Stata Project 4: Testing Coefficients

Econ 330: Econometrics
Professor Lemke
Fall 2008

Due: Thursday, November 20

The data for this problem are in Stata format: project4.dta. The data set contains five variables on 704 individuals. The variables are race (1=hispanic, 2=black, 3=white), age, school (years of schooling), sex (F=female, M=male), and annual labor income. For this assignment, complete each of the parts below. Write a program that executes the entire problem set. Turn in a hard copy of your program. Also turn in a hard copy of the actual answers, edited and explained clearly.

  1. Create dummy variables for race (hispanic, black, and white) and sex (female and male). Also create age2 to equal the square of age, and create lnwage to equal the natural log of annual earnings. Keep (and order) wage, lnwage, age, age2, school, hispanic, black, white, female, and male. Provide the summary statistics for this data set. Save this dataset as coeftests2.dta.

  2. Regress wages on age, age squared, years of schooling, race (omit white), and sex (omit male). Given what you know about wages, do the results generally make sense? Summarize the residuals of the regression. Plot the residuals from the regression against age. (Include the graph in your answers.) Explain why the residuals should make one question the model specification.

  3. Regress logged wages on age, age squared, years of schooling, race (omit white), and sex (omit male). (Let this be called Model 3, as this is problem 3.) Given what you know about wages, do the results generally make sense? Summarize the residuals of the regression. Plot the residuals from the regression against age. (Include the graph in your answers.) Explain why the residuals might give one more confidence in this model over the one in problem 2.

  4. Re-estimate Model 3, then answer the following questions.
    1. Test the claim that there is no difference between being black or hispanic on wages.
    2. Test the claim that there is no effect of race of wages.
    3. Test the claim that each year of additional schooling increases expected wages by nine percent.
    4. Test the claim that the gender differential is ten percent.
    5. Describe the predicted relationship between age and ln(wages) as completely as possible.

  5. Using Model 3, again test the claim that the return to each additional year of schooling is nine percent, but this time do not use Stata's test command. Rather, estimate an unrestricted model and a restricted model to obtain the sum of squared residuals. Then calculate the F-statistic and (ball-park or calculate precisely) the p-value. (Extra credit to anyone who can program Stata to do these calculations -- without using the test or any similar command.)

  6. Using Model 3, conduct the F-test that all variables have no effect. Do not rely on Stata's output of this statistic, but rather compute it by estimating a restricted and unrestricted model. Then calculate the F-statistic and (ball-park or calculate precisely) the p-value. (If you are hoping to receive extra credit in problem 5, then you must also program Stata to calulate the F-statistic and p-value for this question.)

  7. Estimate a model wherein ln(wages) depends on age, age-squared, schooling, and sex. Test the claim (using a Chow test) that the coefficients of this model are the same regardless of race. (Hint: this will require four regressions.)

  8. Estimate a model that includes age, age squared, and sex and allows for a different intercept and a different return for each year of schooling by race, then answer the following questions.
    1. Test the claim that there is no difference in the return to each year of schooling for the three races.
    2. Test the claim that there is no difference in the return to each year of schooling for blacks and hispanics.

  9. Estimate a model that allows all coefficients on age, age-squared, schooling, and sex to vary by race. Then test (using Stata's test command) whether the gender differential is statistically different between whites and blacks; between blacks and hispanics; between whites and hispanics; and between all three races.