determinant of schooling outcomes due to school resources (Krueger 2003), and in part because of its availability across countries and time. There are some legitimate concerns of simultaneity bias in including this variable: Countries with higher incomes per capita are likely to be able to afford to increase schooling resources, lowering the pupil-teacher ratio. Without a measure of school inputs, the tradeoff is reduced efficiency of the estimates due to a poorer fit in the first stage; we report specifications with and without the inclusion of this variable.

The remaining endogeneity issue is that of omitted variable bias. While it is possible that government effectiveness or the consumption-investment ratio can influence income per capita through an intervening omitted variable, or is affected by an omitted variable that also affects income per capita, this is not suggested by our theoretical model. Moreover, we are inclined toward a fairly parsimonious model, given the general lack of robustness of other, atheoretical explanatory variables that have been advanced in the literature. In any case, we take steps to address this issue in our robustness section.

Estimation of the model is via two-stage least squares, using two-step GMM and adjusted for heteroskedasticity-robust standard errors. For robustness tests using panel data, we run both fixed effects IV-GMM with correction for heteroskedasticity and serial correlation, and system GMM using the orthogonal deviations transformation for the endogenous regressors (Arellano & Bover 1995) and Windmeijer-corrected standard errors.<sup>10</sup> In most of our specifications, our model is overidentified, and we accordingly report the Hansen _J_ -test of overidentifying restrictions.<sup>11</sup>

# **3.3 Data Description**

Our cross-country macroeconomic data are drawn mainly from the World Bank’s _World Development Indicators_ . This includes the main controls: the investment share of output, and the net rate of depreciation (which is the sum of the population growth rate and 0.05, as discussed in Section 2). We supplement these with data from several other sources. Our primary measure of the human capital stock is the Barro & Lee (2001) dataset on educational attainment, which captures the average educational attainment of the population aged 15 and older. Our supplementary educational data—such as the pupil-teacher ratio and educational expenditures—were mainly from the UNESCO Institute for Statistics’ _Global Education Statistics_ database. Our primary governance

> 10System GMM allows for control of (weak) endogeneity using internal instruments, which is a distinct advantage for addressing possible endogeneity in the governance variable. System GMM was chosen over difference GMM (Arellano & Bond 1991) due to the discontinuous nature of the discontinuities nature the annual data.

> 11There are additional issues associated with the practical estimation of the augmented Solow model, many of which have been raised before by other authors (Dowrick & Rogers 2002; Hall & Jones 1999). These include, _inter alia_ , assumptions of homogeneous cross-country technology and a failure to distinguish between the effects of diminishing returns and technology transfer. We do not propose to resolve these additional issues here—doing so would go far beyond the scope of this paper—but we wish to reiterate that the focus here is on resolving the human capital puzzle, not on testing the Solow model.

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