Skip to content

Jales paper on discontinuity in density published in Journal of Business & Economic Statistics

Jul 4, 2019

Minimum Contrast Empirical Likelihood Inference of Discontinuity in Density

Jun Ma, Hugo Jales & Zhengfei Yu

Journal of Business and Economic Statistics, July 2019

Hugo Jales

Hugo Jales

This paper investigates the asymptotic properties of a simple empirical-likelihood-based inference method for discontinuity in density. The parameter of interest is a function of two one-sided limits of the probability density function at (possibly) two cut-off points. The authors' approach is based on the first order conditions from a minimum contrast problem. They investigate both first order and second order properties of the proposed method. They characterize the leading coverage error of their inference method and propose a coverage-error-optimal (CE-optimal, hereafter) bandwidth selector. They show that the empirical likelihood ratio statistic is Bartlett correctable.


An important special case is the manipulation testing problem in a regression discontinuity design (RDD), where the parameter of interest is the density difference at a known threshold. In RDD, the continuity of the density of the assignment variable at the threshold is considered as a “no-manipulation” behavioral assumption, which is a testable implication of an identifying condition for the local average treatment effect. When specialized to the manipulation testing problem, the CE-optimal bandwidth selector has an explicit form. The authors propose a data-driven CE-optimal bandwidth selector for use in practice. Results from Monte Carlo simulations are presented. Usefulness of their method is illustrated by an empirical example.