IMPORT DEMAND ELASTICITIES: ESTIMATES AND DETERMINANTS Lant Pritchett Division Working Paper No. 1987-4 February 1987 Country Analysis and Projections Division Economic Analysis and Projections Department The World Bank Division Working Papers report on work in progress and are circulated for Bank staff use to stimulate discussion and comment. The World Bank does not accept responsibility for the views expressed herein which are those of the author(s) and should not be attributed to the World Bank or to its affiliated organizatiQns. The findings, interpretations, and conclusions are the results of research supported by the Bank; they do not necessarily represent official policy of the Bank. The designations employed, the presentation of material, and any maps used in this document are solely for the convenience of the reader and do not imply the expression of any opinion whatsoever on the part of the World Bank or its affiliates concerning the legal status of any country, territory, city, area, or of its authorities, or concerning the delimitation of its boundaries, or national affiliation. Division Working Paper 1987-4 February 1987 IMPORT DEMAND ELASTICITIES: ESTIMATES AND DETERMINANTS* LANT PRITCHETT Country Analysis and Projections Division Economic Analysis and Projections Department Economics and Research Staff, World Bank I would like to thank Riccardo Faini, Fernando Clavijo, Fahrettin Yagci, E.C. Hwa and the participants in an EPDCO Seminar for helpful comments on an earlier draft. Summary This paper reports the results of the estimation and testing of traditional import demand equations for fifty developing countries. Specification tests are reported and price and income elasticity estimates are reported for thirty countries. It is found that the income elasticities are generally precisely estimated and substantially greater than one. The price elasticities are significant but usually less than unity. The second part of the paper examines the variation of the estimated elasticities with respect to certain characteristics of the countries. A country's per capita income, size, and share of trade in total output ate found to be important d-eterminants of its import elasticities. The countries' income elasticities increase with increasing income from low levels of per capita income up to about 2800$ per capita then decrease at higher incomes. Price elasticity increases significantly with a higher trade share for a given income and size. TABLE OF CONTENTS Page No; Part I .......... **............................ . ..........1 The Estimation ...........................10 . . 2 The RCocusl ..... ..*.....e. - ... ...600**0000 .... g....3 Part II .......g... ........ .............e eee............. .........86 Income Elasticity.. . e.................- .. g... g ............... 7-9 Price Elasticity.e . ..e.e.e............e.e.....eee- .. g ..e. -10 Conclusion .. ......... *........ ev*o..... o... * .... e-vre13 Table 2b.................... * . *................ 1 -5 Table la ndi .1-....... ....... . .. . . . ... .. o......e.e..14. 6 Table lbThe Da.............e............e ........................ 7 Figure.2a *The Spcfc o.. ............................... o.- e.. 11 Figure 2bndx T . 1....o.........e e ...e *..e.e.o.Ie..e...... . 16 Appendix Table 1.. ... ..... ....... ........ -14 Ap The Datable1 .2.......... - ........e ..... o............. .14 B. Th e Specification .................................. . 2914 Appendix Table 2................................ . Appendix Table sn ................... * ........................517 Appendix TabLe 1.2..... e* .............. evv*.ee -1l Appendix Table 1.3 ........ o..........****@*c4 Appendix 2 .......... . o ........ ........ ............... .......35 A. The Testing, ....... ....... o ... . . . . . .. - . .-35 I. Residual Serial Correlation .................. 35 II. Stability.. ............................e e ee35 III. Homogeneity... .. . o .......................... 36 Appendix 3 ......... o.... ....... e-...e...................... .37 Appendix Table 3.1. . e..e.........................e..... e .... 39 Appendix Table 3.2......eg...... o..... . o*eo .... .............. -40 Appendix Table 3.3 eg........................................ 41 Bibliography ........................4 2........ 42 Part I In the formulation of trade policy, an accurate knowledge of the response of imports and exports to incame, relative price and policy changes is important. Therefore, the specification, econometric estimation and testing of import demand, export demand and export supply functions, is an important component of the formulation of any policy model. This paper deals with two aspects of the overall goal. First, the estimation and testing of a traditional import demand function for a broad cross section of developing countries, and secondly, the investigation of the structural determinants of the elasticities. We find that both income and price elasticities are affected both by structural changes and policy actions. In most developing countries, the government plays a large role in the determination of the level and the composition of imports. The instruments used to control' the aggregate level of imports include quantitative restrictions, licensing, prohibitive lists, as well as various types of foreign exchange controls. The impact of these controls is often difficult to assess and almost impossible to boil down into a single quantitative measure that could be used in a regression framework. (For attempts in that direction see Bertola and Faini, 1986, on Moroccan imports and Faini and Pritchett, 1986, on Turkish imports). However, estimation that ignores these government controls is subject to the Lucas critique (Lucas, 1976) that the resulting parameters are not invariant with respect to changes in government policy. In other words, a liberalization of trade would cause a change in the observed elasticities of import demand. The approach pursued in -2- this paper is to first recover the historically stable responsiveness of imports to income and relative price changes and address to issue of government policy in a second stage. The Estimation For each of fifty countries the following equation was estimated: 2 2 Mt O+ iyoit-.i+ 6i it-i+ mt-l it i=0 i=0 where all variables are in logarithims and mt : quantity of imports Yt e income (GNP) in constant prices Pt : relative price of imports. The data used and the choice of specification is discussed in Appendix 1. Each of these. equations was then subjected to a battery of tests of mis-specification. These tests attempted to identify these countries for which stable, accurate estimates could be attained. The tests were of three types. The residuals were tested for serial correlation. As noted in Khan (1974) if the stringency of government control over imports is serially correlated then exclusion of these government controls in a regression would induce serial correlation in the residuals. Secondly, each country's equation was tested for stability. If the government control of imports had undergone a shift during the estimation period then this is one factor that could induce instability in the estimated equation. Finally equations were tested for homogeneity of prices. Certain types of import that controls depend -3- on foreign exchange prevent crnsumers from responding symmetrically to changes in the relative price of imports coming through import price increases or domestic price decreases. The statistical properties of the tests as well as a more complete specification of the null hypotheses tested can be found in Appendix 2. The R:sults Thirty of the fifty countries estimated had regressions which were broadly acceptable and from which the resulting parameters can be taken as historically stable indicators of the responsiveness of imports to income and relative prices. A listing of which countries passed which set of tests in Appendix Table 1.1; the results of all the tests for each country can be found in Appendix Table 1.2 and in Appendix Table 1.3 is shown the lag structure of prices and income for each country. Table One shows each countries income and price e elasticities. In Figure la we see the. distribution of price elasticitics for the thirty countries with each country identified by a three letter abbreviation with its the standard error in parenthesis. The income elasticities are displayed in Figure lb. The estimated income elasticities were usually precisely estimated and generally quite high. The mean of the thirty country sample was 1.4. Only two countries had income elasticities significantly less than one whereas 13 of the thirty countries had income elasticities significantly greater than one.. Price elasticities were generally less precisely estimated. The average price elasticity was -.63, a substantial responsiveness, but well below one. Several general features of the results are worth emphasizing. First import determination in the countries which failed -4- the tests is by no means uninteresting, it is just that government behavior will have to be explicitly incorporated into the analysis to recover usable estimates. Extension of the import model to include exchange rationing along the lines of Hemphill (Hemphill, 1974) or Moran (Moran, 1986) might prove interesting. Secondly, a common practice in macro models at the Bank and elsewhere, is to calculate imports as a constant percentage of income and ignore relative prices. The joint hypothesis of unit income and zero price elasticity that is implied by this approach was tested. This procedure could be statistically rejected as a model of import determination for 21 of 30 countries. Thirdly, although prices do matter, elasticities are not large. Twelve of 30 had price elasticities significantly different from zero. However, only two countries had price elasticities significantly greater than one whereas nine were -significantly less than one. Most were in the zero to one range that indicates the price responsiveness is present and significant but not large. We then carried the results and estimated parameters for these 30 countries to a next stage where we investigate the determinants of the elasticities themselves. -5- Table 1 Country Price Elasticity (Std-error) Income Elasticity Latin American and Caribbean Argentina -2.1 (.67) 2.56 (.63) Bolivia -.44 (.21) 1.11 (.102) Brazil -1.1 (2.1) .63 (.88) Chile -.32 (.12) 2.21 (.16) Colombia -.52 (.35) 1.25 (.08 Paraguay -.56 (.45) 1.42 (.36) Peru -.40 (.20) 1.66 (.17) Uruguay -.35 (.17) 2.12 (.15) Honduras 1.2 (1.2) 1.08 (.29) Jamaica -.18 (.16) 1.12 (.24) Asia Bangladesh -.36 (.12) 1.52 (.17) India .74 (.55) 1.05 (.39) Indonesia -1.5 (1.1) 1.02 (.92) Korea -.22 (.54) 1.50 (.16) Malaysia -2.3 (1.7) 1.67 (.37) Pakistan -.48 (.08) .76 (.135) Philippines -.56 (.34) 1.2 (.2) Thailand -.67 (.23) 1.25 (.086) Middle East and North Africa Israel -.66 (.22) 1.43 (.05) Morocco -.42 (.43) 1.38 (.24) Syria .43 (.38) 1.44 (.07) Tunisia -.25 (2.08) 1.43 (.39) Sub-Saharan Africa Benin -1.6 (1.4) 2.9 (.25) E.A.F. -1.87 (.26) .57 (.10) Gabon -1.23 (..) 1.49 (..) Gambia .002(1.2) .9 (.53) Kenya -1.48 (.34) 1.37 (.26) Zambia -1.14 (.123) .78 (.28) Southern Europe Greece .013 (.34) 1.37 (.07) Yugoslavia -.74 (.85) .86 )(.43) -6- Table la: Price Elasticities (30 Countries) MAR -.42 (.43) BGD PAK PHL -.36 -.48 -.561 (.12) (.08) (.84) .-- --- ----------------- --- --------------------- -------------------------- -- ------- --- --- ---------------------------------- ------ ------------ ----------- IND GRC TUN URY PER PRY ISR ZMB .74 .013 -.25 -.35 -.4 -.56 -.66 -1.14 (.55) (.34) (2.08) (.17) (.20) (.45) (.22) (.123) ------------------------ ------------------------------------------------- -------------------------------- --------------------------------. HND SYR GMB JAM KOR CHL BOL COL THA YUG BRA GAB KEN IDN BEN CAF ARG MYS 1.2 .43 .002 -.18 -.22 -.32 -.438 -.52 -.67 -.74 -1.11 -1.23 -1.46 -1.5 -1.6 -1.87 -2.1 -2.3 (1.16) (.36) (1.2) (.16) (.54) (.117) (.208) (.35) (.23) (.85)' (2.1) (.59) (.34) (1.1) (.4) (.26) (.67) (1.7) ------------------------------------------------------------------------------------------------------------------------ -------------------------------- <.4 .3 .2 .1 0 -.1 -.2 -.3 -.4 -.5 -.6 -.7 -.8 -.9 -1 1.1 1.2 1.3 >1.4 --------------------------------------------------------------------------------------------------------------------------------------------------------- -7- Table lb: Income Elasticities (30 Countries) SYR 1.44 (.07) ISR 1.43 (.05) IND THA GRC 1.05 1.85 1.37 (.39) (.086) (.09) ZMB IDN JAM PAK KEN TUN BGD MYS .78 1.02 1.107 1.2 1.37 1.43 1.52 1.67 (.28) (.92) (.24) (2) (.26) (.39) (.17) (.34) CAF BRA PAK YUG GMB HND BOL COL MAR PER KOR PRY URY CHL ARG BEN .57 .63 .75 .86 .90 1.05 1.11 1.25 1.38 1.42 1.5 1.46 2.89 2.21 2.56 2.9 (.10) (.88) (.135) (.43) (.52) (.89) (.102) (.089) (.24) (.36) (.16) (.168) (.15) (.166)' (.63) (.247) .6 .7 .8 .9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 -8 Part II Previous studies have shown that countries of similar size and income levels to also show other similar economic features. Both the sectoral composition of production (Chenery and Syrquin, 1975) as well as trade patterns (McCarthy, Taylor and Alikhani, 1984) have been shown to be systematically related to per capita income and population levels. In this study we investigate import responsiveness and its relation to three country characteristics; per capita income, population and trade openness, as measured by the share of imports and exports in total output. The main interests of this type of study are twofold. First, we establish a standard elasticity for countries of similar characteristics. Secondly, the openness variable gives an indication of the direction and magnitude of changes in import responsiveness as a country becomes more open at given income and population levels, as might be brought about through a liberal policy towards trade. In effect this is a backhanded response to the Lucas critique. Even though we could not directly observe the impact of government policy on import determination we can observe the effect of different openness levels on elasticities. For our sample of thirty countries we perform the following regression for the price elasticities (E) A ° 1RPCYi+ A2RPCYDd.+ A3POPNi+ A4SHRTRDi+ i -9- where: RPCY all per capita income in 1980 $. RFCYSd = square of real per capita income POPN = 1980 population in millions - - SHRTRD = imports + exports GNP and a similar regression for income elasticities. Since each observation (Ce, n) was created by a previous regression we also had an estimate of its standard error which was used to correct for heteroskedasticity. Income Elasticity The results of the regression on income elasticities were (t statistics in pareni..Lasis): A 7 r.= .72 + .0075 RPCY + (1.33 x 10 ) RPCYSA ' (3.09) (3.47) (-3.16) + .004 POPN - .0004 * SHRTRD (.31) (-.018) .t2= .954 DW = 2.5 SER - 2.26 As can be seen value this equation has surprisingly good fit for a cross section regression of this type. The joint F-test for inclusion of the poptalation and opennes's terms' is .055 so we may confidently conclude they play no tole in the determination of income elasticities. Per capita incom' is very important. Income elasticity first increases with per capita incoie up to income levels of 2800 $ then decreases with per c.apita income increases beyond thaI point. The pattern of predicted values is shown in Figure 2a. I~ I. -, , - -' A - - - - - - 10 - Price Elasticity The results for the price elasticity were leil = .65 - (.00054)RPCY.+ (8.53 x 10 )RPCYSd+ (.79) SHRTRD (3.32) (2.74) (1O9) 2. 58 (.79) -(.0002) * POPN (1.61) R -79 DW = 1.91 SER= 1.49 This regression also has quite good fit considering the cross section nature sample and -how few variables were included. Price elasticity (referring to absolute values) falls as income increases up to point and increases thereafter. Price elasticity is higher, the greater to openness of the economy. A ten percent rise in trade share (at the means of all variables) give rise to a 7% increase in the price elasticity. This indicates that as a country pursues a more outward oriented trade policy that increases its trade share then elasticitie-s, price responsiveness, will also increase. In the case of a trade liberalization the post- libralization trade elasticities would tend to be underestimated by the historically estimated elasticities that ignored the government control over imports. Three empirical relationships are established by these regressions. An inverted U shaped response of income elasticity to per capita income, a U shaped response of price elasticity to per capita income, and a positive relationship between price elasticity and a countries openness. What would explain these patterns? A positive relationship between price responsiveness and a higherishare in trade is to be expected. Government report control mechanisms tend to reduce Figure 2a Responses of Income Elasticity to Per Capita Income I ncome Elasticity 2.1 URY (2.12) 1.8 KOR 1.5 1.5 THA 1.2 *' ( 1 .25) R SYR /O( t.44) .9. GRC (1.37) PAK (.76) .3 >RPCY W190 I I T 19805 300 1 300 2!800 4500 Figure 2b Response of Price elasti'city to Per Capita Income (at means of other variables) Phfci BEN Elasticity (1.6) 1.2 ZMB 1 < (1.14) .8 PRY (.56) iSR .6 MR (.66) (.42) .4 % URY .2 I I I80 300 1300 3100 4500 - 12 - import responsiveness. Therefore higher trade share, for a given level of income and size, may indicate a more liberal trade response, one that allows more adjustment of imports to income and telative price shifts. The pattern of income elasticities first rising then falling with per capita income may be explained by sectoral differences imports and production at different income levels. At very low levels of income imports may consist of food and other necessary intermediates which have less than unit elasticity. At higher income levels more sophisticated investment and intermediate inputs are imported, goods with higher elasticities. This is similar to the CEPAL explanation of high (greater than unit) income elasticity of imports for import substituting countries due to the multiplier effect of imports of capital goods (see Rodriquez, 1980). Another possible explanation depends on differences in consumption patterns as income grows. At low levels of income high income elasticity goods are neither produced nor consumed. At middle levels of income high elasticity goods are imported, they are consumed but not produced. Finally as an economy matures the production structure matches the 3onsumption structure and high elasticity goods are domestically produced, lowering their share in imports. The explanation of the relationship between price elasticities and per capita income is tentative. At low income levels countries import only non-competing imports and are constrained by goven amount of available foreign exchange and they are not free to borrow. Therefore they are forced to be at least unit elastic with respect to a change in foreign (dollar) import prices since the total amount spent is constrained. At higher per capita income levels countries may borrow more freely and therefore are less elastic, as they no longer are forced - 13 - to maintain total foreign exchange spent constant in the lack of import price increases. But at middle per capita income levels countries import price inelastic goods as they are not domestic substitutes. At high per capita income levels countries both may borrow and lend and produce a broader range of goods as import substitutes, this leads to higher price elasticity. Conclusion This paper has reported import demand elasticity estimates for 30 countries. Income elasticities in these countries tend to be greater than one where price elasticities tend to fall between zero and one. A second part of the paper showed that variation in income elasticities were explained by differences in per capita income. Also price elasticity increases significantly with an increasing trade share of a given level of income and population. r f9. Appendix 1 A) The Data I. The income or activity variable used was GDP measured in local currency constant prices as extracted from the BESD database at the World Bank. The terms of trade adjusted measure GNY was also tried but led to no significant improvements. II. The imports data for the regressions in the text was imports of goods and non-factor services in local currency constant prices available in the BESD database. Regressions were also preformed using imports taken from the IMF Balance of Payments and deflated to constant values by a dollar price deflator described below. These results are discussed in Appendix 3. III. The relative price measure used for the regressions in the text was the rati,o of the National Accounts deflators for imports and GNP. This has some risks as the data are country reported with no check on methodology or accuracy. Therefore all the regressions were also run using a dollar import price deflator constructed directly from commodity prices and a manufacturing unit value index (See Moran and Park, 1986). The results were remarkably similar and are discussed and compared in Appendix 3. B) The Specification The partial adjustment model is a common way of dealing with a variable that responds only with a lag to changes in its determinants. This leads to inclusion with only a lagged dependent variable. However in our case we introduced lags in the independent variables (prices and income) as well as the lagged dependent. This was done for three reasons, first for a significant portion of the countries we could - 15 - reject the null hypotheses of joint exclusion of the lagged values of the independent variables. Secondly, we were only interested in the long run elasticities, not the lag pattern. The problems of the precise estimation of individual coefficients therefore were not an issue. Lastly, in order to make the results comparable across countries we used exactly the same specification and so used the most general lag structure feasible. - 16 - Appendix Table 1: Country Regressions and Tests Passed All Passed All But Passed All But Failed Chow (73) Failed Too Tests At 10% Hendry 1% Hendry 1%, and Hendry Many (Hendry 1%) Short-run Homogeneity ---------------------------------------------------------------------------------------------------- Chile (Post 73) Argentina (66-84) Bolivia (63-81) Mexico Ecuador ------------------------ ------------------------------------------------------------------ Peru Brazil Paraguay Costa Rica Venezuela ------------------------------------------------------------,-----------------,,----------------------- Jamaica Colombia Uruguay Libya Dom. Republic --------------------------------------------------------------,,,,,------------------------------------- Honduras Morocco * Phil-ippines Nigeria El Salvador --------------------------------------------------------------------------X-------------------------- Korea Thailand Ghana Panama ---------------------------------------------------------------------------------------------------- Malaypia Kenya * CIV Egypt -------s-------------------------------------------------------------------------------------------- India Madagascar Algeria ------------------- -------------------------------------------------------------I------------------- Pakistan Ethiopia ---------------------------------------------------------------------e------------------------------- Bangladesh * Cameroon -----------------------------------------------------------------------------------------.----------- Tunisia Liberia ---------------------------------------------------------------------------------------------------- Indonesia (66-84) Senegal ---------------------------------------------------------------------------------------------------- Gambia Portugal ---------------------------------------------------------------------------------------------------- Gabon Somalia --------------------------~----~--------------------------------------------~-----~-------------------- * Has a dummy * Fails Chow (79) * Fails Chow (79) for '77 - 17 - Appendix Table 1.1: Country Regressions and Tests (continued) ------------------------------------------------------------------------------------ Passed All Passed All But Passed All But Failed Chow (73) Failed Too Tests At 10% Hendry 1% Hendry 1%, and Hendry Many (Hendry 1%) Short-run Homogeneity --------------------------------------------------------------------------------------------------- CAF ---------------------------------------------------------------------------------------------------- Benin ------------, ----------------------------------------------------------------------------------------- Zambia --------------------------------------------------------------------------I ----------------------- Israel ----------- --------------------------------------------------------- Syria Greece ** ---------------------------------------------------------------------------------------------------- Yugoslavia ---------------------------------------------------------------------------------------------------- Total 20 6 4 7 13 -----^--------------------------------------------------------------------------------------------7-- ** Failed SR Homogeneity - 18 - Appendix Table 1.2: South America ----------------------------------------------------------------------------------------------------------------------- Country, Variables, Long-run Price (s ) Long-run Income (Tn ) Parameter Tests Specification Period (Std. Error) (Std. Error) H0 Is 0 Tests H0: 6.= 0 V. H0: 1 1 H e 0= 0, = I Test H0: e O Test H0 = I H0 Long-run Homogeneity -------------------------------- ------------------ ---------- -----------------------------------------O-- Argentina F(1,11).= 28 (.000)* LRM .04 (.832) (ARG) -2.14 2.56 F(3,11) = 16 (.000)* Chow (79) .9 (.53) IMP,DF,GNP (.67) (.63) X 2(2) = 10.13 (.001)* Chow (66,75,84) .162 (.979) F(1,8) = .004 (.95) Homog. .889 (.489) 66-84 x 2(1) = 10 (.001)* x 2 (1) 6.5 (.013)* Hendry (79) (000)* Bolivia F(1,11) = 3.02 (.110) LRM .319 (.571) (BOL) -.438 1.11 F(3,11) = 2.28 (.136) Chow (79) 1.186 (.20) IMP, DF, GNP (.208) (.102) x 2(2) = 4.44 (.10)* Chow (73) .636 (.73) F(1,8) = 3.04 (.592) Homog 6.13 (.010)* 63-81 x 2(1) = 4.4 (.035) x2(1) = 1.35 (1.24) Hendry X 2(2)=13.5 (.001) ----------------------------------------------------------- :------------------------------------------------------------- F(1,11) = .714 (.416) LRM .082 (.77) Brazil -1.1 .63 F(3,11) = .724 (.559) Chow (79) 1.04 (.47) (BRA) (2.15) (.88) x 2(2) = .27 (.87) Chow (66,75,84) 12.73 (.03) IMP,DF,GNP F(1M8) = .004 (.94) Homog 1.22 (.360) 66-84 x 2(1) = .26 (.60) x 2(1) = .17 (.68) Hendry 35 (.000)* F(1,14) = 1.5 (.23) LRM .307 (.58) Colombia -.517 1.25 F(3,14) = .67 (.58) Chow (79) 1.12 (.48) (COL) (.35) (.084) x 2(2) = 8.86 (.011)* Chow (73) .57 (688) IMP,DF,GNP F(l,11) = .17 (.68) Homog .13 (.87) 63-84 x 2(1) = 2.18 (.14) x 2(1) = 8.8 (.002)* Hendry 185 (.000)* ------------------------------------------------------------------------------------------------------------------- - 19 - Appendix Table 1.2: (continued) South America --------------- ----------------------------------- -------------------- --------- -- - ------- --------------------------. Country, Variables, Long-run Price Long-run income Parameter Tests Specification Period (Std. Error) (Std. Error) Ho 2Is 0 Tests 1 1 H0: = O = Test H :Test H :H Test H = 0 ° n H 1 : Long-run Homogeneity --------------------------------u.------------------------------------------------------------------------ F(1,14) = 8.44 (.011) LRM (1.05) (.29) Chile -.32 2.21 Chow (79) 1.1 (.41) CHI) (.117) (.166) Chow (73) .62 (.68) IMP,DF,GNP, (DUM POST) F(1,11) = .027 (.87) Homog .62 (.54) 73 63-84 x2(1) = 9.71 (.001)* Hendry 18.7 (.002) ----------------"---------------------------------------------------------------------- -------------------------------- F(1,14) = 1.23 (.28) LRM .009 (.92) Paraguay -.56 1.66 . F(3,14) = 1.7 (.21) Chow (79) .97- (54) (PRY) (.45) (.168) x (2) = 85 (.000)* Chow (73) .92 (53) IMP, DF, GNP F(1,11) = 3.3 (.09)* Homog 3.36 (.05)* 63-84 X 2(1)= 1.53 (.214) x 2(1) = 15.6 (.OQ0)* Hendry 6.52 (.258) ---------------------------------------------------------------------------------------------------------------------- F(1,14) = .901 (.359) LRM .868 (.351) Peru -.4 1.42 F(3,14) = 2.7 (.002)* Chow (79) .346 (.87) (PER) (.20) (.36) x 2(2) = 3.70 (.15) Chow (73) 2. (.19) IMP, DF, GNP F(1,11) = .04 (.846) Homog 1.09 (.39) 63-84 x 2(1) 322 (.22)* X2(1) = 1.4 (.23) Hendry 6.52 (.258) t----------------------------------------------------------------------------------------------------------------------- - 20 - Appendix Table 1.2: (continued) South America --------------------------------------------------------------------------------------------------------------------N---- Country, Variables, Long-run Price (e) Long-run income (11) Parameter Tests Specification Period (Std. Error) (Std. Error) Ho Isi 0 Tests H = 0 V. 0* Ho = °71n = 1 Test H aC= 0 Test H n =n 1 HO: Long-run Homogeneity -------------------------0---------------------------------------------------------------------------------------------- F(1,14) = 4.5 (Q055)* LRM .514 (.472) Uruguay -.35 2.12 F(3,14) = 2,44 (.10)* Chow (79) 1.87 (.25) (URY) (.17) (.15) X 2(2) = 51 (.000)* Chow (73) 1.66 (.275) IMP, DF, GNP F(1,11) = 1.95 (.667) HOMOG 4.36 (.054)* 63-84 x 2(1) = 3.96 (.096)* x 2(1) = 50 (.000) HENDRY 17.7 (eO03)* ------------------------ ------------------------------------------------------------------------------------------- F(1,14) = 0.34 (.56) LRM .72 (.395) Jamaica F(3,14-) = 0.84 (0.49) Chow (79) .36 (.86) (JAM) X2(2) = 1.59 (.449) Chow (73) 1.88 (.22) IMP, DF, GNP -.186 1;107 F(3,11) = 0.035 (.856) Homog .93 (.455) 63-84 (.168) (.24) X 2(1) 1.22 (0.268) x 2(1) .198 (.656) Hendry 6.5 (.25) ---------------------------------------------------------------------------------------------------------------------- Honduras F(1,14) = 1.126 (0.307) LRM .05 (.82) (HND) F(3,14) = 1.61 (0.23) Chow (79) 0.9 (0.51) IMP, DF, GNP 1.209 1.086 x (2) = 3.86 (.145) Chow (73) 0.79 ( .63) (1.16) (.289) F(1,11) = 0.051 (0.826) Homog 1.49 ( .27) 63-84 X 2(1) = 1.07 x 2(1) = .089 (.76) Hendry 9.35 (.095)*,t --------------------------------------------------------------------------------------------------------------------- - 21 - Appendix Table 1.2: East Asia ------------------------------------------------------------------------------------------------------------------- Country, Variables, Long-run Price (e) Long-run income (11) Parameter Tests Specification Period (Std. Error) (Std. Error) Ho 2Is 0 Tests 3 = 0 V. H0 0, 11 Test H a 0 Test H n 1 0 Long-run Homogeneity -------------------------- ------------------- ------------------------------------------------------------- Indonesia F(1,14) = 69 (0)* LRM .14 ( 69) (IDN) -1.51 1.02 F(3,14) = 1.9 (.18) Chow (79) 1.1 (.44) IMP,DF,GNP (1.13) (.923) x 2(2) = 28 (0)* Homog .79 (.58) 66-84 Chow (66,75,84) .39 (.87) X 2(1) = 1.77 (.182) x 2(1) = 00 (97) Hendry 23 (Q003)* F(1,14) = .118 (.738) LRM .39 (.84) Korea -.22 1.51 F(3,14) = .805 (.517) Chow (79) .89 (.54) (KOR) (.541) (.157) X 2(2) = 26 (0)* Chow (73)-4.4 (.124) IMP,DF,GNP F(1,8) = .987 (.35 Homog 4.13 (.047)* 66-84 x 2(1) = .1712 (.68) X 2(2) 10.99 (,O00)* Hendry 8.39 (.135) Malaysia F(1,14) = 3.12 (.099)* LRM .21 (.643) (MYS) -2.3 1.67 F(3,14) = 3.98 (.03)* Chow (79) 1.95 (.258) IMP,DF,GNP (1.72) (.343) X (2) = 4.9 (.085)* CHOW (73) .90 (.54) 63-84 F(2,11) = .02 (.81) HOMOG 2.7 (.092)* X 2(1) = 1.81 (.173) x 2(2) = 3.83 (.65) Hen ry 13.62 (.018)* Philippines F(1,14) -4.1 (.062)* LRM .628 (.427) (PHL) -.561 1.2 F(3,14) = 3.65 (.049)* Chow (79) 1.6 (.30) IMP,DF,GNP (.342) (.201) X 2(2) = 4.05 (.13) Chow (73) 4.38 (.019) 63-84 F(1,11) = .058 (.814) Homog (3.1) (.063)* x 2(1) = 2.68 (.10)* x 2(1) = 1.07 (.29) Hendry 90 (.000)* - 22 - 2?\ Appendix Table 1.2: (continued) East Asia ------------------------------------------------------------------------------------------------- Country, Variables, Long-run Price (e) Long-run income (rn) Parameter Tests Specifitation Period (Std. Error) (Std. Error) H: 0 6. 0 Tests Ho 6e = V. H': s= °111= 0. Test H: Test H: H: Long-run Homogeneity ------------------------------------------------------------------------------------------------- F(1,14) = 5.2 (.037)* LRM 1.44 (.22) Thailand -.67 1.25 F(3,14) = 6.8 (.008)* Chow (79) 2.79 (.134) THA) (.23) (.086) X (2) 11 (.004)* Chow (73) 1.07 (.44) IMP, DF, GNP F(1,11) = .011 (.92) Homog 3.18 (.072)* 63-84 x 2(1) = 8e6 (.003)* x 2(1) = 8.8 (.002)* Hendry X 2(15)=15 (.007)* -------------------------------------------------------------------- ----------.--------------i-------------------- Appendix Table 1.2: South Asia -------------------------------------------------------------t--.------------------------------------^----------- Country, Variables, Long-run Price (e) Long-run income (7n) Parameter Tests Specification Period (Stde Error) (Std. Error) 'H0 26. 0 Tests H ^ . = 0 v. H = 0, rl= 1 Test H 0: a 0 Test H' r 1 H0 Long-run Homogeneity --------------------------------------------------------------------------------s------------------------------. India F(1,14) = 13 (.271) LRM .063 (.81) IND) .738 1.05 F(3,14) = 5.46 (.011)* Chow (79) .49 (.77) IMP,DF, GNP (.558) (.39) 2 (2) = 2.96 (.22) Chow (73) .67 (.70) 63-84 F(1,11) = 1.99 (.185) Homog 5.05 (.019)i x2(1) - 1.7 (.186) X 2(1) = .017 (.89) Hendry 6.5 (.26) ------------------------------------------------------h------------------------------------------------------------,----<. / 23- , ' 'S. .t h A S i a,,, Appendix Table 1.2: (continuo) South Aia . - - -- - -- -- -- -- -- -- -- -- -- -- -- -- - -- -................................... -- -- -- -- -.- --- -- -- -- -- -- -- -- -- --,- -- - -- -- - - - - - - - - - - - - - - - - -- ---------- Country, Variables, Long-run Price (0) Long-run income ( RParafetef Teits Specification Period (Std. Error) (S+d' Errc7); ) - : ° ! Tests 9'H0:y6.=0 v. Test H a Tes-IH; H T 'I H : Long-ruh Horrcigeneeify !' \ , I F(1.14) = 2.9,(.11) ,LRM 1.81 (.177) Pakistan -.439 .76 l F(3,14) I 4.5 (.02)* Chow (79) .78 (.58) (PAK) (.116) ( 135 -x 2(2) 132 (.000)* ChOW (73) .70 (.683) IMP, DF, GNP F(1,11) .588 (471) HOMOG .66 (.683) 63-84 x2(1) = 3.5 (.000)* x2(1) a 2.9 (.08)* HENDRY 13.3 (.020)* --------------------------------------------------- -......-.......---------------....................--......----------------------------------------------------....... -. -. -------.------ -------------- F(1 .14) = 5.S<1 (.029)* LRM .79 (.38) Bangladesh -.32 1.52 f .S,14) - 3.9 (.031)* Chow (74) 1.93 (.184) (BGD) (.15) (.172) x 2(2) = 2.57 (.008)* Chow (73) .94 (.592) F(1,11) = 1.4 (.25) Homog 4.65 (.046)* x2(1) = 4.3 (.037)* X 2 <) 9.3 (1 . / -. -Wez-dry 3.7 (.000)* --------------------------s------------------------- --------- -----------------------------.---------- --------------------------- -24- Appendix Table 1.2: North Africa ------------------------------------------------------------------------------------------------------------------ ------ Country, Variables, Long-run Price (e) Long-run income (Tn ) Parameter Tests Specification Period (Std. Error) (Std. Error) H: Is.= 0 Tests H : . = 0 v. H 0 , i I1 Test H0 a O Test H0: n 1 H0 Long-run Homogeneity Morocco F(1,14) = .414 (.53) LRM (1.66) (.19) (MAR) -.419 1.38 F(3,14) = 2.22 (.14) Chow (79) 4.23 (.029)* IMP, GNP, DF (.435) (.24) x 2(2) = 2.58 (.24) Chow (73) 1.81 (.24) F(l,11) = .12 (.735) Homog. .602 (.626) 63-84 .929 (.335) 2.47 (.115) Hendry 171 (.000)* --------------------------------------------------------------------------------------.-------------------------------- Tunisia F(1,14) = .035 (.85) LRM .317 (.573) '(TUN) -.25 1.43 F(3,14L= 1.51 (.25) Chow (79) .309 (.89) IMP, GNP, DF (2.08) (.395) x 2(2) = 8.18 (.016)* Chow (73) .972 (.529) 63-84 F(1,11) = .001 (.978) Homog 1.01 (.422) X 2(1) = .014 (.902) x 2(1) = 1.99 (.297) Hendry 4.34 (.500) - 25 - Appendix Table 1.2: continued North Africa --------O--- -------------------------------------------------------------------------------------------------------------- Country, Variables, Long-run Price (e) Long-run income (in) Parameter Tests Specification Period (Std. Error) (Std. Error) Ho 0 Is 0 Tests H: S. = 0 v. H0: e1= 0 1= 1 Test H0: a 0 Test H: n - 1 H: Long-run Homogeneity Chow (73) 32.005 (.008)* Benin F(l,11) = 1.61 (.23) LRM 7.5 (.006)* (BEN) -1.57 2.87 F(3,11) - 3.99 (.036)* Chow (79) 1.77 (.22) IMP, DF, GNP (1.03) (.64) X 2(2) = 8.73 (.012)* Homog 3.3 (.077)* 63-81 x (2) = 2.28 (.13) x 2(1) = 8.43 (.003)* Hendry X (2)] 4.49 (10.95) F(1,14) = 7.2 (.018)* LRM 1.41 (.23) Zambia -1.14 .78 F(3,14) = 4.5 (.020)* Chow (79) .98 (.47) (ZMB) (.123) (.28) x 2(2) = 96 (.000)* Chow (73) .43 (.86) IMP, DF, GNP F(1,11) = 1.11 (.314) Homog 1.88 (.19) 63-84 x 2 = 86 (.000)* x 2(1) - 6 (.438) Hendry 7.28 (.200) - 26 - Appendix Table 1.2: Africa ---------------------------------------------------------------------------------------------------------------------- Country, Variables, Long-run Price (e) Long-run income (n) Parameter Tests Specification Period (Std. Error) (Std. Error) H0 di= 0 Tests H = 0 v. H e 1 0, n 1 1 Test H: a = 0 Test HO = 1 H0 Long-run Homogeneity -------------------------------------------------------------------------------------------------------------------- Gambia F(1,11) = .000 (.998) LRM 1.02 (.31) (GMB) .002 .905 F(3,11) = 1.9 (.186) Chow (79) .22 (.88) IMP, DF, GNP (1.2) (.535) x 2(2) = .15 (.926) Chow (63,71,81) 2.37 (.257 63-81 F(1,8) = .056 (.819) Homog .94 (.464) x 2(1) = .000 (.998) x 2(1) = .031 (.86) HendryX 2(2) = .8 (.66) -------------------------------------------------------------------------------------------------------------------- F(1,14) = 6.04 (.02)* LRM .19 (.65) Kenya ,.t.48 T.37 F(3,13) = 1.9 (.004)* Chow (79) 3.30 (.057)* (KEN) (.34) (.26) X2(2) 140 (.000)* Chow (73) 1.53 (.32) IMP, DF, GNP F(1,9) = .325 (.58) Homog 76T (.54) 63-84 X 2(1) = 19.1 (.000)* X 2(1) = 2.02 (15) Hendry X 2(2) 38 (,Q00)* ----------------------------------------------------------------------------------------------------------------------- F(1,12) = 11.28 (.006)* LRMI .082 (.77) Gabon -1.33 1.53 F(3,12) = 7.34 (.005)* Chow (79) .99 (.46) (GAB) (.587) (.057) X (2) = 140 (.000)* Chow (73) .262 (.949) IMP, IX, GNP F (1,9) = Homog .77 (.58) 64-83 x 2(1) = 514 (.023)* X2(1) = 86 (.000) Hendr-y (X 2(4)]= 5.7 (.21) --------------------------------------------------- ------------------------------------------------------------------- - 27 - Appendix Table 1.2: South Europe ----------------------------------------------------------------------------------------------------------------------- Country, Variables, Long-ruo Price (£) Long-run income (rn) Parameter Tests Specificatior Period (Std. Error) (Std. Error) H0 Is.= 0 Tesrs H0: 6. =0 v. H 0 = n 1 0, Test H a Test H0 n 1 H* Long-run Homogeneity --------------------------------- ------------------------------------------------------------------------------ F(1,13) = .001 (.97) LRM 2.5 (.113) Greece .013 1.37 F(3,13) = .146 (.93) Chow (79) 1.09 (.42) GRC) (.338) (.07) x (2.) = 25.7 (000)* Chow (73) 1.73 (.28) 63-83 F(1,10) = .001 (.974) Homog 10.22 (.002)* IMP, DF, GNP x2(1) = .001 (.96) X2(1) = 25 (.000)* Hendry 7.8 (.16) ----------------------------------------------------------------------------------------------------------------------. Yugoslavia F(1,14) = .59 (.45) LRM .99 (.322) (YUG) -.74 .86 F(3,14) = 1.32 (.30) Chow (79) .91 (.512) IMP, OF, GNP (.85) (.43) X 2(2) = .97 (.61) Chow (73) 1.59 (.293) 63-84 F(1,11) = 1.92 (.67) Homog .56 (.65) X (1)= .75 (.38) x2(1) = .09 (.75) Hendryr 11.53 (.041)* --------------------------------------------------------------------------------------------------- -^i-------------- - 28 - Appendix Table 1.2: Middle East --------------------------------------------|-------------------------------------------------------------------- Country, Variables, Long-run Price (£) Long-run income (T) Parameter Tests Specification Period (Std. Error) (Std. Error) Ho 16.= 0 Tests H0:. H e= 0, = 1 0* Test H: a = 0 Test H: n = I H: Long-iuh Homogeneity --------------------------------------------------------------------------------------------------------- ------------- Israel F(1,14) = 11.2 (.005)* LRM 10.36 (o001)* (ISR) -.665 1.43 R(3,14) = 2.6 (*09)* Chow (79) .23 (.936) IMP, DF, GNP (.216) (.052) X 2(2) = .69 (eOOO)* Chow (73) .95 (.542) F(1,11) = .004 (.951) Homog .536 (.665) 63-84 x 2(1) = 9.4 (.002)* x 2(1 = 69 (.000)* Hendry 2.6 (.76) Syria F(1,12) = 1.01 (.33) - LRM .006 (.935) (SYR) .43 1.44 F(3,12) = .58 (.678) Chow (79) .80 (.519) IMP, DF, GNP (.38) (.069) X (2) = 42.6 (.000)* Chow (74) 2.16 (.23) F(1,9) = .322 (.584) ,Homog. 1.32 (.32) 65-84 x2(1) = 1.3 (.25) x (1) = 42 (.000)* Hendry 13.85 (.016)* ------------ --------------------------------------------------------------------------------------------- -------------- - 29 - Appendix Table 1.3 Page 1 of 6 COUNTRY: LATIN AMERICA Date: 10/10/86 Variables and Coefficient Estimates Period Long Long -2 IMP, DF, GNPKP M-1 Y Y Y-2 Pt - P 2 Price Income R ARG 66-84 .53 3.46 -1.8 -.44 -.78 -.08 -.11 -2.14 2.56 .96 (Std. Error) (.19) (.72) (.89) (.59) (.12) (.19) (.18) (.67) (.63) Bolivia 63-81 .15 2.65 -1.55 -.16 -.39 -.18 .21 1.11 -.438 .942 (.33 (.70) (1.67) (.96) (.19) .23) .213) (.102) (.208) Brazil 66-84 .72 2.13 -1.89 .10 -.31 -1.1 .63 .978 (.10) (.58) (.53) (.16) (.178 Chi le Colombia 63-84 .022 2.07 -2.5 1.66 -.24 -.18 -.08 -.52 1.25 (.305)(1.3) (2.35) (1.33) (.45) (.512) (.402) (.35) (.084) -30 - Appendix Table 1.3 (continued) Page 2 of 6 COUNTRY: LATIN AMERICA Date: 10/10/86 Variables and Coefficient Estimates Period Long Long -2 IMP, DF, GNPKP Mt-I Yt yt-1 rt-2 Pt Pt-I Pt-2 Price Income R Paraguay 63-84 .36 .816 -.43 .68 -.52 -.17 .3 -.56 1.66 .983 (.26) (.72) (1.2) (.72) (.30) .39) .32) (.45) (.168) Peru 63-84 .49 1.53 .092 -.9 -.486 -.068 .349 -.4 1.42 .843 (.25) (.54) .85) (.55) .27) (.354) (.216) (.20) (.36) Uruguay 63-84 .37 1.55 .40 -.62 -.22 .089 -.09 -.35 2.12 .962 a .962 a 3 - (.17) (.27) (.40) (.31) (.098)(.12) (.10) .27) (.15) 5 Jamaica 63-84 .44. .96 -.06 -.29 -.22 .19 -.07 -.186 .1.107 .887 (.32) (.36) (.48) (.27) (.15) (.23) (.17) (.168) (.24) - - Honduras 63-84 .58 3.48 -2.02 -1.01 .47 .59 -.56 1.2 1.08 .953 (.15) (.83) (1.15) (.67) (.40) (.53) (.47) (1.16) (.289) Applldhix Tabl1u 1.3 (>uaj I-nued) - 31 Appendix Table 1.3 (continued) Page 3 of 6 COUNTRY: VARIOUS (EAST ASIA) Date: 1O/G/d6 Variables and Coefficient Estimates Period Long Long -2 IMP, DF, GNPKP Mt-1 Yt Yt-P t-2 Pt, Pt-1 Pt-2 Price Income R Indonesia 66-84 .30 .097 .42 .196 -.79 -.15 -.09 -1.51 1.02 .992 (.35) (1.28) (1.25) (1.13)w ....... (.67) (.25) (.12) (1.13) (.92) Korea 66-84 .53 1.95 -1.46 .20 .176 -.47 .19 -.22 1.51 .996 (.15) (.47) (.75) (.48) (.31) (.39) (.30) (.54) (.15) Malaysia, 63-84 .70 1.47 -.08 -.89 -.90 -.11 .33 -2.3 1.67 .982 (.17) (.81) (1.13) (.79) (.32) (.37) (.39) (1;7) (.34) Philippines .- 63-84 .39 1.03 1.15 -1.45 -.39 -.14 .20 -.561 1.2 .962 (.29) (.75) (1.73) (1.24) (.20) (.21) (.116) (.34) (.201) Thailand 63-84 .36 .60 1.68 -1.49 -.92 .25 .23 -.67 1.25 .980 (.22) (1.) (1.5) (1.05) (.22) (.33) (.18) (.23) (.086) - 32 - Appendix Table 1.3 (continued) Page 4 of 6 COUNTRY: SOUTH ASIA AND SOUTHERN EUROPE Date: 10/10/86 Variables and Coefficient Estimates Period Long Long -2 IMP, DF, GNPKP M1 Yt yt1 Y Pt P P Price Income R t-1 t-2 Bangladesh 63-84 -.018 1.37 -.91 1.13 -.40 -.08 .15 -.32 1.52 .861 (.20) (.43) (.60) (.40) (.13) (.17) (.14) (.15) (.172) India 63-84 .742 .36 -2.1 2.05 -.27 .16 .30 .738 1.05 .942 (.10) (.46) (.57) (.45) (.15) (.22) (.16) (.55) (.39) Pakistan 63-84 .096 2.53 .28 -2.12 -.59 .25 -.04 -.43 .79 .766 (.22) (.85) (1.2) (.88) (.22) (.39) (.23) (.116) (.13) Greece 63-83 .22 1.42 -.23 -.12 -.16 .27 -.10 .013 1.37 .982 (.36) (.62) (1.07) (.52) (.38 (.426) (.27) (.33) (.07) Yugoslavia 63-84 .78 1.5 -.81 -.50 -.28 .27 -.15 -.74 .86 .952 (.16) (.57) (.69) (.57) (.16) (.20) (.21) (.85) (.43) - 33 - Appendix Table 1.3: (continued) Page 5 of 6 COUNTRY: MIDEAST AND N. AFRICA Date: 10/10/86 Variables and Coefficient Estimates Period Long Long -2 IMP, OF, GNPKP M Yt. Y-1 Yt-2 P Price Income R Israel 63-84 -.034 1.29 .56 -.37 -.19 -.16 -.32 -.665 1.43 .981 (.27) (.49) (.65) (.41) (.26) (.27) (.20) (.210) (.052) Syria 65-84 .007 1.98 -.157 .13 .003 .08 .35 .43 1.44 .967 (.32) (.40) (.56) (.36) (.37) (.47) (.44) (.38) (.069) Morocco 63-84 .39 1.75 -.59 -.31 -.88 .95 -.32 -.42 1.38 .927 (.29) (.8) (1.15) (.69) (.37) (.51) (.39) (.43) (.25) Tunisia 63-84 .68 .44 .15 -.14 -.33 .83 -.58 -.25 1,43 .985 (.18) (.42) (.51) (.48) (.43) (.40) (.42) (2.08) (.39) - 34 - Appendix Table 1.3 (continued) Page 6 of 6 COUNTRY: SUB-SAHARAN AFRICA Date: 10/10/86 Variables and Coefficient Estimates Period Long Long -2 IMP, DF, GNPKP Mti Yt Y Yt2 P Pt1 P Price Income R t-I t-I t-2 t-I t-2 Benin 63-81 .65 1.61 -1.12 .50 -1.26 .86 -.14 -1.57 2.87 .946 (.18) (1.22) (1.38) (.91) (.37) (.54) (.42) (1.03) (.64) CAF 63-84 -.2 .16 1.31 -.71 -1.3 -.19 -.37 -1.55 .63 .781 (.26) (.76) (1.14) (.75) (.29) (.31) (.204) (.25) (.12) Gabon 64-83 .13 1.46 -.18 .05 .35 -.08 -1.42 -1.33 1.53 .986 (Uses RPIMPIX) -(.15) (.21) (.27) (.19) (.34) (.37) (.34) (.58) (.057) Gambia 63-81 .46 -.09 1.14 -.57 .11 -.97 .86 .002 .905 .757 (.25) (.55) (.63) (.67) (.44) (.50) (.55) (1.2) (.53) Kenya 63-84 .35 .31 -.06 .64 -.38 -.95 .37 -1.48 1.37 .785 (.24) (.51) (.65) (.53) (.33) (.49) (.39) (.34) (.26) Zambia 63-84 .327 .68 .11 -.27 -.24 -.47 -,05 -1.14 .78 .921 (.27) (.47) (.47) (.41) (.21) (.27) (.28) (.123) 1.28 -J - 35 - Appendix 2 A. Testing I. Residual Serial Correlation Since, as is well known, the presence of a lagged dependent variable biases the standard Durban Watson statistic towards 2 we use a Lagrange Multiplier test. This involves regressing the residuals on the regressors and the lagged residuaL and comparing the R values of that regression times the number of observations and comparing it: to values from a chi square distribution of one degree of freedom (See B3reusch and Godfrey, 1980). II. Stability Three tests of stability are performed. A standard Chow test for sub-sample stability, a Chow post-sample stability test, and a Hendry test of post sample predictive accuracy. The Chow test of sub-sample stability tests to equality of the vector of coefficients estimated in two different sample periods. In this case the sample period 1963-1984 was divided into 1963-1973 and 1974-1984 and the equality of parameters across these sample periods was compared. Failure to reject this test implies that there is no evidence of change in the responsiveness of imports over the sample period. A second Chow test was used to test the stability of the regression estimated over the 1963-1979 period for the five remaining years of the sample. This test is intended to detect out of sample failure of the regression that may be due to mis-specification. This test has notoriously low statistical power and so was used in conjunction with the Hendry test of post-sample predictive accuracy. The test of post-sample predictive accuracy used in the five observations from 1979 to 1984 as a post-sample period and constructed - 36 2 a x (5) test. This test has only asymptotic justification and is, in small samples too powerful (its actual size exceeds nominal size in small samples). As a practical matter this was taken into account by using a 1% significance level for this test (as opposed to the low 10% level used on all other tests) and when the Chow and Hendry tests disagreed basing the inclusion of the country in the sample on the other tests goodness of fit criteria. III. Homogeneity If we write the model as. 2 2 t 0 1 t-il :-i I i t-i i=0 i=0 2D SiPD t-i 1i i=0 where: PI : import prices PD : domestic prices, then the tests of homogeneity are: A) A long run test for equality of the effect of domestic vs import price changes is: 2 2 i=O i=O A test for the equality of price effected period by period is: I D S= -6. for all i i i Acceptance of this homogeneity tests indicates conformity of the import demand functions to the homogeneity of degree zero of demand functions with respect to prices. -r37 Appendix 3 The regressions reported in' L'e text' aLl usd data from the National Accounts as reporLed by the countries. The' reported price deflator was calculated as the ratio of current to const-ant price figures for imports. Fortunately t,Ie ce is acnothe.r source for data on import and export prices which we' can use, to comrn.are to resul'ts to re- assure ourselves that the results'given ,'i the t"I!'re not dependent in any way on the quirks ,of t4e data cho.3-en. In this case we have imports t~~~~ ~ ~ X I in current dollars reportd'I'in the TIm.'dBalance of,- Payments Sttatistics. A dollar price deflator for imports t6r 39 developring countrie. has been constructed (see Moran and Park, I ') 8 £) i: e t Iy from commodity price data and a manufacturing unit value ,indf.x. Thererore we replicated all of the. regressions a.nd tests in the teiit:uzng these alternate imports and price measures. The results were quite:reas!L7rtir1gr kco. n untry wcse import demand regressions were originally,cdeermed acceptable :ubsequently should have been excluded from the sampln. The rezalts comparing the values of the estimates of price elasWicities u in g the different price measures are reported in Appendix TaLle 3.1. e .eassuri.ngl1y for many countries the point estimates are quite close. F'or other countries, there were considerable numerical difference;s` but -generally not outside the range of sampling variation. Only six countries had point estimates with more than a standard error, difference and none cf tie estimat'es were more than two standard errors away. The dif.erences in price elasticity estimates were not significant. The sudm of the differences across all thirty countries was .015, heaLthy reassurance that the differences were random.More important to the message of this paper than single country - ', 5 , -38- differences are the results of the subsequent regressions. These regressions were carried out using the new price and income elasticity estimates. Since in the regression reported in the text we used weighted least squares because of heteroskedasticity here we are faced with two measures of the elasticities as the dependent variable (using the two different measures of prices and the two different measures of imports) and three choices for weights (no weights, and the two sets of standard errors from the different regressions). We decided to use each of them and ran six regressions for both income and price elasticities. Using the three possible weights of estimates from the regressions using the national accounts and deflator point estimates and using the price index and BOP point estimates. In Appendix Table 3.2 we see the results for the income elasticity regression. The estimated turning point of the quadratic varies only from 2825$ to 2857$ with the two different measures using their own standard errors and the fit is almost equally as good for both measures. The results for the price measure are presented in Appendix Table 3.2. All possible regressions still show a U-shaped pattern of response of price elasticity t,o per-capita income and the share of trade in output variable has a negative sign in all six regressions. We can firmly conclude that none of the cross section regression results were at all dependent on the choice of data source for imports or on the choice of import price measure. - 39 - Appendix Table 3.1: PRICE ELASTICITIES Estimated w/ of Estimated w/ of Estimated w/ IMPDEFL/GNPFL PIMPIX * EXCHIDX/ PIMPIX*EXCHIDX GDPDEFL CPI (UNCTAD) (UNCTAD) ARG -2.1 (.67) -2.51 (2.14) -1.57 BOL -.44 (.21) -.438 (.152) -.26. (.09) BRA -1.1 (2.1) -1.02 (1.94) -1.27 (1.5) CHL -.32 (.12) -.146 (.10) COL -.52 (.35) -.628 (.229) -.607 (.20) PRY -.56 (.45) -.351 (.313) -.28 (.34) PER -.40 (.20) -.284 (.156) -.26 (.16) URY -.35 (.17) -.363 (.120) -.203 (.152) JAM -.18 (.16) *-.274 (.188) -.31 (.28)* HND 1.2 (1.2) *.134 (.386) .22 (.36)* iDN -1.5 (1.1) .607 (.488) .34 (.83) KOR -.22 (.54) .3077 (.543) -1.14 (.78) MYS -2.3 (1.7) .982 (1.27) 1.3 (.88) PHL -.56 (.34) -.247 (.486) -.41 (.415) THA -.67 (.23) -.579 (.32) -.46 (.5365) BGD -.36 (.12) *.048 (.194) .04 (.247)* IND .74 (.55) .727 (.644) 1.00 (.68) PAK -.48 (.08) -.404 (.132) -.387 (.13) ISR -.66 (.22) -.363 (.126) -.341 (.115 MAR -.42 (.43) -.44 (.551) -.178 (.65) SYR .43 (.38) *.108 (.365) -.04 (*305)* TUN -.25 (2.08) .268 (1.23) .98 (.74) BEN -1.6 (1.4) *1.3 (2.49) -3.10 (5.5) CAF -1.87 (.26) *-1 .45 (.268) -2.16 (,49)* GAB -1.23 ( ... ) -.88 (.383) -1 .33 (.58) GMB .002 (1.2) -.631 (2.76) -2.81 2.6) KEN -1.48 (.34) -1,68 (.500) -2.2 (1.7) ZMB -1.14 (.123) *-1.59 (.4C5) -3.81 (1.42)* GRC .013 (.34) -.037 (.175) .011 (.17) YUG -.74 (.85) .424 (.550) .47 (.64) * Used UNCTAD dollar import price index. - 40 - Appendix Table 3.2: Income Elasticity Dependent Variable Coefficient on: Measures/ 2 SER Weights RPCY RPCYSA POPN SHRTRD RER Deflator/OLS .00038 -6.56 x 10 8 -.0004 .005 .113 .53 (.00029) (6.35 x 108 (.0008) (.34) Deflator (Deflator) .00074 -1.3 x 107 .00034 -65 X 105 .96 2.3 (.00022) (4.2 x 10-8) (.001) (.25) Deflator (Index) .0011 -1e91 x 10 .0004 -.173 .98 1.29 (.0001) (28 x 108 ) (.0013) (.23) Index (OLS) 1.26 x 10-6 -1.21 x 108 eOO -.294 .095 .74 (.0004) (8.7 x 108 ) (.001) (.482) Index (Deflator) .000979 -1.85 x 10 -.0004 .076 .91 3.7 (.00086) (7.01 x 10-8) (.002) (.41) Index (Index) .000668 -1.09 x 10 .00133 -.146 .945 2.43 (.00027) (53 x 10-8) (.002) 1.43) - 41 - Appendix Tabla 3.3: Price Elasticity Dependent Variable Coefficient on: Measures/ Weights RPCY RPCYSA POPN SHRTRD R2 (SER) Deflator (OLS) -.000148 3.53 x 108 .001 -.55 .113 (.0004) (9.4 x 10 ) (.0013) (.51) (.79) Deflator (.eflator) .000589 -9.4 x 10o8 .0021 -.84 .82 (.00018) (4.16 x 10 ) (.0011) (.28) (1.38) Deflator (Index) .00015 -2.019 x 10i8 .000669 -.43 .66 (.00022) (4.4 x 10 8) (.001) (-.37) (1.56) Index (OLS) .00116 -2.14 x 10 7 .0038 -.032 .198 (.0006) (1.42 x 10 ) (.002) (.78) (1.20) Index (Deflator) .00018 -2.51 x 108 .0014 -.36 .49 (.00019) (3.96 x 10- (.0013) (.33) (1.38) Index (Index) .00093 -805.0 x 107 .0033 -3.23 .66 (.0005) (1.2' x 107) (.003) (.62) (4.01) - 42 - Bibliography Breusch, T.S. and Godfrey, L.G., 1980, "A Review of Recent Work on Testing for Autocorrelation in Dynamic Economic Models", University of Southampton Discussion Papers in Economics and Econometrics, #8017. 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