Use GPA3.RAW for this exercise. The data set is for 366 student-athletes from a large university for fall and spring semesters. [A similar analysis is in Maloney and McCormick (1993), but here we use a true panel data set.] Because you have two terms of data for each student, an unobserved effects model is appropriate. The primary question of interest is this: Do athletes perform more poorly in school during the semester their sport is in season?
(i) Use pooled OLS to estimate a model with term GPA (trmgpa) as the dependent variable. The explanatory variables are spring, sat, hsperc, female, black, white, frstsem, tothrs, crsgpa, and season. Interpret the coefficient on season. Is it statistically significant?
(ii) Most of the athletes who play their sport only in the fall are football players. Suppose the ability levels of football players differ systematically from those of other athletes. If ability is not adequately captured by SAT score and high school percentile, explain why the pooled OLS estimators will be biased.
(iii) Now, use the data differenced across the two terms. Which variables drop out? Now, test for an in-season effect.
(iv) Can you think of one or more potentially important, time-varying variables that have been omitted from the analysis?