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Identification and estimation in a correlated random coefficients binary response model

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  • Hoderlein, Stefan
  • Sherman, Robert

Abstract

We study a linear index binary response model with random coefficients B allowed to be correlated with regressors X. We identify the mean of the distribution of B and show how the mean can be interpreted as a vector of expected relative effects. We use instruments and a control vector V to make X independent of B given V. This leads to a localize-then-average approach to both identification and estimation. We develop a n-consistent and asymptotically normal estimator of a trimmed mean of the distribution of B, explore its small sample performance through simulations, and present an application.

Suggested Citation

  • Hoderlein, Stefan & Sherman, Robert, 2015. "Identification and estimation in a correlated random coefficients binary response model," Journal of Econometrics, Elsevier, vol. 188(1), pages 135-149.
    • Handle: RePEc:eee:econom:v:188:y:2015:i:1:p:135-149
    DOI: 10.1016/j.jeconom.2015.03.044
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    Cited by:

    1. Hoderlein, Stefan & Holzmann, Hajo & Meister, Alexander, 2017. "The triangular model with random coefficients," Journal of Econometrics, Elsevier, vol. 201(1), pages 144-169.
    2. Christoph Breunig & Stefan Hoderlein, 2018. "Specification testing in random coefficient models," Quantitative Economics, Econometric Society, vol. 9(3), pages 1371-1417, November.
    3. Stefan Hoderlein & Hajo Holzmann & Alexander Meister, 2015. "The triangular model with random coefficients," CeMMAP working papers 33/15, Institute for Fiscal Studies.
    4. Fabian Dunker & Stefan Hoderlein & Hiroaki Kaido, 2013. "Random coefficients in static games of complete information," CeMMAP working papers CWP12/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Juan Carlos Escanciano, 2020. "Irregular Identification of Structural Models with Nonparametric Unobserved Heterogeneity," Papers 2005.08611, arXiv.org.
    6. Marbac, Matthieu & Sedki, Mohammed, 2017. "A family of block-wise one-factor distributions for modeling high-dimensional binary data," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 130-145.
    7. Christoph Breunig & Stefan Hoderlein, 2016. "Nonparametric Specification Testing in Random Parameter Models," Boston College Working Papers in Economics 897, Boston College Department of Economics.
    8. Amaresh K Tiwari, 2021. "A Control Function Approach to Estimate Panel Data Binary Response Model," Papers 2102.12927, arXiv.org, revised Sep 2021.
    9. Escanciano, Juan Carlos, 2023. "Irregular identification of structural models with nonparametric unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 234(1), pages 106-127.
    10. Guo, Jing & Wang, Lei & Zhang, Zhengyu, 2022. "Identification and estimation of a heteroskedastic censored regression model with random coefficient dummy endogenous regressors," Economic Modelling, Elsevier, vol. 110(C).

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    More about this item

    Keywords

    Correlated random coefficients binary response model; Instrumental variables; Control variables; Conditional median restrictions; Localize-then-average strategy;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • 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
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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