03 Jun Question 1. The table below presents the sample means and regression results from a study of the gender gap in hourly wages among workers with
Question
1. The table below presents the sample means and regression results from a study of the gender gap in hourly wages among workers with more than a high school education. The Armed Forces Qualifying Test (AFQT) is a test used to determine if an individual has the mental ability to be in the military. It is a cross between an IQ test and the SAT. The numbers in parentheses are standard errors.
Use these data to decompose the gender gap into the portion “explained” by the included variables and the portion left “unexplained”. You can do the decompositions using log wages or convert the estimates to wages first. Please show or explain your calculations. (You do not need to decompose the “explained” portion by variable types.)
2. I would like you to use the NJ 2012 dataset posted on the course website to run two simple wage regressions and then interpret the results.
a. Restricting your sample to full-year (wkswork2>5), full-time (uhrswork >34) workers, estimate a regression where the dependent variable is the natural log of wage and salary income [ln(incwage)] and the explanatory variables are age, age-squared, and an indicator variable for whether an individual is female. [Define female = 1 if sex=2, and female = 0 if sex =1.]
Interpret the results. What do estimates reveal about how wages vary with age and sex?
b. Again restricting your sample to full-year (wkswork2>5), full-time (uhrswork >34) workers, estimate a regression where the dependent variable is the log of wage and salary income [log(incwage)] and the explanatory variables are age, age-squared, the indicator variable for whether an individual is female, and indicator variables for the completed level of education. Here are the variables you should use to capture an individual’s level of education:
The education categories defined by these variables are “mutually exclusive.” That is, an individual can only belong to one of these groups (so only one of these variables can be equal to 1 for any given observation).
The “excluded” category (the category for which all of these variables are equal to zero) is high school graduates with less than a year of college (educ00 = 9 or 10). The coefficients on the education variables indicate the difference between the specified group and the excluded category, high school graduates.
Interpret the results of this regression. What do the estimates reveal about how wages vary with the level of education?
c. What happens to the coefficient on the female indicator variable between regression (a) and regression (b)? What does that tell us about the role education levels play in explaining the gender gap?
d. What happens to the R-squared between regression (a) and regression (b)? What does this change reveal?
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