Angrist and Pischke \({ }^{29}\) report estimation results of log-earnings equations using a large sample of college graduates. The predictors of interest (there are others included in their model) are the indicator variable PRIVATE ( \(=1\) if the individual attended a private college or university,\(=0\) if the individual attended a public college or university) and \(S A T / 100\), the individual's SAT score divided by 100. In the estimated regression equations, the dependent variable is \(\ln\) (EARNINGS) and they include an intercept. The coefficient estimates, with standard errors in brackets, for two regressions that they estimate, are as follows.

a. In each model, what is the approximate effect on earnings of attending a private university rather than a public university?

b. In the second model, what is the predicted effect on earnings of a 100-point increase in SAT score?

c. The estimated coefficient of PRIVATE is smaller in the second model than in the first model. Use the concept of "omitted variables bias" to explain this result.

d. What should happen to the estimated coefficients in equation (XR7.4.2) if parental income is included as an explanatory variable? Explain.

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0.212[0.060]PRIVATE 0.152 [0.057]PRIVATE +0.051 [0.008] (SAT/100) (XR7.4.1) (XR7.4.2)