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A consistent bootstrap procedure for the maximum score estimator

Author

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  • Patra, Rohit Kumar
  • Seijo, Emilio
  • Sen, Bodhisattva

Abstract

In this paper we propose a new model-based smoothed bootstrap procedure for making inference on the maximum score estimator of Manski (1975, 1985) and prove its consistency. We provide a set of sufficient conditions for the consistency of any bootstrap procedure in this problem. We compare the finite sample performance of different bootstrap procedures through simulation studies. The results indicate that our proposed smoothed bootstrap outperforms other bootstrap schemes, including the m-out-of-n bootstrap. Additionally, we prove a convergence theorem for triangular arrays of random variables arising from binary choice models, which may be of independent interest.

Suggested Citation

  • Patra, Rohit Kumar & Seijo, Emilio & Sen, Bodhisattva, 2018. "A consistent bootstrap procedure for the maximum score estimator," Journal of Econometrics, Elsevier, vol. 205(2), pages 488-507.
    • Handle: RePEc:eee:econom:v:205:y:2018:i:2:p:488-507
    DOI: 10.1016/j.jeconom.2018.04.001
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    Citations

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    Cited by:

    1. Babii, Andrii & Kumar, Rohit, 2023. "Isotonic regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 234(2), pages 371-393.
    2. Chen, Le-Yu & Oparina, Ekaterina & Powdthavee, Nattavudh & Srisuma, Sorawoot, 2019. "Have Econometric Analyses of Happiness Data Been Futile? A Simple Truth about Happiness Scales," IZA Discussion Papers 12152, Institute of Labor Economics (IZA).
    3. Matias D. Cattaneo & Michael Jansson & Kenichi Nagasawa, 2020. "Bootstrap‐Based Inference for Cube Root Asymptotics," Econometrica, Econometric Society, vol. 88(5), pages 2203-2219, September.
    4. Adam M. Rosen & Takuya Ura, 2019. "Finite Sample Inference for the Maximum Score Estimand," Papers 1903.01511, arXiv.org, revised May 2020.
    5. Chen, Le-Yu & Oparina, Ekaterina & Powdthavee, Nattavudh & Srisuma, Sorawoot, 2022. "Robust Ranking of Happiness Outcomes: A Median Regression Perspective," Journal of Economic Behavior & Organization, Elsevier, vol. 200(C), pages 672-686.
    6. Joel L. Horowitz, 2018. "Bootstrap Methods in Econometrics," Papers 1809.04016, arXiv.org.
    7. Fu Ouyang & Thomas Tao Yang, 2022. "Semiparametric Estimation of Dynamic Binary Choice Panel Data Models," Papers 2202.12062, arXiv.org, revised Feb 2024.
    8. Wied, Dominik, 2024. "Semiparametric distribution regression with instruments and monotonicity," Labour Economics, Elsevier, vol. 90(C).
    9. 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.
    10. 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.
    11. Han, Jinyue & Wang, Jun & Gao, Wei & Tang, Man-Lai, 2023. "Estimation of the directions for unknown parameters in semiparametric models," MPRA Paper 116365, University Library of Munich, Germany.
    12. Joel L. Horowitz, 2018. "Bootstrap methods in econometrics," CeMMAP working papers CWP53/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

    More about this item

    Keywords

    Binary choice model; Cube-root asymptotics; (In)-consistency of the bootstrap; Latent variable model; Smoothed bootstrap;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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