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Robust Data-Driven Inference for Density-Weighted Average Derivatives

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  • Cattaneo, Matias D.
  • Crump, Richard K.
  • Jansson, Michael

Abstract

This paper presents a new data-driven bandwidth selector compatible with the small bandwidth asymptotics developed in Cattaneo, Crump, and Jansson (2009) for density-weighted average derivatives. The new bandwidth selector is of the plug-in variety, and is obtained based on a mean squared error expansion of the estimator of interest. An extensive Monte Carlo experiment shows a remarkable improvement in performance when the bandwidth-dependent robust inference procedure proposed by Cattaneo, Crump, and Jansson (2009) is coupled with this new data-driven bandwidth selector. The resulting robust data-driven confidence intervals compare favorably to the alternative procedures available in the literature.
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  • Cattaneo, Matias D. & Crump, Richard K. & Jansson, Michael, 2010. "Robust Data-Driven Inference for Density-Weighted Average Derivatives," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1070-1083.
    • Handle: RePEc:bes:jnlasa:v:105:i:491:y:2010:p:1070-1083
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    7. Ichimura, Hidehiko & Todd, Petra E., 2007. "Implementing Nonparametric and Semiparametric Estimators," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 74, Elsevier.
    8. Horowitz, Joel & Hardle, Wolfgang, 1994. "Direct Semiparametric Estimation of Single-Index Models With Discrete Covariates," Working Papers 94-22, University of Iowa, Department of Economics.
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    Cited by:

    1. Kaido, Hiroaki, 2017. "Asymptotically Efficient Estimation Of Weighted Average Derivatives With An Interval Censored Variable," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1218-1241, October.
    2. Matias D. Cattaneo & Max H. Farrell & Michael Jansson & Ricardo Masini, 2022. "Higher-order Refinements of Small Bandwidth Asymptotics for Density-Weighted Average Derivative Estimators," Papers 2301.00277, arXiv.org, revised Feb 2024.
    3. Cattaneo, Matias D. & Jansson, Michael & Newey, Whitney K., 2018. "Alternative Asymptotics And The Partially Linear Model With Many Regressors," Econometric Theory, Cambridge University Press, vol. 34(2), pages 277-301, April.
    4. Matias D Cattaneo & Michael Jansson & Xinwei Ma, 2019. "Two-Step Estimation and Inference with Possibly Many Included Covariates," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(3), pages 1095-1122.
    5. Cattaneo, Matias D. & Crump, Richard K. & Jansson, Michael, 2014. "Small Bandwidth Asymptotics For Density-Weighted Average Derivatives," Econometric Theory, Cambridge University Press, vol. 30(1), pages 176-200, February.
    6. Belloni, Alexandre & Chernozhukov, Victor & Chetverikov, Denis & Fernández-Val, Iván, 2019. "Conditional quantile processes based on series or many regressors," Journal of Econometrics, Elsevier, vol. 213(1), pages 4-29.
    7. Dong, Hao & Otsu, Taisuke & Taylor, Luke, 2021. "Average Derivative Estimation Under Measurement Error," Econometric Theory, Cambridge University Press, vol. 37(5), pages 1004-1033, October.
    8. Atchadé, Yves F. & Cattaneo, Matias D., 2014. "A martingale decomposition for quadratic forms of Markov chains (with applications)," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 646-677.
    9. Dennis Kristensen, 2009. "Semiparametric modelling and estimation (in Russian)," Quantile, Quantile, issue 7, pages 53-83, September.
    10. Andrews, Donald W.K. & Shi, Xiaoxia, 2014. "Nonparametric inference based on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 179(1), pages 31-45.
    11. Yukitoshi Matsushita & Taisuke Otsu, 2018. "Likelihood Inference on Semiparametric Models: Average Derivative and Treatment Effect," The Japanese Economic Review, Japanese Economic Association, vol. 69(2), pages 133-155, June.
    12. Yukitoshi Matsushita & Taisuke Otsu, 2018. "Likelihood Inference on Semiparametric Models: Average Derivative and Treatment Effect," The Japanese Economic Review, Springer, vol. 69(2), pages 133-155, June.
    13. Yukitoshi Matsushita & Taisuke Otsu, 2019. "Jackknife, small bandwidth and high-dimensional asymptotics," STICERD - Econometrics Paper Series 605, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    14. Valeri Voev, 2009. "On the Economic Evaluation of Volatility Forecasts," CREATES Research Papers 2009-56, Department of Economics and Business Economics, Aarhus University.
    15. Matias D. Cattaneo & Richard K. Crump & Michael Jansson, 2013. "Rejoinder," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1265-1268, December.
    16. Matias D. Cattaneo & Richard K. Crump & Max H. Farrell & Ernst Schaumburg, 2020. "Characteristic-Sorted Portfolios: Estimation and Inference," The Review of Economics and Statistics, MIT Press, vol. 102(3), pages 531-551, July.
    17. Ulrich K. Müller & Yulong Wang, 2017. "Fixed- Asymptotic Inference About Tail Properties," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1334-1343, July.

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models

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