Question

We consider a randomized experiment, the Tennessee STAR experiment, where students and teachers are randomly assigned to either a small class (15 students) and a regular class (24 students).

We want to estimate the effect of smaller class in primary school and use the following linear model:
Score = β0 + β1ClassSize + Controls + u,
where Score is student’s academic score, Class Size is dummy for small class, and controls includes free lunch status, race, gender, teacher characteristics and so on.

However, you estimate the following model instead:
Score = α0 + α1ClassSize + v

A. Provide the conditions for the OLS estimator for α1 to be unbiased.
B. Provide the Gauss-Markov assumptions for the OLS estimator for α1.
C. Evaluate the sign and the magnitude of bias α1 if teacher’s experience has positive effect on score and more experienced teachers are more likely to be assigned to regular class.
D. Suppose that teachers and students are randomly assigned to either a small class (15 students) or a regular class. Compare α1 to β1.
E. How does the OLS estimator for β1 change as we additionally include parental characteristics as Controls?

Answer 1