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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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    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. Arai, Yoichi & Ichimura, Hidehiko, 2016. "Optimal bandwidth selection for the fuzzy regression discontinuity estimator," Economics Letters, Elsevier, vol. 141(C), pages 103-106.
    10. 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).
    11. 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.
    12. 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.
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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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