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

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?

2. Replication of Card and Krueger (1996) analysis. The below table presents findings from a
replication of the Card and Krueger’s analysis, but for two different southern states (Alabama and
Mississippi) and for a different measure of school resources (average term length, measured in days).
Answer the following questions using the information reported in this table and the data on the
“question 1” worksheet of exercise2.xls.
a.

Using the data given in the question 1 worksheet, plot average term length for blacks in Alabama
and for blacks Mississippi (y-axis) against year (x-axis). (Note: The resulting figure will look
something like Figure 3 in the original paper, but with only 2 lines. To create this graph, use
Chart Wizard in Microsoft Excel, and choose line graph.)

b. On the basis of the graph created in part (a), would you say that school resources have
historically been lower for blacks in Alabama or in Mississippi?
c. Mississippi produced more cotton than Alabama during the antebellum (pre Civil War) period.
i. Does this help to explain the trends seen in the figure produced in part (a)? Explain.

ii. Suppose that the cropping patterns in Alabama and Mississippi were largely a result of differences in soil types or climate. Describe how this historical accident might create a “natural experiment” that can be used to estimate the effect of school resources on skill.
d. Using the data given in the question 1 worksheet, plot average educational attainment against birth cohort by state of birth for blacks. Do the trends in educational attainment appear to be consistent with the trends in term length described in part (b)? Explain. (Note: The resulting figure will look something like Figure 4 in the original paper. To create this graph, use Chart Wizard in Excel, and choose line graph.)
e. The attached table shows the differences between Alabama and Mississippi in average educational attainment and average term length for five birth cohorts, separately by race. Using this table, answer each of the questions below.
i. For blacks, which of the differences in average educational attainment are statistically significant?
ii. What is the implied effect of term length on educational attainment for blacks? [For each cohort, find the ratio of the AL-MS difference in educational attainment to the AL-MS difference in term length.]

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

GPAi = ? 0 + ?1GPAir + ? 2 SATir + ? 3 SATi + ?i
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.

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