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Estimation of Binary Choice Models with Linear Index and Dummy Endogenous Variables

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  • Nese Yildiz

    () (University of Rochester, Department of Economics)

Abstract

This paper presents computationally simple estimators for the index coefficients in a binary choice model with a binary endogenous regressor without relying on distributional assumptions or on large support conditions and yields root-n consistent and asymptotically normal estimators. We develop a multi-step method for estimating the parameters in a triangular, linear index, threshold-crossing model with two equations. Such an econometric model might be used in testing for moral hazard while allowing for asymmetric information in insurance markets. In outlining this new estimation method two contributions are made. The first one is proposing a novel ”matching” estimator for the coefficient on the binary endogenous variable in the outcome equation. Second, in order to establish the asymptotic properties of the proposed estimators for the coefficients of the exogenous regressors in the outcome equation, the results of Powell, Stock and Stoker (1989) are extended to cover the case where the average derivative estimation requires a first step semi-parametric procedure.

Suggested Citation

  • Nese Yildiz, 2012. "Estimation of Binary Choice Models with Linear Index and Dummy Endogenous Variables," Koç University-TUSIAD Economic Research Forum Working Papers 1202, Koc University-TUSIAD Economic Research Forum.
  • Handle: RePEc:koc:wpaper:1202
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    File URL: http://eaf.ku.edu.tr/sites/eaf.ku.edu.tr/files/erf_wp_1202.pdf
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    References listed on IDEAS

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    1. Jun, Sung Jae, 2009. "Local structural quantile effects in a model with a nonseparable control variable," Journal of Econometrics, Elsevier, vol. 151(1), pages 82-97, July.
    2. Richard W. Blundell & James L. Powell, 2004. "Endogeneity in Semiparametric Binary Response Models," Review of Economic Studies, Oxford University Press, vol. 71(3), pages 655-679.
    3. Ma, Lingjie & Koenker, Roger, 2006. "Quantile regression methods for recursive structural equation models," Journal of Econometrics, Elsevier, vol. 134(2), pages 471-506, October.
    4. Chen, Songnian, 1999. "Semiparametric Estimation Of A Location Parameter In The Binary Choice Model," Econometric Theory, Cambridge University Press, vol. 15(01), pages 79-98, February.
    5. Richard Blundell & James L. Powell, 2001. "Endogeneity in nonparametric and semiparametric regression models," CeMMAP working papers CWP09/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Horowitz, J. L. & Härdle, Wolfgang, 1994. "Direct Semiparametric Estimation of Single - Index Models with Discrete Covariates," SFB 373 Discussion Papers 1994,36, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    7. Joseph G. Altonji & Rosa L. Matzkin, 2001. "Panel Data Estimators for Nonseparable Models with Endogenous Regressors," NBER Technical Working Papers 0267, National Bureau of Economic Research, Inc.
    8. Lewbel, Arthur, 2000. "Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables," Journal of Econometrics, Elsevier, vol. 97(1), pages 145-177, July.
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