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Table 3 presents a series of reduced form education and earnings equations and the correpondin structural estimates of the return to education, using college proximity as an instrumental variable completed education. Columns 1 and 2 show the coefficients of an indicator for college proximity in models for years of schooling. Columns 3 and 4 show the coefficients of the college proximity variable in reduced form wage equations ( i.e models that exclude education). Finally, columns 5 and 6 report the iv estimates of the return to education: these are simply the ratios of the corresponding reduced form coefficients in the earnings and schooling equations. The modes in columns 1, 3 and 5 exclude parental education and family structure variable while the models in colums 2, 4 and 6 include these variables.
Two alternative specifications are reported in the upper and lower panels of the table. The models in the upper panel (panel A) include the conventional measures of experience and experience – squared constructed from observerd age and education.
If schooling is measured with error, however, then experience is also mismeasured --- suggesting possible biases in the reduced form models in panel A. By the same token, if education is truly endogenous in the earnings equation, the so is experience, since experience is mechanically related to education. Therefore, in the lower panel (panel B) I have estimad models that instrument experience and experience – squared with age and age – squared.
Regardless of the inclusion or exclusion of family background variables, and irrespective of the treatment of experience, the conclusions from table 3 are similar. Growing up near a college has strong positive effect on both education (0.32 to 0.38 years of schooling) and earnings (4.2 to 4.8 percent). The use of college proximity as an exogenous determiant of schooling yields IV estimates of the return to education in the range of 0.12 to 0.14. These estimates are 50 -60 percent higher than the corresponding ols estimates----about the same relative ratio as reported by butcher and case (1993), Kane and Rouse (1993), and Angrist and Krueguer /1993). Nevertheless, the standard error of the IV estimates are relatively large, and one cannot reject the hypothesis that differences between the IVand OLS estimates are due to sampling error.
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Under the null hypothesis that the OLS estimates are consistent the variance of the difference between the IV and OLS estimates of the return to education is the difference in their variances, which is approximately equal to the variance of the IV estimate.