the data, and then spits out policy solutions. Policy decisions draw on a variety of information and remain the domain of that most elusive of qualities: good human judgment. REFERENCE Hall, Robert. 1990. "Invariance Properties of Solow's Productivity Residual." In Peter Diamond, ed., Growth/Productivity/Unemployment: Essays to CelebrateBob Solowv's Birtbday. Cambridge, Mass: MIT Press, pp. 71-112. THE WORLD BANKECONOMICREVIEW,VOL. 15, NO. 2 Z77-Z82 Whathave we learnedfrom a decade of empiricalresearchon growth? Comment on "Growth Empirics and Reality," by William A. Brock and Steven N. Durlauf Xavier Sala-i-Martin William Brock and Steven Durlauf's article nicely summarizes sorne of the re- cent research on Bayesian model averaging. They make a number of important points. One is that the empirics of growth face three key problems: model un- certainty, parameter uncertainty, and endogeneity. They argue that theory un- certainty can be dealt with using Bayesian model averaging methods. Their key equations are 16, 17, and 18, for which the interpretation isas follows. Suppose you are interested in the distribution of the partial derivative of the growth rate with respect to variable z, b,. Let each set of every possible combination of ex- planatory variables be called a "model." Conditional on each model there is a distribution of b, for a given data set. Equation 17 says that the posterior distri- bution of b, isa weighted average of all these individual distributions, where the weights are proportional to the likelihoods of the models. Equation 18 says that the mean of this distribution isthe weighted average of the ordinary least squares (OLS) estimates of all these models, where the weights are propottional to the likelihoods. Equation 19 makes a similar claim about the variance. The assumption that weights are proportional to the likelihoods is an impor- tant one. In fact, it may drive the authors' first key empirical result-that East- erly and Levine's (1997) regression of growth on ethnolinguistic fractionaliza- tion (ELF) is "robust" to Bayesian model averaging analysis. It is important to remember that models with more explanatory variables have larger likelihoods. It isalso important to remember that Brock and Durlauf perform Bayesianmodel averaging analysis by combining the explanatory variables of the Easterly and Levine paper in all possible ways: sets of one right-hand-side variable, sets of two, sets of three, and, eventually, one set with all the right-hand-side variables. This last model is the one run by Easterly and Levineand the largest model run by Brock and Durlauf (and therefore the one that is likely to have the largest likelihood and that gets the largest weight). Hence, it is not surprising that the weighted average of all the models is simi- lar to that for Easterly and Levine's model, because most of the weight of the average goes to Easterly and Levine's specification, by construction. In other words, the finding that Easterly and Levine's regression results (column 1in table Xavier Sala-i-Martin is atColumbia University and UPF. © 2001 The International Bank for Reconstruction andDevelopment / THE WORLD BANK 277 278 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. 2 1) are "robust" to the Bayesian model averaging analysis because the weighted average of models (column 2) is virtually identical is likely to be an artifact of the weights used. I should confess that these are also the weights I used in a 1997 paper (which has equations 16 and 17 in exactly the same form). However, in that work I averaged only regressions with a fixed set of explanatory variables, so I did not have the problem that I am pointing out here. Doppelhofer, Miller, and Sala-i- Martin (2000) derive an alternative weighting scheme. The posterior density of model Mmisproportional to the likelihood (sum of squares of residuals, or SSEm- T12), multipliedby T-kmI2,where T is the number of observations and km is the number of explanatory variables in model m: Y(MJID) =U(MJT SSEM Zp(M, )Tk1 2.SSE7T12 i=l Note that this weighting scheme penalizes larger models. It would be interesting to see whether column 1 still looks verymuch like column 2 when these alterna- tive weights are used. A second important assumption is the prior that allows Brock and Durlauf to eliminate the si(Mm)from equation 15 to derive equation 16. They use the prior that "all modelsare equally likely." Imagine that we had 32 possible right- hand-side variables. If we believe that all models are equally likely, the prior distribution of model sizes is as shown in figure 1. The average model size is 16. If instead we had 10 explanatory variables, the implicit assumption would be that the average model size of the prior distribution of cross-country re- gressions is 5. The problem is that Brock and Durlauf propose that when analyzing (or dis- cussing) a paper like Easterly and Levine (1997), we take the key regression in that paper and perform Bayesian model averaging analysis with it. If we take FIGURE 1. Prior Probabilities by Model Size: Equal Model Probabilities 0.2 1 -- 0.15 0.05 0 e v Sala-i-Martin 279 this proposal literally,we would implicitly assume that the average model size of "the growth regression" is 5 when the original paper had 10 variables, and 16 when the original paper had 32 variables. Besides being arbitrary, this as- sumption does not make sense: The prior model size should be invariant to the paper being discussed. One solution to this problem, following Doppelhofer, Miller, and Sala-i-Martin (2000), would be to specify the model prior probabilities by choosing a prior mean model size, k, with each variable having a prior probability K'IK of being included, independent of the inclusion of any other variables, where K isthe total number of potential regressors (figure 2). Equal probability for each possible model isthe special case in which K= K/2. The prior distribution of model sizes would be invariant to the paper analyzed. Moreover, the robustness of this prior could be checked by redoing the Bayesian model averaging exercise (or better yet, Bayesian averaging of classical estimates) for different values of K. My third comment relates to the treatment of parameter uncertainty. I agree with the authors that this problem is analogous to that of theory uncertainty. But if so, why do they propose a different solution? Ifwe think that Africa needs a different slope for variable z, all we need to do is to construct a new variable (ztimes one for countries in Africa and z times zero otherwise) and put this new variable in the pool of potential variables to be included in the Bayesian model averaging analysis. Rather than columns 3-6, table 2 should include a row pre- senting the distribution of the P3j<21for this new variable, as a regular additional variable subject to theory uncertainty. When we think of parameter uncertainty as another form of theory uncer- tainty, an additional problem comes to mind. Why do we think that Africa needs its own slope? Why don't we have a special slope for Christian countries? Or hot countries? Or small countries? Of course, we do not know whether or not special slopes are needed (we do not have a theory, or we can have many open- ended theories that would call for a special slope for each of these country groups). However, in the spirit of Durlauf and Johnson (1995), shouldn't we then per- FIGURE 2. Prior Probabilities by Model Size (K 7) 0.2 0.15 - 0.1 0.05 _ 0 .___ O ? 61 9 7 280 THE WORLD BANK ECONOMIC REVIEW, VOL. I5, NO. Z form Bayesian model averaging or Bayesian averaging of classical estimates for each group of countries? How would we go about that? A perhaps related question is that of nonlinearities, which Brock and Durlauf do not allow for in their article. It isclear that African countries have both lower average growth and greater ethnolinguistic fractionalization. The conditional data might therefore look like figure 3. If we think about the implications of figure 3, we arrive at the conclusion that if we could somehow reduce ELF for African countries, Africa will conditionally grow faster than the rest of the world for- ever (that is, we would move the African data points to the left along the steeper regression line). Becausewe do not have a theory of ELF, we do not know whether this is sensible or not. Alternatively, we could think that the partial relationship between growth and ELF looks like figure 4. In fact, the data points in figures 3 and 4 are exactly the same. The only thing that differs is the functional form of the regression curve. Under this interpretation, if Africa manages to get the same ELF as the rest of the world, its growth rate will also be similar. Hence the economic implications of a separate slope for Africa are very different from those of a nonlinear relation- ship. It would have been interesting to incorporate nonlinearities in the analysis. Finally, the claim that growth economists have not dealt with parameter un- certainty is not quite true. In fact, parameter uncertainty is a particular form of what economists usually label interaction terms. For example, suppose a claim is made that the partial derivative of growth with respect to z depends on variable y: Og, - az,,p +i YIY FIGURE 3. g ROW (slope=p3) Africa (slope=P3+P2) 0~~~~~ _ < \ ~ ~ELF Sala-i-Martin 281 FIGURE4. g 0 *X _ * \ ~~~ELF The way to test this claim would be to run a regression of growth with z as an explanatory variable and with an additional variable that isa countr-y-by-country product of z times y. That is, we should introduce interaction terms. It should be clear that parameter uncertainty is nothing but an interaction terirnwhen vari- able y is simply a dummy variable for a region (in this case, Sub-Sahiaran Africa). To the extent that growth economists have introduced interaction terms, there- fore, they have allowed for parameter heterogeneity. I conclude with two sources of disappointment about this otherwise excellent article. First, the articleisnot really about the empirics of economilcgrowth. All empirical analyses are subject to the problems it discusses,especially those forced to use small data sets. In this sense the title, though cute, is highly misleading and, to the extent that it leads future researchers away from econiomicgrowth analysis, potentially damaging. Amore appropriate title would be "Small-Sample Econometrics," because the problems discussed are common to all empirical analyses with small samples (which include all cross-country analyses in any field). After all, if we had a huge data set with zillions of observations, we could simply throw in all potential variables, with particular slopes for each potential set of coutris, ithall potential nonlinearities, and so on-and the data would tell us which coefficients are zero and which are not. The fact that we have more potential variables than we have countries prevents us from followringthis strat- egy,and this is where the problem starts. But this is a problem of small samples, not growth econometrics. Second, although the authors introduce endogeneity as an important prob- lem early in their article, I was disappointed to find that they went no further. Given the authors' reputation, I was excited when I started reading the article about the prospect of a potential solution, perhaps along the lines of Bayesian model averaging. But no solution was offered. 282 THE WORLDBANKECONOMICREVIEW,VOL. I5, NO. I REFERENCES Doppelhofer, G., R. Miller, and X. Sala-i-Martin.2000. "Determinants of Long-Term Growth: A BayesianAveraging of Classical Estimates(BACE)Approach." NBER Work- ing Paper no. 7750,National Bureau of Economic Research, Washington, D.C. Durlauf, S., and P.Johnson. 1995. "Multiple Regimes and Cross-Country Growth Be- havior."Journalof AppliedEconometrics10:365-84. Easterly, W., and R.Levine. 1997. "Africa'sGrowth Tragedy: Policiesand Ethnic Divi- sions." QuarterlyJournal of Economics 112(4):1203-50. Sala-i-Martin, X. 1997."I Just Ran Two Million Regresssions." AmericanEconomic Review, Papers and Proceedings 87:178-83. THEWORLD BANKECONOMICREVIEW,VOL. 15, NO. z 2.83-z88 What have we learnedfrom a decade of empirical researchon growth? Applying Growth Theory across Countries Robert M. Solow I am broadly in sympathy with the spirit of the article byWilliam Brock and Steven Durlauf and that by William Easterly and Ross Levine. They are trying to move the literature in the right direction. I say this even though I have been skeptical from the beginning about the interpretation of cross-country growth regressions. The potential problem of reverse causality has been obvious to everyone. It has usually been met with the standard econometric dodge: using lagged values of slow-moving variables as instruments. But this cannot be a serious solution to the problem. The causality issue points to a deeper question: Do cross-country regressions define a meaningful surface along which countries can move back and forth at will? If this is the idea, what mechanism could underlie such a sur- face? Brock and Durlauf call such a regression a "model." I suppose in a statis- tical sense it is. But an economic model should have some internal structure; its causal arrows should rest on some sort of behavioral mechanism, and that seems to be missing in this literature. I think I had this prejudice even before cross-country regressions became fash- ionable. I thought of growth theory as the search for a dynamic model that could explain the evolution of one economy over time. There were no explicit cross- sectional implications. Were there implicit ones? Certainly, and my comments bear on the question of what they might be. A JUSTIFICATION FOR MULTIVARIABLE CROSS-COUNTRY GROWTH REGRESSIONS? In my view growth theory was conceived as a model of the growth of an indus- trial economy. Its parameters certainly could not be regarded as fixed forever, but maybe they would need to bereconsidered only over intervals of 30-50 years, long enough so that the differences between endpoints could not be dominated by demand-driven business cycles. So far as I can remember, I Ihavenever ap- plied such a model to a developing economy, because I thought the underlying machinery would apply mainly to a planned economy or a well-developed mar- ket economy. This is not a matter of principle, just wariness. Robert M. Solow is with the Department of Economics at the Massachusetts Institute of Technol- ogy. An earlierversion of this articlewas presented at the World Bank conference "What Have We .200t. Learned from a Decade of Empirical Research on Growth?" held on 26 February © 2001 The International Bank for Reconstruction and Development / THE WORLD BANK 283 284 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. 2 Now suppose that you want to compare several such economies and make inferences from the comparison. I use these general terms to emphasize that the cross-country regression is not the only way to make comparisons. You could intend just to interpret parallel time series for a small group of countries, with the goal of understanding the source of differences among them. What back- ground assumptions do you have to make if such a comparison is to be sensible? The economies you are comparing must have something in common, some part of the driving mechanism. If Robert Summers and Alan Heston were sud- denly to discover national income and product accounts from an economy that existed on Mars a million years ago, you would not expect that economy to fit neatly into a Barro regression. So the economies must have some things in com- mon, but not everything. One possible specification that early writers tended to make in this spirit, perhaps automatically, and that some perhaps still make, is that the economies in question share common technological knowledge. The normal justification for this assumption was that technological handbooks were easily available everywhere, even before the Internet. Sothe basic commonality could be the knowledge of a production function F(K,L,H;A), not necessarily Cobb-Douglas in form. Of course, countries would have different values of K, L, and H, but a strict interpretation would give them the same value of A(t). Within the model, which leavesonly the saving-investmentpattern, thegrowth rate of employment, and the rate of depreciation-as well as initial conditions, of course-to differ from country to country. Those are the implications to be explored. We are all familiar with exercises like this. Right or wrong, they are coherent. But then what is the role of all the other right-hand-side variables- openness to trade, size of government, black market premium, and degree of inequality, to name just a few that appear frequently? Maybe we should regard them as purely descriptive, a search for empirical correlations with no analytical implications. That would be a respectable occupation. But to stay within the model, we have to think about the role of total factor productivity (TFP) or A(t). When I used to teach growth theory, I would always begin by saying, "Let's imagine a toy economy that produces only one homogeneous good, using as inputs just (the services of) a stock of the good itself and a flow of labor." In that context it isnatural to think of A(t) in purely technological terms. That may be how the habit was established of supposing that the shape of the production function and the path of A(t) were common across countries. But soon ques- tions would arise; if they didn't, I would raise them myself. For example, someone would be sure to wonder if there really is significant substitutability between labor and capital, at least enough to make the model interesting. The routine reply is, "That is an empirical question, so we have to go outside the narrow model." Empirically speaking, every industrial economy produces not one but thousands of different goods and services. Even if each of them operates with a Leontief technology, they exhibit a wide variety of capital- labor ratios, from the very labor-intensive, such as personal services, to the very capital-intensive, like electricity generation. The economy as a whole-what the Solow 285 toy economy symbolizes-can substitute between capital and labor by changing the composition of output in the obvious way. Moreover-and this is very im- portant-there isan elementary market mechanism to make this happen: Ifcapital becomes scarce, its rental price will rise relative to the wage; the price of capital- intensive goods will rise relative to the price of labor-intensive goods; demand will shift to labor-intensive goods; and the aggregate capital-labor ratio will fall. (And that is not the end of the process.) Once you go down that road, you have to rethink the production function and especially the role of A(t). It is certainly unwise to assume that all econo- mies are equally efficient at reallocating inputs across industries. Tlhisdifference in efficiency would be reflected in A(t), and maybe not only there. As soon as that thought enters your mind, it immediately occurs to you that thLereare many other nontechnological factors that could influence the leveland growth of TFP. They would include the intensity of competition-domestic or foreign-because that would influence the amount of waste and slack in various industries, the alacrity with which the national economy adopts new technology, and thus the leveland growth of TFP. You can just as easilyimaginethat the amount and nature of regulation in a country can affect the efficiency of resource allocation, and thus the "effective" levelof TFP and quite possibly its rate of growth. Evenamong Organization for Economic Co-operation and Development (OECD) countries analysts have found that substantial international differences in productivity can persist even within a narrowly defined industry. It is easiestto think of such institutional differences as ifthey could be summed up as international differences in TFP, but the situation could be more compli- cated. We usually model TFP as if it were a Hicks-neutral multiplicative factor. That might be harmless if the production function is Cobb-Douglas. But that assumption israrely tested. (MichaelBoskin and LawrenceLau [2000] have tested it in a cross-country panel context involving a dozen or so countries and a translog technology, and they reject it strongly.) One obvious generalization is to allow arbitrary factor augmenting technological change, so that the production func- tion would be written as F(A(t)K, B(t)L, C(t)H). Does this line of thought provide a justification for multivariable cross-coun- try regressions? Probably. But it also suggests focusing more directly on TFP or factor augmentation functions as the proper left-hand-side variables in empiri- cal work and thinking more seriously about right-hand-side variables that might legitimately account for differencesin TFP or inA(t), B(t), and C(t). Current prac- tice seems to be much too haphazard. GROWTH THEORY AS THE THEORY OF THE EVOLUTION OF POTENTIAL OUTPUT One might protest that only pure labor augmentation allows the existence of a steady-state growth path. Maybe that should not be a concern. Easterly and Levine point out that observed growth paths do not look like steady states, ex- 286 THE WORLD BANK ECONOMIC REVIEW, VOL. 15, NO. 2 cept perhaps in the United States. This could be related to the nature of factor augmentation. In heavily agricultural economies, for instance, weather and dis- ease could play the role of disturbances to steady-state growth, and their effects would not be represented as Hicks-neutral. But an old Keynesian like me sus- pects that deviations from steady-state growth are often related to deviations of output from potential output-often demand failures with sticky prices, possi- bly export failures with sticky prices. A serious attempt to study the nontechnological components of TFP should also get away from the indefensible presumption that actual output is always close to potential output. In poor countries, especially monocultural primary producers, the choice of off-potential end points, even 20-30 years apart, can materially distort the measured growth of output and maybe even more so the measured growth of TFP. Industrial countries have been less vulnerable to this problem in the postwar period. But Japan has produced nowhere near its poten- tial output for a decade, and I have my doubts about contemporary Europe. This point may be worth developing. I think of growth theory as precisely the theory of the evolution of potential output. So it is mostly concerned with the supply side of the macroeconomy. Deviations are demand driven. In advanced industrial countries we have ways of estimating the growth of potential output. Some depend on a version of Okun's Law; others work directly with production functions. But all are explicitly trying to measure potential output. That is why I think of real-business-cyclemodels and the indiscriminate use of the Hodrick- Prescott filter as intellectually backward steps. For other contexts we need other methods. To take the simplest example, agricultural economies, especially single-crop ones, are subject to large fluctua- tions in output and output growth stemming from such things as droughts and pests. Easterly and Levine provide examples. How should we deal with such observations? We can define potential output as the output that could be pro- duced with normal weather. An estimate of that quantity (or the TFP derived from it) should be on the left-hand side of a growth regression. Or else we need a weather or disease prevalence variable on the right-hand side. In the first case weather-induced fluctuations are just removed; in the second case they are in- cluded in TFP but segregated. Without such makeshifts, we are asking for trouble in cross-country studies that include many countries at different stages of devel- opment. If those studies are growth-oriented, they should be aimed at explain- ing potential output or TFP. In effect I am agreeing strongly with the advice of Easterly and Levine: Com- parative growth studies should focus on understanding and analyzing the vari- ous sources of differences in TFP and the policies that might affect them. This goes for both technological and nontechnological factors in TFP. My residual doubt is whether using cross-country regressions involving large numbers of countries with different institutional histories is the best way to go about this task. I would prefer to start with qualitative studies of basically similar coun- tries, extended over time and space. Solow 287 This could be taken as a step toward endogenous growth theory, and so it is. The good thing about the fox that Paul Romer started chasing more than 15 years ago isthat it leads us to focus on the analysis of the economic incentivesto create new technology. I have two suggestions for those engaged in this hunt. First, close attention to what goes on in research and development enterprises might pay off more at this stage than simple mechanical modeling that may be off the mark. I once had the opportunity to observe the General Motors research laboratories at close hand; the incentivesand responses were anything but simple. Second, the nontechnological sources of differences in TFP may be more im- portant than the technological ones. Indeed, they may control the technological ones, especially in developing countries. Obvious examples include things like the security of contracts, the intensity of competition, and respect for instrumental rationality as a mode of behavior. There may be less obvious ones. CONCLUSION I conclude by returning to an old hobbyhorse of mine. Our modeling exercises are usuallycarefully tailored to lead, all too transparently, to a steady-state growth rate. This habit induces analysts to make gratuitous linearity assumptions and to impose other more or less arbitrary restrictions on models. But maybe, as Easterly and Levine argue, steady-state behavior is a rarity outside a few suc- cessful advanced industrial countries. Nicholas Kaldor's stylized facts may still have relevance, but not everywhere. One of the advantages of vast computer power is that theory does not need easy special cases, such as purely labor augmenting technological change or the analogous assumption that allows a steady state to be an attractor even without constant returns to scale. Numerical integration or iteration can answer the kinds of questions we want to ask of a model, even if the model is not tractable with pencil and paper. Correspondingly, it is probably not a good idea to set cross- country regressions the task of explaining the rate of growth or some other sta- tionary characteristic. It is time paths that need to be modeled and studied. Circumstances have given these remarks a discursive character. So I would like to end by distilling my three main points: * Ifthey mean anything at all, those many right-hand-side variables in growth regressions are determinants of TFP. But then they should be selected with that function in mind, and TFP (or its growth rate) should be the left-hand- side variable. Moreover, some of those factors could affecl other charac- teristics of the aggregate production function. Allowing for separate factor augmentation functions would be a first step, but there are other possibili- ties. It may be necessary to think about genuine estimation of the underly- ing production function. * The proper measure of output underlying the left-hand-side variable is potential output. In industrial countries there are standard methods of 288 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. 2 approximation (not all of which are satisfactory).The deviation of actual from potential output is mainly demand driven. Some of the sharpest de- viations of actualfrom potential output occur in primary producing coun- tries. These deviations may be related to weather fluctuations or disease, but export failures may be a demand-side source. There are various think- able ways to deal with this issue;they need to be systematized. * The exponential steady state isa theoretical convenience. But many coun- tries, much of the time, are nowhere near steady-state growth. This sug- gests that comparative studiesshould focus lesson the growth rate and more on comparing and understanding whole time paths. REFERENCE Boskin, Michael, and Lawrence J. Lau. 2000. "Generalized Solow-Neutral Technical Progress and Postwar Economic Growth." Discussion Paper 00-12. StanfordInsti- tute for Economic Policy Research,Stanford University, and Working Paper 8023, National Bureau of Economic Research, Cambridge, Mass. THE WORLD BANKECONOMICREVIEW,VOL. I5, NO. 2 z89-3]14 Crisis Transmission: Evidence from the Debt, Tequila, and Asian Flu Crises Jose De Gregorioand Rodrigo 0. Valdes This article analyzes how external crises spread across countries. The authors analyze the behavior of four alternative crisis indicators in a sample of 20 countries; during three well-known crises: the 1982 debt crisis, the 1994 Mexican crisis, and the 1997 Asian crisis. The objective istwofold: to revisit the transmission channels of crises, and to ana- lyzewhether capital controls, exchange rate flexibility, and debt maturity structure affect the extent of contagion. The results indicate that there is a strong neighborhood effect. Trade links and similarity in precrisis growth also explain (to a lesser extent) which countries suffer more contagion. Both debt composition and exchange rate flexibility to some extent limit contagion, whereas capital controls do not appear to curb it. The increasing globalization of the economy has put the issue of transmission of crises across countries in the front line. Although the word contagion is a rather new concept in international finance, it has been the focus of a large number of policy-oriented seminars and debates. Both regional and time clustering of cur- rency crises are at the heart of the discussion. There are several important ques- tions that need to be answered. In this article, we focus on two of them. First, what are the propagation channels of international crises across countries (other than common shocks)? Second, are there useful policy instruments for shielding countries from contagion? In particular, do capital controls, exchange rate flex- ibility and the external debt maturity structure affect contagion? We seek to answer these questions using evidence from three key events: the 1982 debt cri- sis, the 1994 Mexican devaluation, and the 1997 Asian crisis. There is an ongoing discussion about the proper definition of contagion (see, for example, Kaminsky and Reinhart 1998; Forbes and Rigob6n 1999). Here we simply refer to it as the co-movement suffered by countries during crisis pe- riods and that is unexplained by initial conditions or common shocks. It is a characteristic of crises because it is precisely during these periods in which the Jose De Gregorio is with the Ministry of Economics, Mining and Energy in Chile, and the Depart- ment of Industrial Engineering at the Universidad de Chile (jdegregorio@minecon.cl). Rodrigo 0. Valdes is with the Ministry of Finance in Chile (rtvaldes@minbnda.cl).This article is part of the wIDER/World Bank research project "Contagion: How It Spreads and How It Can Be Stopped." Rodrigo 0. Valdes acknowledges partial financial support from FONDECYT grant 1990338. The authors thank Ilan Goldfajn, Leonardo Hernandez, Guillermo Perry, Carmen Reinhart, Roberto Rigob6n, and two anonymous ref- erees for helpful suggestions, and Pamela Mellado for excellent research assistance. O 2001 The International Bank for Reconstruction and Development / THE WORLD BANK 289 290 THE WORLD BANK ECONOMIC REVIEW, VOL. 15, NO. Z issue is important from a policy perspective. Nevertheless, as Rigob6n (1999) emphasizes, contagion could be confused with the presence of a large common shock. In our empirical investigation, we attempt to separate the effectsof conta- gion from other large common shocks. However, because we select crisis periods, we cannot strictly compare whether they are essentiallyof a different nature than tranquil times. This issue has led many to question the view that contagion is a particular phenomenon during crisis and isdifferent from simpleinterdependence. We do not solvethis problem, although we compare differenttransmission mecha- nisms through which interdependence across countries occurs.' This article is closely related to other studies of contagion, particularly those that analyze the existenceof contagion and the likelihood of alternative propaga- tion channels by examining a number of currency crises. According to Eichengreen, Rose, and Wyplosz (1997) and Glick and Rose (1998), trade links are the key transmission channel of crises across countries. While the first study focuses on Organisation for Economic Co-operation and Development (OECD) countries, the second studies five international crises using a narrower form of contagion than the one weuse,namely, contagion originating from "ground zero." Kaminsky and Reinhart (1998) claimthat financial links are potentially an important trans- mission mechanism. However, they argue that because of the high correlation between trade and financial links, it is difficultto distinguish between both chan- nels. We revisit the existence of contagion as well as the most likely transmis- sion channels. Instead of focusing on transmission from ground-zero countries to the rest of the world, we look at the impact of crises elsewhere on the likelihood that a country will suffer a crisis. This allows us to study the fact that many times contagion happens from country A to country B, but what may cause prob- lems in country C is not a crisis in A, but the problems in B. A typical case we have in mind isthat a crisis in Mexico may affect Chile more through its impact on Argentina and Brazil than through the crisis in Mexico itself. For this rea- son, focusing on ground-zero countries could give an incomplete picture of the evidence. Section I discusses our basic empirical approach. Section II provides evidence of the existence of contagion and investigates the transmission channels behind this phenomenon. Section III investigates the extent to which capital controls, exchange rate flexibility, and debt structure shield countries against contagion effects. Section IV presents concluding remarks. I. EMPIRICAL APPROACH This section describesour empiricalmethodology. To measure contagion or trans- mission of crises across countries, we follow an approach that combines previ- ous work by Sachs, Tornell, and Velasco (1996); Eichengreen, Rose, and Wyplosz 1. We use indistinctly theexpressions contagion, interdependence, and co-movements. De Gregorio and Valdes 291 (1997); and Glick and Rose (1998). In particular, we try to explain the cross- sectional variation in alternative crisis indicators during particular events using (i) a set of initialmacroeconomic conditions, and (ii) a weighted average of the evolution of the crisis indicator in other countries. With (i), we seek to control for country-specific characteristics that may directly explain the extent of crises as well as common factors that affect countries differently depending on macro- economic characteristics (forexample, an international interest rate shock). With (ii), we seek to measure and characterize contagion. Because alternative weight- ing schemes can be associated a priori with different transmission channels, we are able to study what may drive contagion. We focus the analysis on three important events of the past 25 years from the perspective of developing countries: crisis 1, the 1982 debt crisis; crisis 2, the 1994 Mexican devaluation; and crisis 3, the 1997 Asian crisis. In the spirit of Glick and Rose (1998), we identify a ground-zero country for each crisis and date the episode accordingly. This is used just to date the beginning of the crisis, not to define how it spreads to other countries. We assume that Whenthe crisis begins, all countries are subject to contagion. We use a dummy to control only for the ground-zero country, which captures the fact that this country by defini- tion cannot suffer from contagion. In the case of the debt crisis, we use Mexico as the ground-zero country and date the initial period of the crisis in August 1982, when Mexico announced a moratorium on its external debt. In the case of the tequila crisis, the ground- zero country is naturally Mexico and the initial date is December 1994. Finally, we consider that the Asian crisis started in Thailand in July 1997. We analyze the performance of four alternative crisis indicators in 20 coun- tries, 8 from Latin America, 6 from Asia, and 6 controls (small, open OECDcoun- tries). Appendix table A-1 lists the countries as well as their neighborhood codes. MeasuringContagion To measure contagion, we explain the performance of crisis indicators in the countries, using particular averages of what happens in other countries. More formally, indexing countries by i (i=1,2,. . ., 20) and crises byj (j= 1, 2, 3), we estimate cross-section models of the following form: i't,j, (1) ACI,,,j t= + PlXj,, + /52 E Mi,k,,ACIk,,,i+ P3E M ,I5CIk,tj + E where ACIj,j denotes the change in crisis indicator CI in country i, during crisis j, between one month before that crisis and month t; Xij is a vector of initial macroeconomic conditions in country i prior to crisis j; Mi,k,1 is a fixed number that weights ex ante the importance of country k in explaining the performance of country i; M1,l is a fixed number that weights equally all countries different from i; and £,,t is a random shock. We construct a series of matrixes with weights Mi,k, to calculate particular linear combinations of other countries' returns. Each linear combination repre- sents a particular theory of contagion. 292 THE WORLD BANK ECONOMIC REVIEW, VOL. 15, NO. 2 The M1lj allows us to control for the effect of the size of each crisis. In other words, it controls for the effect of the common shock that occurs elsewhere. After normalizing the weights, this is equivalent to adding for each country the average crisis in all other countries. If we had a very large sample, this could be approxi- mated by the average across countries, and solved by including a dummy variable for each crisis. However, in our sample, this could lead to biases as long as coun- tries subject to large shocks-that is, large changes in the crisis indicator-also have a large weight in the average change in the crisis indicator. There would be an obvious and strong upward bias because the country with a large weight would be included in both the left- and right-side variables. For this reason, we exclude the country when computing the average external shock for each observation. When the true /39is positive (that is, there is contagion) and the Mik, weights are nonnegative, the ordinary least squares (OLS) estimation of equation I has a positive bias.2 A shock in e i,t, that triggers a crisisin a country will affect, through contagion, the performance of other countries; the other countries, in turn, will affect country i's performance, introducing a positive correlation between the error term (E j) and one of the regressors (Xk1iMi,k, ACIkt,). However, because this bias is monotonic in /82and hence there is no bias when I62is zero (and there is negative bias when /B2< 0), the issue isnot a serious problem for our particular purposes. As long as we focus on comparing alternative models, it is valid to compare different OLSestimates of A3.The same is true when we compare alter- native measures for curbing contagion. In a very large sample, this effect would not exist because the feedback from a single country to others would be small. Here we presume this is also small; as long as there are about 20 countries per episode, the effect of a particular en., should be small. We consider the following four crisis indicators: * A foreign exchange market pressure index at a three-month horizon after the crisis, denoted by Pi-3. * A foreign exchange market pressure index at a 12-month horizon after the crisis, denoted by Pi-12. * The level of the real exchange rate 12 months after the crisis, denoted by RER. * A credit rating indicator, denoted by CR. When using indicators with the same time horizon in different crises, we are implicitly assuming that the three crises have similar contagion patterns in the time dimension. This does not need to be the case. The credit rating measure partially takes into account this issue. In constructing Pi-3and Pi-12, we follow the standard procedure of calculat- ing a weighted average of changes in the real exchange rate and the stock of international reserves in each country/observation. In the case of crises 2 and 3, we also include (minus) the change in the real interest rate with respect to the 12- 2. We consider onlynonnegative M,k, weights. De Gregorio and Valds 293 month average level observed prior to the crisis. As in Kaminsky and Reinhart (1999), we weight each component of the index such that each one has equal (cri- sis-specific) volatility. A negative change in PI shows an increase in market pres- 3 sure that may arise from any of the three components. We use data from Interna- tional Monetary Fund (IMF;various years) for international reserves, interest rates (short-run deposits), and inflation. We use the JP Morgan database for real ex- change rates, in which a downward movement in RERmeans depreciation.4 For credit rating, we use the credit risk indicator compiled by Institutional Investor. Because it is published only in March and September of each year, we are not able to have a perfect dating for each crisis. However, this allows us to select the horizon we consider more appropriate in each crisis. For crisis 1, we use the 1-year change in the index published in March 1983; for crisis 2, we use the 6-month change published in September 1995 (which seems to better cap- ture the Mexican downgrade); and for crisis 3, we use the 12-month change published in March 1998. The 60 x 60 matrix with weights M,, Xcan take several forms. However, be- cause cross-crisis contagion makes little economic sense,we restrict it to a block diagonal with three 20 x 20 submatrixes. Moreover, because we are not inter- ested in explaining contagion suffered by ground-zero countries, the matrixes have zeros in the respective row. Furthermore, to avoid running regressions in which an independent variable is a function of that same dependent variable, we restrict the main diagonal to be zero. We follow the same procedure when constructing the Ml,, matrix of equal weights. In any case, the concept of own contagion does not make sense. Depending on the exact definition of contagion, there are two alternative classes of weighting matrixes. If contagion is defined as occurring exclusively from the ground-zero country to other countries, then the matrix has to have nonzero elements only in the columns corresponding to the ground-zero coun- try. This is the approach taken by Glick and Rose (1998). Alternatively, if con- tagion is defined more broadly as transmission of crises from a particular set of countries to others, then the nonzero elements could appear anyvwherein the 20 x 20 matrixes, except in the row of the ground-zero country. This isthe approach followed by Eichengreen, Rose, and Wyplosz (1997) in trying to explain the probability of crisis (a binary variable) in a group of OECDcountries. They con- sider that there is contagion as long as a weighted "crises elsewhere" variable 5 affects the probability of crisis in an individual country. We focus our analysis on the second type of contagion, although we also analyze the first type. 3. None of the results change in any important way if we exclude from Pi interest rates for crises2 and 3. 4. Because of dramatic jumps unrelated to the crises, we excluded international reserves from the indicators for South Africa in crises 2 and 3 and the real interest rate for Brazil in crisis2. 5. The approach taken by Kaminsky and Reinhart (1998) is conceptually similar although formally different. They estimate the incidence of crises as a function of fundamentals and the number of crises in alternative clusters of countries. This is equivalent to having matrixes with ones in particular entries. 294 THE WORLD BANK ECONOMIC REVIEW,VOL. I5, NO. I To test for the presence of contagion, we check whether 82 in equation 1 is significantly different from zero. To compare the strength of contagion across different weighting matrixes (of the second type), we rescale them such that each row adds up to one. Thus, f2 shows the impact of a particular weighted average of crisis indicators elsewhere in the crisis indicators of the average (not ground- zero) country. Then different weighting matrixes allow us to identify the most important transmission channels. MacroeconomicFundamentals The vector X,,, of initial macroeconomic conditions includes country-specific characteristics that may explain the extent of the crises in each country. Specifi- cally, we consider a set of variables that are typically related to currency attacks and balance of payments crises according to standard models (first, second, and later generations) and the existing empirical evidence.6 The list of variables is the following: 1. Credit boom 1. Total credit to the private sector (as a percentage of gross domestic product, GDP) in excess of the long-run trend of the ratio credit/ GDPcalculated using a Hodrik-Prescott filter (seeGourinchas, Landerretche, and Valdes 2001). We consider 1981, 1994, and 1996 as the initial condi- tions for crises 1, 2, and 3, respectively. 2. Credit boom 2. Total credit (as a percentage of GDP) in excess of the long- run trend of the ratio credit/ GDP, for the same years as for credit boom 1. 3. RER overvaluation. Twelve-month average of RER misalignment prior to each crisis calculated using as equilibrium RER an HP filter with information up to the month before each crisis (therefore the filter is one-sided). 4. Fiscalbalance/GDP.Fiscal balance as a percentage ofGDP, for the sameyears as for credit booms. 5. Currentaccount/GDP. Current account balance as a percentage of GDP, for the same years as for credit booms. 6. GDP growth. GDP annual growth rate, for the sameyears as for credit booms. 7. Debt/GDP. Debt to GDP ratio. For OECD countries, we estimate the stock of debt by adding up current account deficits since 1950. This is for the same years as for credit booms. 8. Inflation. Consumer price index 12-month inflation measured inthe month before each crisis (measured as p/(1 + p), where p is the rate of inflation). Beforeanalyzing the presenceof contagion, it isinteresting to evaluate whether these macroeconomic fundamentals matter in explaining which countries suffer stronger crises (or a crisis at all) during an international crisis. Sachs, Tornell, and Velasco (1996) address this issue, although they focus only on the Tequila crisis. Their main result is that excess credit creation and RERmisalignment are 6. See Eichengreen, Rose,and Wyplosz (1997); Kaminsky, Lizondo, and Reinhart(1998); and the comprehensive study by Berg and Pattillo (1998) fordetails. De Gregorio and Valdes 295 the most important variables in explaining the extent of crises across countries. They do not find any relevant role for the current account deficit. Bergand Pattillo (1998) find similar results using several alternative methodologies. They find that the most important indicators of vulnerabilities are the rate of growth of do- mestic credit, a measure of real exchange rate overvaluation, and the ratio of deficit, the reserves to the M2 money supply. They find that the current account of budget deficit, and the composition of external liabilities are good predictors external fragilities only in some cases (estimations). Table 1 presents the results of estimating equation 1 without contagion ef- fects. In the equation, we include ground-zero countries, so we estimate a stan- balance dard crisis-prediction equation. In our estimations, the current account appears as a highly significant explanatory variable in Pi-3, Pi-12, and RER (the "objective" indicators). Credit boom (private credit), RER overvaluation, fiscal balance, and GDP growth are significant in some of the crisis indicators. In the case of the RER depreciation indicator, it is interesting to note that the signs of the current account balance and the fiscal balance are opposite. This indicates that an increase in the current account increases the real depreciation 12 months later, but the converse occurs with the fiscal balance. The interpretation is not deficit straightforward. By accounting, we can decompose the current account An in- into private and public components, the latter being the budget balance. TABLE 1. Crisis Indicators and Initial Conditions Crisis indicator Change in credit rating Change in RERc Variable Change in pi-3a Change in Pi-12b -1.92 -1.25 Constant -0.08 -4.62 (-0.68) (-0.04) (-2.94) (-2.41) -44.35 Credit boom -30.82 - -15.92 (-2.27) (-1.64) (-1.75) - - RER overvaluation -0.24 -0.45 (-1.43) (-2.63) -0.77 Fiscalbudget/GDP - - - (-2.14) - 1.04 Current account/GDP 0.44 0.67 (1.70) (2.54) (3.49) - - GDPgrowth - 1.50 (3.22) 0.05 0.29 R2 0.17 0.31 0.09 0.00 F-statistic p-value 0.02 0.00 60 60 Observations 60 60 and text for crisis Note: Data are for 20 countries for three crisisperiods. See table A-1 for countries t-tests are in periods. Values are from OLS regressions with constants (not reported). White's robust parentheses. We report variables with at least 80 percent significance. aForeign exchange market pressure index three months after the crisis. bForeign exchange market pressure index 12 months after the crisis. cLevel of the realexchange rate 12 months after the crisis. Source: Authors' calculations. 296 THE WORLDBANKECONOMICREVIEW,VOL. I5, NO. Z crease in the budget deficit would raise the current account deficit, deteriorating the RER indicator, but there is a direct effectpartially offsetting the current ac- count effect. An interesting result is that, other than credit boom, macro-variables do not explain changes in credit rating. Credit rating is a "subjective" crisis indicator because it is based on the assessment of vulnerabilities assigned by the market. Neither the debt/GDP ratio nor inflation has significant effects in explaining any of the crisis indicators. As shown by the R2 statistics, the macroeconomic fundamentals we consider have a limited capability for explaining the cross-coun- try experience during crisis periods, a result consistent with the already large literature on crisis forecasting. II. CONTAGION AND TRANSMISSION CHANNELS This section investigates the presence of contagion in the three crises we study and analyzes the likelihood of alternative transmission channels. It discusses the construction of alternative weighting matrixes and presents some empirical results. WeightingMatrixes There are several potential channels for the propagation of contagion. The most important are direct trade links, trade competition in third markets, macroeco- nomic similarities, and financial links. Eichengreen, Rose, and Wyplosz (1997) and Glick and Rose (1998) find evidence that trade links are the most important channel of propagation. Kaminsky and Reinhart (1998) also find strong evidence of regional contagion. They conclude that this pattern could be associated with trade links as well as with financial links. A key problem is that the two are cor- related. An additional problem isthat measures to control for financial links are limited. Controlling for the average shock elsewhere is a form of controlling for the international environment. In addition, we may capture the channels through which interdependence or contagion occurs by weighting the shocks elsewhere by some characteristics of the relationship among countries. Thus, different weighting matrixes Mik,j allow us to investigate the importance of alternative transmission channels of contagion (from country i to country k). We consider the following matrixes: 1. Equal weights for all countries k, allowing us to control for differences across crises. 2. Direct trade links measured by the ratio of bilateral trade between coun- tries i and k to total trade of country i. This set of weights is motivated by trade-based contagion theories, such as competitive devaluation. 3. Trade competition in third markets measured through a similarity index of the trade pattern based on the relative importance in total exports of De Gregorio ancdValdes 297 six sectors (agriculture, food, fuel, ores, high-tech manufactur-ing,and low- tech manufacturing). This matrix has the same motivation as in point 2. 4. Neighborhood (regional) dummies for Latin American, Asian, and indus- trial countries (seeappendix table A-1 for details). This matrix ismotivated by the presumption that contagion is regional (explained primarily by fi- nancial links after controlling for trade links). 5. An overall macroeconomic similarity index that combines RER misalign- ment, current account balance, credit boom, fiscal balance, and GDPgrowth. Macroeconomic similarities may explain contagion if, for tistance, inves- tors learn and update their priors during a crisis (that is, there is a "wake- up call" during crisis). 6. Specific macroeconomic similarity indexes, including external similarity (encompassing RER and current account), credit boom, and GDP growth. 7. All of the above measures, but with respect to only neighboring countries. This allows us to evaluate the alternative contagion channels at the regional level. Both trade-pattern similarity, because of data availability, and neighbor dummy matrixes, by definition, are constant across crises. The rest of the matrixes are crisis-specific. All the matrixes are symmetric, except the one with direct trade links. The reason for the lack of symmetry of the trade-link matrix is that trade is measured with respect to total trade of the country; thus, bilateral trade is symmetric, not its importance with respect to each country. To construct a similarity index between countries i and k when considering a single variable (for example, GDP growth or credit boom), we calculate:7 (2) Oi,k,, = exp(-xijj - Xk,1I), where x, is the standardized variable under analysis in country i. The standard- ization is based on cross-country, crisis-specific observations.8 When constructing similarity indexes that combine multiple variables (for example, trade pattern, external conditions, and overall macroeconomic simi- larity), we calculate: (3) Oik, = exp(-Ix,j,, - Xs,k,jI), where s indexes the different variables entering the index and x is the stan- dardized variable s in country i and crisis j. 0 To facilitate comparability across different matrixes, we rescale the i,kj'S so that maximum similarity takes the value 1 and minimum similarity takes the value 0. Thus, we calculate the weight Mi,k,jas follows: 7. The procedure for constructing similarityindexes is somewhat ad hoc because it introduces some nonlinear transformations in the data; however, it allows us to reduce the effect of outliers. 8. By standardized variable, we refer to a variable in a given crisis minus its mean divided by its standard deviation. 298 THE WORLD BANK ECONOMIC REVIEW, VOL. 15, NO. 2 (4) M ,k,j - min(Oi,k',i) ' max(ei.,k.,,) - min(0i ,k,j) 6 where i', k', and j represent all possible country combinations in crisis j. Fur- thermore, for a straightforward interpretation of the results,we rescaleMi.k,iagain so that -i Mik,j = 1. Thus, 12 reflects the impact of a weighted average of what is happening elsewhere on the average country. EmpiricalResults Tables 2 to 5 present the estimation of equation 1using Pi-3, Pi-12, RER, and CR, respectively, and with alternative weighting matrixes for each crisis indicator. The variable "contagion index" corresponds to 82,while "equal weight" corre- sponds to P3. All regressions include a constant and dummies for the ground- zero countries (not reported). The results for the Pi-3 indicator show that contagion is strongly and almost exclusively driven by neighborhood and direct trade effects. None of the "wider" matrixes (those considering not only neighbors) yields a significant coefficient that could indicate the presence contagion. Indeed, when constraining weight- ing matrixes to neighboring countries, most of the results are significant. The point estimate of direct trade links is smaller than that of the neighbor dummies, and, because we are constraining weights to be one, we can conclude that the neighbor effect is quantitatively stronger than that of direct trade. This prob- ably reflectsthe closetrade linksthat exist between neighbors rather than a proper propagation channel. In fact, when we consider direct trade with neighboring countries only, the estimate is highly significant, but the point estimate is still smaller than what the neighbor dummymatrix yields.Interestingly,neithermacroeconomic similarities nor the common shock proxy plays any role in explaining the cross- country propagation of contagion at this three-month horizon. None of the parameters corresponding to the variables measuring macroeco- nomic initial conditions, except for credit boom, changes in any important way when we incorporate the contagion index. In fact, credit boom ceases to be sig- nificant in all specifications. Consequently, once the effects of interdependence across crises are included, the R2 increases from 0.17 in table 1 to values around 0.5. This reveals the importance that contagion and transmission of crisis across countries have on the vulnerability to external crisis.9 The results for Pi-12 show a different picture (table 3). For this indicator, we observe that a real exchange rate overvaluation, a current account deficit, and low growth increase the (absolute) value of the crisis indicator, that is, increase the incidence of crisis. After controlling for the equal-weight matrix, the R2s increase with respect to the value reported in table 1, but the marginal explana- tory power of this variable is not as large as that of the three-month exchange 9. It is also worth mentioning that, aside from the Pi-12 indicator, resultsdo not change if we ex- clude the M 1,jAcik,1,,term in the regressions. Total Contagion TABLE 2. Three-Month Change in Foreign Exchange Market Pressure Index and Weighting matrix Trade Trade pattern Credit Growth with with Direct Trade Neighbor Macro External similarity similarity similarity neighbors neighbors Variable trade pattern dummy similarity -21.92 -12.55 -2.09 -3.34 Creditboom -5.32 -13.22 0.68 -13.07 -15.45 (-0.96) (-0.74) (-0.14) (-0.21) (-0.33) (-0.78) (0.05) (-0.68) (-0.91) -0.25 -0.26 -0.25 -0.21 -0.21 RER overvaluationa -0.24 -0.26 -0.21 -0.25 (-1.79) (-1.72) (-1.63) (-1.61) (-1.73) (-1.78) (-1.75) (-1.71) (-1.74) 0.27 0.26 0.27 0.49 0.40 Current account/GDP 0.45 0.24 0.41 0.28 (1.15) (1.20) (2.30) (1.87) (1.98) (1.00) (2.05) (1.18) (1.18) -3.40 -1.24 -0.73 0.61 0.47 Contagion index 0.63 -0.54 0.71 -0.18 (-0.65) (-0.38) (3.50) (2.91) (2.37) (-0.52) (4.29) (-0.12) (-1.14) 3.80 1.91 1.21 -0.02 0.10 Equal weight -0.06 1.05 -0.08 0.71 (0.89) (0.67) (-0.07) (0.31) (-0.14) (1.01) (-0.26) (0.45) (1.31) 0.56 0.53 R2 0.46 0.46 0.51 0.46 0.60 0.46 0.47 0.00 0.00 0.00 0.00 0.00 F-statistic p-value 0.00 0.00 0.00 0.00 60 60 60 60 60 Observations 60 60 60 60 periods. Values are from OLSregres- Note: Data are for 20 countriesfor three crisisperiods. See tableA-1 for countries and text for crisis countries (not robust t-testsare in parentheses.Ex- sions with constants and dummy variables in the three ground-zero reported). White's ternal similaritycombines current account and RER overvaluation sirnilIarity. aSeetext for definition. Source: Authors' calculations. TABLE 3. Twelve-Month Change in Foreign Exchange Market Pressure Index and Total Contagion Weighting matrix External similarity Growth Direct Trade Neighbor Macro External Credit Growth Variable of of trade pattern dummy similarity similarity similarity similarity neighbors neighbors RER overvaluationa -0.46 -0.42 -0.45 -0.51 -0.44 -0.46 -0.46 -0.52 -0.43 (-2.66) (-2.60) (-2.98) (-2.96) (-2.32) (-2.68) (-2.64) Current account/GDP (-3.17) (-2.79) 0.45 0.48 0.39 0.53 0.47 0.48 0.47 0.39 0.41 (1.56) (1.87) (1.59) (1.94) (1.73) (1.75) (1.68) (1.50) GDPgrowth (1.63) 1.31 1.18 1.53 1.49 1.26 1.26 1.12 1.36 1.84 (2.62) (2.59) (3.51) (2.97) (2.63) (2.64) (1.46) Contagion index (2.98) (3.94) -0.13 -2.80 -1.72 -3.03 0.15 -0.49 0.42 -1.08 -1.41 (-0.34) (-2.46) (-3.50) (-1.33) (0.06) (-0.33) (0.22) Equal weight (-2.42) (-3.37) 0.72 3.31 2.28 3.51 0.45 1.10 0.18 1.60 2.00 (1.63) (2.93) (4.26) (1.59) (0.18) (0.72) (0.10) (3.31) R2 (4.18) 0.40 0.46 0.52 0.42 0.40 0.40 0.40 F-statistic p-value 0.46 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Observations 0.00 60 60 60 60 60 60 60 60 60 Note: Data are for 20 countriesfor three crisis periods. See tableA-1 for countries and text for sions with constants crisis periods. and dummy variables Values are from ol.s regres- in the three ground-zero countries (not reported). White's ternal similarity robust t-tests are in parentheses. combines current Ex- account and RER overvaluation similarity. 'See text for definition. Source: Authors' calculations. De Gregorio and Valdes 301 market pressures indicator. We find that for this indicator, co-movement is al- most exclusively driven by the common shock (proxied by the equal-weight matrix, that is, crisis elsewhere). Transmission through trade, neighbor effects, and similarities do not appear to play an important additional role. In fact, none of the weighting matrixes yields significantly positive parameters. If we do not control for the equal-weight matrix, the results change dramatically, with sev- eral weighting matrixes having significantly positive results. However, this fol- lows from the fact that the equal weight and other matrixes are collinear across crises. In what follows, we no longer consider Pi-12in the analysis and conclude that there is no particular form of contagion in this indicator beyond the exist- ence of common shocks (although there isa high degree of co-movement across countries).10 In the case of the indicator based on 12-month RER depreciation (table 4), we find that contagion indexes are significantly positive when we consider direct trade links, neighbors, and growth similarity. The strong negative sign for trade pattern similarity indicates that there is evidence against third-market competi- tion being an important transmission mechanism of crises. Conventional wisdom indicates that when a country has a currency crisis, a real depreciation will hurt competitors in those markets, leading to competitive devaluations. However, because a crisis in a country is usually coupled with an output collapse, it may create opportunities for the country's main competitors. This may be what ishappening with the reverse signwe find, at least at the one- year horizon. It might also be that trade pattern similarity is not appropriately measuring third-market competition, and perhaps third-market competition could be better proxied by some regional effect. We still find that initial condi- tions measured by the current account deficit and budget deficit help to explain 12-month RER depreciation. Credit boom isthe only initial macroeconomic vari- able that looses significance in the RER equation when we include contagion. Finally, in the case of change in credit rating (table 5), we find that the direct trade links, neighbors, overall macro similarity, and growth similarity matrixes yield significant contagion coefficients. When considering only similarities with neighboring countries, we find that both trade and external macroeconomic simi- larity appear to bevery important channels of contagion. As in the previous case, initial conditions measured by credit boom looses significance w]henwe include contagion. With the CR index, we find no initial condition to be significant when we include contagion. The evidence presented so far is not able to discriminate completely among (statistically significant) competing weighting matrixes. Following Eichengreen, Rose, and Wyplosz (1997), table 6 presents the results of estimating equation 1 10. We look again at P1-12 only when examining contagion from ground-zero countries because the specification andthe implication of theresults are different.In addition, in the remaining results, we exclude the equal-weight matrix from the analysis because it is not significantfor indicators other than Pl-12. TABLE 4. Real Exchange Rate Depreciation and Total Contagion Weighting matrix External similarity Growth Direct Trade Neighbor Macro External Credit Growth of of Variable trade pattern dummy similarity similarity similarity similarity neighbors neighbors Credit boom -14.77 -23.81 -9.55 -10.78 -20.24 -13.95 -11.33 -7.25 -9.34 (-0.77) (-1.23) (-0.49) (-0.51) (-1.02) (-0.60) (-0.61) (-0.37) (-0.48) Fiscalbudget/GDP -0.65 -0.96 -0.68 -0.77 -0.90 -0.86 -0.52 -0.63 -0.68 (-1.95) (-2.90) (-2.06) (-2.26) (-2.60) (-2.54) (-1.57) (-1.92) (-2.05) Current account/GDP 1.08 0.94 1.09 1.07 1.03 1.02 1.14 1.08 1.09 (4.02) (3.47) (4.12) (3.84) (3.72) (3.69) (4.34) (4.11) (4.07) Contagion index 0.65 -2.39 0.60 1.52 -1.57 0.67 4.14 0.64 0.56 (2.17) (-1.99) (2.36) (1.14) (-0.68) (0.48) (2.81) (2.53) (2.13) Equal weight 0.10 3.09 0.26 -0.76 2.37 0.06 -3.08 0.21 0.33 (0.26) (2.58) (0.72) (-0.55) (1.01) (0.04) (-2.21) (0.60) (0.95) R2 0.49 0.48 0.49 0.45 0.44 0.44 0.51 0.50 0.48 F-statistic p-value 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Observations 60 60 60 60 60 60 60 60 60 Note: Data are for 20 countries forthree crisis periods.See table A-1 for countries and textfor crisis periods. Valuesare from OLS regres- sions with constants and dummy variables in the three ground-zero countries (not reported). White's robust t-tests are in parentheses. ternal similarity combines Ex- current account and RER overvaluation similarity. Source: Authors' calculations. and Total Contagion TABLE 5. Change in Credit Rating Weighting matrix External Trade similarity with of Direct Trade Neighbor Macro External Credit Growth similarity neighbors neighbors Variable trade pattern dummy similarity similarity similarity -3.80 1.58 3.63 Credit boom -0.95 -8.21 1.28 0.41 -7.10 -24.71 (0.24) (0.58) (-0.12) (-1.06) (0.19) (0.05) (-0.86) (-2.41) (-0.49) 2.15 -0.38 -6.63 2.33 0.82 0.83 w Contagion index 0.75 -2.09 0.74 (-0.20) (-2.59) (2.16) (5.11) (6.10) w (2.70) (-2.01) (5.34) (1.82) -1.51 0.09 0.02 Equal weight 0.10 2.59 0.04 -1.23 0.99 7.46 (0.10) (0.33) (2.59) (0.16) (-1.16) (0.58) (2.82) (-1.47) (0.39) R2 0.65 0.48 0.45 0.62 0.45 0.41 0.48 0.46 0.61 0.00 0.00 0.00 F-statistic p-value 0.00 0.00 0.00 0.00 0.00 0.00 60 60 60 60 Observations 60 60 60 60 60 Values are from OLS regres- Note: Data are for 20 countries for three crisis periods. See tableA-1 for countries and text for crisis periods. White's robust t-tests are in parentheses. Ex- sions with constants and dummy variables in the three ground-zero countries (not reported). ternal similarity combines current account and RER overvaluation similarity. Source: Authors' calculations. 304 THEF WORLDBANKECONOMICREVIEW,VOL. 15, NO. 2 TABLE 6. Contagion and Competing Weighting Matrixes Pressure indicator Change in pj-31 Change in RERb Change in credit rating Variable (1) (2) (1) (2) (3) (1) (2) (3) (4) Credit boom 0.00 0.01 -0.13 -0.10 -0.08 0.01 0.02 0.07 0.04 (0.02) (0.05) (-0.69) (-0.54) (-0.44) (0.12) (0.26) (1.2) (0.59) RER overvaluationb -0.21 -0.22 - - - - - - - (-1.74) (-1.78) Fiscal budget/GDP - - -0.68 -0.62 -0.68 - - - (-2.07) (-1.92) (-2.10) Current account/GDP 0.37 0.38 1.08 1.10 1.10 - - - - (1.95) (1.92) (4.06) (4.19) (4.17) Direct trade matrix -0.22 - 0.50 0.37 - -0.12 - - - (-0.74) (1.47) (1.12) (-0.42) Neighbor dummy 0.82 0.76 - 0.41 0.50 0.81 0.71 -2.00 - matrix (3.48) (2.22) ----- (1.26) (1.91) (4.36) (5.09) (-2.62) Macrosimilarity - - - - - - 0.13 matrix (0.48) Growth similarity - - 0.40 - 0.47 - matrix (0.89) (1.22) Tradewith - -0.08 - - - - - - 1.04 neighbors (-0.24) (2.83) Externalsimilarity - - 2.90 -0.25 with neighbors (3.64) (-0.61) matrix R7 0.60 0.60 0.49 0.50 0.50 0.58 0.62 0.69 0.66 F-statistic p-value 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Observations 60 60 60 60 60 60 60 60 60 Note: Data are for 20 countries for three crisis periods. See table A-1 for countries and text for crisis periods. Values are from OLS regressions with constants and dummy variables in the three ground-zero countries (not reported). White's robust t-tests are in parentheses. External similarity combines current account and RER overvaluation similarity. 'Foreign exchange market pressure index three months after the crisis. bLevel of the real exchange rate 12 months after the crisis. Source: Authors' calculations. simultaneously including competing relevant contagion indexes. We consider some of the matrixes that appeared as more relevant in tables 2-5 in pairs, using the same initial macroeconomic conditions as before. The results show that in the cases of indicators based on Pi-3and country CR, the identification is straightforward. In both cases, the neighborhood effect ap- pears as the most relevant propagation mechanism for contagion. In the second case, we also observe that external similarities with respect to neighbors appears to be a strong mechanism (which is a particular form of a neighborhood effect). Trade links no longer appear important in these two cases when we control for the effect of neighbors. Although trade links and neighbor effects are highly De Gregorioand Valdes 305 correlated, our results suggest that the prime candidate for contagion is not trade, as documented in other papers, but geographical proximity."' Thle results are less clear-cut in the case of the indicators based on RER. Because of strong col- linearity, some times we observe that a pair of matrixes is highly significant when considered individually, but is no longer significant (individually) wvhenconsid- ered together. Despite this issue, it ispossible to exclude some explanations and rank others informally according to point estimates. Direct trade linlksand neigh- bors appear as the two most relevant matrixes.12 Contagionfrom Ground-Zero Countries An alternative way of defining contagion is to limit it to propagating from ground-zero countries only. In this case, we try to explain the cross-country variation of our crisis indicators using different weights of ground zero for each country. This definition of contagion is obviously more restrictive than the previous approach. Moreover, it is potentially misleading if the ground-zero country is not correctly identified. However, this exercise is useful for testing the robustness of our results. Because the temporal evolution of the ground-zero country can be very dif- ferent from what actually happened in other countries, we modify our strategy slightly. In particular, we analyze whether a weighted change in Pr-3 at ground zero is able to explain changes in Pi-12, RER, and CR. The weighting matrixes are similar to those we used in the previous subsection, although we no longer have the straightforward intuition for the estimated parameter we htad before (a weighted average of what is happening elsewhere). Therefore, we use standard- ized parameters. Table 7 presents the results for the cases in which we find statisiticallysignifi- cant contagion. It showsthat with the Pi-12 indicator, contagion marginally arises only when we consider the equal-weight matrix. This result is proof of co- movement, perhaps caused by a large shock, which isdifferent across crises, but it is not necessarily evidence of contagion. With the indicator based on the RER, direct trade ties between countries and the ground-zero country appear to gen- erate contagion. Finally, changes in credit rating can be explained for countries that are neighbors of the ground-zero country (especiallyifthey have similarinitial external macroeconomic conditions) or have direct trade links with it. 11. We cannot avoid making references to the case of Chile, which suffered contagion from Asia due to high trade links, but is alsodependent on movements in Latin America, a region with weak trade links. Chile's trade with Argentina and Brazil, its main trade partners in the region, is well below 10 percent. 12. One can further analyze this issue of collinearity by estimating a model of the following form: ACI,,t,l=0 +P J; + /2 X (y I Mi,kjACIkjt,+ (1- k M,,k,jACIk,t.,) Mr) +Ei,tj where ymeasures the relative importance of M,,k, vis-a-vis M',k*,.Theresults forRER (not reported) show a significant p2 but very impreciseestimates of r,showing that any combination of the two matrixes would be valid. TABLE 7. Contagion from a Ground-Zero Country Pressure indicator and weighting matrix Change in Change in credit rating/ Change in Change in --- Change in Change in credit rating/ external credit rating/ Pi-12/equal RER/direct credit rating/ neighbor similarity of trade with Variable weights, tradeb direct trade dummy neighbors neighbors Creditboom - -0.23 -0.06 -0.04 -0.02 -0.05 (-1.12) (-0.80) (-0.62) (-0.46) (-0.69) RERovervaluationb -0.48 - - - - (-2.79) Fiscalbudget/GDP - -0.57 (-1.58) Current account/GDP 0.50 1.04 (1.77) (3.67) GDPgrowth 1.44 - - - - - (3.03) Contagion index 0.24 1.78 0.27 0.43 0.45 0.29 (1.69) (2.04) (2.53) (4.38) (4.72) (2.76) R2 0.37 0.41 0.41 0.52 0.54 0.43 F-statistic p-value 0.00 0.00 0.00 0.00 0.00 0.00 Observations 60 60 60 60 60 60 Note: Data are for 20 countries for three crisis periods. See table A-1 for countries and text for crisis periods. Values are OLS regressions with constants and dummy variables in the three ground-zero countries (not reported). White's robust t-tests are in parentheses. Contagion index corresponds to the standardized parameter of a weighted average of change in ri-3 according to a particular matrix M. External similarity combines current account and RER overvaluation similarity. 'Foreign exchange market pressure index three months after the crisis. "Level of the real exchange rate 12 months after the crisis. Source: Authors' calculations. De Gregorio and Valdes 307 III. POLICIES TO CURB CONTAGION One key policy question is how countries can curb (or even stop) contagion. A leading prescription is to limit financial integration. Other policy prescriptions to limit the extent of contagion are exchange rate flexibility and avoiding short- term debt. The issue of contagion and alternative policies is an empirical one. This section evaluates the usefulness of these three policy measures in curbing contagion. Capital Controls and Contagion Capital controls could curb contagion if financial links are an important propa- gation channel. However, the usefulness of limiting financial integration is less clear if contagion arises due to trade links, or if initial similarity in macroeco- nomic conditions and crises are the consequence of real shocks. Nevertheless, it could be argued that capital controls might help an orderly adjustment, avoid- ing typical problems that an unregulated financial sector often produces, such as overshooting the exchange rate. Of course, capital controls have costs in tran- quil times because the country does not take full advantage of capital movements. However, defenders of capital controls point to contagion as one of the reasons for having capital controls as a preventive measure. Edwards (1999)evaluates whether capital controls in Chilewere a useful device for avoiding contagion. He measures contagion as the correlation between do- mestic and Asian interest rates (specifically, interest rates in Hong Kong), con- trolling for domestic devaluation and exchange rates in the United States. He concludes that controls on capital inflows may have been able to protect Chile from relatively small shocks, but were not able to prevent contagion stemming from large external shocks. It should be mentioned that the objective of capital control measures goes beyond avoiding contagion. Among other objectives, capital controls have been used to avoid excess real exchange rate appreciation, to curb capital inflows, and to modify the foreign debt term structure.13 To evaluate whether financial integration facilitates contagion, we use a stan- dard capital control index and analyze whether contagion is weaker in coun- tries with a higher index. In particular, we estimate models of the following form: (5) ACI,,,= Pb+PlXA,+ [P2+ 33CCi ]M,,k,,ACIkj,, + Eijq, 1 where cc,, is a capital control index of country i during crisis j. If capital con- trols were effective in curbing contagion, the estimation should yield a negative and significant/3. To construct the capital control index, we use the standard dummy variables that appear in IMF (various years). For restrictions on payments on capital trans- actions and the surrender requirement of export proceeds, we assign values of 13. See De Gregorio,Edwards, and Vald6s (2000) for an evaluationof the Chilean experience. 308 THEWORLDBANKECONOMICREVIEW,VOL. 15, NO. 2 0, 1, or 2, depending on whether neither, one, or both of the restrictions apply. We consider the status as of December in 1981, 1994, and 1996 for the corre- sponding crises. Table 8presents the results of the estimation of equation 5 for our three crisis indicators that show contagion and for the same weighting matrixes used in last section. The results show that capital controls do not have any relevant effect in limiting contagion. Indeed, the associated parameter is generally not significantly different from zero. It has to be noted, however, that we use a broad definition of capital controls, and the most commonly used and specific forms of controls or regulations cannot be captured with these 0, 1, 2 indicators. However, the results indicate that countries that had more pervasive forms of control did not avoid contagion more than countries with looser controls. Exchange Rate Flexibility and Contagion Exchange rate flexibility is expected to reduce contagion by avoiding some of the overvaluation episodes to begin with and limiting the scope of speculation. To evaluate the effect of exchange rate flexibility on contagion, we use the same approach as with capital controls. In particular, we estimate an equation similar to equation 5, but with an indicator of exchange rate flexibility for country i in crisis j instead ofcc,,. We use a 0, 1, 2 indicator (2 is maximum flexibility) based on data gathered by Goldfajn and Vald6s (1999). The data wereconstructed using IMF (various years). That report groups exchange rate regimes into three catego- ries: fixed (including narrow bands), flexible, and floating. Table 9 presents the results. They show that flexibility has a significant effect in limiting contagion only when we measure contagion using changes in credit ratings. Point estimates show a large effect: Moving from a fixed exchange rate regime to a floating one reduces contagion by two-thirds. This result is robust to alternative weighting matrixes. It is interesting because it indicates that the market evaluates better and islessvulnerable to economies with flexibleexchange rate regimes. When measuring contagion with real depreciation, we find that flexibility increasescontagion, although this result ismarginally significant under only two weighting matrixes. This latter result is not surprising because the exchange rate is the variable that adjusts when external shocks hit the economy. Moreover, part of the adjustment may be an overshooting of the real exchange rate. We do not find significant effects of flexibility in the case of Pi-3. Overall, we can conclude only for the CR indicator that having a flexible ex- change rate may reduce contagion. Debt Maturity Structureand Contagion Having debt maturity tilted toward the long run would limit the scope of finan- cial runs against a particular country. To evaluate whether the debt maturity structure has any impact on the extent of contagion, we run an equation similar to equation 5, but with the ratio of short-term debt to total debt for country i in TABLE 8. Capital Controls and Contagion Pressure indicator and weighting matrix Change in Change in Change in credit rating/ Change in Change in Pr-3/trade Change in Change in Change in Change in credit rating/ external Pi-3/direct ri-31 with RER/direct RERI RER/ growth credit rating/ trade with similarity Variable trade, neighbors, neighborsa tradeb neighborsb similarityh direct trade neighbors of neighbors Credit boom -0.04 0.01 -0.02 -0.16 -0.13 -0.17 -0.01 0.02 0.04 (-0.23) (0.07) (-0.12) (-0.86) (-0.70) (-0.84) (-0.11) (0.26) (0.58) RER overvaluationb -0.26 -0.23 -0.22 - - - (-1.86) (-1.76) (-1.65) Fiscalbudget/GDP - - - -0.57 -0.56 -0.76 (-1.69) (-1.75) (-2.26) o Current account/GDP 0.38 0.37 0.46 1.09 1.18 1.05 - - - (1.67) (1.79) (2.15) (4.10) (4.42) (3.87) Contagion index 0.48 0.64 0.56 0.82 0.94 1.00 0.84 1.12 0.92 (1.65) (2.77) (2.36) (3.19) (3.71) (2.71) (2.64) (4.95) (4.69) Contagion x 0.14 0.04 0.04 -0.15 -0.35 -0.06 -0.03 -0.23 -0.08 capital controls (0.64) (0.23) (0.23) (-0.69) (-1.45) (-0.20) (-0.15) (-1.53) (-0.56) R2 0.51 0.60 0.56 0.49 0.51 0.47 0.48 0.62 0.66 F-statistic p-value 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Observations 60 60 60 60 60 60 60 60 60 Note: Data are for 20 countries for threecrisis periods. See table A-I for countries and text for crisis periods. Values arefrom oi.s regressions with constants and dummy variables in the three ground-zero countries (not reported). White's robust t-tests are in parentheses. External similaritycombines current account and RER overvaluation similarity. Foreign exchange market pressure index three months after the crisis. bLevel of the real exchange rate 12 months after the crisis. Source: Authors' calculations. TABLE 9. Exchange Rate Flexibility and Contagion Pressure indicator and weighting matrix Change in Change in Change in credit rating/ Change in Change in pi-3/trade Change in --- Change in Change in Change in credit rating/ external Pi-3/direct Pi-31 with RER/direct RERI RERI growth credit rating/ trade with similarity Variable tradea neighborsa neighborsa tradeb neighborsb similarityb direct trade neighbors of neighbors Credit boom -0.05 0.02 -0.01 -0.18 -0.11 -0.23 -0.21 -0.05 -0.02 (-0.30) (0.14) (-0.07) (-0.92) (-0.60) (-1.19) (-0.28) (-0.67) (-0.26) RER overvaluationb -0.22 -0.22 -0.23 - - - - - - (-1.58) (-1.79) (-1.75) Fiscalbudget/GDP - - - -0.60 -0.62 -0.72 (-1.85) (-1.96) (-2.27) w Current account/GDP 0.43 0.40 0.50 1.04 1.10 1.00 - - - (2.06) (2.09) (2.50) (3.90) (4.23) (3.78) Contagion index 0.74 0.62 0.44 0.40 0.18 0.35 1.54 1.36 1.23 (1.97) (2.42) (1.62) (1.03) (0.50) (0.79) (4.50) (4.92) (5.87) Contagion x -0.12 0.07 0.17 0.23 0.46 0.52 -0.68 -0.54 -0.43 exchange rate (-0.42) (0.31) (0.71) (0.94) (1.74) (1.81) (-2.67) (-2.12) (-2.27) flexibility R2 0.51 0.60 0.57 0.49 0.52 0.50 0.54 0.64 0.69 F-statistic p-value 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Observations 60 60 60 60 60 60 60 60 60 Note: Data are for 20 countries for three crisis periods. See table A-1 for countries and text for crisis periods. Values are from OLS regressionswith constants and dummy variables in the three ground-zero countries (not reported). White's robust t-tests are in parentheses. External similarity combines current account and RER overvaluation similarity. 'Foreign exchange market pressure index three months after the crisis. bLevel of the real exchange rate 12 months after the crisis. Source: Authors' calculations. De Gregorio and Valdes 311 crisis j instead of cc,,. We use data from the Bank of International Settlements (Bis) (various years) and consider the short term to be less than a year. Two of the countries in our sample (Swedenand Finland) have positive net external assets and report to the BISfrom "within," and one country (Singapore) is considered a banking center and thus is highly leveraged. For these countries, we consider a zero in the ratio short debt/total debt and include a special dumrmyvariable in the equation multiplying the contagion index. Table 10 shows that a tilt toward short-term financing increases contagion when we measure it using changes in credit rating. The effects are economically relevant, highly significant, and robust to alternative weighting matrixes. With 12-month real depreciation and direct trade, there is a marginally significant positive effect. IV. CONCLUDING REMARKS This article has examined the channels through which crises spread across coun- tries. For this purpose, we examined the behavior of crisis indicators as a function of initial conditions and the average of crisisindicators elsewhere. The latter vari- ableattempts to capture interdependenceor co-movements.This relationship could be simply the result of common shocks hitting a number of countries. To under- stand how theseexternal common shocks and shocks originating in other countries spread to other places, weconstructed a weighted average of crisis indicators else- where. The weighting schemes attempt to capture different transmission mecha- nisms. We used the importance of bilateral (also called direct) trade, competition in third markets, regional relationship, and indexes of similarities. We found that the channel of propagation of crises depends on both indica- tors and horizons. Three months after a crisis, there are strong neighborhood effects. Rather than trade links and/or macroeconomic similarities, what seems to better explain cross-country correlation is the proximity of countries or re- gional effects. The same happens when we analyze changes in country credit ratings at longer horizons (6 to 12 months). Thus the regional weighting scheme is the strongest quantitatively and is sta- tistically the most robust. This impliesthat crisis spread mainly, but not uniquely, as the Russian crisis in 1998 witnessed, through regions. No wonder the debt crisis was centered inLatin America and the 1997 crisis in Asia. Part of thiscould be explained by direct trade links, because regions tend to have irnportant trade relationships. But the effect of trade links,although important, cannot account for the whole regional effect. Another candidate for explaining this regional ef- fect is financial links, through cross-border ownership of assets, stock market links, and others. At this stage, we do not have good indicators for constructing weighting matrixes to control for financial links. This is clearly an area that deserves further research. A question that arises in most of the literature on currency crisis and contagion is whether crises are triggered by bad sentiments or by self-fulfilling prophecies. In TABLE 10. Composition of Capital Inflows and Contagion Pressure indicator and weighting matrix Change in Change in Change in credit rating/ Change in Change in Pi-3/trade Change in Change in Change in Change in credit rating/ external Pt-3/direct Pi-3/ with RER/direct RERI RERI growth credit rating/ trade with Variable similarity tradea neighborsa neighborsa tradeb neighborsb similarityb direct trade neighbors of neighbors Credit boom -0.05 -0.01 -0.03 -0.09 -0.07 -0.17 0.04 0.01 0.03 (-0.28) (-0.04) (-0.16) (-0.45) (-0.34) (-0.78) RERovervaluation (0.60) (0.21) -0.23 (0.51) -0.22 -0.21 - - - - - - (-1.72) (-1.76) (-1.65) Fiscalbudget/GDP - - - -0.60 -0.55 -0.74 ul (-1.83) (-1.69) (-2.22) |9 Currentaccount/GDP 0.47 0.34 0.45 1.08 1.11 1.05 - - - (2.04) (1.61) (2.07) (3.99) (4.10) (3.77) Contagion index 0.70 0.53 0.50 0.75 3.86 1.17 0.35 0.35 0.34 (1.79) (1.32) (1.50) (1.96) (1.74) (2.02) (0.84) (1.20) Contagion x (1.15) 0.57 -0.58 -0.51 3.60 -2.26 1.73 4.38 3.95 Short-term debt 2.47 (0.27) (-0.40) (-0.33) (1.71) (-1.68) (0.79) (2.91) (4.14) R2 (2.32) 0.51 0.60 0.56 0.51 0.52 0.48 0.57 0.72 0.70 F-statistic p-value 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Observations 0.00 60 60 60 60 60 60 60 60 60 Note: Data are for 20 countries forthree crisis periods. See table A-I forcountries and text for crisis periods.Values are from dummy variables OLsregressions with in the three ground-zero constants and countries (not reported). White's robust t-tests are in parentheses. External similarity overvaluation similarity. combines current account and RER Source: Authors' calculations. De Gregorio and Valdes 313 TABLE A-1. Country List Neighborhood Country code Argentina 1 Brazil 1 Chile 1 Colombia 1 Ecuador 1 Mexico 1 Peru 1 Venezuela 1 Indonesia 2 Korea 2 Malaysia 2 Philippines 2 Singapore 2 Thailand 2 Sweden 3 Finland 3 Portugal 3 Australia 3 New Zealand 3 South Africa 3 the context of contagion, this impliesthat a crisiscould occur just because of con- tagion. In this article, we show that, although the crisis indicatorsare affected by contagion, fundamentals explain a large fraction of the crises. In particular, the current account deficit, exchange rate overvaluation, and credit boom affect our market pressure indicators. Giventhe sample size,the results change in some speci- fications and some caveats could be added, but we can conclude that fundamen- tals matter and it isnot just what is going on elsewherethat causescrisisto happen. At a 12-month horizon, fundamentals matter and both trade links and initial macroeconomic conditions explain which countries suffer stronger contagion. We find that the cross-country variation of a 12-month real exchange rate de- preciation depends on growth and external similarities (overvaluation and cur- rent account deficit) and direct trade links. At this horizon, neighborhood (re- gional) effectsare stillimportant. Common shocks seemto explain cross-country correlation of a 12-month change in a foreign exchange market pressure index. For the other indicators of crisis we use-the 3-month change in foreign exchange market pressure index, the 12-month real exchange rate depreciation, and the change in the credit rating-we find that co-movements explained by specific forms of contagion are more important. To this end, we conclude that although crises may be triggered by common shocks, transmission across countries de- pends on regional, trade, and macroeconomic characteristics of the countries. A policy issue that has been in the middle of the discussion on contagion is the way inwhich linksacross countriescould be limitedduring crisis periods. The issue of the optimality of contagion should be addressed first, but at this stage we have 314 THE WORLD BANK ECONOMIC REVIEW, VOL. I5, NO. 2 taken a practical view in analyzing whether there may be policies that could curb contagion. To this end, we analyze the impact of capital controls, exchange rate flexibility, and debt composition. We find that capital controls do not affect con- tagion. Exchange rate flexibility and the structure of external debt have effects on some of our crisis indicators, affecting the country credit rating. Exchange rate flexibility also affects the real depreciation after 12 months. REFERENCES Berg, Andrew, and Catherine Pattillo. 1998. "Are Currency Crises Predictable? A Test." IlNF Working Paper WP/98/154. Bank of International Settlements (BIS).Various years. The Maturity, Sectorial and Na- tionalityDistributionof InternationalBank Lending.Basle:BIS. De Gregorio, Jose, Sebastian Edwards, and Rodrigo 0. Vald6s. 2000. "Capital Controls: Do TheyWork?"Journal of Development Economics 63(1):59-83. Edwards, Sebastian. 1999. "How EffectiveAre Capital Controls?" Journal of Economic Perspectives 14(4):65-84. Eichengreen,Barry, Andrew K. Rose,and Charles Wyplosz. 1997. "Contagious Currency Crises." Mimeo, University of California, Berkeley, July. Available online at http:/H haas.berkeley.edu/-arose. Forbes, Kristin, and Roberto Rigob6n. 1999. "Measuring Contagion: Conceptual and Empirical Issues." Mimeo, MIT. Glick, Reuven, and Andrew K. Rose. 1998. "Contagion and Trade: Why Are Currency CrisesRegional?" Mimeo, University of California, Berkeley,August. Available online at http://haas.berkeley.edu/-arose. Gourinchas, Pierre Olivier, Oscar Landerretche, and Rodrigo 0. Valdes. 2001. "Credit Booms: Is Latin America Different?" Economia 1(2):47-99. Goldfajn, Ilan, and Rodrigo 0. Valdes. 1999. "The Aftermath of Appreciations." Quar- terly Journal of Economics 114(1):229-62. International Monetary Fund (IEIF).Various years.Exchange Arrangements and Exchange Restrictions. Washington, D.C.: IMF. . Various years. International Financial Statistics. Washington, D.C.: INIF. Kaminsky, Graciela L., and Carmen M. Reinhart. 1999. "The Twin Crises: The Causes of Banking and Balance of Payments Problems." American Economic Review 89(3):473- 500. . 1998. "On Crises, Contagion, and Confusion." Mimeo, University of Maryland, November. Kaminsky, Graciela L., Saul Lizondo, and Carmen M. Reinhart. 1998. "Leading Indica- tors of Currency Crises." IMF Staff Papers, March. Rigob6n, Roberto. 1999. "On the Measurement of the International Propagation of Shocks." Mimeo, MIT. Sachs, Jeffrey, Aaron Tornell, and Andres Velasco. 1996. "Financial Crises in Emerging Markets: The Lessons from 1995." Brookings Papers on1Economic Activity 1. THE WORLD BANK ECONOMIC REVIEW, VOL. I5, NO. 2 315-340 Mutual Fund Investment in Emerging Markets: An Overview GracielaL. Kaminsky, Richard K. Lyons, and SergioL. Schbnukler International mutual funds are key contributors to the globalization of financial markets and one of the main sources of capital flows to emerging economies. I)espite their importance in emerging markets, little is known about their investment allocation and strategies. This article provides an overview of mutual fund activity in emerging markets. It describes their size, asset allocation, and country allocation and then focuses on their at both the behavior during crises in emerging markets in the 1990s. It analyzes data fund-manager and fund-investor levels. Due to large redemptions and injections, funds' flows are not stable. Withdrawals from emerging markets during recent crises were large, which is consistent with the evidence on financial contagion. One of the most remarkable characteristics of the financial crises of the 1990s is the speed at which they spread to other countries. The Mexican crisis in Decem- ber 1994 prompted speculative attacks in Argentina and Brazil during the first quarter of 1995. The 1997 Thai crisis reached Malaysia, Indonesia, and the was Philippines within days. Unlike these earlier crises, the 1998 Russian crisis not confined to regional borders; it spread quicklyto countries as distant as Brazil de- and Pakistan. Even developed countries were affected, with the default and valuation reverberating in financial markets in Germany, the United States, and the United Kingdom. The time clustering of crises in different countries has generated a vast litera- ture on contagion (a term broadly understood as the cross-country spillover of is graciela@givu.edi. Graciela L. Kaminsky is with George Washington University. Her e-mail address Bureau of Economic Richard K. Lyons is with University of California, Berkeley, and the National Research. His e-mail address is Iyons@haas.berkeley.edii. Sergio L. Schmukler is with the World Bank. His e-mail address is sschmukler@worldbank.org. The authors thank Francois Bourguignon and two comments from Stijn anonymous referees for numerous helpful suggestions. They also benefited from and participants at the Inter- Claessens, Kristin Forbes, Jonathan Garner, Andrew Karolyi, Subir Lall, INIF/WorldBank Brown Bag national Monetary Fund (InIF)/World Bank conference on "Contagion," For help with Lunch, and a workshop at the Institute of Development Studies, University of Sussex. data the authors thank Erik Sirri of the U.S. Securities and Exchange Commission, Konstantinos excellent research Tsatsaronis from the Bls, and Ian Wilson from Emerging Market Funds Research. For assistance we thank Cicilia Harun, Sergio Kurlat, and Jon Tong. For financial support they thank the National Science Foundation, the World Bank (Latin American Regional Studies Program and Research Support Budget), and the World Bank Research Advisory Unit. (2001 The International Bank for Reconstruction and Development / THE WORI BANK 315 316 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. Z crises).' Many of these studies focus on the role of financial links. There isevi- dence, for example, that banks were important in spreading the 1997 crisis, due to the "common-lender channel" (Kaminsky and Reinhart 2000; Van Rijckeghem and Weder 2000).2 The role of portfolio investors (foreign and domestic) during crises has also been under scrutiny,3 with some researchers finding evidence of institutional panic and herding. This type of behavior might have helpedspread crises even to countries with strong fundamentals. Kaminsky, Lyons, and Schmukler (2000b) note that individuals, too, can contribute to in- stitutional panic by fleeingfrom funds-particularly mutual funds-forcing fund managers to sell when fundamentals do not warrant selling. Although research on portfolio flows and the role of institutional investors has expanded dramatically in the late 1990s, information on the importance and evolution of institutional investors in emerging markets is still fragmented. Moreover, the role of mutual funds in capital-flow reversals during crises has not yet been documented. This article complements previous research in these two areas. First, it provides an overview of the importance and behavior of international mutual funds in emerging markets.4 Second, it examines whether mutual fund investment tends to be stable over time and during crises. There are two key advantages-beyond growing importance-to studying mutual funds rather than other institutional investors. The first is data quality. U.S.-based mutual funds report holdings to the U.S. Securities and Exchange Commission (U.S. SEC) semi-annually. In addition, private companies compile mutual fund data at higher frequencies, typically quarterly, through surveys. These data enable both cross-sectional and time-series analysis. In contrast, other institutional investors, like pension funds and hedge funds, are not required to disclose holdings. (Nor do there seem to be sources that compile data for these investor types from voluntary disclosures.5) The second key advantage to study- ing mutual funds is that their allocations to emerging markets have grown con- siderably in scope and size. There are now specialized subcategories within the broader mutual fund category. Some funds specialize in a particular country, some within a region, and some specificallyin emerging markets, whereas some invest in emerging markets as part of a global strategy. 1. Many of the papers are available at www.worldbank.org/contagion. 2. The common-lender channel refers to cases in which common international banks lend to differ- ent countries, which consequently become linked. When a crisis hits the common lenders, all countries tend to be affected by the crisis. 3. See, for example, Cumby and Glen (1990); Bekaert and Urias (1996); Brown, Goetzmann, and Park (1998); Eichengreen and Mathieson (1998); Frankel and Schmukler (1996,1998,2000); Levy Yeyati and Ubide (1998); Bowe and Domuta (1999); Borensztein and Gelos (1999); Kaminsky, Lyons, and Schmukler (2000a, 2000b); and Pan, Cham, and Wright (2001). 4. Mutual funds from developing countries are also becoming important in some countries, helping develop local capitalmarkets. Those funds are not covered in this study, however. 5. To study the behavior of pension or hedge funds one would need estimates of portfolio changes. Brown, Goetzmann, and Park (1998) provide such estimates for hedge funds during the Asian crisis. Kaminsky, Lyons, and Schmukler 317 I. BRIEF HISTORY OF CAPITAL FLOWS Private capital flows have become the main source of external financing for developing countries, far surpassing public funds and accounting for some 80 percent of all flows to developing countries.6 The first increase in capital flows occurred in the 1970s (seefigure 1),triggered bythe 1973-74 oilshock and ampli- fied by the growth of the Eurodollar market and a spurt in bank lending during 1979-81. Latin America was the main recipient, with net flows peaking at $41 billion in 1981. Flows in this episode took the form mainly of syndicated bank loans (figure2). The pace of international lending came to an abrupt halt in 1982 with the increase in world real interest rates to levels not seen since the 1930s. By the late 1980s, there was a revival of international lending.,with capital flows to Latin America making a tremendous comeback. Capital flows to Asia also surged, increasing tenfold from their averages in the late 1980s. The com- position of capital flows changed dramatically, with bank lending replaced by foreign direct investment and portfolio investment. Bank lending to both East Asia and Latin America declined from 70 percent of net private capital flows in the 1970s to about 20 percent in the 1990s (see figure 2). While foreign direct investment in East Asia and Latin America constitutes the largest share of capi- tal flows, portfolio investment (bonds and equity) has also increased substan- tially, accounting for about 30 percent of capital flows in the 199CIs.In absolute values, bond and equity flows to each region-excluding those counted as for- eign direct investment-increased from $1 billion in 1990 to $40 billion in 1996, with bond flows exceeding equity flows in Latin America since 1994. (Reported equity flows are underestimated: Any equity flow meant to acquire more than 10 percent of a company's outstanding shares is recorded as foreign direct in- vestment, which accounts for around 50 percent of total capital flows.) In the 1990s, as in the 1980s, booms were followed by a slowdown of capital inflows.7 The first episode occurred in the immediate aftermath of Mexico's currency crisis in December 1994. Capital inflows resumed for mnostcountries within six months and returned to their peak values soon thereafter. The crisis was confined to a small number of Latin American countries. Capital flows to Asian economies were largely unaffected. The second, more severe slowdown came in 1997, during the Asian crisis. The Russian default in August 1998 ac- centuated this slowdown, as capital flows collapsed. The change in inflows was similar in magnitude to that after the 1982 debt crisis, with total capital inflows declining about 35 percent to both Latin America and Asia.8 6. The data on capital flows come from World Bank databases. For more detailed description of capital flows, see World Bank (1997, 2000). 7. The term reversal is used in the literature in various ways. For some, a reversal is a shift from inflows to outflows. For others, a reversal is a reduction in inflowsrelative to what is expected. 8. During the debt crisis, capital inflowsdeclined about 24 percent in the first year of thecrisis and 53 percent in the second year. FIGURE 1. Total Net Private Capital Flows to Developing Countries, by Region 1972-98 (billions of U.S. dollars) East Asia and Pacific 140--- 1 120 1 100~ _ _ _ _ 80 60 40 20 N t co co 0 cm ' T co 0 N 0- (0 co N- OCO 0- 0- co 00 co00 C) 0) 0) 0) 0) Eastern Europeand CentralAsia 50 40 30- 20 10_0 N\ (D co 0 CN t (C CO o c\ t co (0 0- r-0 - l- 0 0 00 00 0 0 C) 0) 0) ) LatinAmericaand the Caribbean 120 100 80 60 NM t ( CO 0C N t tD CO 0 N\ N- ( N- \ N- CD O N- CD CD 't CD O 0) 0) 0) c0 0) CI 0) C0 0 0) 00 0 0D OD 0 C) C Cm0 Notes: Net capital flows to developing countries include bank and trade-related lending, portfolio equity and bond flows, and foreign direct investment. The countries comprising Latin America and the Caribbean are Antigua and Barbuda, Argentina, Barbados, Belize, Bolivia, Brazil, Chile, Columbia, Costa Rica, Cuba, Dominica, Dominican Rebublic, Ecuador, El Salvador, Grenada, Guadeloupe, Gua- temala, Guyana, Haiti, Honduras, Jamaica, Mexico, Nicaragua, Panama, Paraguay, Peru, Puerto Rico, St. Kitts and Nevis, St. Lucia, St. Vincent and the Grenadines, Suriname, Trinidad and Tobago, Uru- guay, and Venezuela. The countries comprising East Asia and Pacific are American Samoa, Cambodia, China, Fiji, Indonesia, Kiribati, Korea, Dem. Rep., Lao PDR, Malaysia, Marshall Islands, Micronesia, Fed. Sts, Mongolia, Myanmar, Palau, Papua, New Guinea, Philippines, Samoa, Soloman Islands, Thai- land, Tonga, Vanuatu, Vietnam. The countries comprising Europe and Central Asia are Albania, Ar- menia, Azerbaijan, Belarus, Bosnia and Herzegovina, Bulgaria, Croatia, Czech Republic, Estonia, Geor- gia, Hungary, Isleof Man, Kazakstan. Kyrgyz Republic, Latvia, Lithuania, Macedonia FYR, Moldova, Poland, Romania, Russian Federation, Slovak Republic, Tajikistan, Turkey, Turkmenistan, Ukraine, Uzbekistan, and Yugoslavia FR (Serbia/Montenegro). 318 Kaminsky, Lyons, and Schmukler 319 FIGURE 2. Type of Net Private Capital Flows to Developing Countries, 1970s to 1990 (billions of U.S. dollars) 700 600 400 300 d 200 100 .,. I'i....,._ 9 8 9 0 1990's 1970's 1980's 1990's 1970's 1 0's 1 9 's 1970's 1980's Latin American & the Caribbean East Asia & Pacific Europe d: CentralAsia *100 * Foreign Direct Investment D Portfolio Bond Flows MPortfolio Equity Flows EDBank & Trade-RelatedLending Notes: See Figure 1 for countries includedin each region. Source: World Bank data. The decline of short-term portfolio flows (bonds, equities, and bank lending) was even more pronounced, with flows fallingabout 60 percent in Latin America in 1998. Overall, bond and equity flows to Latin America declined from about $44 billion in 1996 to about $15 billion in 1998. Bond and equity flows to Asia collapsed in 1998 to $9 billion, from their peak in 1996 of $38 billion. In sum, portfolio flows have become an important source of external financ- ing in emerging markets. These flows have been unstable, with booms followed by pronounced reversals, and they have been channeled mainly through institu- tional investors, particularly mutual funds. II. MUTUAL FUND INVESTMENT Different data sources are needed to study the role of institutional investors. Unlike data on capital flows, which the World Bank collects on a regular basis, 320 THE WORLD BANK ECONOMIC REVIEW, VOL. I5, NO. 2 no agency has full detailed information on institutional investors. Institutions and companies like the Organisation for Economic Co-operation and Development (OECD), the U.S. SEC, the Investment Company Institute, Morningstar, Emerging Market Funds Research, Frank Russell, AMG Data Services,Lipper Analytical Services, and State Street Bank have partial information on institutional investors. The International Finance Corporation (IFC) has data on total market capitaliza- tion by country. Emerging Market Funds Research compiles data on dedicated emerging market funds. Morningstar and the U.S. SECcollect data on U.S. mu- tual funds. Data from the World Bank and the Bank for International Settlements (BIS) can be found elsewhere in the published literature in a similar format. Getting an overall picture requires analyzing and combining data from vari- ous sources. This article contributes to the literature by compiling information from different sources and displaying it systematically and by presenting new evidence, though parts of the data are displayed elsewhere in a different format. The appendix summarizes the data sets used in this study and their sources. Size of Mutual Fundsand InstitutionalInvestors Institutional investors-including mutual funds, pension funds, hedge funds, and insurance companies-are a growing force in developed markets. Institutional investors held almost $11 trillion in the United States alone in 1995 (table 1). U.S.institutional investors accounted for more than half the assets held by insti- tutions across the world. When individual investors choose to allocate part of their portfolios to emerg- ing markets, they typically make their purchase through mutual funds. In ac- tively managed funds, it is the fund manager who ultimately determines the portfolio allocation by choosing how the fund invests its assets (within the lim- its of the fund's defined scope). In index funds, the manager's role is passive, aimed at replicating a predetermined index.9 Mutual funds based in developed countries have become one of the main in- struments for investingin emerging markets.10 The first funds, in the 1980s, were closed-end funds, which are well suited for investing in illiquid markets because their shares cannot beredeemed. As liquidity increased in emerging markets, the most widely used instrument became open-end funds. Mutual fund investors include other institutional investors as well as individual investors. For example, more than half of pension funds invest in emerging markets through existing mutual funds, for both liquidity and cost reasons (less expensive than giving specific mandates to fund managers). Therefore, in examining mutual funds, much of pension fund investment in emergingmarkets iscovered as well. AWorld Bank (1997) survey estimates that pension funds hold around 1.5 to 2 percent of their portfolios ($50-$70 billion) in assets from emerging markets. 9. In all cases, butparticularly for ofindex funds, fund managers tend to be evaluated against some benchmark indices. As a consequence, the behavior of managers is likely affected bythese evaluations. 10. See New York Stock Exchange (2000) on U.S. investors in emerging market shares. Kaminsky, Lyons, and Schmukler 321 TABLE 1. Share of Global Assets Held by U.S.- and European-Based International Institutional Investors, 1995 (percent) Institutional investor U.S.-based European-based Pension funds 66 24 Insurance companies 37 37 Life insurance 35 36 Non-life insurance 45 37 Mutual funds 59 33 Open-end 65 34 Closed-end 57 41 Aggregate 52 32 Assets (billions of 10,994 6,666 U.S. dollars) Source:BIS 1998. Hedge funds are a newer type of institutional investor. Still smrallrelative to other institutional investors, hedge funds held estimated total assets of $81 bil- lion by year-end 1997, only a small fraction of which is investedlin emerging markets."1 Like other institutional investors, insurance companies likely invest only a small proportion of their assets in emerging markets. However, unlike hedge funds, their asset holdings are large. More evidence on thieinvestment allocation of this industry is needed.12 Of course, institutional investors in developed countries invest internation- ally not only in emerging markets but also in other developed economies. These broader, international portfolios are more concentrated in equities than in bonds (figure 3). Banks, for their part, tend to invest a bit more of their own assets and some of their clients' in foreign bonds. Despite the broader, international diver- sification of institutional investors, their portfolios still exhibit a strong home bias. For example, accordingto the World Bank (1997), U.S.equity pension funds held less than 9 percent of their assets in international instruments and around 2 percent in emerging markets (in 1994). Even when international institutional investors hold only a small fraction of their portfolio in emerging markets, they have an important presence in these economies, given the relatively small size of their capital markets. Funds dedi- cated to emerging markets alone hold on average between 4 and 15 percent of the Asian, Latin American, and transition economies' market capitalization (table 2). By comparison, holdings of U.S. mutual funds accounted for 15 per- cent of the U.S. market capitalization in 1996 (see table 3). In Japan and the United Kingdom, domestic mutual funds held 4 and 8 percent of the local mar- ket capitalization that same year. 11. See Eichengreen and Mathieson (1998) for a detailed study of hedge funds. 12. Beyond institutional investors, it is difficult to determine the direct holdings ofindividual in- vestors. No regulatory agencies (like the U.S. SEC or the BIS) or private companies (like Morningstar or Lipper Analytical Services) keep such records. FIGURE 3. Distribution of U.S. Mutual Fund Assets by Fund Type as of December 31, 1998 Distribution by instrument AllU.S.Funds AsiaPacificFunds EmergingMarketFunds LatinAmericanFunds GlobalFunds 2%* A-seRs S. 79-O 13 O s.h d") t 0o/ogX ) 130rs<4 | Bonc A~ 9 3 jivX~~~~4 (tSfQ \~; N k\ 8 63% 5~~~~~~~~2% Distribution by country QQ or region AllU.S.Funds AsiaPacificFunds EmergingMarketFunds LatinAmericanFunds GlobalFunds Sand Other~~~~~~. Lat saAe " USar Erlhope Cand U5% E- e aAnrarsa 20% 2% Oth.r1 CandaOte 1 % Uad0 Ae 29% Canda Notes: Morningstar classifies the assets as being invested in one of six countries or regions: United States and Canada, Japan, Asia (excluding Latin America, or Japan), Europe, other. Holdings are classified in one of four asset classes: cash, stocks, bonds, or other. The Morningstar universe includes funds except money market all types of mutual funds. Funds that invest primarily outside the United States are mostly equity funds. Source: Morningstar. Karninsky, Lyons, and Scbnmukler 323 The estimates of the importance of mutual funds in emergingmarkets are quite conservative because they include only the holdings of dedicated emerging mar- ket equity funds.e3 Excluded are the holdings of global funds, which account for a substantially larger share of the stock market capitalization of emerging mar- kets. Even though global funds hold only a small share of their assets in emerg- ing markets, they are substantially larger than dedicated emerging market funds giving them a stronger presence.'4 Moreover, some of the outstanding equity in emergingmarkets-as well as inmany developed countries-is not publicly traded because it belongs to families or corporations that control the companies. So international mutual funds hold a large and significant proportion of the pub- licly available equity, even though the total amount is not known. The importance of mutual funds varied substantially during the 1990s (see table 2). Though net equity flows declined from their 1993 peak-about $27 billion to Latin America and $21 billion to Asia-the relative importance of mutual funds increased until 1997. For example, dedicated emerging market equity funds held $22 billion in Latin American stocks at the end of 1995 and nearly double that, $40 billion, by December 1997. Though mutual fund growth was less pronounced in Asia, mutual funds are still important in many coun- tries. Overall, dedicated emerging market mutual funds held $77 billion in Asia at the onset of the crisis (December 1996). While the absolute amount of mutual fund investment in transition economies is not comparable to that in Asia and Latin America, fund growth in these transition economies has been remarkable. In market capitalization terms, mutual funds have become big players in these markets, with especially large positions in markets in Hungary and Poland. The mutual fund industry specializing in emerging markets has a very con- centrated portfolio by economies. At least half their total portfolio is invested in just six markets: Brazil, Hong Kong (China), Republic of Korea, Malaysia, Mexico, and Taiwan (China). Country shares have varied, sometimes substan- tially, in the 1990s. For example, Malaysia attracted about 12 percent of all the funds allocated to Asia in 1995 but only 4 percent after the crisis. In contrast, the share allocated to Indian assets increased from 7 percent to 14 percent. The proportion of assets allocated to countries in Latin America has been less vola- tile, with Brazil's share of the funds allocated to the region holding at about 40 13. Data on dedicated funds come from Emerging Market Funds Research, which collects aggre- gate data of emerging market mutual funds. They track the net cash flows of nearly 1,400 international emerging market equity funds, with an average position of about $120 billion in 1996. The data cover both U.S.-registered and offshore funds as well as funds registered in Luxembourg, the United King- dom, Ireland, Cayman Islands, Canada, and Switzerland. It includes both open- and closed-end funds. The data set used in thisarticle starts with the Mexican crisis of 1995 and ends in March 1999; it there- fore includes observations on the major currency crises of the 1990s. 14. For example, estimates for the mutual fund industry more broadly suggest that international funds hold between 60 percent and 70 percent of the market capitalization in Hungary, in contrast to the estimates in table 3,which are all below 30 percent. We thank Jonathan Garner, from Dij, for this information. TABLE2. Holdings of Dedicated Emerging Market Fund Assets and Their Share of Market Capitalization, by Country and Region, 1995-98 1995 1996 1997 1998 End-of-year Share of End-of-year Share of End-of-year Share of End-of-year Share of holdings market holdings market holdings market holdings market (billions of capitalization, (billions of capitalizationa (billions of capitalizationa (billions of capitalization, Economy U.S. dollars) (percent) U.S. dollars) (percent) U.S. dollars) (percent) U.S. dollars) (percent) China 1.9 4 2.3 3 3.1 2 1.9 Hong Kong 1 12.6 n.a. 20.4 n.a. 13.2 n.a. 9.4 India n.a. 4.5 3 6.1 4 7.4 5 5.6 Indonesia 5 4.5 9 5.5 7 1.9 2 1.3 Korea, Rep. of 7 10.3 6 7.7 5 2.5 2 7.3 Malaysia 11 8.2 4 12.0 4 2.4 1 1.5 Pakistan 2 0.6 6 0.5 5 0.8 7 0.2 Philippines 3 3.4 6 4.2 6 1.7 3 1.9 Singapore 6 5.1 n.a. 5.3 n.a. 3.0 n.a. 3.8 Sri Lanka n.a. 0.2 9 0.1 5 0.2 10 0.1 Taiwan, China 7 4.6 2 7.2 3 5.9 2 5.7 Thailand 2 9.8 7 5.9 4 2.2 4 3.1 Total Asia 10 65.7 6 77.2 5 44.2 4 41.7 5 W Argentina 3.1 9 3.3 8 4.6 9 3.1 Brazil 6 8.1 5 11.5 6 15.4 6 8.3 Chile 4 3.4 5 2.9 4 3.4 4 2.6 Colombia 4 0.4 2 0.6 4 0.6 3 0.3 Mexico 2 5.5 6 7.8 7 13.4 10 7.9 Peru 7 0.7 7 0.9 7 1.1 6 0.7 Venezuela 5 0.3 6 0.7 12 1.2 9 0.5 Total Latin American 5 21.5 6 27.7 7 39.7 7 23.2 5 Czech Republic 0.5 3 1.0 6 1.0 6 0.7 Hungary 6 0.4 25 1.2 29 2.3 26 2.2 Poland 16 0.7 18 1.5 20 1.9 17 2.2 Russiab 14 1.0 n.a. 2.6 10 7.5 7 1.7 Slovak Republic 3 0.1 n.a. 0.1 4 0.1 5 0.1 Total transition 8 2.7 15 6.4 14 12.8 12 7.0 economies 10 n.a. is not available. Note: Data cover only the holdings of the dedicated emerging market funds(basedinside and outside the United States). Thus in each country is the importance of all significantlylarger in foreign mutual funds most cases.The International Finance Corporation database does not containmarket capitalization in the table). for some countries (shown as n.a. aShareof country's stock market capitalization. blncludesother members of the Commonwealth of Independent States. Source:Emerging Market Funds Research and International Finance Corporation. Kaminsky, Lyons, and Schmukler 325 TABLE 3. Share of Total Mutual Fund Assets Held by Selectled Developed Country-Based Funds, by Asset Type, 1996 (percent) United States Japan United Kingdom France Money market funds 25 29 0 45 Bond funds 22 45 5 29 Equity funds 49 24 88 11 Balanced funds 3 2 6 14 Share of total 76 9 4 11 As percent of GDP 46 9 16 34 As percent of market 15 4 8 18 capitalization Source: BIS 1998. percent. Among transition economies, five countries account for most mutual fund investment: the Czech Republic, Hungary, Poland, Russia (and other mem- bers of the Commonwealth of Independent States), and the Slovak Republic. Again, the shares of crisis countries in the mutual fund portfolio swing substan- tially; Russian holdings varied from 25 percent to 59 percent of mutual funds' portfolios in transition economies. Mutual funds also hold large positions in American and Global Depositary Receipts, (ADRs and GDRS), typically traded on the New York Stock Exchange, NASDAQ, and the American Stock Exchange. Therefore, mutual funds often do not trade in the local stock markets when investing abroad.15 Holdingsof U.S.-BasedMutual Funds U.S.-based mutual funds accounted for almost 60 percent of world mutual funds in 1995 (seetable 1).The U.S.mutual fund industry expanded significantlyduring the 1990s (table 4). From 1991 to 1998 the number of bond and stock funds increased from 2,355 to 10,144 net assets rose from $705 billion to $3.6 tril- lion. The 20 largest U.S. mutual funds capture only a small proportion of all the assets of the U.S. mutual funds industry (not more than 4 percent). The exposure of U.S. mutual funds to emerging markets increased substan- tially during the 1990s (seetable 4). U.S.-based, open-end mutual funds (includ- ing Asia Pacific, Latin American, and emerging market funds) had around $35 billion by the end of 1996, up from about $1 billion at the end of 1991. As Asia Pacific funds grew from 11 funds in 1991 to 154 in 1998, their net assets rose from $1 billion in 1991 to $16.4 billion in 1996 and then fell to $6.5 billion in 1998 following the Asian crisis. Mutual funds specializing in emerging markets increased from 3 funds in 1991 to 165 funds in 1998, with total net assets rising 15. See Karolyi (1998) for a broad-based survey of global cross-listings.Also see Smith and Sofianos (1997) for a study of the effects ofdepositary-receipt listing in the New York Stock Exchange. TABLE 4. Size of Mutual Fund Universe, as of December 31, 1991-98 1991 1992 1993 1994 1995 1996 1997 1998 All U.S. funds Net assets (billions of U.S. dollars) 705 933 1,338 1,428 1,838 2,335 2,954 3,570 Number of funds 2,355 2,522 3,422 5,594 6,937 7,746 8,655 10,144 Net assets of 20 largest funds as 2 2 3 4 3 4 4 3 percentage of all U.S. funds Asia Pacific funds Net assets (billions of U.S. dollars) 1.1 1.4 8.4 11.9 12.1 16.4 9.0 6.5 Number of funds 11 14 27 59 79 106 127 154 Net assets of 20 largest funds 100 100 97 94 94 93 90 82 as percentage of all Asia Pacific funds Emerging market funds Net assets (billions of U.S. dollars) 0.1 0.5 3.7 8.7 8.5 15.6 16.9 13.5 Number of funds 3 7 10 32 64 94 119 165 Net assets of 20 largest funds 100 100 100 92 89 72 71 67 as percentage of emerging market funds Latin American funds Net assets (billions of U.S. dollars) 0.04 0.2 1.3 3.9 2.5 2.9 4.1 1.8 Number of funds 1 3 5 15 25 28 35 47 Net assets of 20 largest funds 100 100 100 100 73 95 97 95 as percentage of Latin American funds Global funds Net assets (billions of U.S. dollars) 16.1 18.3 28.1 45.4 58.1 82.0 108.1 125.4 Number of funds 52 56 78 143 180 198 223 273 Net assets of 20 largest funds as 81 80 74 73 71 76 79 77 percentage of world funds Source: Morningstar. Kaminsky, Lyons, and Schmukler 327 from $142 million in 1991 to $13.5 billion in 1998 (after peaking at $17 billion in late 1997). The number of Latin American funds increased from 1 to 47, and their net assets rose dramatically from $44 million to $1.8 billion. Global funds increased from 52 to 273, with total net assets rising from $16 billion to $125 billion. With the exception of mutual fund investment in U.S.assets, the mutual fund industry is highly concentrated, with the largest 20 funds holding about 80 percent or more of all assets. Until 1993 bonds constituted the largestshare of mutual fund portfolios. After that, equities began to predominate. By 1998, for mutual funds overall, about 68 percent of their portfolio was allocated to stocks; most of the rest (between 24 and 40 percent) was allocated to bonds (seefigure 3). The proportion of as- sets held in stocks is substantially larger for mutual funds specializing in emerg- ing markets (including Asia Pacific and Latin America), varying from 83 per- cent to 92 percent. Global funds also hold a large share of their assets in stocks (86 percent). The country or regional composition of the total U.S. mutual (und portfolio in 1998 was 83 percent U.S. and Canadian stocks, 12 percent European stocks, 1 percent Japanese assets, 2 percent Asian assets, and 0.9 percent Latin Ameri- can assets. Although the percentage dedicated to emerging markets is small, the large size of the U.S.mutual fund industry implies that the dollar amount held in assets from emerging countries is significant. III. BEHAVIOR OF MUTUAL FUNDS DURING CRISES The financial crises of the 1990s spread beyond the country and even the region of origin. Financial disruption spread to countries as far apart as Argentina, the CzechRepublic, and SouthAfrica. Crisesbefore 1990 had also led tocontagion- witness the debt crisis in 1982-but that contagion had tended to be regional until recently (with some exceptions). That changed inthe 1990s. The East Asian crisis triggered financialdisruption as far away as Argentina, Mexico, and Chile. The speculative attack on the Hong Kong dollar in October 1997 also spilled over into other markets. Even the U.S. stock market suffered sizable losses after the Hang Seng index fell 15 percent. The cross-country effects became more widespread following the Russian default in August 1998, with stock prices in all industrial countries declining between 20 percent and 50 percent. Contagion in these recent crises has been partly attributed to global financial links. Studies have shown that the behavior of mutual funds and contagion may be linked, either because funds generate cross-country spillovers or because funds engage in feedback trading (trading in response to past returns, such as selling when past returns are low). International mutual funds can contribute to the spread of crises across countries through spillover effectsif, for example, investors holding fund shares decideto selltheir Asian funds when Russia devaluesits currency. Or if managers of Latin American funds sell assets in Brazil when a crisis hits Mexico. These need not be irrational responses: New models of rational herding explain 328 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. 2 the transmission of crises through financial links. These models involve asymmet- ric information and cross-market hedging.16 If mutual fund investors or managers also engage in feedback trading, their behavior can appear consistent with conta- gion even though mutual funds may not be the main force driving the spillovers. Institutional investors, such as mutual funds, can also be a stabilizing force. If investors buy mutual fund shares for long-run gains, they might not withdraw their investments during a crisis. Marcis, West, and Leonard-Chambers (1995) and Rea (1996)find that shareholders did not redeemshares during crisesperiods. They find that net inflows to emerging markets are usually steady, and crisis- period outflows are small and short lived (at least during Mexico's crisis). Froot, O'Connell, and Seasholes(2001) present a related picture, but without focusing on institutional investors. Though net flows into individual emerging markets decreased during the Mexican and Asian crises, Froot, O'Connell, and Seasholes find little evidence of net outflows.17 This section provides evidence on the stability of mutual fund investment and the behavior of mutual funds following speculative attacks, distinguishing where possible between the behavior of mutual fund managers and underlying investors.' 8 Mutual FundFlows On balance, flows of dedicated emerging market mutual funds to Asia, Latin America, and transition economies (data from EmergingMarket Funds Research) since 1995 have been muted, reaching about $20 billion, with booms in capital inflows followed by pronounced outflows (figure 4). Outflows from Latin America reached about $4 billion in 1995, but mutual funds increased their positions in Latin America by about $2 billion in the first half of 1996. The Mexico crisis did not spill over to Asia or the transition economies. In fact, flows to Asia ballooned to almost $11 billion, whereas flows to transition economies remained stable throughout 1995-96. The picture changes during the currency turmoil in Asia in the second half of 1997. This time, mutual funds pulled out not only from Asia but from Latin 16. For example, in the Calvo and Mendoza (1998) model, the costs of gathering country-specific information induce rational investors to follow the herd. In the Calvo (1998) model, uninformed inves- tors replicate selling by liquidity-squeezed informed investors, because the uninformed investors mistak- enly (but rationally) believe that these sales are signaling worsening fundamentals. Kodres and Pritsker (1999) focus on investors who engage in cross-market hedging of macroeconomic risks. They find that international market co-movement can occur in the absence of any relevant information, even in the ab- sence of direct common factors across countries. For example, a negative shock to one country can lead informed investors to sell that country's assets and buy assets of another country, increasing their expo- sure to the idiosyncraticfactor of the second country. Investors then hedge this new position by selling the assets of a third country, completing the chain of contagion from the first country to the third. 17. Froot, O'Connell, and Seasholes (2001) and Choe, Kho, and Stulz (1999) are able to study the dynamics of capital flows during crises using higher-frequency data. But their data are aggregated across types of investors, so they cannot focus on the role of different kinds of institutional investors, as is done here. 18. This section examines data sets from various sources, including the Emerging Market Funds Research, Morningstar, the U.S. SEC, and the Bis. Kaminsky, Lyons, and Schmukler 329 FIGURE 4. Mutual Fund Quaterly Flows to Emerging Market Economies (billions of U.S. dollars) LatinAmericaneconomies 20 = 0 . - - - - - , 0 - ---- -- - - - - Tsan boe on_mle Il---l 200 l I 50 ---- I 00 OO . Singaporee , T nSri La , adn T ( e) . T > e es e e b 1 50. y nds a So-Market eE Funds -------- Research.- R 50u i c.- - - osn ------------------------------------------------------------------------- 2 Ix -r - - - ---- -- - - - - - -- - - - - - - - - - - - - 200 ; Notes: Latin America includes Argentina, Brazil, Chile, Colombia, Mexico, Peru, and Venezuela. Asia includes China, Hong Kong, India, Indonesia, Republic of Korea, Malaysia, Pakistan, Philippines, Singapore, Sri Lanka, Taiwan (China), and Thailand. Transition economies includJe Czech Republic, Hungary, Poland, Russia and other members of the Commonwealth of Independent States, and the Slovak Republic. Source. Emerging Market Funds Research. 330 THE WORLDBANKECONOMICREVIEW,VOL. r5, NO. 2 America as well, with net outflows from Latin America reaching about $1 bil- lion in the six months followingthe collapse of the baht. In Asia, flowsrebounded brieflyin the first quarter of 1998 but declined thereafter. Overall in 1998, mutual fund withdrawals took a turn for the worse, reaching about $4 billion in Asia, with substantial outflows from Latin America and transition economies. A closer look at the spillover effects surrounding the Mexican, Thai, and Rus- sian crises shows how a crisis in one country triggers withdrawals in other coun- tries. To isolate the behavior of mutual funds in crisis times, the average quarterly mean flow (as a percentage of funds' initial positions) during the entire sample period (1995-99) is subtracted from net buying or selling (see figure 5).19For example, following the Mexican devaluation, mutual funds sold about 5 per- cent of their Brazilian positions relative to their average quarterly buying and sellingduring 1995-99. Thus Brazil experienced unusual withdrawals of about 5 percent in the aftermath of the Mexican devaluation. Looking at country data according to the severity of the outflows conveys more clearly the extent of con- tagion across regions following the initial speculative attack. Thus, for example, Malaysia was most affected in the aftermath of the Russian crisis, with abnor- mal outflows of approximately 30 percent. The repercussions of the three crisis episodes were dramatically different. The Mexican crisis was concentrated in Latin America and was confined to a hand- ful of countries. Only Brazil and Venezuela-in addition to the crisis country, Mexico-suffered abnormal average withdrawals (of 5 percent and 2 percent) in the two quarters following the devaluation. Mutual funds increased their exposure to Asian countries and transition economies, with (above-trend) flows of around 4 percent for Asia and 11 percent for the transition economies. The aftermath of the collapse of the Thai baht presents a different picture, with signsof a moregeneralretrenchment ofmutual funds inemergingmarkets. Mutual fund flows to Asian economies were basically all well below trend in the two quar- ters following the collapse of the Thai baht, except for flows to China, Pakistan, and Sri Lanka, which were above average. Withdrawals were also substantial from Hong Kong (12 percent), Singapore (7 percent), and Taiwan, China (12 percent). This time the retrenchment also reached Latin America and the transition econo- mies,with average quarterly withdrawals reaching about 6 percent for Colombia and 4 percent for the Czech Republic during the two quarters following the out- break of the Thai crisis. Colombia, the Czech Republic, Hungary, and Peru were most affectedin this episode, with outflows of 3 percent or more above average. Even more pronounced was the flight away from emerging during the Rus- sian crisis. About half the countries in the sample experienced abnormal with- drawals of 10 percent or more. In some cases, withdrawals were massive: 30 percent in Malaysia and 16 percent in the Czech Republic. Some Latin Ameri- can countries were also dramatically affected. Colombia and Venezuela suffered 19. Models of asset trade (such as microstructure finance models) provide a theoretical basis for focusing on changesin flow relative to whatis expected, which here is proxied by average flow. Kaminsky, Lyons, and Schmukler 331 FIGURE5. Mutual Fund Net Buying or Selling Following Recent Crises, by Country Afterthe MexicanCrisis 01 0% -20Zc -30% ' ~ ~ ~ Nd:, 1/ V r : = :: A C _ U E . A 0: 0 . C 2 C. ~ $. ~~~~~ V 0 0.C 0 u Hi' M U AftertheThaiCrisis(July1997) '0' 0j7c -20%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -30% ~~~~U H ~O C 0 V- AftertheRussianCrisistAugust1998) 20% 10%1 0%tE 20Zo -30% - ] m c 0, A 0 C C Notes: The figures show the spillover of crises to other developing countries. The figures display average mutual fund flows (net buying or selling as a percentage of the end of the preceeding quarter the sample average holdings) in the two quarters following the outbreak of the crisis, after subtracting for the study period. Source: Emerging Market Funds Research. 332 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. 2 average quarterly outflows of about 8 percent. Only Mexico and Peru did not suffer following the worldwide financial disruption triggered by the Russian default. In fact, inflows to Mexico were 5 percent above average flows. Several different factors seem to affect the varied pattern of responses in mu- tual fund flows across countries after a crisis erupts, including economic vul- nerability and liquidity of financial markets.20 Other risk factors-such as a possible change in political authority, severe new restrictions on purchases and sale of assets, or a debt moratorium-might also affect mutual fund invest- ment behavior. Not surprisingly, analysis shows that economic vulnerability matters. For example, the Czech Republic and Russia suffered severe outflows in 1997 and 1998, when both countries were in economic distress. Kaminsky, Lyons, and Schmukler (2000a) find that other factors also influence investors' withdrawals from emerging markets. In the caseof China, for example, devaluation fearswere widespread among investors and the vulnerability of its financial system was widely known, yet it did not suffer from the Asian crisis. In contrast, Singapore, Taiwan (China), and Hong Kong-the most liquid markets in Asia-suffered pronounced capital-flow reversals, even though their economies looked far healthier than China's. Though lessimportant, risk factors, such as attacks against foreign investors and political instability, helped explain the outflows in Paki- stan and Malaysia during the Russian crisis. Moreover, the crises that began in Mexico, Thailand, and Russia also showed increasing degrees of spillover, point- ing to systemic factors in addition to country-specific factors. Investorsand Managers Though mutual funds are commonly included among institutional investors, they differ from hedge funds, pension funds, and insurance companies in how much control underlying investors have over portfolio size. Fund behavior is thus de- termined by the decisions of both managers and investors.21 This hybrid nature affects mutual fund flows to countries and regions. This characteristic provides an opportunity to study in detail the behavior of these two groups of agents. Kaminsky, Lyons, and Schmukler (2000b) focus on whether the trading strategies of these two groups are driven by current and past returns (positive-feedbacktrading-the buying of past winners and sellingof past losers). This section provides additional evidence on the influence of each group, using detailed data from the BISand the U.S. SEC, which help isolate the behavior of the two groups. 20. See Kaminsky, Lyons, and Schmukler (2000a) for more detail on the probable determinants of mutual fund behavior in crises. 21. Mutual funds here means open-end, nonindex funds, which account for most of the funds that invest in emerging markets. In closed-end funds, investors do not control portfoliosize. In index funds, managers have littlecontrol over portfolio holdings. Kaminsky, Lyons, and Schmukler 333 INVESTORS. The behavior of underlying investors is described in figures 6 and 7. Cash flows to Asian mutual funds (from U.S.-and the U.K.-based funds), a decision belonging to investors, were high before the Asian crisis, particularly in 1995-96. After the Thai devaluation of 1997, large outflows began and contin- ued in 1998. Outflows were particularly large for U.S.-based funds after the Russian crisis. Equity FIGURE 6. Injections and Redemptions in U.S.- and U.K.-Based Asian Mutual Funds (average monthly cash flow) U.S.-based funds (millions U.S. dollars) 350 250 150 50 A -A -50 -150 ~c ~o'c 00 o0 't I 't V% W Wf o ' c tE r- r- r- o c o0 so > D t0 sa > D > z 0 .0> b0 > - D L ct 2S 0 D s > > > 0 > D o s > 0 0 0 ) 00 0 0) 0 0 0 0) 0 0 00 0 0 0 0 Note: Positive figures are injections; negative figures are redemptions. Source: BIS 1998. 334 THE WORLD BANK ECONOMIC REVIEW, VOL. 15, NO. 2 FIGURE 7. Net Assetsand Injections and Redemptions in U.S.-Based Latin American Funds W~~~~ ------- 0.50 X I0.30 -. . --- 0.20-... 0.00 II m m- -0.30 - Ql Q2 Q3 Q4 Ql Q2 Q3 Q4 Ql Q2 Q3 Q4 Ql Q2 Q3 Q4 Ql 1995 1995 1995 1995 1996 1996 1996 1996 1997 1997 1997 1997 1998 1998 1998 1998 1999 * PercentQuarterlyInjections/Redemptions G NetAssetsin BillionsU.S. Dollars Note: All funds are open-end. The figure reports net assets and aggregate values (across funds) of quarterly injections or redemptions. Injections reflect percentage increases in thenumber of outstand- ing shares; redemptions reflect net decreases. For injections and redemptions, a value of 0.1 stands for 10 percent. For net assets (in billions of U.S. dollars)a value of 0.1 stands for $100 million. Source: Morningstar and U.S. Securities and Exchange Commission. Injections and redemptions for 13 Latin American mutual funds,22 again, part of the investors' decision set, show a pattern of inflows and outflows consistent with the broad features of the recent crises reviewed above (see figure 7). Injec- tions are measured by the percentage increase in the number of shares held by each mutual fund and redemptions by the percentage decrease, to control for fund-size changes due to capital gains and losses. Large redemptions from Latin American funds accounted for 25 percent of the outstanding shares in the first 22. The data come from Morningstar and the U.S. SEC. The sample here includes holdings of the largest 13 Latin-America equity funds (open-end) from April 1993 to January 1999 (24 quarters): Fi- delity Latin America, Morgan Stanley Dean Witter Institutional Latin America, Van Kampen Latin America (formerly Morgan Stanley), BT Investment Latin America Equity, TCW Galileo Latin America Equity, Tcw/Dean Witter Latin America Growth, Excelsior Latin America, Govett Latin America, Ivy South America, Scudder Latin America, T. Rowe Price Latin America, Merrill Lynch Latin America, and Templeton Latin America. These funds did not all exist from the beginning of our sample; on av- erage we have about 10 quarters of data (out of a possible 24) per fund. Kaminsky, Lyons, and Schbmikler 335 quarter of 1995 during the Mexican crisis. Thereafter, injections resumed to Latin American funds until the last quarter of 1997, during the Asian crisis. Redemp- tions continued during 1998, increasing during the Russian crisis, reaching 20 percent in late 1998 and early 1999. Fluctuations in injections and redemptions influence the funds' net assets, which are also determined by movements in un- derlying stock prices. The patterns in figures 6 and 7 are closely associated with those in figure 4 on average quarterly flows. During the Mexican crisis, as investors pulled out of Latin American funds, there was a large outflow from Latin American countries. Then investors and flows returned to Latin American countries until the last quarter of 1997, when the Thai crisis expanded to other countries. In Asia, there are no signs of fund outflows or investor redemptions during the Mexican cri- sis, but there are large effects during the Asian crisis. This pattern suggests that investors' decisions influence fund flows. MANAGERS. Managers cannot control the injections or redemptions of under- lying investors. What they can control is the use of cash or short-term positions (for example, U.S.Treasury bills),which help buffer portfolios from the effects of redemptions. Holding assets that are highly liquid allows managers to meet redemptions without selling less liquid assets. In principle, this can mute the volatility caused by investment outflows. However, managers can also reinforce investors' actions and amplify volatility if they increase their liquidity positions in times of investor retrenchment. In multiple-country portfolios, managers make the decision about which country to withdraw from.23 Interestingly, managers' choices about short-term positions do not change as funds experience redemptions or injections (table 5). On average, the funds in the sample hold 5 percent of their assets in liquid positions. Examining short- term positions in more detail by size of the fund shows that large funds hold a larger share of their positions in liquid assets. This finding is somewhat unex- pected because large funds are likely to have better access to bank credit lines than smaller funds and thus not to need to hold large liquid positions. Both large and small mutual funds hold smaller liquid positions in times of redemption, indicating that fund managers' behavior helps smooth the effects of investors' withdrawals on equity markets in Latin America. Bycontrast, medium-size funds hold more liquid assets in times of redemption, thus magnifying investors' with- drawals from emerging markets. 23. Investors obviously determine the withdrawal country in the case of single-country funds. There are two drawbacks to this data set. First, the data are only froml.atin American funds. In the future, it will be interesting to study thebehavior of managers by considering a broader set of mutual fund types. Second, the data do not provide a complete picture of managers' responses to liquidity squeezes be- cause information on funds' credit lines with banks is lacking. Funds facing large redemptions may have resorted to using such credit lines. 336 THE WORLD BANK ECONOMIC REVIEW, VOL. 15, NO. 2 TABLE 5. Average Short-Term Positions of U.S.-Based Latin American Funds, 1995-98 (percentage of total net assets) All times Injection times Redemption times All funds 4.44 4.57 4.37 Large funds 6.97 8.40 5.22 Medium funds 3.81 2.24 4.40 Small funds 4.16 4.48 3.61 Note: Injection times are defined as periods when the number of the fund's outstanding shares increases; redemption times as periods when the number decreases. See appendix table for list of companies in each fundsize category. Source: U.S. SEC. IV. CONCLUSIONS The increasing globalization of financial markets and the crises of the 1990s have spawned a vigorous literature on financial integration, international financial architecture, and contagion. A central element of the debate is the behavior of financial markets. In particular, many have argued that financial markets are volatile and prone to contagion. Most of the literature has focused on market imperfections and how they lead to herding behavior and financial cycles that are unrelated to market fundamentals. Though studies have covered several dimensions of foreign investors' role in emerging markets, this article provides an overview of a missing dimension- the behavior of international mutual funds. Institutional investors are the main channel of financial flows to emerging markets, and mutual funds are a large part of institutional investors. They are the only class of institutional investors for which reliable data are available on an ongoing basis. Several general findings emerged. Equity investment in emerging markets has grown rapidly in the 1990s. A significant proportion of that equity flow is chan- neled through mutual funds. Collectively, these funds are large investors and hold a sizable share of market capitalization in emerging markets. Among mutual funds, Asian and Latin American funds achieved the fastest growth. Their size remains small, however, compared with domestic U.S. funds and global funds. When investingabroad, U.S.mutual fundshold mostlyequity rather than bonds. Global funds invest mainly in developed nations (the United States, Canada, Eu- rope, and Japan), with just 10 percent of their investment devoted to Asia and Latin America. Mutual funds generally invest in a subset of countries within each region. In Latin America, they invest primarily in Brazil and Mexico, then in Ar- gentina and Chile. In Asia, the largest shares are in Hong Kong, India, Korea, Malaysia, Taiwan (China), and Thailand. In transition economies, mutual funds invest most of their assets in the Czech Republic, Hungary, Poland, and Russia (and other members of the Commonwealth of Independent States). Kaminsky, Lyons, and Schmukler 337 Mutual fund investment was veryresponsive during the crisesof the 1990s. The Mexican crisis affected mostly Latin America, and the Asian and Russian crises had a large impact on Asian and Latin American funds. These findings are consis- tent with previous findings on contagion and with reports by industry analysts. Investment by underlying investors of Asian and Latin American funds is volatile. Injections andredemptions are large relative to total funclsunder man- agement. The cash held by managers during injections and redemptions does not fluctuate significantly, soinvestors' actions are typically reflected in emerging market inflows and outflows. Many questions remain that could be addressed in future research. To test theories of financial crises, it would be valuable to examine the link between institutional investor behavior and country and market characteristics. It would also be useful to compare the behavior of different fund types-such as global, emerging market, and regional funds-to provide evidence for discussions of international financial architecture.These are areas that we arecurrently research- ing. Beyond studying institutional investors, it would also be interesting to ana- lyze the behavior of banks' proprietary trading in emerging markets. This is an area where hard evidence is almost completely lacking. APPENDIX. Data Sets and Sources Data set Source Use Description Net private capital World Bank Figure 1 Net capital flows to developing countries, including the so-called emerging economies, flows Figure 2 typically middle-income developing countries. The amounts include bank and trade- related lending, portfolio equity and bond flows, and foreign direct investment. The countries included in each region are detailed in the figures. International BIS, 68th Annual Table 1, Distribution of institutional investors between the U.S. and Europe in 1995. Monthly institutional Report Table 2, averages of cash to and from Asian funds in the United States and the United Kingdom. investors Figure 6 Size of the mutual fund industry in the United States, Japan, the United Kingdom, and France. Dedicated emerging Emerging Market Table 3, Country holdings of dedicated emerging market funds, based inside and outside the United market funds Funds Research Figure 4, States. The data are aggregate, tracking nearly 1,400 international emerging market Figure 5 equity funds, with an average position of about $120 billion in 1996. The data set covers both U.S. registered and offshore funds as well as funds registered in Luxem- 0c bourg, United Kingdom, Ireland, Cayman Islands, Canada, and Switzerland. It includes both open- and closed-end funds. Market capitalization International Table 3 Total market capitalization by country. Finance Corporation U.S. mutual funds Morningstar Table 4, Net asset value and number of U.S.-based mutual funds. The funds are divided in five Figure 3 categories by investment allocation: all funds, Asia Pacific funds, emerging market funds, Latin America funds, and world funds. Latin American Morningstar and Figure 7 Aggregate values (across funds) of quarterly injections / redemptions and the net asset mutual funds U.S. SEC values of U.S.-based Latin American mutual funds. Injections reflect percentage increases in the number of the funds' outstanding shares; redemptions reflect decreases. Short-term positions U.S. SEC Table 5 Average short-term positions (mostly in cash) held by Latin American mutual funds. Large of Latin American mutual funds are Merrill Lynch Latin America, Fidelity Latin America and Scudder funds Latin America. Medium mutual fund is TCW/Dean Witter Latin America Growth. Small mutual funds are BT Investment Latin America Equity, Excelsior Latin America, Govett Latin America, Ivy South America, Morgan Stanley Dean Witter Institutional Latin America, TCW Galileo Latin America Equity. Kaminsky, Lyons, and Schmukler 339 REFERENCES BIS(Bank for International Settlements). 1998. 68th Annual Report. Basel, Switzerland. Bekaert, Geert, and Michael Urias. 1996. "Diversification, Integration, and Emerging Market Closed-End Funds." Journal of Finance 51:835-69. Borensztein, Eduardo, and Gaston Gelos. 1999. "A Panic-Prone Pack? The Behavior of Emerging Market Mutual Funds." International Monetary Fund, Washington, D.C. Bowe, Michael, and Daniel Domuta. 1999. "Foreign Investor Behaviour and the Asian Financial Crisis." Working Paper. University of Manchester. Brown, S., W. Goetzmann, and J. Park. 1998. "Hedge Funds and the Asian Currency Crisis of 1997." NBERWorking Paper 6427. National Bureau of Economic Research, Cambridge, Mass. Calvo, Guillermo. 1998. "Capital Market Contagion and Recession: An Explanation of the Russian Virus." Working Paper. University of Maryland, College Park. Calvo, Guillermo, and Enrique Mendoza. 2000. "Rational Herd Behavior and the Glo- balization of Securities Markets." Journal of International Economics 51(1):79-113. Choe, Hyuk, Kho, Bong-Chan, and Rene Stulz. 1999. "Do Foreign Investors Destabilize Stock Markets? The Korean Experience in 1997." Jotirnal of Financial Economics 54(2):227-64. Cumby, Robert, and Jack Glen. 1990. "Evaluating the Performance of International Mutual Funds." Journal of Finance 45:497-521. Eichengreen, Barry, and Donald Mathieson. 1998. "Hedge Funds and Financial Market Dynamics." INIF,Occasional Paper No. 166. Frankel, Jeffrey, and Sergio Schmukler. 1996. "Country Fund Discounts and the Mexi- can Crisis of December 1994: Did Local Residents Turn Pessimistic Before Interna- tional Investors?" Open Economies Review 7:511-534. . 1998. "Crisis, Contagion, and Country Funds." In R. Glick (ed.), Managing Capital Flows and Exchange Rates. New York: Cambridge University Press. . 2000. "Country Funds and Asymmetric Information." International Journal of Finance and Economics 5:177-95. Froot, K., P. O'Connell, and M. Seasholes. 2001. "The Portfolio Flows of International Investors,I." Journalof FinancialEconomics59:151-93. Kaminsky, Graciela, and Carmen Reinhart. 2000. "On Crises, Contagion, and Confu- sion."Journalof InternationalEconomics51(1):145-68. Kaminsky, Graciela, Richard Lyons, and Sergio Schmukler. 2000a, "Liquidity, Fragil- ity, and Risk: The Behavior of Mutual Funds during Crises." Available online at www.worl dbank.org/research/bios/schmukler.htm. 2000b, "Managers, Investors, and Crises:Mutual Fund Strategies in Emerging Markets." World Bank PolicyResearch Working Paper 2399, Washington, D.C., and NBERWorking Paper 7855, National Bureau of EconomicResearch, Cambridge, Mass. Karolyi, Andrew. 1998. "Why Do Companies List Their Shares Abroad? A Survey on the Evidence and Its Managerial Implications." New York University Salomon Bros. Center Monograph, vol. 7, no. 1. Kodres, L., and M. Pritsker. 1999. "A Rational Expectations Model of Financial Conta- gion." International Monetary Fund, Washington, D.C. Levy Yeyati, Eduardo, and Angel Ubide. 1998. "Crises, Contagion, and the Closed-End Country Fund Puzzle." 1.MFWorking Paper 98-143. Washington, D.C. 340 THE WORLDBANKECONOMICREVIEW,VOL. 15, NO. 2 Marcis, R., S. West, and V. Leonard-Chambers. 1995. "Mutual Fund Shareholder Re- sponse to Market Disruptions." Perspective 1(1). New York Stock Exchange. 2000. Shareownership Study. Availableonlineat www.nyse. com. Pan, Ming-Shiun, Kam Cham, and David Wright. 2001. "Divergent Expectations and the Asian Financial Crisis of 1997." Journal ofFinancialResearch. Forthcoming. Rea, J., 1996. "U.S. Emerging Market Funds: Hot Money or Stable Source of Invest- ment Capital?" Perspective2(6). Smith, Katherine, and George Sofianos. 1997. "The Impact of an NYSE Listing on the Global Trading of Non-U.S. Stocks." NYSEWorking Paper No. 97-02. Van Rijckeghem, Caroline, and Beatrice Weder. 2000. "Financial Contagion:Spillovers through Banking Centers." International Monetary Fund, Washington, D.C. World Bank. 2000. Global Development Finance:Analysis and Summary Tables. Wash- ington, D.C. - . 1997. Private CapitalFlows to Developing Countries. World Bank Policy Re- search Series. Washington, D.C. Introduce YourLibrary to OXFORD THE WORLD BANK _ UNIVERSITY PRESS ECONOMIC REVIEW Paris EDITOR: FranSois Bourguignon, The World Bank, WBERisthe most widely read scholarly economic journal in the world and specializes in quantitative development policy analysis. For more information, visit our website at: www.wber.oupjournals.org If you feel that a subscription would benefit students and colleagues, photocopy this page, fill in the name and address, and Oxford University Press will send a FREE sample copy of The World Bank Economic Review without obligation! Institution*_ Librarian: Address: City: Zip:__ _ State: Country: C!104intlib/linwber ==2.e ~~~~~~~~Elsewhere: _ - ~~~~~~~~~~~~Oxford UniversityPress _XUfftA1 ~~~~~~~~Great ClarendonStreet,Oxford OX2 6DP.UK Fax:(91t9)677-1714 Tel:+44 (0) 186S26790t ;EM@.-!FW fi.QJj f :x: -MMA-1g. ~~~~E-mail: jn1.orders@otip.co.uk Journalsin EconomicsfroM OXFORD UNIVERSITY PlRESS Jouirnal of Intermational Econo,nii Laiw c ,trb ~ tu redqto oudgir rkaJughltaidandw snclha:enrun. l _ -to Lhereham .n c.lLatvro,Lntean mceon. nTucacmV a S _ i A_iwww.cj ielpoupjournals.org oContt O'tfor timpormni Econor i R-A. 1,u nmL h'mEic:itinzc % 31 LesI n' icn mrn ai i'mn a, C- . a C atr,buti° WcLi-, .4pieheconomicandarna'mcmnitnwwlop L.oupourn oldsi5d No po\rnva.cep.oupjoul -n CoeRtrileeftioncs to Politacnl Economy A\Ilim I r 3dta I i rric Urambin olongeenrhIeorer. and nrgnmlrn tas siue . \ rromhn,ks |f thousgh aioidC erK 1t3,J-t -. , Ih \ cO.-IllmjliMJIAILKuer- and%ir:ma Ectngonzis~~~~~~~~' Inqui Swap 1{ssp W%vpeoupiournals.o.rg .oupjournals.org reh m:- -x-Lrs ~m . tr, fihe -,S. - or eapnn ar. ; ..)% 4 - al TeI:(9i9)67rr Renoal est3ilEcon b daji ppn. d ccose omSo 1,-Lrnl o e -il pu nhomira ind ro-noIka rywir- * s -4()8568 z- .- IIIIiYW OkforfEconoic w-.vv.oeproupoupj)rna1s.org PIper 1.1.1ir \e c cn,sic.> .ao * lI n InvLt-.L a. Q'.L2D 4 b (91)wel: u6pjournals4 O)186o2648 I _ Coming in the next issueof THE WORLD BANK ECONOMIC REVIEW Volume 15, Number 3, 2001 * Capital Account Liberalization: What Do Cross-Country Studies Tell Us? BarryEichengreen * Where Has All the Education Gone? Lant Pritchett * Measuring the Dynamic Gains from Trade Romain Wacziarg * Ownership and Growth ThorvaldurGy/fason,Tryggvi ThorHerbertsson,and Gyfi Zoega * Infrastructure, Geographical Disadvantage, Transport Costs, and Trade Nuno Limdo andAnthonyJ Venables * Deposit Insurance around the World: A Database As/i Demirgiuf-Kuntand TolgaSobaci TlWE WORLD BANK 1818 Il Strect, NWV Washint-ton, DC 20433, USA NVorld WVide \Veb: http)://Nw\vwv.vorldbanki.orgr/ E-mail: kvbcravworldhank.orgr 13 0 PREMH#NGToND o 78011 19 8031 3 86 5 WASHING-195 DC 0 ISBN 0-1985-0907-3