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Introduction to Modern Economic Growth schooling are as important as private returns (which would correspond to very large externalities) Rauch estimated significant external returns, with the magnitude of the external returns often exceeding the private returns External returns of this magnitude would imply that human capital differences could play a much more important role as a proximate source of cross-country differences in income per capita than implied by the computations in Chapter However, Rauch’s regressions exploited differences in average schooling levels across cities, which could reflect many factors that also directly affect wages For example, wages are much higher in New York City than Ames, Iowa, but this is not only the result of the higher average education of New Yorkers A more convincing estimate of external returns necessitates a source of exogenous variation in average schooling Acemoglu and Angrist (2000) exploited differences in average schooling levels across states and cohorts resulting from changes in compulsory schooling and child labor laws These laws appear to have had a large effect on schooling, especially at the high school margin Exploiting changes in average schooling in state labor markets driven by these law changes, Acemoglu and Angrist estimate external returns to schooling that are typically around or percent and statistically insignificant (as compared to private returns of about 10%) These results suggest that there are relatively small human capital externalities in local labor markets This result is confirmed by a study by Duflo (2004) using Indonesian data and by Ciccone and Perri (2006) Moretti (2002) also estimates human capital externalities, and he finds larger effects This may be because he focuses on college graduation, but also partly reflects the fact that the source of variation that he exploits, changes in age composition and the presence of land-grant colleges, may have other effects on average earnings in area Overall, the evidence appears to suggest that local human capital externalities are not very large, and calibration exercises as those in Chapter that ignore these externalities are unlikely to lead to significant downward bias in the contribution of human capital to cross-country income differences The qualification “local” in the above discussion has to be emphasized, however The estimates discussed above focus on local externalities originally emphasized by Jacobs Nevertheless, if a few very talented scientists and engineers, or other very 494

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