Introduction to Econometrics 3rd Edition by James Stock, Mark Watson

Exercise 17

This exercise uses the same data as Empirical Exercise 1.
a. Estimate a probit model using the same regressors as in Empirical Exercise 2.
b. Test the hypothesis that the coefficient on smkban is zero in the population version of this probit regression against the alternative that it is nonzero, at the 5% significance level. Compare your t -statistic and your conclusion with those of Empirical Exercise 3 based on the linear probability model.
c. Test the hypothesis that the probability of smoking does not depend on the level of education in this probit model. Compare your results with those in Empirical Exercise 11.1(e) using the linear probability model.
d. Mr. A is white, non-Hispanic, 20 years old, and a high school dropout. Using the probit regression from (a) and assuming that Mr. A is not subject to a workplace smoking ban, calculate the probability that Mr. A smokes. Carry out the calculation again assuming that he is subject to a workplace smoking ban. What is the effect of the smoking ban on the probability of smoking
e. Repeat (d) for Ms. B, a female, black, 40-year-old college graduate.
f. Repeat (d) and (e) using the linear probability model from Empirical Exercise 2.
g. Based on the answers to (d) through (f), do the probit and linear probability model results differ If they do, which results make more sense Are the estimated effects large in a real-world sense
h. Are there important remaining threats to internal validity
Exercise 1
Based on the following scenario: Four hundred driver's license applicants were randomly selected and asked whether they passed their driving test ( Pass i = 1) or failed their test ( Pass i = 0); data were also collected on their gender ( Male i = 1 if male and = 0 if female) and their years of driving experience ( Experience i in years). The following table summarizes several estimated models.
Using the results in column (1):
a. Does the probability of passing the test depend on Experience Explain.
b. Matthew has 10 years of driving experience. What is the probability that he will pass the test
c. Christopher is a new driver (zero years of experience). What is the probability that he will pass the test
d. The sample included values of Experience between 0 and 40 years, and only four people in the sample had more than 30 years of driving expe-lienee. Jed is 95 years old and has been driving since he was 15. What is the model's prediction for the probability that Jed will pass the test Do you think that this prediction is reliable Why or why not
Exercise 2
Christopher is a new driver (zero years of experience). What is the probability that he will pass the test
Exercise 3
The sample included values of Experience between 0 and 40 years, and only four people in the sample had more than 30 years of driving expe-lienee. Jed is 95 years old and has been driving since he was 15. What is the model's prediction for the probability that Jed will pass the test Do you think that this prediction is reliable Why or why not