Abstract

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.

摘要

本文研究了一种简单的基于经验似然性的密度不连续性推断方法的渐近性质。感兴趣的参数是概率密度函数（可能）在两个截止点的两个单边限制的函数。我们的方法基于最小对比度问题的一阶条件。我们研究了该方法的一阶和二阶性质。我们表征了我们的推理方法的领先覆盖误差，并提出了一个覆盖误差最优（CE最优，以下称）带宽选择器。我们证明经验似然比统计量是巴特利特可校正的。一个重要的特殊情况是回归不连续设计（RDD）中的操纵测试问题，其中感兴趣的参数是已知阈值处的密度差。在RDD中，阈值处分配变量密度的连续性被视为“无操纵”行为假设，这是对局部平均治疗效果的识别条件的可检验含义。当专门针对操纵测试问题时，CE最佳带宽选择器具有显式形式。我们建议在实践中使用数据驱动的CE最佳带宽选择器。给出了蒙特卡洛模拟的结果。一个经验例子说明了我们方法的有效性。CE最佳带宽选择器具有显式形式。我们建议在实践中使用数据驱动的CE最佳带宽选择器。给出了蒙特卡洛模拟的结果。一个经验例子说明了我们方法的有效性。CE最佳带宽选择器具有显式形式。我们建议在实践中使用数据驱动的CE最佳带宽选择器。给出了蒙特卡洛模拟的结果。一个经验例子说明了我们方法的有效性。