To keep the problem of assessing instrument strength over this proliferation of possible instrument sets manageable, I consider only a subset of these possibilities. In the differenced equation, I consider instrument sets consisting of the second to ���1�<sup>��</sup> lags of income and the Gini, for a total of �<sup>�</sup> possible combinations of instruments. Similarly, in the levels equation, I consider instrument sets including the first to �<sup>��</sup> lagged differences of income and the Gini, for a total of �<sup>�</sup> combinations of instruments for this equation as well. In addition, for each of these �<sup>�</sup> ��<sup>�</sup> ��<sup>�</sup> combinations of instruments for the levels and differenced equations together, I consider both the “collapsed” and non‐ “collapsed” versions of the instruments, for a total of 2�<sup>�</sup> possible instrument sets. In the results below, I set ��5 so there are 1250 different possible specifications corresponding to 1250 different instrument sets. These break down into 50 distinct instrument sets for the differenced equation, and 50 distinct instrument sets for the levels equation.

I implement this robustness analysis using the OBT data set as an illustration. As noted above, I consider the minimal specification of a regression of growth on lagged per capita GDP and lagged inequality, and so I drop the redistribution variable included in their main regressions. Since this variable does not enter significantly in their benchmark specification, dropping it has little effect on their main finding of a negative and significant effect of net inequality on growth. For each instrument set, I implement the SYS‐GMM estimator and retrieve the estimated coefficient on inequality, together with its standard error. Table 6 summarizes the distribution of point estimates of the growth effects of inequality, together with the absolute value of their conventional t‐statistics. Consistent with the benchmark specification in OBT, the estimated effect of inequality on growth from the SYS‐GMM estimator, reported in the top panel of Table 6, is significantly negative in nearly all specifications. The SYS‐GMM point estimates range from ‐1.4 (at the 10<sup>th</sup> percentile) to 0.43 (at the 90<sup>th</sup> percentile), with a median value of ‐0.8 which is very close to the OBT benchmark estimates of around ‐0.7.<sup>13</sup> The table also distinguishes between models with “GMM‐style” and “collapsed” instrument sets, with slightly more negative effects when the instrument set is collapsed. The distribution of t‐statistics shows that in

> 13 It is worth noting that the OBT benchmark specification reported in Table 2 does not appear among the 1250 models summarized in Table 5.  This is due to three different reasons:  (a) as noted previously I do not include the lagged redistribution variable that is in OBT’s benchmark specification, (b) OBT do not include the lagged change in log GDP per capita in the instrument set for the levels equation, whereas in my robustness analysis here I always include at least one lag, and (c) I include the first and higher lags of the change in inequality in the instrument set for the levels equation whereas OBT start with the second lag.

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