Question

The Ministry of Education wants to know whether attending a private school has a positive causal effect on student test scores. The Ministry provides you with data that covers all students in the province of Ontario. The data include each student's grade average and whether he or she attends a public or private school. Note that attending a private school is an active choice made by students and parents (all students are guaranteed a spot in a public school) and students are required to pay tuition to attend (public schools are free).

You define the independent variable of interest as

??=   1 if student attends a private school

  0 otherwise

Let ??? denote the grade average of student ?. You consider estimating the following regression in order to evaluate the effect of attending a private school on student grade average:

???=?0+?1??+??

Please answer the following questions.

a/ Interpret the parameter ?0. What does it represent?

b/ Interpret the parameter ?1. What does it represent?

c/Using the econometric model given by the equation above (???=?0+?1??+??), write down (mathematically) the condition that must be satisfied for OLS estimation of this model to result in an unbiased estimate of ?1. Now interpret this condition (in words). Do you think the condition is satisfied?

d/ Would your answer to question (1c) above change if heteroskedasticity was present in this model? If so, explain how. If not, why not? Make sure to (briefly) define heteroskedasticity in your answer.

Answer 1