set: limiting the instrument matrix to a single lag (top-right panel), collapsing the matrix of instruments (bottom-left), and limiting and collapsing the instruments at the same time (bottomright).<sup>27</sup> For first difference GMM, we use two lags in the matrix of instruments so as to have the same number of orthogonality conditions as in the system GMM estimation in the top-right panel, thus making the results more easily comparable.<sup>28</sup> The p-values of the Hansen tests shown in Table 3 suggest that in virtually every case the null of joint validity of all instruments cannot be rejected. Moreover, the Difference-in-Hansen test results, whose p-values always exceed 0.10 (in most cases by a large amount) point towards the superiority of system GMM over first difference GMM.

The parameter estimates of the variables of interest follow the pattern found earlier. The coefficient on the poverty headcount is consistently negative and highly significant, regardless of the model and specification estimated. In contrast, the coefficient of the inequality variable varies in sign and significance depending on the GMM approach and the controls used in the estimation. It is positive and, in most cases, significant for first difference GMM, consistent with our results for the withingroup estimates in Table 3 and part of the earlier literature (e.g., Forbes, 2000). However, it is negative and, in some cases, significant for system GMM, consistent with our results for pooledOLS and another strand of the literature (e.g., Berg et al., 2018, and references therein).<sup>29</sup> The tentative conclusion is that the negative effect of poverty on growth is robust to changes in model specification and estimation method, while the effect of inequality on growth, which has been the focus of a massive literature, is not.

# **IV.3. Weak instruments analysis**

System GMM relies on lagged levels and differences of the regressors as internal instruments. Bazzi and Clemens (2013) and Kraay (2015) have recently raised the potential problem of weak instruments when using system GMM estimation in growth regressions. Weak identification arises

> 27 The conclusions do not change if we take orthogonal deviations instead of first differences to remove the fixed effects in (12). The results are available upon request.

> 28 Data for the infrastructure index included in Model M4 are available for only 88 countries under the system GMM specification and 79 under the first difference GMM specification. Thus, the estimates of this model shown in the top panel feature a number of instruments exceeding the cross-section dimension of the data. However, reducing the number of instruments by collapsing the matrix of instruments (as in the bottom panel) or erasing instruments manually from the matrix of instruments (for example, using instruments for lagged income, Gini and poverty only) leads to results (available upon request) very similar to those shown in the table.

> 29 Since the coefficient estimates on the controls themselves are of no direct interest here, they are omitted from the table to save space. However, it is worth noting that in most cases they are not significant. The main exception is lagged income, as well as lagged infrastructure and lagged female education in model M4.

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