the logo after 1 em space; see diagram B), or under the logo the right of the logo (centered vertically along the height of (the space between the logo and the words "THE WORLD the logo after 1 em space; see diagram B), or under the logo BANK" should be the same as the cap height of the words, (the space between the logo and the words "THE WORLD aligned flush left; see diagram C). When the logo is placed 46269 BANK" should be the same as the cap height of the words, on aalignedorflush dark black background, the logo should reverse to left; see diagram C). When the logo is placed whiteon(see diagram D). a dark or black background, the logo should reverse to PRMED Knowledge Brief white (see diagram D). 2. The words "THE WORLD BANK" should be set in ALL HumanIncomeCAPS,and Economic Growth CapitalConvergence 2. The words "THE WORLD BANK" should be set in ALL Univers Bold. The size of the type in relation to the logoCAPS, remainBold. shouldUnivers constant. Always use the art provided in The size of the type in relation to the an electronic file or in CRC. logo should remain constant. Always use the art provided in Jes´us Crespo Cuaresma Jesús Crespo Cuaresma Department of Economics, University of Innsbruck, Austria an electronic file or in CRC. Department of Economics, University of Innsbruck, Austria jesus.crespo-cuaresma@uibk.ac.at jesus.crespo-cuaresma@uibk.ac.at Placement of Logo Placement of Logo All World Bank books must display the World Bank logo on All World Bank books must display the World Bank logo on The Solow model of economic growth (Solow, 1956, Swan, 1956) concludes that poorer countries will The positive relationship between years of education and income at the individual level is a well the front and back covers, the spine, and the title page. the front and back covers, the spine, and the title page. tend toestablished empiricalricher ones--provided that countriesofshare the same production function, grow faster than relationship. Decades of estimations Mincerian wage regressions have lead savingstorate and population growth, and labour-augmenting technology grows at the same rate in a plethora of estimates of the elasticitycovercover to additional years of educational attainment. FrontFront of wages all countries. The existence of income convergence has thus been usually taken to be a test of At the macroeconomic level, however, nding a robust empirical relationship between measures of On the front cover, the logo should be placed at either the On the front cover, the logo should be placed at either the exogenous growth model versus endogenous growth models--that do not necessarily conclude on the educational attainment and long-runlowerlower growth turns out to be an extremely dicult task. economicor or upper left corner and should be accompanied by the upper left corner and should be accompanied by the This note summarizes the eorts of the recent literature on the macroeconomic relationship between words "THE WORLD BANK." Placement of the World Bank words "THE WORLD BANK." Placement of the World Bank existence of convergence in income per capita among economies. Here we describe different concepts education and long-run economic growth. logo logo blockthe front cover should bebe as follows:the outside block on on the front cover should as follows: the outside of convergence used in the empirical literature edgeeconomic growth and summarize the results of this edge onthe logo (the outer box) should be between 2.25 picas of of the logo (the outer box) should be between 2.25 picas literature. (3/8 inch) and 3.75 picas (5/8 inch) from the trim. The logo (3/8 inch) and 3.75 picas (5/8 inch) from the trim. The logo should be placed equidistant from both trim and spine. See should be placed equidistant from both trim and spine. See Theoretical setting(s) samples on next page. samples on next page. The Solow model and incomeWorld Human capital as an input ofTheproduction The World Bank logo is the only logo to appear on front covers convergence Bank logo is the only logo to appear on front covers and spines of publications published by EXTOP. Any exception and spines of publications published by EXTOP. Any exception Total output (Y ) is assumed to depend on physical capital (Kt), labour input (Lt) and (labour- to this guideline needs to be approved by the publisher. Mankiw ett alia (1992) present a straightforward generalization of the Solow model of economic to this guideline needs to be approved by the publisher. Additional logos (for cosponsors or copublishers) appear at the augmenting) technology (At) accordingAdditional growth including human capital as anbottomlogos to a Cobb-Douglas production function with costant extra production factor, which is able to account for of the back cover, along with the World Bank logo. (for cosponsors or copublishers) appear at the returnslarger cross-country dierences in income emmanating from dierences in investment rates than to scale on all inputs, bottom of the back cover, along with the World Bank logo. the basic Solow model. Using aYsimple Cobb-Douglas production function, total output (Yt) t = Kt (AtLt)1 - , where (0,1). Labour input and technology are assumed to grow at constant rates n and g, is assumed to depend on physical capital (Kt), human capital (Ht), labour input (Lt) and respectively. Physical capital is accumulated through savings ,(with a constant savings rate s) technology (At), and depreciates at a constant rate , Yt = Kt Ht (AtLt)1 -- where + < 1, (0,1) anddKt=(0,1)=Labour input and technology are assumed to grow . at constant rates n and g, respectively.KPhysical and human capital evolve according to dt t (1) We can write (1) in terms of effective labour=dKt sYt - Kt. dt asK t = skYt - Kt (1) and kt = sytt-=(Ht+=s+Yg)-ktHt, dH n , (2) dt h t (2) where kwhereKstk/(isAthe)savingsy rateYton(Aphysical capital, shsteady state level ofascapital per unit of t = t t L and = / t t L ) = kt . The can be interpreted the savings rate on effectivehuman capitalcanas the proportion of input 0, whichthe human capital production function labour (k) or be found by setting kt = used in leads to (human capital is assumed to be produced with the same technology as output) and is the depreciation rate of physical and human capital. In terms of eective labour, we can write(3) s(k) = (n + + g)k. (1) Graphically, the equilibrium level of k is given by the intersection point of the investment per and (2) as unit of effective labour curve, s(k), with the break-even investment line, [(n++g)k], as shown (3) in Figure 1.1 Countries with levels of capital per tunit of effectivet labour below k (see k1 in Fig- ure 1) present positive growth in the stock of capital per unit of effective labour (see (2)), while h t = shy - (n + + g)h , kt = skyt - (n + + g)kt, (4) where ht = Ht/[AtLt], kt = Kt/[AtLt] and y = Yt/[AtLt] = kt ht . This implies that the steady countries to the right of k will tend to decrease their stock of capital per unit of effective labour. state level of capital and human capital per unit of eective labour is given by the solution to kt = 0 and h t = 0. Denoting equilibrium variables with an asterisk, Log-linearizing around the steady state level of incomeper unit of effective labour, ln y = ln k + ln h = + ln(n + + g). dln(yt) 1 - - dt = [ln(y) 1--ln(yt)], ln sk + - ln sh - 1 - - (4) 1 1The break-even investment line represents the investment needed to avoid the capital stock from falling. lny = lnk + lnh = + 1 - - lnsk + 1 - - lnsh - 1 - - ln(n + + g). This expression nests the results for the standard Solow model (without human capital) for This expression nests the results for the standard Solow model (without human capital) for = 0. Notice the value of the elasticity of income to (physical capital) savings,11-- = 0. Notice the value of the elasticity of income to (physical capital) savings, > . - Using the data in Mankiw et alia (1992) for 106 countries in the period 1965-1985,-Figure 1 >11- Using the data in Mankiw et alia (1992) for 106 countries in the period 1965-1985, Figure 1 - . presents the scatterplot of per capita income (after controlling for investment and population presents the scatterplot of per capita (after controlling for investment and population growth) against schooling rates of the working age population (after controlling for investment growth) against schooling rates of population (after controlling for investment and population growth) and income growth andschooling (where initial income isisalso controlled and population growth) and income oling (where initial income also controlled for), which clearly shows a positive and signicant relationship between both variables and the for), which clearly shows a positive significant relationship between both variables and the schooling measure. schooling measure. Figure 1: Income and income growth versus schooling: Mankiw et alia (1992) data Figure 1: Income and income growth versus schooling: Mankiw et alia (1992) data 4 1.2 3 0.8 2 0.4 (residuals) (residuals) 1 0.0 growth 0 -0.4 Income -1 Income -0.8 -2 -1.2 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -1.6 -1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 Schooling (residuals) Schooling (residuals) Human capital as a determinant of technology adoption Human capital as a determinant of technology adoption The model with human capital as an input of production hypothesizes level eects of human The model with human capital as an input of production hypothesizes level effects of human capital on GDP per capita. Education, however, has long been considered a determinant of capital on GDP per capita. Education, however, has long been considered a determinant of technology adoption/innovation (the so-called Nelson-Phelps hypothesis, Nelson and Phelps, technology adoption/innovation (the so-called Nelson-Phelps hypothesis, Nelson and Phelps, 1966). This can be modelled by including a specication for technology such as (Benhabib and 1966). This can be modelled by including a specification for technology such as (Benhabib and Spiegel, 1994), Spiegel, 1994), Att A = g(Ht) + c(Ht) = g(Ht) + c(Ht) Aft Aft At At At At -1 , -1 , where Aft is the level of technology of the leading country (technology frontier) and g(·) and c(·) are assumed to be linear functions proxying the innovation and diffusion process of technology, where Aft is the level of technology of the leading country (technology frontier) and g(·) and c(·) are assumed to be linear functions proxying the innovation and diusion process of technology, respectively. Benhabib and Spiegel (1994) consider two alternative production functions, one respectively. Benhabib and Spiegel (1994) consider two alternative production functions, one where human capital is a standard production input, where human capital is a standard production input, Yt = AtKtt Htt Ltt , Yt = AtKHL, and one where human capital determines technology diusion, and one where human capital determines technology diffusion, At At Aft YYtt= AtKttLtt, = AtKL, = g(Ht) + c(Ht) = g(Ht) + c(Ht) , , At At At Aft--11 At which imply the following models for the growth rate of GDP: which imply the following models for the growth rate of GDP: YYtt At = = At + K + H + L , Ktt Htt Ltt YYtt At At + K + H + LLtt, Ktt Htt and Yt 2 = g(Ht) + c(Ht) Aft Yt At -1 +Kt +Lt. Kt Lt Table 1 presents OLS estimates of alternative models (including the two above) for the data of Benhabib and Spiegel (1994), which uses the data on average years of schooling by Kyriacou 2 (1991) as a proxy for human capital. The results in Table 1 show that, in this dataset, changes in averages years of schooling are not positively related to economic growth, while there is evidence of human capital aecting technology diusion and innovation. Table 1: Model estimates: Benhabib and Spiegel (1994) data (1) (2) (3) (4) (5) (6) K t/Kt 0.46 (5.36) 0.50 (5.01) 0.54 (8.31) 0.50 (5.01) 0.49 (6.50) 0.44 (4.23) H t/Ht 0.06 (0.80) -0.06 (-1.02) Lt/Lt 0.21 (1.01) 0.11 (0.52) 0.13 (0.79) 0.11 (0.52) 0.27 (1.62) 0.17 (0.77) Ht -0.10 (-1.48) -0.10 (-1.48) 0.16 (2.32) 0.38 (2.91) 0.04 (3.31) (Aft/At - 1) Ht (Aft/At - 1) 0.19 (5.26) 0.24 (5.43) R2/Obs. 0.52/78 0.53/78 0.68/78 0.53/78 0.69/78 0.62/78 Robust t-statistics in parenthesis. Education data: Problems and solutions The striking lack of empirical relationship between changes in years of education and subsequent economic growth has led to a number of studies trying to assess the problem by improving the available data on education measures. While Temple (1999) claims that the lack of relationship may be due to outliers, most of the literature attributes the existence of the puzzle to deciencies in the human capital data (see Krueger and Lindahl 2001, De la Fuente and Domenech, 2006, or Cohen and Soto 2007). Crespo Cuaresma (2005) analyzes the evolution of (the second moment of) the distribution of educational attainment across OECD countries and nds enormous dierences depending on the dataset used. In particular, the three datasets analyzed (Barro-Lee, Cohen-Soto and De la Fuente-Domenech) provide contradictory conclusions on the existence and evolution of convergence of educational attainment across industrialized countries. The issue is of special relevance, since convergence in schooling levels has been usually claimed to be partly responsible for the convergence process in labour productivity across OECD countries. Recently, Lutz et alia (2008) present a new dataset of educational attainment by ve-year age groups for 120 countries for the period 1970-2000 (see also Lutz et alia, 2007, for a techni- cal discussion of the reconstruction exercise). The dataset is reconstructed using demographic methods to back-project the population by four levels of educational attainment and sex along cohort lines. Unlike earlier reconstruction eorts, these data also incorporate the fact that peo- ple with dierent levels of education tend to have dierent mortality rates. While some studies show evidence of signicant eects of the demographic structure of the working age population on economic growth (see for example Lindh and Malmberg, 1999), the existing data was not able to disentangle quantity eects (from non-education related productivity dierentials across age groups) from quality eects (from education-related dierences aecting productivity and technology adoption/innovation). Lutz et alia (2008) show that considering dierences in hu- man capital across age groups is highly important in order to assess the eect of education on economic growth. In particular, Lutz et alia (2008) show that secondary education of the older age groups and tertiary education of younger age groups tend to be important for technology adoption and innovation. 3 Education quality and economic growth The quality of schooling can be considered as important as the quantity, measured, for instance, by years of attainment. Although comparable cross-country data on international test scores are only available for a limited number of countries, some studies have been able to establish a positive relationship between quality of schooling and income growth. Hanushek and Kimko (2000) and Barro (2001) nd that scores on international examinations have quantitatively bigger eects on economic growth than years of attainment. This eect is more relevant for scores in science examinations. References [1] Barro (2001), Human capital and growth. American Economic Review, Papers and Proceedings , 91, 12-17. [2] Benhabib, J. and M. Spiegel (1994), The role of human capital in economic development: Evidence from aggregate cross-country data. Journal of Monetary Economics , 34, 143-173. [3] Cohen D. and M. Soto (2007), Growth and human capital: good data, good results, Journal of Economic Growth ,12, 51-76. [4] Crespo Cuaresma, J. (2005), Convergence of educational attainment levels in the OECD: More data, more problems?, Economics of Education Review , 25, 173-178. [5] De la Fuente, A. and R. Domenech (2006), Human capital in growth regressions: How much dier- ence does data quality make? Journal of the European Economic Association , 4, 1-36. [6] Hanushek, E. and D. Kimko (2000), Schooling, labor-force quality, and the growth of nations. American Economic Review , 90, 11841208. [7] Krueger, A. and M. Lindahl (2001), Education for growth: Why for whom? Journal of Economic Literature, 39, 1101-1136. [8] Kyriacou, G. (1991), Level and growth eects of human capital, A cross-country study of the convergence hypothesis. New York: New York University, Mimeo. [9] Lindh, T. and B. Malmberg (1999), Age structure eects and growth in the OECD, 1950-1990. Journal of Population Economics , 12, 431-449. [10] Lutz, W., A. Goujon, S. K.C., and W. Sanderson (2007), Reconstruction of populations by age, sex and level of educational attainment for 120 countries for 1970-2000. IIASA Interim Report IR-07-002. Laxenburg, Austria: International Institute for Applied Systems Analysis. [11] Lutz, W., Crespo Cuaresma, J. and W. Sanderson (2008), The demography of educational attain- ment and economic growth. Science, 319, 1047-1048. [12] Mankiw, N.G., D. Romer and D.N. Weil (1992), A contribution to the empirics of economic growth. Quarterly Journal of Economics , 107, 407-37. [13] Nelson, R. and E. Phelps (1966), Investment in humans, technological diusion, and economic growth. American Economic Review, Papers and Proceedings , 56, 69- 75. [14] Temple, J. (1999), A positive eect of human capital on growth. Economics Letters , 65, 131-134. 4