This exercise uses data from the STAR experiment introduced in Chapter 7, Sections 7.5.3 and 7.5.4. In the STAR experiment children were randomly assigned within schools into three types of classes: small classes with 13–17 students, regular-sized classes with 22–25 students, and regular-sized classes with a full-time teacher aide to assist the teacher. Student scores on achievement tests were recorded, as was some information about the students, teachers, and schools. Data for the kindergarten classes is contained in the data file star.dat.

(a) Estimate a regression equation (with no fixed or random effects) where MATHSCORE is related to SMALL, AIDE, TCHEXPER, BOY, and WHITE_ASIAN. Discuss the results. Do students perform better at math when they are in small classes? Does a teacher’s aide improve scores? Do the students of more experienced teachers score higher on math tests? Does gender or race make a difference?

(b) Re-estimate the model in part

(a) with school fixed effects. Compare the results with those in part (a). Have any of your conclusions changed?

(c) Test for the significance of the school fixed effects. Under what conditions would we expect the inclusion of significant fixed effects to have little influence on the coefficient estimates of the remaining variables?

(d) Re-estimate the model in part

(a) with school random effects. Compare the results with those from parts

(a) and (b). Are there any variables in the equation that might be correlated with the school effects?

(e) Using the t-test statistic in (15.37) and a 5% significance level, test whether there are any significant differences between the fixed effects and random effects estimates of the coefficients on SMALL, AIDE, TCHEXPER, and WHITE_ASIAN.

What are the implications of the test outcomes? What happens if we apply the test to the fixed and random effects estimates of the coefficient on BOY?

(f) Estimate a random effects model omitting AIDE and including TCHMASTERS and SCHURBAN. What do you conclude about the effect of the two new variables on MATHSCORE? What happens if you try to get fixed effects estimates of this model?