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460 Chapter 11 Regression with a Binary Dependent Variable

11.5 Using the results in column (7):

a. Akira is a man with 10 years of schooling. What is the probability that
the government will employ him?

b. Jane is a woman with 12 years of schooling. What is the probability
that the government will employ her?

c. Does the effect of the years of schooling on employment in the gov-
ernment depend on gender? Explain.

11.6 Use the estimated probit model in Equation (11.8) to answer the following
questions:

a. A black mortgage applicant has a P/I ratio of 0.35. What is the prob-
ability that his application will be denied?

b. Suppose that the applicant reduced this ratio to 0.30. What effect
would this have on his probability of being denied a mortgage?

c. Repeat (a) and (b) for a white applicant.
d. Does the marginal effect of the P/I ratio on the probability of mortgage

denial depend on race? Explain.

11.7 Repeat Exercise 11.6 using the logit model in Equation (11.10). Are the
logit and probit results similar? Explain.

11.8 Consider the linear probability model Yi = b0 + b1Xi + ui, where
Pr(Yi = 1 ͉ Xi) = b0 + b1Xi.

a. Show that E(ui ͉ Xi) = 0.
b. Show that var(ui ͉ Xi) = (b0 + b1Xi)[1 - (b0 + b1Xi)]. [Hint: Review

Equation (2.7).]
c. Is ui heteroskedastic? Explain.
d. (Requires Section 11.3) Derive the likelihood function.

11.9 Use the estimated linear probability model shown in column (1) of
Table 11.2 to answer the following:

a. Two applicants—one self-employed and one salaried—apply for a
mortgage. They have the same values for all the regressors other than
employment status. How much more likely is it for the self-employed
applicant to be denied a mortgage?

b. Construct a 95% confidence interval for your answer to (a).

c. Think of an important omitted variable that might create a bias in the
answer to part (a). What is the variable, and how would it create a
bias in the results?