Minimum Contrast Empirical Likelihood Inference of Discontinuity in Density* |
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Authors: | Jun Ma Hugo Jales Zhengfei Yu |
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Institution: | 1. School of Economics, Renmin University of China, 59 Zhongguancun Street, Haidian District, Beijing 100872, China;2. Department of Economics, Syracuse University, 426 Eggers Hall, Syracuse, NY 13244;3. Faculty of Humanities and Social Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8571, Japan |
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Abstract: | AbstractThis 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. |
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Keywords: | Bandwidth selection Discontinuity in density Empirical likelihood |
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