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Simple Local Polynomial Density Estimators

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  • Matias D. Cattaneo
  • Michael Jansson
  • Xinwei Ma

Abstract

This article introduces an intuitive and easy-to-implement nonparametric density estimator based on local polynomial techniques. The estimator is fully boundary adaptive and automatic, but does not require prebinning or any other transformation of the data. We study the main asymptotic properties of the estimator, and use these results to provide principled estimation, inference, and bandwidth selection methods. As a substantive application of our results, we develop a novel discontinuity in density testing procedure, an important problem in regression discontinuity designs and other program evaluation settings. An illustrative empirical application is given. Two companion Stata and R software packages are provided.

Suggested Citation

  • Matias D. Cattaneo & Michael Jansson & Xinwei Ma, 2020. "Simple Local Polynomial Density Estimators," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(531), pages 1449-1455, July.
    • Handle: RePEc:taf:jnlasa:v:115:y:2020:i:531:p:1449-1455
    DOI: 10.1080/01621459.2019.1635480
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    1. Jens Ludwig & Douglas L. Miller, 2007. "Does Head Start Improve Children's Life Chances? Evidence from a Regression Discontinuity Design," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(1), pages 159-208.
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    3. 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.
    4. Burt S. Barnow & Matias D. Cattaneo & Rocío Titiunik & Gonzalo Vazquez‐Bare, 2017. "Comparing Inference Approaches for RD Designs: A Reexamination of the Effect of Head Start on Child Mortality," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 36(3), pages 643-681, June.
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