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


  • Koenker, Roger
  • Yoon, Jungmo


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.

Suggested Citation

  • Koenker, Roger & Yoon, Jungmo, 2009. "Parametric links for binary choice models: A Fisherian-Bayesian colloquy," Journal of Econometrics, Elsevier, vol. 152(2), pages 120-130, October.
  • Handle: RePEc:eee:econom:v:152:y:2009:i:2:p:120-130

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    References listed on IDEAS

    1. LaLonde, Robert J, 1986. "Evaluating the Econometric Evaluations of Training Programs with Experimental Data," American Economic Review, American Economic Association, vol. 76(4), pages 604-620, September.
    2. A. Smith, Jeffrey & E. Todd, Petra, 2005. "Does matching overcome LaLonde's critique of nonexperimental estimators?," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 305-353.
    3. Rajeev H. Dehejia & Sadek Wahba, 2002. "Propensity Score-Matching Methods For Nonexperimental Causal Studies," The Review of Economics and Statistics, MIT Press, vol. 84(1), pages 151-161, February.
    4. 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.
    5. Dehejia, Rajeev, 2005. "Practical propensity score matching: a reply to Smith and Todd," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 355-364.
    6. Roger Klein & Richard Spady & Andrew Weiss, 1991. "Factors Affecting the Output and Quit Propensities of Production Workers," Review of Economic Studies, Oxford University Press, vol. 58(5), pages 929-953.
    7. 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.
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    Cited by:

    1. Victor Chernozhukov & Iván Fernández‐Val & Blaise Melly, 2013. "Inference on Counterfactual Distributions," Econometrica, Econometric Society, vol. 81(6), pages 2205-2268, November.
    2. Chu-Ping C. Vijverberg & Wim P. M. Vijverberg, 2016. "Pregibit: a family of binary choice models," Empirical Economics, Springer, vol. 50(3), pages 901-932, May.
    3. Esmeralda A. Ramalho & Joaquim J. S. Ramalho & José M. R. Murteira, 2014. "A Generalized Goodness-of-functional Form Test for Binary and Fractional Regression Models," Manchester School, University of Manchester, vol. 82(4), pages 488-507, July.
    4. Vijverberg, Chu-Ping C. & Vijverberg, Wim P.M. & Taşpınar, Süleyman, 2016. "Linking Tukey’s legacy to financial risk measurement," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 595-615.
    5. Rainer Winkelmann, 2009. "Copula-based bivariate binary response models," SOI - Working Papers 0913, Socioeconomic Institute - University of Zurich.
    6. 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.
    7. Wang-Sheng Lee, 2013. "Propensity score matching and variations on the balancing test," Empirical Economics, Springer, vol. 44(1), pages 47-80, February.
    8. Proietti, Tommaso & Luati, Alessandra, 2013. "The Exponential Model for the Spectrum of a Time Series: Extensions and Applications," MPRA Paper 45280, University Library of Munich, Germany.
    9. Philipp Doebler & Heinz Holling, 2015. "Meta-analysis of Diagnostic Accuracy and ROC Curves with Covariate Adjusted Semiparametric Mixtures," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 1084-1104, December.
    10. Hess Wolfgang & Tutz Gerhard & Gertheiss Jan, 2016. "A Flexible Link Function for Discrete-Time Duration Models," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 236(4), pages 455-481, August.
    11. Lahiri, Kajal & Yang, Liu, 2013. "Forecasting Binary Outcomes," Handbook of Economic Forecasting, Elsevier.
    12. 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).
    13. 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).
    14. Subramanian, Sundarraman, 2016. "Bootstrap likelihood ratio confidence bands for survival functions under random censorship and its semiparametric extension," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 58-81.
    15. Fábio Bayer & Francisco Cribari-Neto, 2015. "Bootstrap-based model selection criteria for beta regressions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 776-795, December.


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