Question

1. Given Assumption 1: Conditional distribution of ui given Xi has mean zero: E[ui |Xi ] = 0

(a) Suppose Xi and ui are independent and that E[ui ] = 0. Show that Assumption 1 holds.

(b) In the late 1980s, the Tennessee government ran project STAR. It cost $12m to implement at the time (the Tennessee budget on K-12 education was $212m in FY 2018-19). In project STAR, students and teachers were randomly assigned small (13-17 students) or large (22-25 students). Given data on 3733 students in the experiment, you wish to estimate Yi = β0 + β1Xi + ui where Yi is the test score for student i, and Xi = 1 if student i was in a small class and 0 if student i was in a large class. Explain why Assumption 1 holds in this setting.

Answer 1