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Endogenous Semiparametric Binary Choice Models with Heteroscedasticity

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  • Stefan Hoderlein

    (Boston College)

Abstract

In this paper we consider endogenous regressors in the binary choice model under a weak median exclusion restriction, but without further specification of the distribution of the unobserved random components. Our reduced form specification with heteroscedastic residuals covers various heterogeneous structural binary choice models. As a particularly relevant example of a structural model where no semiparametric estimator has of yet been analyzed, we consider the binary random utility model with endogenous regressors and heterogeneous parameters. We employ a control function IV assumption to establish identification of a slope parameter beta by the mean ratio of derivatives of two functions of the instruments. We propose an estimator based on direct sample counterparts, and discuss the large sample behavior of this estimator. In particular, we show root-n consistency and derive the asymptotic distribution. In the same framework, we propose tests for heteroscedasticity, overidentification and endogeneity. We analyze the small sample performance through a simulation study. An application of the model to discrete choice demand data concludes this paper.

Suggested Citation

  • Stefan Hoderlein, 2009. "Endogenous Semiparametric Binary Choice Models with Heteroscedasticity," Boston College Working Papers in Economics 747, Boston College Department of Economics, revised 29 Sep 2014.
  • Handle: RePEc:boc:bocoec:747
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    Citations

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    Cited by:

    1. Yingying Dong & Arthur Lewbel, 2015. "A Simple Estimator for Binary Choice Models with Endogenous Regressors," Econometric Reviews, Taylor & Francis Journals, vol. 34(1-2), pages 82-105, February.
    2. Stefan Hoderlein & Robert Sherman, 2012. "Identification and estimation in a correlated random coefficients binary response model," CeMMAP working papers CWP42/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Andrew Chesher & Adam Rosen, 2012. "An instrumental variable random coefficients model for binary outcomes," CeMMAP working papers CWP34/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. 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.
    5. Yingying Dong & Arthur Lewbel & Thomas Tao Yang, 2012. "Comparing Features of Convenient Estimators for Binary Choice Models With Endogenous Regressors," Boston College Working Papers in Economics 789, Boston College Department of Economics, revised 15 May 2012.
    6. Andrew Chesher & Adam M. Rosen, 2014. "An instrumental variable random‐coefficients model for binary outcomes," Econometrics Journal, Royal Economic Society, vol. 17(2), pages 1-19, June.
    7. Michelle R. Garfinkel & Michael McBride & Stergios Skaperdas, 2012. "Governance and Norms as Determinants of Arming," Revue d'économie politique, Dalloz, pages 197-212.
    8. Arthur Lewbel & Yingying Dong & Thomas Tao Yang, 2012. "Viewpoint: Comparing features of convenient estimators for binary choice models with endogenous regressors," Canadian Journal of Economics, Canadian Economics Association, vol. 45(3), pages 809-829, August.

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