Tests for detecting probability mass points

Byung Hill Jun, Hosin Song

Research output: Contribution to journalArticlepeer-review

Abstract

The objective of this paper is developing test statistics to detect the presence of mass points when data are possibly generated by a mixture of a continuous and a discrete distribution. To serve our purpose we propose two versions of the probability mass point (PMP) test. We derive the limiting distributions of the PMP test statistics under the null and alternative hypothesis by exploiting the asymptotic difference between two kernel density estimators with different bandwidths. Specifically, the proposed PMP test statistic is shown to converge to either the standard normal distribution or a linear transformation of a positive Poisson distribution at a non-mass point depending on bandwidths choice, while it diverges to infinity at a mass point. Numerical experiments are conducted to demonstrate the validity of our proposed tests. Korean taxpayers’ bunching behavior is considered as an empirical application.

Original languageEnglish
Pages (from-to)205-248
Number of pages44
JournalKorean Economic Review
Volume35
Issue number1
DOIs
StatePublished - 2019

Bibliographical note

Funding Information:
We are grateful for the helpful comments from two anonymous referees and seminar participants at the Asian Meeting of the Econometric Society, WEAI 89th Annual Conference, the 2016 China Meeting of the Econometric Society, the 2017 Autumn Meeting of JAAE, and the 2018 Annual Meeting of the Korean Econometric Society. This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2014S1A5A8018660) and by the Hankuk University of Foreign Studies Research Fund.

Funding Information:
* We are grateful for the helpful comments from two anonymous referees and seminar participants at the Asian Meeting of the Econometric Society, WEAI 89th Annual Conference, the 2016 China Meeting of the Econometric Society, the 2017 Autumn Meeting of JAAE, and the 2018 Annual Meeting of the Korean Econometric Society. This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2014S1A5A8018660) and by the Hankuk University of Foreign Studies Research Fund. ** First Author, Associate Professor, Department of International Economics and Law, Hankuk University of Foreign Studies, 107 Imun-ro, Dongdaemun-gu, Seoul, 02450, Korea. E-mail: bjun@hufs.ac.kr. *** Corresponding Author, Associate Professor, Department of Economics, Ewha Womans University, 52 Ewhayeodae-gil, Seodaemun-gu, Seoul, 03760, Korea. E-mail:hsong@ewha.ac.kr.

Publisher Copyright:
© 2019, Korean Economic Association. All rights reserved.

Keywords

  • Bunching
  • Kernel Density Estimator
  • Probability Mass Point Test

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