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ESTIMATION OF BINARY CHOICE MODELS WITH LINEAR INDEX AND DUMMY ENDOGENOUS VARIABLES

Published online by Cambridge University Press:  28 March 2013

Neşe Yildiz
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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 multistep 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, Econometrica 75, 1403–1430) are extended to cover the case where the average derivative estimation requires a first-step semiparametric procedure.

Type
Articles
Information
Econometric Theory , Volume 29 , Issue 2 , April 2013 , pp. 354 - 392
Copyright
Copyright © Cambridge University Press 2013 

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Footnotes

I would like to thank Takeshi Amemiya, Aprajit Mahajan, Edward Vytlacil, James Powell, and Todd Elder for very helpful comments and questions on this paper.

References

REFERENCES

Altonji, J. & Matzkin, R.L. (2005) Cross section and panel data estimators for nonseparable models with endogenous regressors. Econometrica 73, 1053–1153.CrossRefGoogle Scholar
Amemiya, T. (1978) The estimation of a simultaneous equation generalized probit model. Econometrica 46, 1193–1205.CrossRefGoogle Scholar
Bhattacharya, J., McCaffrey, D., & Goldman, D. (2006) Estimating probit models with self-selected treatment. Statistics in Medicine 25, 389–413.Google Scholar
Blundell, R. & Powell, J. (2003) Endogeneity in nonparametric and semiparametric regression models. In Dewatripont, M., Hansen, L.P., & Turnovsky, S.J. (eds.), Advances in Economics and Econometrics: Theory and Applications, Eighth World Congress, vol. II. Cambridge University Press.Google Scholar
Blundell, R. & Powell, J. (2004) Endogeneity in semiparametric binary response models. Review of Economic Studies 71, 581–593.CrossRefGoogle Scholar
Chen, S. (1999) Semiparametric estimation of a location parameter in the binary choice model. Econometric Theory 15, 79–98.CrossRefGoogle Scholar
Chen, X. & Vytlacil, E. (2005) Nonlinear Panel Data Models with Lagged Dependent Variables. Manuscript, Stanford University.Google Scholar
Chernozhukov, V. & Hansen, C. (2005) An IV model of quantile treatment effects. Econometrica 73, 245–261.CrossRefGoogle Scholar
Chesher, A. (2003) Identification in nonseparable models. Econometrica 71, 1405–1441.CrossRefGoogle Scholar
Chesher, A. (2005) Nonparametric identification under discrete variation. Econometrica 73, 1525–1550.CrossRefGoogle Scholar
Giné, E. & Guillou, A. (2002) Rates of strong uniform consistency for multivariate kernel density estimators. Annals of H. Poincaré PR-38, 907–921.CrossRefGoogle Scholar
Heckman, J. (1978) Dummy endogenous variables in a simultaneous equation system. Econometrica 46, 931–959.CrossRefGoogle Scholar
Heckman, J., Ichimura, H., & Todd, P. (1998) Matching as an econometric evaluation estimator. Review of Economic Studies 65, 261–294.CrossRefGoogle Scholar
Horowitz, J.L. & Härdle, W. (1996) Direct semiparametric estimation of single index models with discrete covariates. Journal of the American Statistical Association 91, 1632–1640.CrossRefGoogle Scholar
Imbens, G. & Newey, W. (2009) Identification and estimation of triangular simultaneous equation models without additivity. Econometrica 77, 1481–1512.Google Scholar
Jun, S.J. (2009) Local structural quantile effects in a model with a nonseparable control variable. Journal of Econometrics 151, 82–97.CrossRefGoogle Scholar
Lewbel, A. (2000) Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables. Journal of Econometrics 97, 145–177.CrossRefGoogle Scholar
Lingjie, Ma & Koenker, R. (2009) Quantile regression methods for recursive structural equation models. Journal of Econometrics 134, 471–506.Google Scholar
Manski, C.F. (1988) Identification of binary response models source. Journal of the American Statistical Association 83, 729–738.Google Scholar
Powell, J.L, Stock, J.H., & Stoker, I.M. (1989) Semiparametric estimation of index coefficients. Econometrica 57, 1403–1430.CrossRefGoogle Scholar
Vytlacil, E. & Yildiz, N. (2004) A Matching Based Estimator of Average Treatment Effect in Weakly Separable Models. Manuscript, Yale University and University of Rochester.Google Scholar
Vytlacil, E. & Yildiz, N. (2007) Dummy endogenous models in weakly separable models. Econometrica 75, 757–779.CrossRefGoogle Scholar