time periods is suspect, and where comparable data are available, they are often only for a very limited set of (mostly developed) countries. Moreover, our instrumental variables strategy already accounts for issues of mismeasurement, conditional on our instruments satisfying the necessary exclusion conditions. Nonetheless, we use a recently-compiled database of comparable achievement data (Altinok & Murseli 2007) to examine how our results change when we utilize a more accurate measure of human capital quality. The results are reported in column ( _Z3_ ).<sup>25</sup> Human capital remains significant, and in this case its contribution more than doubles, so that a 1 percent increase in human capital leads to an almost 8 percent increase in output per worker. We do note the far poorer fit of the specification, however, which we feel justifies our decision not to use this measure as our primary measure of human capital.

The microeconometric literature on education production functions suggests that, in addition to the pupil-teacher ratio, several other inputs have been important (Hanushek 2003; Pritchett & Filmer 1999). We include, as additional instruments, a selection of the determinants that have been found to be more consistently significant: The percentage of trained teachers (as a macroeconomic proxy for teacher ability, usually measured with teachers’ years of schooling or experience), and public education expenditures (a macroeconomic proxy for resources devoted to teacher salaries and school infrastructure). This specification is reported in column ( _Z4_ ).<sup>26</sup> Although the results are once again similar, we note that the specification suffers from a small sample problem, which may limit inference.<sup>27</sup> The next three columns, ( _Z5_ )–( _Z7_ ), introduce interaction terms between governance and resource inputs. These are for governance and school inputs, governance and family inputs, and family and school inputs, respectively. Although not fully justified by our theoretical model, the interaction term allows for the possibility that the efficacy of school inputs may be conditional on the institutional environment. This is intuitively plausible, and the interaction term also serves as a possible instrument that is orthogonal to the error term in the second stage. Adding these interaction terms, however, does not modify our principal conclusions concerning the coefficient for human capital, which remains relatively stable throughout. Note, however, that ( _Z5_ ) does not satisfy the overidentification test.

Our final three specifications endogenize the most potentially problematic instrumental variable: Government effectiveness. Column ( _Z8_ ) uses lagged government effectiveness (from 1996) as an instrument for contemporaneous (year 2000) governance. The magnitude of the human capital contribution falls, but remains significant at the 1 percent level, while the coefficient for physical

> 25We are again forced, by virtue of satisfying the overidentification test, to exclude family inputs from the instrument set.

> 26The microeconomic literature also finds that teacher quality is a very important source of variation in student performance (Hanushek 2003). Unfortunately, there is close to no international data available for teacher quality.

> 27Other permutations and combinations of these additional school inputs yielded similar significant coefficients for human capital, but typically did not satisfy the overidentification test.

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