Minimum Contrast Empirical Likelihood Inference of Discontinuity in Density*

Jun Ma, Hugo Borges Jales, Zhengfei Yu

Research output: Contribution to journalArticle


This article 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. Our approach is based on the first-order conditions from a minimum contrast problem. We investigate both first-order and second-order properties of the proposed method. We characterize the leading coverage error of our inference method and propose a coverage-error-optimal (CE-optimal, hereafter) bandwidth selector. We 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. 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 an empirical example.

Original languageEnglish (US)
JournalJournal of Business and Economic Statistics
StatePublished - Jan 1 2019


  • Bandwidth selection
  • Discontinuity in density
  • Empirical likelihood

ASJC Scopus subject areas

  • Statistics and Probability
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

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