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Tests for Detecting Probability Mass Points

Author

Listed:
  • Byung-hill Jun

    (Hankuk University of Foreign Studies)

  • Hosin Song

    (Ewha Womans University,)

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.

Suggested Citation

  • Byung-hill Jun & Hosin Song, 2019. "Tests for Detecting Probability Mass Points," Korean Economic Review, Korean Economic Association, vol. 35, pages 205-248.
  • Handle: RePEc:kea:keappr:ker-20190101-35-1-08
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    as
    1. Chirok Han & Jin Seo Cho & Peter C. B. Phillips, 2011. "Infinite Density at the Median and the Typical Shape of Stock Return Distributions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(2), pages 282-294, April.
    2. Zinde-Walsh, Victoria, 2008. "Kernel Estimation When Density May Not Exist," Econometric Theory, Cambridge University Press, vol. 24(3), pages 696-725, June.
    3. Pudney, Stephen, 2008. "Heaping and leaping: survey response behaviour and the dynamics of self-reported consumption expenditure," ISER Working Paper Series 2008-09, Institute for Social and Economic Research.
    4. Raj Chetty & John N. Friedman & Tore Olsen & Luigi Pistaferri, 2011. "Adjustment Costs, Firm Responses, and Micro vs. Macro Labor Supply Elasticities: Evidence from Danish Tax Records," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 126(2), pages 749-804.
    5. Cho, Jin Seo & White, Halbert, 2010. "Testing for unobserved heterogeneity in exponential and Weibull duration models," Journal of Econometrics, Elsevier, vol. 157(2), pages 458-480, August.
    6. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, September.
    7. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(4), pages 631-653.
    8. Bastani, Spencer & Selin, Håkan, 2014. "Bunching and non-bunching at kink points of the Swedish tax schedule," Journal of Public Economics, Elsevier, vol. 109(C), pages 36-49.
    9. Emmanuel Saez, 2010. "Do Taxpayers Bunch at Kink Points?," American Economic Journal: Economic Policy, American Economic Association, vol. 2(3), pages 180-212, August.
    10. Miguel Almunia & David Lopez-Rodriguez, 2018. "Under the Radar: The Effects of Monitoring Firms on Tax Compliance," American Economic Journal: Economic Policy, American Economic Association, vol. 10(1), pages 1-38, February.
    11. Steffen Otterbach & Alfonso Sousa-Poza, 2010. "How Accurate are German Work-time Data? A Comparison of Time-diary Reports and Stylized Estimates," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 97(3), pages 325-339, July.
    12. Henrik Jacobsen Kleven & Camille Landais & Esben Schultz, 2014. "Migration and Wage Effects of Taxing Top Earners: Evidence from the Foreigners' Tax Scheme in Denmark," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(1), pages 333-378.
    13. Taisuke Otsu & Ke-Li Xu & Yukitoshi Matsushita, 2013. "Estimation and Inference of Discontinuity in Density," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(4), pages 507-524, October.
    14. Arulampalam, Wiji & Corradi, Valentina & Gutknecht, Daniel, 2017. "Modeling heaped duration data: An application to neonatal mortality," Journal of Econometrics, Elsevier, vol. 200(2), pages 363-377.
    15. Donald W. K. Andrews, 1986. "Complete Consistency: A Testing Analogue of Estimator Consistency," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(2), pages 263-269.
    16. Petoussis, Kos & Gill, Richard & Zeelenberg, Kees, 1997. "Statistical analysis of heaped duration data," MPRA Paper 89263, University Library of Munich, Germany.
    17. Burgstahler, David & Dichev, Ilia, 1997. "Earnings management to avoid earnings decreases and losses," Journal of Accounting and Economics, Elsevier, vol. 24(1), pages 99-126, December.
    18. Wändi Bruine de Bruin & Paul S. Fischbeck & Neil A. Stiber & Baruch Fischhoff, 2002. "What Number is “Fifty‐Fifty”?: Redistributing Excessive 50% Responses in Elicited Probabilities," Risk Analysis, John Wiley & Sons, vol. 22(4), pages 713-723, August.
    19. McCrary, Justin, 2008. "Manipulation of the running variable in the regression discontinuity design: A density test," Journal of Econometrics, Elsevier, vol. 142(2), pages 698-714, February.
    20. S. Zinn & A. Würbach, 2016. "A statistical approach to address the problem of heaping in self-reported income data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(4), pages 682-703, March.
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    More about this item

    Keywords

    Bunching; Kernel Density Estimator; Probability Mass Point Test;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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