Run a regression of average hourly earnings AHE on age AGE.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Use the Assignment I data set 1 which contain data for full-time workers. Data are provided for workers whose highest educational achievement is either a high school degree or a bachelor’s degree. The variables are:

 

FEMALE: 1 if female; 0 if male; 

AHE : Average Hourly Earnings; 

BACHELOR: 1 if worker has a bachelor’s degree; 0 if worker has a high school degree AGE: workers age 25-34 years. 

This assignment is about predicting the earnings of the workers by investigating the relationship between worker’s age, gender and education. Answer the following questions in word file and insert the stata output in your word file. Keep all works in a log file and submit the log file as well. 

a. Run a regression of average hourly earnings AHE on age AGE. What is the value of the estimated intercept. What is the value of the estimated slope? Using the estimated regression answer this question: How much do earnings increase as workers age increases by one year.

b. Suppose Bob is a 26-year-old worker. Predict Bob’s earnings using the estimated regression. Alexis is a 30-years-old worker. Predict Alexis’ earnings using the regression.

c. Does AGE account for a large fraction of the variance in earnings across individuals? Explain

d. Now suppose earnings depend on age and also on the gender and education of the worker. Run a regression of AHE on AGE, FEMALE (i.e., gender), and BACHELOR (i.e., education). Construct a 95% confidence interval for the coefficient of AGE in the regression.

e. Are the results from regression in (d) substantially different from the results in (a) regarding the effects of AGE on AHE? Do you think the regression of (a) suffers from the omitted variable bias? Explain, without any tests.

f. Bob is a 26-year-old male worker with a high school degree. Predict Bob’s earnings using the estimated regression in (d). Alexis is a 30-year-old female worker with a bachelor degree. Predict Alexis’ earnings using the regression in (d)

g. Compare the fit of the regressions in (a) and (d) using adjusted R2. Can you explain why the R2 and adjusted R2 so similar in the regression in (d).

h. Are gender and education important determinant of earnings? Test the null hypothesis at 0.05 significance that FEMALE can be deleted from the regression (i.e., FEMALE = 0). Test the null hypothesis at 0.05 significance that BACHELOR can be deleted from the regression. Test the null hypothesis at 0.05 significance that both FEMALE and BACHELOR can be deleted from the regression.

i. Perform diagnostic tests on regression (d). Specifically, perform heteroskedasticity test, omitted variable bias test and multicollinearity test. What do you find? Explain what problems your regression in (d) are suffering from. Give recommendation about what solutions there might be.

j. Suppose that the correct specification of earnings equation is nonlinear in both log of the dependent variables and polynomial in age. Create a new variable ln(AHE) which is log of AHE and another variable that is square of age, i.e., AGE2 (i.e., AGE× AGE). Now run a regression of ln(AHE) on AGE, AGE2, FEMALE, BACHELOR. Alexis is a 30-year-old female worker with a bachelor degree. What does the regression predict for the value of her ln(AHE). Bob is a 26-year-old male worker with a high school degree. What does the regression predict for the value of her ln(AHE).

 

k. Create a new variable which is an interaction term by multiplying FEMALE × BACHELOR. 

Now run a regression of ln(AHE) on AGE, AGE2, FEMALE, BACHELOR and the interaction term FEMALE × BACHELOR. Alexis is a 30-year-old female worker with a bachelor degree. What does the regression predict for the value of her ln(AHE). Bob is a 26-year-old male worker with a high school degree. What does the regression predict for the value of her ln(AHE).

 

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