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Optimal bandwidth selection for local linear estimation of discontinuity in density

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  • Jales, Hugo
  • Ma, Jun
  • Yu, Zhengfei

Abstract

We derive an optimal bandwidth selection rule for estimating a function of two one-sided limits of the probability density function at two cut-off points by the local linear estimation method. Our rule follows Arai and Ichimura (2015, AI, hereafter)’s principle and selects two bandwidths simultaneously, one for each cut-off point. Simulation results are presented. We also illustrate the usefulness of the method in an empirical application.

Suggested Citation

  • Jales, Hugo & Ma, Jun & Yu, Zhengfei, 2017. "Optimal bandwidth selection for local linear estimation of discontinuity in density," Economics Letters, Elsevier, vol. 153(C), pages 23-27.
    • Handle: RePEc:eee:ecolet:v:153:y:2017:i:c:p:23-27
    DOI: 10.1016/j.econlet.2017.01.024
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    References listed on IDEAS

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    1. Yoichi Arai & Hidehiko Ichimura, 2018. "Simultaneous selection of optimal bandwidths for the sharp regression discontinuity estimator," Quantitative Economics, Econometric Society, vol. 9(1), pages 441-482, March.
    2. Arai, Yoichi & Ichimura, Hidehiko, 2016. "Optimal bandwidth selection for the fuzzy regression discontinuity estimator," Economics Letters, Elsevier, vol. 141(C), pages 103-106.
    3. Gerard, Francois & Rokkanen, Miikka & Rothe, Christoph, 2015. "Identification and Inference in Regression Discontinuity Designs with a Manipulated Running Variable," IZA Discussion Papers 9604, Institute of Labor Economics (IZA).
    4. Wojciech Kopczuk & David Munroe, 2015. "Mansion Tax: The Effect of Transfer Taxes on the Residential Real Estate Market," American Economic Journal: Economic Policy, American Economic Association, vol. 7(2), pages 214-257, May.
    5. Sebastian Calonico & Matias D. Cattaneo & Rocio Titiunik, 2014. "Robust Nonparametric Confidence Intervals for Regression‐Discontinuity Designs," Econometrica, Econometric Society, vol. 82, pages 2295-2326, November.
    6. Hugo Jales, 2018. "Estimating the effects of the minimum wage in a developing country: A density discontinuity design approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(1), pages 29-51, January.
    7. 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.
    8. Emmanuel Saez, 2010. "Do Taxpayers Bunch at Kink Points?," American Economic Journal: Economic Policy, American Economic Association, vol. 2(3), pages 180-212, August.
    9. Hugo Jales & Zhengfei Yu, 2017. "Identification and Estimation Using a Density Discontinuity Approach," Advances in Econometrics, in: Regression Discontinuity Designs, volume 38, pages 29-72, Emerald Group Publishing Limited.
    10. Patrick Bajari & Han Hong & Minjung Park & Robert Town, 2011. "Regression Discontinuity Designs with an Endogenous Forcing Variable and an Application to Contracting in Health Care," NBER Working Papers 17643, National Bureau of Economic Research, Inc.
    11. 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.
    12. Yoichi Arai & Hidehiko Ichimura, 2013. "Optimal Bandwidth Selection for Differences of Nonparametric Estimators with an Application to the Sharp Regression Discontinuity Design," CIRJE F-Series CIRJE-F-889, CIRJE, Faculty of Economics, University of Tokyo.
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    Cited by:

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    3. Rajesh, Richu & G., Rajesh & Sunoj, S.M., 2022. "Kernel estimation of extropy function under length-biased sampling," Statistics & Probability Letters, Elsevier, vol. 181(C).

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    More about this item

    Keywords

    Bandwidth selection; Density discontinuity; Local linear estimation;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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