Minimum Contrast Empirical Likelihood Inference of Discontinuity in Density*

Jun Ma, Hugo Borges Jales, Zhengfei Yu

Research output: Contribution to journalArticle

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.

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

Fingerprint

Likelihood Inference
Empirical Likelihood
Optimal Bandwidth
Selector
Discontinuity
manipulation
Manipulation
Coverage
One-sided limit
Regression
coverage
Average Treatment Effect
First-order
regression
Testing
Order Conditions
Likelihood Ratio Statistic
Data-driven
Probability density function
Asymptotic Properties

Keywords

  • Bandwidth selection
  • Discontinuity in density
  • Empirical likelihood

ASJC Scopus subject areas

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

Cite this

Minimum Contrast Empirical Likelihood Inference of Discontinuity in Density*. / Ma, Jun; Borges Jales, Hugo; Yu, Zhengfei.

In: Journal of Business and Economic Statistics, 01.01.2019.

Research output: Contribution to journalArticle

@article{dd94f090d2574fe8a47cf5e35ec5708a,
title = "Minimum Contrast Empirical Likelihood Inference of Discontinuity in Density*",
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.",
keywords = "Bandwidth selection, Discontinuity in density, Empirical likelihood",
author = "Jun Ma and {Borges Jales}, Hugo and Zhengfei Yu",
year = "2019",
month = "1",
day = "1",
doi = "10.1080/07350015.2019.1617155",
language = "English (US)",
journal = "Journal of Business and Economic Statistics",
issn = "0735-0015",
publisher = "American Statistical Association",

}

TY - JOUR

T1 - Minimum Contrast Empirical Likelihood Inference of Discontinuity in Density*

AU - Ma, Jun

AU - Borges Jales, Hugo

AU - Yu, Zhengfei

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Bandwidth selection

KW - Discontinuity in density

KW - Empirical likelihood

UR - http://www.scopus.com/inward/record.url?scp=85068548796&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85068548796&partnerID=8YFLogxK

U2 - 10.1080/07350015.2019.1617155

DO - 10.1080/07350015.2019.1617155

M3 - Article

JO - Journal of Business and Economic Statistics

JF - Journal of Business and Economic Statistics

SN - 0735-0015

ER -