15 principal components in Columns (5)-(7). Table A3 reports the coefficient estimates for inequality, their 95% confidence intervals, and the associated Hansen J-test p-values for additional limits on the instrument set. All estimates use the one-step System-GMM estimator.<sup>26</sup> As the first-difference transform is affected by gaps in the panel data, orthogonal deviations transformation was used for robustness checks in the DHS data set, which contains gaps in the panel for three countries. This issue does not affect our findings.<sup>27</sup> We report standard errors clustered at the country level that are robust to heteroskedasticity and autocorrelation.<sup>28</sup> For each GMM specification, we report the Hansen J-test of instrument validity, and Arellano-Bond (1991) autocorrelation tests. We also report the numbers of observations, countries, instruments, and, when relevant, principal components.

We start by discussing the relationship between total inequality and growth (equation 5), presented in Table 3. This helps place our findings in the preceding literature by allowing comparisons with previous findings before we proceed to examine the same relationship for the two distinct components of overall inequality – namely inequality of opportunity and a residual term (a proxy for inequality due to effort). As in Forbes (2000), whose empirical specification is identical to the one we use here, we find signs of conditional convergence: the sign of the coefficient on initial income is always negative and significant at the 95% level or confidence or above for three of the seven specifications.<sup>29</sup> The coefficient estimates for male and female education and the price level of investment are also similar to those in Forbes (2000). When it comes to the conditional correlation between inequality and growth, however, our results diverge: whereas Forbes (2000) reports a coefficient on inequality that is always positive and significant in four different specifications, our estimates are always negative and significant at the 90% confidence level or above in five of the seven specifications. The difference-GMM specification in Forbes (2000) (Table 3, column 4) implies a 1.3% increase in average growth over the next five-year period for a 10-point increase in the initial Gini coefficient, while the same estimate from our study is a 2.2% decrease for a 10-point increase in initial mean log deviation (Table 3, column 4). A more conservative estimate using system-GMM suggests a 1% decline in growth for the same change in initial inequality (Table 3, column 5).

Two issues are worth additional discussion regarding the findings presented in Table 3. First, regression diagnostics, particularly the Hansen J-test suggests that the validity of the instrument set is called into question when we limit the number of instruments using the _collapse_ or the _pca_ options discussed above (columns 6 & 7).<sup>30</sup> These p-values continue jumping around when we limit the number of

> 26 While the two-step estimator is more efficient, it has been shown that any gains are small (Bond et al. 2001). The two-step estimator converges relatively slowly to its asymptotic distribution. Furthermore, the one-step standard errors are more robust for inference in finite samples (Blundell and Bond, 1998).

> 27 Results are available from the authors upon request. The IES data set contains no gaps.

> 28 Of course, for the long-run OLS, which uses a cross-section of countries, one cannot cluster at the country level and we use robust standard errors.

29 The only difference between our empirical specification and Forbes (2000) is the measure of inequality used: we use mean log deviation while Forbes (2000) employs the Gini coefficient available in the Deininger and Squire (1996) data set. Our findings are not qualitatively different if we use the Gini index instead of Theil (L). Readers should note, however, that we are not trying to replicate Forbes (2000) here: Since the focus of our paper is as much on inequality of opportunity as it is on overall inequality, the set of countries in our sample is restricted by the availability of data on circumstances.

30 The p-values that are less than 0.0001 for Hansen J-tests in columns 7 of Tables 3 and 5 seem to be due to the presence of an outlier in the value of mean log deviation. Mean log deviation in Bolivia in 2000 is 0.978, which lies