Economics of Education Assignment

1. Education Production Functions. Consider the following education production function:

test i = b 1 + b 2 class _ size i + b 3 free _ lunch i + b 4 class _ size i ∗ free _ lunch ,
ˆ
where test i represents student i’s predicted test score in percentil points, class _ size i is i’s class size,  and free _ lunch i equals 1 if i receives a federally subsidized lunch at school, 0 otherwise.
a. Suppose that b3 = 0.05 . Interpret this finding. (Hint: Evaluate the production function for
free _ lunchi = 0 and for free _ lunchi = 1 .)

b. Suppose that b2 = −0.01 and b4 = −0.005 . Interpret this finding. Are the class size effects
larger for students on free lunch, larger for students not on free lunch, or the same for both?
Explain. (Hint: Same as above.)
c. Suppose that the education production function above is estimated using data from Project
STAR. Does b 2 give a biased estimate of the true causal effect of class size on test scores? Why
or why not?

d. Suppose once again that the education production function above is estimated using data from
Project STAR. Does b 2 tell us anything about how test scores would be affected by a large-scale
class-size reduction program? Why or why not?

3. Understanding Peer Effects and the Social Multiplier. Sacerdote (QJE, 2001) estimates the following equation:

GPAi = φ 0 + φ1GPAir + φ 2 SATir + φ 3 SATi + εi
where GPAi represents student i’s predicted grade point average, GPAir is i’s roommates’ GPA and
SAT represents scores on the Scholastic Aptitude Test.

a. How do you interpret φ 2 the coefficient on roommate SAT. If individuals chose their roommates in the sample, would you be concerned with the estimate of φ 2 ? Why or why not?

b. Now suppose that roommates are randomly assigned. How do you interpret φ1 the coefficient on roommate GPA? What concerns might you have regarding potential biases in this estimate?
c. Now suppose the equation is re-estimated excluding roommate GPA and, φ 2 , the coefficient on roommate SAT is positive and statistically significant. Could the University use this information to better sort individuals into roommate pairs? Why or why not? Fully explain.