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Robust Data-Driven Inference for Density-Weighted Average Derivatives

Author

Listed:
  • Matias D. Cattaneo

    (Department of Economics, University of Michigan)

  • Richard K. Crump

    (Federal Reserve Bank of New York)

  • Michael Jansson

    () (Department of Economics, UC Berkeley and CREATES)

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.

Suggested Citation

  • Matias D. Cattaneo & Richard K. Crump & Michael Jansson, 2009. "Robust Data-Driven Inference for Density-Weighted Average Derivatives," CREATES Research Papers 2009-46, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2009-46
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    References listed on IDEAS

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    1. Horowitz, J. L. & Härdle, Wolfgang, 1994. "Direct Semiparametric Estimation of Single - Index Models with Discrete Covariates," SFB 373 Discussion Papers 1994,36, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Hardle, Wolfgang & Tsybakov, A. B., 1993. "How sensitive are average derivatives?," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 31-48, July.
    3. Y. Nishiyama & P. M. Robinson, 2000. "Edgeworth Expansions for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 68(4), pages 931-980, July.
    4. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    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(01), pages 176-200, February.
    6. Hardle, W. & Hart, J. & Marron, J. & Tsybakov, A., 1991. "Bandwidth choice for average derivative estimation," CORE Discussion Papers 1991049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Whitney K. Newey & Fushing Hsieh & James M. Robins, 2004. "Twicing Kernels and a Small Bias Property of Semiparametric Estimators," Econometrica, Econometric Society, vol. 72(3), pages 947-962, May.
    8. Robinson, P M, 1995. "The Normal Approximation for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 63(3), pages 667-680, May.
    9. 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.
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    Citations

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    Cited by:

    1. repec:bla:jecrev:v:69:y:2018:i:2:p:133-155 is not listed on IDEAS
    2. 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(02), pages 277-301, April.
    3. repec:taf:jnlasa:v:112:y:2017:i:519:p:1334-1343 is not listed on IDEAS
    4. 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.
    5. 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.
    6. Matias D. Cattaneo & Michael Jansson & Xinwei Ma, 2018. "Two-Step Estimation and Inference with Possibly Many Included Covariates," Papers 1807.10100, arXiv.org.
    7. Andrews, Donald W.K. & Shi, Xiaoxia, 2014. "Nonparametric inference based on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 179(1), pages 31-45.
    8. Alexandre Belloni & Victor Chernozhukov & Ivan Fernandez-Val, 2011. "Conditional quantile processes based on series or many regressors," CeMMAP working papers CWP19/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. Kaido, Hiroaki, 2017. "Asymptotically Efficient Estimation Of Weighted Average Derivatives With An Interval Censored Variable," Econometric Theory, Cambridge University Press, vol. 33(05), pages 1218-1241, October.
    10. 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.
    11. 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.

    More about this item

    Keywords

    Average derivatives; Bandwidth selection; Robust inference; Small bandwidth asymptotics;

    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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