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# For this assignment, we will use the data set voucher posted on Canvas

INSTRUCTIONS TO CANDIDATES

1. Private schools, academic achievement, and instrumental variables

For this assignment, we will use the data set voucher posted on Canvas. This data was used in an influential economics paper to estimate the effect of attending a private school on students’ academic achievement (Rouse 1998). In 1990, the city of Milwaukee in the United States began providing vouchers for students to attend private schools. Public schools are free in the U.S. but private schools often charge large fees. In this exercise, we will consider how attending one of these private schools affected students’ test scores using instrumental variables.

The variable choiceyrs indicates the number of years that a student attended a private school. This is our treatment. The city used a lottery program to select students to receive a voucher to pay for the cost of private school attendance. The variable selectyrs indicates the number of years that a student was selected by lottery to get a voucher. This variable will serve as our instrument. The data span 1991-1994, so each of these variables can take on numbers from zero to four. Our outcome of interest is students’ percentile score on a math test administered in 1994. This variable is called mnce.

a. We would like to estimate the relationship between the number of years a student attended the private school (choiceyrs) and their score on a standardized math test (mnce). One possible estimating equation is the following:

ππππππ  = π½0 + π½1πβππππππ¦ππ  + ππππ

However, we have seen in class that we cannot obtain an unbiased or consistent estimate of π½1 if πβππππππ¦ππ  is correlated with the error term. Why might πβππππππ¦ππ  be correlated with the error term in this case? (This is a conceptual question; you do not need to use Stata to answer it, just think about reasons why attending a private school might be correlated with other factors that could affect math scores.) (3 points)

b. Of the 990 students in the sample, how many were never awarded a voucher? How many had a voucher available for four years? How many students actually attended a choice school for four years? (Hint: Try using the tabulate command in Stata.) (3 points)

c. Now let’s consider whether selectyrs is a good instrument for choiceyrs. Run a regression of choiceyrs on selectyrs. Interpret the coefficient on selectyrs and say whether the sign of this relationship is what you expected. Which of the three conditions for selectyrs to be a good instrument are we testing with this regression? Does selectyrs appear to satisfy this condition? (4 points)

d. Estimate the equation in part (a) without using an instrumental variable. Interpret the coefficient on choiceyrs. What do your results say about the relationship between private school attendance and math scores? (3 points)

e. Suppose that selectyrs meets all of the conditions to be an instrument for choiceyrs. (Because it is a random lottery, we can safely assume that it is uncorrelated with the error term and satisfies the exclusion restriction.)

Estimate the equation in part (a) using instrumental variables with selectyrs as the IV for choiceyrs. Does using IV produce a positive effect of attending a private school on math scores? (Hint: You will use a Stata command called ivgregress 2sls for this problem. Use the command help ivregress 2sls to read the Stata manual’s instructions for how to use this command.) (2 points)

f. Do you think the coefficient on choiceyrs in part (d) or part (e) provides a better estimate of the effect of attending a private school on math scores? Please explain. (2 points)

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