16 components further by retaining the components with the largest eigenvalues (Table A3, panel A). The p-values for the Hansen J-test are better for the difference-GMM and system-GMM specification using the full set of available instruments, while the Arellano-Bond autocorrelation tests suggest no problems with any of the GMM specifications. Nonetheless, the coefficient estimates of inequality from the four GMM specifications are relatively stable – suggesting a negative conditional correlation between 1.0% and 2.4%.

Second, while our findings are not robust enough to allow us to conclude that the conditional correlation between initial inequality and growth is negative in this data set, we can nonetheless state with some confidence that they are not consistent with the findings in Forbes (2000). This may reflect differences in the country and period coverage of the two samples: we have 118 observations for 42 countries, whereas Forbes has 135 observations (in the GMM specification) for 45 countries. 24 countries are present in both Forbes’s and our IES sample. Periods also differ, with these ranging from 1961-65 to 1986-1990 in Forbes (2000), compared to 1981-1985 to 2001-2005 in our study.<sup>31</sup> In addition, as noted earlier, not only the inequality measures used are different (Gini vs. Theil (L)), but also our inequality measures arguably satisfy a higher standard of international comparability, since they were all computed under exactly the same criteria and using the same routines directly from the microdata, whereas Forbes (2000) relied on Gini coefficients available in the Deininger and Squire (1996) data set. Whatever the reasons for the differences, it is fair to conclude that the relationship between inequality and growth is not robust to changes in either data sources/periods or seemingly small changes in empirical specifications.

As described in the previous section, the IES data set is comprised of 23 high-income countries and 19 low- and middle-income (LMIC) countries. In contrast, our DHS data set is comprised entirely of developing countries from Africa, Asia, and Latin America. Although we constructed our DHS data set because of its perceived advantage in containing more observed circumstance variables, it is still interesting to examine the overall inequality-growth relationship in that data set, which we present in Table 4. The findings here are much more equivocal than those presented in Table 3: while there are still signs of conditional convergence, we find no statistically significant coefficient estimates for total inequality (measured by the variance of the wealth index). For the difference-GMM and system-GMM using the full set of instruments, signs of instrument proliferation are apparent: 52 and 73 instruments, respectively, producing unusually high p-values of 0.965 and 0.999 for the Hansen J-test of instrument validity (columns 4 & 5). The coefficient estimates, all of which are close to zero and about half of which are negative, suggest no apparent relationship between inequality and growth in this data set.

Our main interest, however, lies in examining whether and how the association between inequality and growth might change when we decompose overall inequality into the opportunity and residual

> well to the right of the next highest value in our data set (0.829 in Panama in 2003). Excluding Bolivia (2000) from our regression analysis brings the p-value to a much more reasonable 0.148 for the specification presented in column 7 of Table 3, but makes little difference to the coefficient estimates for initial income and total inequality. We present the findings for the full data set to avoid ad hoc exclusion of observations from our analysis. 31 Clearly, neither sample of countries is representative of the world, since they are driven entirely by survey availability, which is evidently non-random. Although our sample covers fewer countries, it has slightly broader regional coverage, including two countries from Africa.