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Nonparametric estimation in random coefficients binary choice models

Author

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  • Eric Gautier

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - IP Paris - Institut Polytechnique de Paris)

  • Yuichi Kitamura

    (Cowles Foundation for Research in Economics - Yale University [New Haven])

Abstract

This paper considers random coefficients binary choice models. The main goal is to estimate the density of the random coefficients nonparametrically. This is an ill-posed inverse problem characterized by an integral transform. A new density estimator for the random coefficients is developed, utilizing Fourier-Laplace series on spheres. This approach offers a clear insight on the identification problem. More importantly, it leads to a closed form estimator formula that yields a simple plug-in procedure requiring no numerical optimization. The new estimator, therefore, is easy to implement in empirical applications, while being flexible about the treatment of unobserved heterogeneity. Extensions including treatments of non-random coefficients and models with endogeneity are discussed.

Suggested Citation

  • Eric Gautier & Yuichi Kitamura, 2011. "Nonparametric estimation in random coefficients binary choice models," Working Papers hal-00403939, HAL.
    • Handle: RePEc:hal:wpaper:hal-00403939
    Note: View the original document on HAL open archive server: https://hal.science/hal-00403939v2
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    References listed on IDEAS

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    More about this item

    Keywords

    Inverse problems; Discrete choice models.;

    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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