Introduction to Econometrics 3rd Edition by James Stock, Mark Watson

Exercise 3

Use the data set CPS08 described in Empirical Exercise 1 to answer the following questions.
a. Run a regression of average hourly earnings ( AHE) on age (Age). What is the estimated intercept What is the estimated slope
b. Run a regression of AHE on Age, gender (Female), and education (Bachelor). What is the estimated effect of Age on earnings Construct a 95% confidence interval for the coefficient on Age in the regression.
c. Are the results from the regression in (b) substantively different from the results in (a) regarding the effects of Age and AHEl Does the regression in (a) seem to suffer from omitted variable bias
d. Bob is a 26-year-old male worker with a high school diploma. Predict Bob's earnings using the estimated regression in (b). Alexis is a 30-year-old female worker with a college degree. Predict Alexis's earnings using the regression.
e. Compare the fit of the regression in (a) and (b) using the regression standard errors, R 2 and R 2. Why are the R 2 and R 2 so similar in regression (b)
f. Are gender and education determinants of earnings Test the null hypothesis that Female can be deleted from the regression. Test the null hypothesis that Bachelor can be deleted from the regression. Test the null hypothesis that both Female and Bachelor can be deleted from the regression.
g. A regression will suffer from omitted variable bias when two conditions hold. What are these two conditions Do these conditions seem to hold here
Exercise 1
Suppose that a researcher, using data on class size ( CS ) and average test scores from 100 third-grade classes, estimates the OLS regression
= 520.4 5.82 X CS, R 2 = 0.08, SER = 11.5.
a. A classroom has 22 students. What is the regression's prediction for that classroom's average test score
b. Last year a classroom had 19 students, and this year it has 23 students. What is the regression's prediction for the change in the classroom average test score
c. The sample average class size across the 100 classrooms is 21.4. What is the sample average of the test scores across the 100 classrooms (Hint: Review the formulas for the OLS estimators.)
d. What is the sample standard deviation of test scores across the 100 classrooms (Hint: Review the formulas for the R 2 and SER.)