Nonparametric Regression with Stochastic Boundary and Regression Discontinuity with Endogenous Cutoff
13 Pages Posted: 23 Jan 2020
Date Written: December 28, 2019
We augment the usual regression discontinuity design model by considering an endogenously chosen cutoﬀ, perhaps chosen to maximize certain criterion that the treatment provider has. This regime faces the challenge that, conditional on realization of the cutoﬀ, observations are no longer i.i.d. We develop conditions under which an asymptotic expansion of the locally linear estimator contains a bias term caused by the endogeneity of order op(h2 +1/√nh). The lower order bias justiﬁes the usual optimal bandwidth selection and bias correction procedures in this setting, though it places constraints on the maximal degree of undersmoothing.
Keywords: Regression discontinuity, Nonparametric regression
JEL Classification: C10, C14
Suggested Citation: Suggested Citation