Econometrics Problem Set #3

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Econometrics

Problem Set #3

Topic 1: Interactions

Suppose you have data on blood pressure and chocolate consumption for a sample of dogs and cats. What regression can you run to determine whether the association between chocolate consumption and blood pressure is different for dogs and for cats? Write down the SRF and the hypothesis test you would need to conduct.

Topic 2: Instrumental Variables

Suppose you wanted to do an instrumental variables analysis of the effect of switching to a higher quality school on students’ test scores. Economist Bruce Sacerdote does precisely this in his paper “When the Saints Go Marching Out: Long-Term Outcomes for Student Evacuees from Hurricanes Katrina and Rita” (American Economic Journal: Applied Economics, 4(1): 109–35.). The paper looks at the impact of two major natural disasters that occurred in 2005 – Hurricanes Katrina and Rita – on school switching. In particular, for people living in the hardest hit areas of Louisiana, entire families were forced to evacuate and relocate.

Sacerdote documents that Katrina evacuees from the New Orleans school district – a predominantly poor and low-scoring district – moved to schools with substantially higher average test scores in the immediate aftermath of the hurricane. The author also shows that New Orleans evacuees attending schools outside the New Orleans metropolitan statistical area (MSA) four years after Katrina experienced significant test score gains between 2005 and 2009, compared with other evacuees and other Louisiana students. However, Sacerdote is concerned that evacuee families who permanently left the New Orleans area after Katrina may be different from those who did not. Therefore, the author uses the severity of hurricane damage in the area where students lived pre-Katrina as an instrument for leaving the New Orleans MSA. The first stage and IV estimates are statistically significant and substantively large – Sacerdote finds that leaving the New Orleans MSA is associated with an increase in both math and English test scores of nearly 0.5 standard deviations.

1) Define the outcome (Y), the endogenous regressor (X), and the instrument (Z) in the context of this study.

2) Is the instrument relevant? Explain why or why not.

3) Describe one specific example that shows the instrument is likely not exogenous.

Topic 3: Oregon Health Experiment

Read the case about Oregon’s Medicaid Expansion.

1) How many Oregon residents volunteered to participate in the Medicaid expansion? What did the State randomly assign to these volunteers?

2) How many volunteers won the lottery? How many of those who won enrolled in Medicaid? Why are these two numbers different?

3) How many of those who lost ended up with insurance by the end of the study? Is this surprising?

4) Based on your answers to parts 1-3, identify the always-takers, never-takers, and compliers. Explain why the compliers drive the results from this study.

5) Exhibit B in the case shows that the Local Average Treatment Effect (LATE) of Medicaid participation on emergency room visits is 0.408. Assume that the impact of winning the lottery on Medicaid participation is 0.3. Calculate the Intent to Treat (ITT) effect of winning the lottery on emergency room visits. (You may ignore statistical significance. Hint: Think about instrumental variables! (IV = RF/FS)

Topic 4: Difference-in-Difference

The Tax Reform Act of 1986 introduced a new tax subsidy for health insurance purchases by the self-employed, starting in 1987. The subsidy did not apply to those employed by others. Gruber and Poterba (1994) analyze the changing patterns of insurance demand before and after the tax reform to estimate how the after-tax price of insurance affects the choice of whether to buy insurance.

The authors use a difference-in-difference (diff-in-diff) model, where the outcome is a dummy variable for whether you are insured:

1) Who is the treatment group and who is the control group in this model?

2) What threats to internal validity does the diff-in-diff strategy address?

3) What threats to internal validity does the diff-in-diff strategy not address?

4) Explain how you would interpret each coefficient.

5) Below is Table VI on page 720, which shows the proportion of individuals who have insurance by time period and self-employment status. Find , and in this table and interpret these statistics in words. Does the subsidy cause more people to buy insurance, and is the effect statistically significant?

6) In 1987, GDP growth slowed down in the U.S. Does this fact create any omitted variable bias in the difference-in-difference model?