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Identification And Estimation In A Correlated Random Coefficients Binary Response Model

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  • Stefan Hoderlein

    (Boston College)

  • Robert Sherman

Abstract

We study identification and estimation in a binary response model with random coefficients B allowed to be correlated with regressors X. Our objective is to identify the mean of the distribution of B and estimate a trimmed mean of this distribution. Like Imbens and Newey (2009), we use instruments Z and a control vector V to make X independent of B given V. A consequent conditional median restriction helps identify the mean of B given V. Averaging over V identifies the mean of B. This leads to an analogous localize-then-average approach to estimation. We estimate conditional means with localized smooth maximum score estimators and average to obtain a root-n-consistent and asymptotically normal estimator of a trimmed mean of the distribution of B. Under the conditional median restrictions, the procedure can be adapted to produce a root-n-consistent and asymptotically normal estimator of the nonrandom regression coefficients in the models of Manski (1975,1985) and Horowitz (1992). We explore small sample performance through simulations, and present an application.

Suggested Citation

  • Stefan Hoderlein & Robert Sherman, 2012. "Identification And Estimation In A Correlated Random Coefficients Binary Response Model," Boston College Working Papers in Economics 837, Boston College Department of Economics.
    • Handle: RePEc:boc:bocoec:837
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    Cited by:

    1. Christoph Breunig & Stefan Hoderlein, 2018. "Specification testing in random coefficient models," Quantitative Economics, Econometric Society, vol. 9(3), pages 1371-1417, November.
    2. Fabian Dunker & Stefan Hoderlein & Hiroaki Kaido, 2013. "Random Coefficients in Static Games of Complete Information," Boston College Working Papers in Economics 835, Boston College Department of Economics.
    3. Stefan Hoderlein & Hajo Holzmann & Alexander Meister, 2015. "The triangular model with random coefficients," CeMMAP working papers 33/15, Institute for Fiscal Studies.
    4. Christoph Breunig & Stefan Hoderlein, 2016. "Nonparametric Specification Testing in Random Parameter Models," Boston College Working Papers in Economics 897, Boston College Department of Economics.
    5. 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.
    6. Hoderlein, Stefan & Holzmann, Hajo & Meister, Alexander, 2017. "The triangular model with random coefficients," Journal of Econometrics, Elsevier, vol. 201(1), pages 144-169.
    7. Escanciano, Juan Carlos, 2023. "Irregular identification of structural models with nonparametric unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 234(1), pages 106-127.
    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. Juan Carlos Escanciano, 2020. "Irregular Identification of Structural Models with Nonparametric Unobserved Heterogeneity," Papers 2005.08611, arXiv.org.
    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

    Heterogeneity; Correlated Random Coefficients; Endogeneity; Binary Response Model; Instrumental Variables; Control Variables; Conditional Median Restrictions.;
    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
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis

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