Question One
Use the data in wage2.dta for this exercise and the option robust.
Estimate the model
〖log(wage)〗_i=β_0+〖β_1 black〗_i+〖β_2 married〗_i+〖β_3 educ〗_i+〖β_4 exper〗_i+〖β_5 tenure〗_i+〖β_6 south〗_i+〖β_7 urban〗_i+u_i.
Holding other factors fixed, what is the approximate difference in monthly salary between blacks and non-blacks? Is this difference statistically significant?
Add the variables 〖exper〗_i^2 and 〖tenure〗_i^2 to the equation and test their join significance.
Extend the original model in (a) to allow the return to education (〖educ〗_i) to depend also on race and test whether the return to education does depend on race.
Re-estimate the original model, but now allow the intercept for the wage equation to differ across the four groups of people: married and black, married and non-black, single and black, and single and non-black.
What is the estimated wage differential between the four groups?
Repeat (d) allowing both the intercept and the return to education (〖educ〗_i) to differ across the four groups of people.
Graph the relationship between (the log of) estimated wages in (f) and the level of education? Use the –margins– and –marginsplot– for this exercise. What do you conclude concerning the relative evolution of wages between the four categories as a function of wages?
Question Two
Exercises (a) through (g) are based on the following scenario: 700 income-earning individuals from a district were randomly selected and asked whether they were employed by the government (Govi = 1) or failed their entrance test (Govi = 0); data were also collected on their gender (Malei = 1) if male and = 0 if female) and their years of schooling (Schoolingi, in years). The following table summarizes several estimated models.
Using the results in column (1):
Does the probability of working in the government depend on Schooling? Explain.
Matthew has 16 years of schooling. What is the probability that he will pass the test?
Christopher never went to college (12 years of schooling). What is the probability that he will get a job with the government?
The sample included values of Schooling between 0 and 18 years, and only five people in the sample had more than 15 years of schooling. Jed has completed a PhD and has been a student for 24 years. What is the model’s prediction for the probability that Jed will get a job with the government? Do you think that this prediction is reliable? Why or why not?
Answer (i) through (iii) in (a) using the results in column (2).
Sketch the predicted probabilities from the probit and logit in columns (1) and (2) for values of Schooling between 0 and 18. Are the probit and logit models similar?
Answer (i) through (iii) in (a) using the results in column (3).
Sketch the predicted probabilities from the probit and linear probability in columns (1) and (3) as a function of Schoolingi for values of Schooling between 0 and 18. Do you think that the linear probability is appropriate here? Why or why not?
Using the results in columns (4) through (6):
Compute the estimated probability of passing the test for men and for women.
Are the models in (4) through (6) different? Why or why not?
Using the results in column (7):
Akira is a man with 10 years of schooling. What is the probability that the government will employ him?
Jane is a woman with 12 years of schooling. What is the probability that the government will employ her?
Does the effect of the years of schooling on employment in the government depend on gender? Explain.
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