Quiz 6

1. Researchers looked to estimate the effect of service on lifetime earnings for veterans following the Vietnam War. Because there is a great deal of endogeneity associated with earnings, they opted to instrument veteran status with draft lottery number. Why would this have been a good instrument?
1. Lottery numbers were randomly assigned to birthdates and men with low lottery numbers were substantially more likely to have served.
2. Lottery numbers were randomly assigned to birthdates and an even mix of drafted men and volunteers joined the military.
3. Men with low lottery numbers were substantially more likely to have served, giving the instrument strong predictive power, but wealthier men were better able to avoid service regardless of their lottery number, potentially linking lottery number to earnings through channels other than service.
4. Men with low lottery numbers were substantially more likely to have served, and because the lottery was public knowledge, anticipating conscription likely strengthened this relationship further.
2. A school gives free after-school tutoring to students who score 50 or below on a midterm math test. You use a regression discontinuity research design to see how tutoring affects math grades at the end of the year. Identify the outcome, treatment, running variable (RV), and cutoff.
1. Cutoff = whether a student scores below 50 on the midterm; RV = final math grade; outcome = midterm scores; treatment = tutoring
2. Cutoff = whether a student passes the class; RV = midterm grade; treatment = tutoring; outcome = final grade
3. Cutoff = midterm score; RV = whether a student scores a 50 or below on the midterm; treatment = tutoring; outcome = final grade
4. Cutoff = whether a student scores below 50 on the midterm; RV = midterm score; treatment = tutoring; outcome = final grade
3. In this case, why might researchers care if the regression discontinuity is fuzzy or sharp?
1. If some students above 50 attended tutoring anyway, or some below 50 did not show up, the jump in outcomes at the cutoff would understate the true effect of tutoring.
2. If students just below 50 differ systematically from those just above in unobserved ways — such as motivation or parental support — the design is fuzzy and the local comparison around the cutoff is no longer credible.
3. If the design is fuzzy, it suggests students or teachers manipulated scores to just below 50 to gain access to tutoring, which would bias the estimated effect upward.
4. A fuzzy design requires researchers to use a wider bandwidth around the cutoff in order to include enough compliers to estimate the effect of tutoring precisely.
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Answer

C

4. Which of the following would not make a good RD design?
1. Estimating the effect of Medicaid eligibility on health outcomes, using the income threshold below which households qualify for coverage.
2. Estimating the effect of alcohol access on traffic accidents, using the minimum legal drinking age of 21.
3. Estimating the effect of prison sentences on recidivism, using the sentencing guidelines score above which judges are required to impose a custodial term.
4. Estimating the effect of attending UVA on lifetime earnings, using the SAT score cutoff above which applicants are admitted upon initially applying.
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Answer

D, because it would be too fuzzy so as not to actually make that much of a difference. Also, the running variable itself may have another impact on the outcome of lifetime earnings.

A paper used results from data on US House elections between 1946 and 1998 to measure the effect of being in office (incumbency) on the likelihood of winning.

1. What is the running variable?
1. Probability of victory in Election t
2. Democratic vote share in Election t
3. Democratic vote share margin of victory in Election t
4. Democratic vote share margin of victory in Election t + 1
2. What is the outcome variable?
1. Probability of victory in Election t
2. Democratic vote share in Election t
3. Democratic vote share margin of victory in Election t
4. Democratic vote share margin of victory in Election t + 1
3. Given the cutoff, what is the treatment?
1. Running as the challenger to the incumbent
2. Running as the incumbent
3. Belonging to the same party as the president
4. Is this a sharp or fuzzy discontinuity?
1. Sharp
2. Fuzzy
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Answer

Trick question: it should be sharp because the treatment is being an incumbent.

5. From the graph, what qualitative conclusion can you draw about the research question?
1. Republicans who barely won an election are just as likely to win the next election as Republicans who barely lost, suggesting there is no incumbency advantage.
2. Democrats who barely won an election are substantially more likely to win the next election than Democrats who barely lost, suggesting a significant incumbency advantage.
3. There are diminishing returns to “winning big” for probability of victory in the next election, suggesting candidates should give up after they have a small lead in the polls.
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Answer

B