Consider a probit model explaining the choice to attend college by high-school graduates. Define (C O L

Question:

Consider a probit model explaining the choice to attend college by high-school graduates. Define $C O L L E G E=1$ if a high-school graduate chooses either a 2-year or 4-year college, and zero otherwise. We use explanatory variables GRADES, 13 point scale with 1 indicating highest grade $(\mathrm{A}+)$ and 13 the lowest (F); FAMINC, gross family income in $\$ 1000$ units; and $B L A C K=1$ if black. Using a sample of $N=1000$ graduates the estimated model is

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a. What information is provided by the signs of the estimated coefficients? Which coefficients are statistically significant at the $5 \%$ level?

b. Estimate the probability of attending college for a white student with $G R A D E S=2(\mathrm{~A})$ and $F A M I N C=50(\$ 50,000)$. Repeat this probability calculation if GRADES $=5(\mathrm{~B})$

c. Estimate the probability of attending college for a black student with $G R A D E S=5(\mathrm{~B})$ and $F A M I N C=50(\$ 50,000)$. Compare this probability to the comparable probability for a white student calculated in part (b).

d. Calculate the marginal effect of an increase in family income of $\$ 1000$ on the probability of attending college for a white student with GRADES $=5(\mathrm{~B})$.

e. The log-likelihood for the model estimated above is -423.36 . Omitting FAMINC and BLACK the $\log$-likelihood of the estimated probit model is -438.26 . Test the joint significance of FAMINC and BLACK at the $1 \%$ level of significance using a likelihood ratio test.

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