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

Exercise 8

Using the data set CollegeDistance described in Empirical Exercise, carry out the following exercises.
a. Run a regression of years of completed education (ED ) on distance to the nearest college (Dist ). What is the estimated slope
b. Run a regression of ED on Dist , but include some additional regressors to control for characteristics of the student, the student's family, and the local labor market. In particular, include as additional regressors Bytest, Female, Black, Hispanic, Incomehi, Ownhome, Dad Coll, Cue80, and Stwmfg80. What is the estimated effect of Dist on EDI
c. Is the estimated effect of Dist on ED in the regression in (b) substantively different from the regression in (a) Based on this, does the regression in (a) seem to suffer from important omitted variable bias
d. Compare the fit of the regression in (a) and (b) using the regression standard errors, R 2 and 2. Why are the R 2 and 2 so similar in regression (b)
e. The value of the coefficient on DadColl is positive. What does this coefficient measure
f. Explain why Cue80 and Swmfg80 appear in the regression. Are the signs of their estimated coefficients (+ or -) what you would have believed Interpret the magnitudes of these coefficients.
g. Bob is a black male. His high school was 20 miles from the nearest college. His base-year composite test score (Bytest ) was 58. His family income in 1980 was $26,000, and his family owned a home. His mother attended college, but his father did not. The unemployment rate in his county was 7.5%, and the state average manufacturing hourly wage was $9.75. Predict Bob's years of completed schooling using the regression in (b).
h. Jim has the same characteristics as Bob except that his high school was 40 miles from the nearest college. Predict Jim's years of completed schooling using the regression in (b).
Empirical Exercise
On the text Web site http://www.pearsonhighered.com/stock_watson/ , you will find a data file CollegeDistance that contains data from a random sample of high school seniors interviewed in 1980 and re-interviewed in 1986. In this exercise, you will use these data to investigate the relationship between the number of completed years of education for young adults and the distance from each student's high school to the nearest four-year college. (Proximity to college lowers the cost of education, so that students ' who live closer to a four-year college should, on average, complete more years of higher education.) A detailed description is given in College Distance_Description, also available on the Web site. 2
a. Run a regression of years of completed education (ED ) on distance to the nearest college (Dist ), where Dist is measured in tens of miles. (For example, Dist = 2 means that the distance is 20 miles.) What is the estimated intercept What is the estimated slope Use the estimated regression to answer this question: How does the average value of years of completed schooling change when colleges are built close to where students go to high school
b. Bob's high school was 20 miles from the nearest college. Predict Bob's years of completed education using the estimated regression. How would the prediction change if Bob lived 10 miles from the nearest college
c. Does distance to college explain a large fraction of the variance in educational attainment across individuals Explain.
d. What is the value of the standard error of the regression What are the units for the standard error (meters, grams, years, dollars, cents, or something else)