NOTE: For questions using Stata, please type your answers into a word processing document (using MS Word or something similar). Insert the
relevant part of your Statalog fileinto your document, and clearly explain how your Stata output answers the question.
1. Estimate the following three regressions using the NLSY dataset:
a. Interpretall of the estimated coefficients (slopes and intercept) for the third model, being as specific as possible. Which of these
coefficients are statistically significant, at a significance level of 0.05? (Note: you will have to generate lwage = log(wage) and also
generate the interaction variable.) (2 points)
b. Show how the coefficients in the third model can be used to exactly recover the coefficients in the first two models.For example, how
are the γcoefficients related to the α and β coefficients?(Note: to get the coefficients in the first two models, type reglwage school if
male==1 and reglwage school if male==0) (2 points).
c. Draw a picture to scale (by hand) based on the estimatesfor the third model, with log(wage) on the y-axis and school on the x-axis.
(1point)
d. Previous studies have found that a year of education increases average wages by approximately 8 percent. Using the second regression
model, test the hypothesis that the coefficient on schoolfor men differs from 0.08. Perform the test using the regression output and issuing a
Stata command (hint: type help test if you don’t remember how to do this…not ttestbut test). Do you reject the hypothesis? Why or why not?
Choose a significance level of 0.05. (2 points)
e. Test the same hypothesis for women. Do you reject the hypothesis? Why or why not? Choose a significance level of 0.05. (2 points)
2. This problem is intended to examine the relationship between education and wages.
a. Run a regression of the log of wages on education (type reglwage school). Draw a picture that represents the regression line (again,
just draw your graphs by hand). (2 points)
b. Create 3 dummy variablesthat represent education categories. The first equals 1 if education is less than 12 years and zero otherwise
(you could call it dropout and code it “gen dropout = (school<12)”, the next equals 1 if education is exactly 12 years and zero otherwise (you
could name it hsgrad and type “gen hsgrad = (school==12)”), and the last equals 1 if education is greater than 12 (you could call it college).
Run a regression of lwage on these dummy variables, remembering to exclude one (it would probably be easiest if you excluded dropout). Add the
estimated regression line to the same picture from part (a). (2 points)
c. Calculate the mean of log wages for individuals in these 3 education categories (for example, “sum lwage if dropout==1”). How do these
compare to the predicted values from the regression that you ran in part (b)?(2 points)
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