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Parametric links for binary choice models: A Fisherian-Bayesian colloquy

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  • Koenker, Roger
  • Yoon, Jungmo
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    Abstract

    The familiar logit and probit models provide convenient settings for many binary response applications, but a larger class of link functions may be occasionally desirable. Two parametric families of link functions are investigated: the Gosset link based on the Student t latent variable model with the degrees of freedom parameter controlling the tail behavior, and the Pregibon link based on the (generalized) Tukey [lambda] family, with two shape parameters controlling skewness and tail behavior. Both Bayesian and maximum likelihood methods for estimation and inference are explored, compared and contrasted. In applications, like the propensity score matching problem discussed below, where it is critical to have accurate estimates of the conditional probabilities, we find that misspecification of the link function can create serious bias. Bayesian point estimation via MCMC performs quite competitively with MLE methods; however nominal coverage of Bayes credible regions is somewhat more problematic.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Econometrics.

    Volume (Year): 152 (2009)
    Issue (Month): 2 (October)
    Pages: 120-130

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    Handle: RePEc:eee:econom:v:152:y:2009:i:2:p:120-130

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    Web page: http://www.elsevier.com/locate/jeconom

    Related research

    Keywords: Binary response model Link function Cauchit Markov chain Monte-Carlo;

    References

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    1. Dehejia, Rajeev, 2005. "Practical propensity score matching: a reply to Smith and Todd," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 355-364.
    2. Jeffrey Smith & Petra Todd, 2003. "Does Matching Overcome Lalonde's Critique of Nonexperimental Estimators?," University of Western Ontario, CIBC Centre for Human Capital and Productivity Working Papers 20035, University of Western Ontario, CIBC Centre for Human Capital and Productivity.
    3. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    4. Dehejia, R.H. & Wahba, S., 1998. "Propensity Score Matching Methods for Non-Experimental Causal Studies," Discussion Papers 1998_02, Columbia University, Department of Economics.
    5. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August.
    6. Klein, Roger & Spady, Richard & Weiss, Andrew, 1991. "Factors Affecting the Output and Quit Propensities of Production Workers," Review of Economic Studies, Wiley Blackwell, vol. 58(5), pages 929-53, October.
    7. LaLonde, Robert J, 1986. "Evaluating the Econometric Evaluations of Training Programs with Experimental Data," American Economic Review, American Economic Association, vol. 76(4), pages 604-20, September.
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    Cited by:
    1. Rainer Winkelmann, 2012. "Copula Bivariate Probit Models: With An Application To Medical Expenditures," Health Economics, John Wiley & Sons, Ltd., vol. 21(12), pages 1444-1455, December.
    2. Vijverberg, Chu-Ping C. & Vijverberg, Wim P., 2012. "Pregibit: A Family of Discrete Choice Models," IZA Discussion Papers 6359, Institute for the Study of Labor (IZA).
    3. Tommaso Proietti & Alessandra Luati, 2013. "The Exponential Model for the Spectrum of a Time Series: Extensions and Applications," CREATES Research Papers 2013-34, School of Economics and Management, University of Aarhus.
    4. Rainer Winkelmann, 2009. "Copula-based bivariate binary response models," SOI - Working Papers 0913, Socioeconomic Institute - University of Zurich.
    5. Esmeralda A. Ramalho & Joaquim J.S. Ramalho & José M.R. Murteira, 2013. "A generalized goodness-of-functional form test for binary and fractional regression models," CEFAGE-UE Working Papers 2013_09, University of Evora, CEFAGE-UE (Portugal).
    6. Victor Chernozhukov & Ivan Fernandez-Val & Blaise Melly, 2008. "Inference On Counterfactual Distributions," Boston University - Department of Economics - Working Papers Series wp2008-005, Boston University - Department of Economics.
    7. Hasebe, Takuya & Vijverberg, Wim P., 2012. "A Flexible Sample Selection Model: A GTL-Copula Approach," IZA Discussion Papers 7003, Institute for the Study of Labor (IZA).
    8. Kajal Lahiri & Liu Yang, 2012. "Forecasting Binary Outcomes," Discussion Papers 12-09, University at Albany, SUNY, Department of Economics.
    9. Wang-Sheng Lee, 2013. "Propensity score matching and variations on the balancing test," Empirical Economics, Springer, vol. 44(1), pages 47-80, February.

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