Minimum Contrast Empirical Likelihood Manipulation Testing for Regression Discontinuity Design

This paper proposes a simple empirical-likelihood-based inference method for discontinuity in density. In a regression discontinuity design (RDD), the continuity of the density of the assignment variable at the threshold is considered as a “nomanipulation” behavioral assumption, which is a testable implication of an identifying condition for the local treatment effect (LATE). Our approach is based on the first-order conditions obtained from a minimum contrast (MC) problem and complements Otsu et al. (2013)’s method. Our inference procedure has three main advantages. Firstly, it requires only one tuning parameter; secondly, it does not require concentrating out any nuisance parameter and therefore is very easily implementable; thirdly, its delicate second-order properties lead to a simple coverage-error-optimal (CE-optimal) bandwidth selection rule. We propose a data-driven CE-optimal bandwidth selector for use in practice. Results from Monte Carlo simulations are presented. Usefulness of our method is illustrated by empirical examples.