Homework assignment due mardi, 8 dec

1. Exercise 10.2: Regression discontinuity analysis: suppose you are trying to evaluate the effect of a new procedure for coronary bypass surgery that is supposed to help with the post-operative healing process. The new procedure is risky, however, and is rarely performed in patients who are over 80 years old. Data from this (hypothetical) example are displayed in Figure 10.10.

(a) Does this seem like an appropriate setting in which to implement a regression discontinuity analysis?

(b) The folder bypass contains data for this example: stay is the length of hospital stay after surgery, age is the age of the patient, and new is the indicator variable indicating that the new surgical procedure was used. Pre-operative disease severity (severity) was unobserved by the researchers but we have access to it for illustrative purposes. Can you find any evidence using these data that the regression discontinuity design is inappropriate?

2. Exercise 10.3: Instrumental variables: come up with a hypothetical example in which it would be appropriate to estimate treatment effects using an instrumental variables strategy. For simplicity, stick to an example with a binary instrument and binary treatment variable.

(a) Simulate data for this imaginary example assuming all the assumptions are met. Estimate the local average treatment effect (LATE) for the data by dividing the intent-to-treat effect by the percentage of compliers. Show that two-stage least squares yields the same point estimate.

(b) Now simulate data in which the exclusion restriction is not met (so, for instance, those whose treatment level is left unaffected by the instrument have a treatment effect of half the magnitude of the compliers) but the instrument is strong (say, 80% of the population are compliers) and see how far off your estimate is.

(c) Finally simulate data in which the exclusion restriction is violated in the same way, however, the instrument is weak (only 20% of the population are compliers) and see how far off your estimate is.