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Bootstrap-Based Inference for Cube Root Consistent Estimators

Author

Listed:
  • Matias D. Cattaneo

    (University of Michigan)

  • Michael Jansson

    (University of California at Berkeley and CREATES)

  • Kenichi Nagasawa

    (University of Michigan)

Abstract

This note proposes a consistent bootstrap-based distributional approximation for cube root consistent estimators such as the maximum score estimator of Manski (1975) and the isotonic density estimator of Grenander (1956). In both cases, the standard nonparametric bootstrap is known to be inconsistent. Our method restores consistency of the nonparametric bootstrap by altering the shape of the criterion function defining the estimator whose distribution we seek to approximate. This modification leads to a generic and easy-to-implement resampling method for inference that is conceptually distinct from other available distributional approximations based on some form of modified bootstrap. We offer simulation evidence showcasing the performance of our inference method in finite samples. An extension of our methodology to general M-estimation problems is also discussed.

Suggested Citation

  • Matias D. Cattaneo & Michael Jansson & Kenichi Nagasawa, 2017. "Bootstrap-Based Inference for Cube Root Consistent Estimators," CREATES Research Papers 2017-18, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2017-18
    as

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    File URL: https://repec.econ.au.dk/repec/creates/rp/17/rp17_18.pdf
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    References listed on IDEAS

    as
    1. Delgado, Miguel A. & Rodriguez-Poo, Juan M. & Wolf, Michael, 2001. "Subsampling inference in cube root asymptotics with an application to Manski's maximum score estimator," Economics Letters, Elsevier, vol. 73(2), pages 241-250, November.
    2. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    3. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August.
    4. Jason Abrevaya & Jian Huang, 2005. "On the Bootstrap of the Maximum Score Estimator," Econometrica, Econometric Society, vol. 73(4), pages 1175-1204, July.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Firpo, Sergio & Galvao, Antonio F. & Kobus, Martyna & Parker, Thomas & Rosa-Dias, Pedro, 2020. "Loss Aversion and the Welfare Ranking of Policy Interventions," IZA Discussion Papers 13176, Institute of Labor Economics (IZA).
    2. Fu Ouyang & Thomas Tao Yang, 2020. "Semiparametric Estimation of Dynamic Binary Choice Panel Data Models," Discussion Papers Series 626, School of Economics, University of Queensland, Australia.
    3. Fu Ouyang & Thomas Tao Yang, 2020. "Semiparametric Estimation of Dynamic Binary Choice Panel Data Models," ANU Working Papers in Economics and Econometrics 2020-671, Australian National University, College of Business and Economics, School of Economics.
    4. Firpo, Sergio & Galvao, Antonio F. & Parker, Thomas, 2023. "Uniform inference for value functions," Journal of Econometrics, Elsevier, vol. 235(2), pages 1680-1699.

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    More about this item

    Keywords

    Cube root asymptotics; Bootstrapping; Maximum score estimation; Isotonic density estimation.;
    All these keywords.

    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

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