Regression Discontinuity Marginal Threshold Treatment Effects

Consider a standard regression discontinuity model, where an outcome Y is determined in part by a binary treatment indicator T, which always (in sharp designs) or sometimes (in fuzzy designs) equals one when a running variable X exceeds a threshold c, and zero otherwise. It is well known that in … these models a local average treatment effect can be nonparametrically identified under very general conditions. We show that the derivative of this treatment effect with respect to the threshold c is also nonparametrically identified in both sharp and fuzzy designs, and can be easily estimated. This marginal threshold treatment effect (MTTE) may be used to estimate the impacts of small changes in the threshold, e.g., we use it to show how raising the age of Medicare eligibility would change the probability of take up of various types of health insurance.