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SNP and SML estimation of univariate and bivariate binary-choice models

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  • Giuseppe De Luca

    () (University of Rome "Tor Vergata")

Abstract

We discuss the semi-nonparametric approach of Gallant and Nychka (1987, Econometrica 55: 363-390), the semiparametric maximum likelihood ap- proach of Klein and Spady (1993, Econometrica 61: 387-421), and a set of new Stata commands for semiparametric estimation of three binary-choice models. The first is a univariate model, while the second and the third are bivariate models without and with sample selection, respectively. The proposed estimators are root-n consistent and asymptotically normal for the model parameters of interest under weak assumptions on the distribution of the underlying error terms. Our Monte Carlo simulations suggest that the efficiency losses of the semi-nonparametric and the semiparametric maximum likelihood estimators relative to a maximum like- lihood correctly specified estimator of a parametric probit are rather small. On the other hand, a comparison of these estimators in non-Gaussian designs suggests that semi-nonparametric and semiparametric maximum likelihood estimators sub- stantially dominate the parametric probit maximum likelihood estimator. Copyright 2008 by StataCorp LP.

Suggested Citation

  • Giuseppe De Luca, 2008. "SNP and SML estimation of univariate and bivariate binary-choice models," Stata Journal, StataCorp LP, vol. 8(2), pages 190-220, June.
  • Handle: RePEc:tsj:stataj:v:8:y:2008:i:2:p:190-220
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    References listed on IDEAS

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    1. Meng, Chun-Lo & Schmidt, Peter, 1985. "On the Cost of Partial Observability in the Bivariate Probit Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(1), pages 71-85, February.
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    5. Gerfin, Michael, 1996. "Parametric and Semi-parametric Estimation of the Binary Response Model of Labor Market Participation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(3), pages 321-339, May-June.
    6. Gabler, Siegfried & Laisney, Francois & Lechner, Michael, 1993. "Seminonparametric Estimation of Binary-Choice Models with an Application to Labor-Force Participation," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 61-80, January.
    7. Lee, Lung-fei, 1995. "Semiparametric maximum likelihood estimation of polychotomous and sequential choice models," Journal of Econometrics, Elsevier, vol. 65(2), pages 381-428, February.
    8. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
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    10. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
    11. Melenberg, B. & van Soest, A.H.O., 1996. "Measuring the costs of children : Parametric and semiparametric estimators," Other publications TiSEM 1227b8b2-0575-4b5d-9bac-7, Tilburg University, School of Economics and Management.
    12. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
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