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Semiparametric Estimation of Random Coefficients in Structural Economic Models

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  • Stefan Hoderlein

    (Boston College)

  • Lars Nesheim

    (University College London)

  • Anna Simoni

    (CNRS - CREST)

Abstract

This paper discusses nonparametric estimation of the distribution of random coefficients in a structural model that is nonlinear in the random coefficients. We establish that the problem of recovering the probability density function (pdf ) of random parameters falls into the class of convexly-constrained inverse problems. The framework offers an estimation method that separates computational solution of the structural model from estimation. We first discuss nonparametric identification. Then, we propose two alternative estimation procedures to estimate the density and derive their asymptotic properties. Our general framework allows us to deal with unobservable nuisance variables, e.g., measurement error, but also covers the case when there are no such nuisance variables. Finally, Monte Carlo experiments for several structural models are provided which illustrate the performance of our estimation procedure.

Suggested Citation

  • Stefan Hoderlein & Lars Nesheim & Anna Simoni, 2015. "Semiparametric Estimation of Random Coefficients in Structural Economic Models," Boston College Working Papers in Economics 895, Boston College Department of Economics, revised 01 Feb 2016.
    • Handle: RePEc:boc:bocoec:895
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    Cited by:

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    2. Florens, Jean-Pierre & Simoni, Anna, 2016. "Regularizing Priors For Linear Inverse Problems," Econometric Theory, Cambridge University Press, vol. 32(1), pages 71-121, February.
    3. Ivan A. Canay & Andres Santos & Azeem M. Shaikh, 2013. "On the Testability of Identification in Some Nonparametric Models With Endogeneity," Econometrica, Econometric Society, vol. 81(6), pages 2535-2559, November.
    4. Botosaru, Irene, 2023. "Time-varying unobserved heterogeneity in earnings shocks," Journal of Econometrics, Elsevier, vol. 235(2), pages 1378-1393.
    5. Arthur Lewbel & Krishna Pendakur, 2017. "Unobserved Preference Heterogeneity in Demand Using Generalized Random Coefficients," Journal of Political Economy, University of Chicago Press, vol. 125(4), pages 1100-1148.
    6. Andrii Babii & Jean-Pierre Florens, 2017. "Is completeness necessary? Estimation in nonidentified linear models," Papers 1709.03473, arXiv.org, revised Nov 2021.
    7. Nagasawa, Kenichi, 2020. "Identification and Estimation of Group-Level Partial Effects," The Warwick Economics Research Paper Series (TWERPS) 1243, University of Warwick, Department of Economics.
    8. Giovanni Compiani & Yuichi Kitamura, 2016. "Using mixtures in econometric models: a brief review and some new results," Econometrics Journal, Royal Economic Society, vol. 19(3), pages 95-127, October.
    9. Shengfang Tang & Zongwu Cai & Ying Fang & Ming Lin, 2019. "Testing Unconfoundedness Assumption Using Auxiliary Variables," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201905, University of Kansas, Department of Economics, revised Mar 2019.
    10. Breunig, Christoph & Mammen, Enno & Simoni, Anna, 2018. "Nonparametric estimation in case of endogenous selection," Journal of Econometrics, Elsevier, vol. 202(2), pages 268-285.
    11. Juan Carlos Escanciano & Wei Li, 2013. "On the identification of structural linear functionals," CeMMAP working papers CWP48/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    12. De Nadai, Michele & Lewbel, Arthur, 2016. "Nonparametric errors in variables models with measurement errors on both sides of the equation," Journal of Econometrics, Elsevier, vol. 191(1), pages 19-32.
    13. Irene Botosaru, 2017. "Identifying Distributions in a Panel Model with Heteroskedasticity: An Application to Earnings Volatility," Discussion Papers dp17-11, Department of Economics, Simon Fraser University.
    14. Nail Kashaev & Bruno Salcedo, 2019. "Discerning Solution Concepts," University of Western Ontario, Departmental Research Report Series 20193, University of Western Ontario, Department of Economics.
    15. Gaurab Aryal & Federico Zincenko, 2014. "Identification and Estimation of Multidimensional Screening," Papers 1411.6250, arXiv.org, revised Mar 2024.

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    Keywords

    Nonlinear random coefficients; mixture models; structural models; heterogeneity; inverse problems;
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