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 postoperative healing process. The new...

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 postoperative 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. Preoperative 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?

(c) Estimate the treatment effect using a regression discontinuity estimate (ignoring) severity. Estimate the treatment effect in any way you like, taking advantage of the information in severity. Explain the discrepancy between these estimates.