17 components, IOpi,t−5 and IRi,t−5 respectively, by estimating equation (6). Table 5 reports results from this regression using the IES country sample.<sup>32</sup> We find no consistent relationship between growth and either inequality between types or inequality within types (as proxies for inequality of opportunity and inequality of effort, respectively): While 13 or the 14 estimates are negative, only one of them is statistically significant at the 90% level of confidence (which happens to be in a specification where the Hansen J-test strongly rejects the validity of the instruments). The coefficient estimates are more scattered for both components of inequality using the DHS data set, but the conclusion is qualitatively the same: one cannot detect any consistent pattern of a relationship between growth and inequality of opportunity (Table 6). As in Tables 3 & 4, some of the GMM specifications suffer from instrument proliferation while in others the validity of the instrument set is rejected. Table A3 confirms these null findings when the instrument set is restricted further using the _pca_ option. These findings are clearly not supportive of the hypothesis that there might be a negative association between inequality _of opportunity_ and growth (and a positive one between the residual inequality and growth) à la Marrero and Rodríguez (2013).

We considered the possibility that these findings might be driven by measurement error. As noted in Section 4, the need for (rough) comparability of circumstance sets across countries led us to use a measure of inequality of opportunity based on a very sparse partition of types. Like other examples of this method, the measure used in the regressions reported in Tables 5 and 6 is a lower-bound indicator. But given the paucity of types, it is arguably a very substantial underestimate of true inequality of opportunity: On average across all the countries and years, our circumstances explain 11.6% of total inequality in the IES and 15.7% in the DHS data sets (See Tables 1 and 2 for details). While it is obviously not the only possible cause, this kind of measurement error would certainly be consistent with substantial amounts of inequality of opportunity (due to omitted circumstances) contaminating the residual component, leading to biased coefficients. The negative coefficient estimates for both the within- and between-type inequality in Table 5 is suggestive of this possibility.

# **6. Conclusions**

In this study, our motivating hypothesis was that the lack of robust conclusions about the association between initial inequality and economic growth in the previous literature might have been driven, at least in part, by the conflation of two different kinds of inequality into the conventional income inequality measure: inequality of opportunities and inequality driven by efforts. Because efforts are notoriously difficult to measure, we have followed the recent literature on the measurement of ex-ante inequality of opportunity, and decomposed overall income inequality into a component associated with opportunities, and a residual component, driven by efforts as well as omitted circumstances.

These decompositions were carried out for the mean logarithmic deviation of household per capita incomes (or expenditures) in 118 household income and expenditure surveys for 42 countries, and for the variance of a wealth index obtained from Demographic and Household Surveys in 134 surveys for 42

> 32 We use the sample that includes region of residence as a circumstance for our default data set. While region of residence is not exogenous, region of birth is missing in many data sets, causing significant underestimation of inequality of opportunity by excluding an important circumstance. Given this tradeoff between underestimation and endogeneity, we report the findings using the data set that excludes region of residence and only utilizes region of birth in Table A4.