Technical Correction Overview and Implications In appendix 1B equation B 5 p 53 relating the inequality parameter of the lognormal distribution to the Gini coef cient contains an error as examined below 1 This parameter is important in estimating the elasticity of poverty with respect to growth This elasticity in turn affects the estimates of the impact of trade liberalization on global poverty It turns out that the correction of the error causes a moderate reduction in the estimate for the long term reduction of global poverty from complete free trade from a central estimate of 540 million people lifted out of poverty to 440 million The corresponding high estimate declines from 680 million to 580 million The broad conclusion remains unchanged that global free trade could lift somewhere in the vicinity of 500 million people out of poverty over the long term An important reason for the limited change in the estimates is that the original estimates imposed a ceiling of 3 5 on the poverty elasticity of growth Most of the Asian countries had estimated elasticities higher than this ceiling so the calculations of their poverty impacts were constrained by the ceiling elasticity With the recalculation of the country poverty elasticities the Asian countries still tend to have relatively high elasticities in the range of 2 5 to 3 table TC 1 in this note The reductions in the calculated poverty effects for these countries are thus not as great as would have been the case if the original calculations had not been constrained by the ceiling elasticity permitted This constraint in turn was adopted based on the judgment that the range of empirical estimates of the elasticity rarely exceeded 3 5 Corrected values for the most important tables affected tables 1 8 1B 1 and 5 3 are presented at the end of this note The range of the poverty elasticity in table 1B 1 p 54 is now from a high of 7 67 to a low of 0 58 instead of the original estimated range from 25 3 to 0 43 Summary table 5 3 p 252 combining static dynamic productivity and dynamic investment effects reports the change in the aggregate poverty effects just described and provides country detail The speci c revised values in tables 4 7 static 4 9 steady state and 5 2 dynamic productivity effects pages 210 215 and 250 respectively are not reported here but can be obtained by replacing the estimated or constrained country speci c poverty elasticities by the revised country speci c poverty elasticities reported here in table TC 1 and then applying the calculations of each of the respective tables Finally the cross section paradox discussed in chapter 1 is also affected by the revision of This paradox is that for countries with per capita incomes above about 1 000 the lognormal predicted incidence of poverty is usually much lower than the observed incidence After the corI am indebted to David Rosnick for calling the error to my attention Note also that in equation B 1 p 52 the minus sign was inadvertently omitted from the exponent Other errata in table 4 1 p 180 GDC should be DGC in table 4 2 p 185 LDC should be DGC 1 rection this diagnosis remains broadly true but is less extreme than before revised table 1 8 The correction reduces the poverty elasticity for Gini coef cients below about 0 5 but raises it for higher Gini coef cients As a result for countries with lower Gini coef cients the corrected predicted poverty incidence is higher than before whereas predicted poverty for high inequality countries is lower than before The most extreme cases of divergence between predicted and actual poverty continue to show large gaps between the two although the gaps are smaller than before Thus for China with actual poverty incidence at 53 7 percent the original predicted level of only 0 5 percent is increased to 3 9 percent leaving unchanged the qualitative diagnosis of a major gap Table TC 1 Original and corrected country speci c poverty elasticities used in calculation of poverty impacts Country Original Revised 3 5 3 5 3 5 3 5 3 5 3 2 3 5 3 0 2 3 2 9 2 5 3 0 3 5 2 7 3 2 2 2 Bangladesh China India Indonesia Korea Malaysia Pakistan Philippines Country Thailand Argentina Brazil Mexico Turkey Mozambique South Africa Tanzania Uganda Original Revised 3 5 3 1 1 0 2 0 3 5 1 4 1 2 1 0 2 3 3 5 2 9 1 5 2 1 3 5 1 0 1 7 1 0 1 4 Corrected Relationship of the Lognormal Distribution Parameter to the Gini Coef cient2 Appendix 1B p 53 states incorrectly that 2 1 G 1 2 2 B 5 where is the standard deviation in the lognormal distribution is the standard normal distribution and the negative exponent indicates inverse function G is the familiar Gini coef cient obtained by taking the ratio of the area between the diagonal and the Lorenz curve to the full area under the diagonal in the diagram of cumulative percent income vertical axis against cumulative percent households horizontal axis This equation was derived from Bourguignon 2002 which was available at the time the original analysis was prepared Cline 2002a 3 In the subsequent published version of the same paper Bourguignon 2003 the relevant equation was corrected The correct version of the underlying equation is G 2 1 2 1 I am grateful to Aart Kraay for clari cations In Bourguignon 2002 it was stated that G 2 2 1 The corrected published version 2003 stated that G 2 2 1 2 3 When this underlying relationship is rearranged and the inverse function applied the corrected equation for becomes 2 1 G 1 2 B 5 In other words the initial equation for was instead the equation for 2 Dollar and Kraay 2001a 12 also give equation B 5 for This relationship between G and can also be con rmed from Aitchison and Brown 1963 8 12 13 in combination with Gastwirth 1972 Aitchison and Brown indicate that for the lognormal distribution the Gini mean difference coef cient pairwise absolute difference between all observations is 1 2 2 2 2 where e 12 2 3 In turn Gastwirth 1972 307 states that for any distribution function the familiar Gini coef cient of relative income inequality i e G equals the absolute mean difference coef cient divided by 2m where m is the mean value of the distribution However because the value of Aitchison and Brown s equation 3 is simply the mean value of the lognormal distribution function equation 2 for mean difference translates directly into equation 1 that is equation 2 divided by 2 becomes equation 1 Thus Aitchison and Brown s value for the mean difference coef cient con rms the corrected value for shown in revised
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