We consider a randomized experiment, the Tennessee STARexperiment, where students and teachers are randomly assigned toeither a small class (15 students) and a regular class (24students).
We want to estimate the e?ect of smaller class in primary schooland use the following linear model:
Score = ?0 + ?1ClassSize + Controls + u,
where Score is student’s academic score, Class Size is dummy forsmall class, and controls includes free lunch status, race, gender,teacher characteristics and so on.
However, you estimate the following model instead:
Score = ?0 + ?1ClassSize + v
A. Provide the conditions for the OLS estimator for ?1 to beunbiased.
B. Provide the Gauss-Markov assumptions for the OLS estimator for?1.
C. Evaluate the sign and the magnitude of bias ?1 if teacher’sexperience has positive e?ect on score and more experiencedteachers are more likely to be assigned to regular class.
D. Suppose that teachers and students are randomly assigned toeither a small class (15 students) or a regular class. Compare ?1to ?1.
E. How does the OLS estimator for ?1 change as we additionallyinclude parental characteristics as Controls?
