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Maximum likelihood estimation of endogenous switching and sample selection models for binary, ordinal, and count variables

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  • Alfonso Miranda

    (Keele University)

  • Sophia Rabe-Hesketh

    (Graduate School of Education, University of California - Berkeley)

Abstract

Studying behavior in economics, sociology, and statistics often involves fitting models in which the response variable depends on a dummy variable- also known as a regime-switch variable- or in which the response variable is observed only if a particular selection condition is met. In either case, standard regression techniques deliver inconsistent estimators if unobserved factors that affect the re- sponse are correlated with unobserved factors that affect the switching or selection variable. Consistent estimators can be obtained by maximum likelihood estimation of a joint model of the outcome and switching or selection variable. This article describes a “wrapper” program, ssm, that calls gllamm (Rabe-Hesketh, Skrondal, and Pickles, GLLAMM Manual [University of California – Berkeley, Division of Bio- statistics, Working Paper Series, Paper No. 160]) to fit such models. The wrapper accepts data in a simple structure, has a straightforward syntax, and reports out- put that is easily interpretable. One important feature of ssm is that the log likelihood can be evaluated using adaptive quadrature (Rabe-Hesketh, Skrondal, and Pickles, Stata Journal 2: 1–21; Journal of Econometrics 128: 301–323). Copyright 2006 by StataCorp LP.

Suggested Citation

  • Alfonso Miranda & Sophia Rabe-Hesketh, 2006. "Maximum likelihood estimation of endogenous switching and sample selection models for binary, ordinal, and count variables," Stata Journal, StataCorp LP, vol. 6(3), pages 285-308, September.
    • Handle: RePEc:tsj:stataj:v:6:y:2006:i:3:p:208-308
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    References listed on IDEAS

    as
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    2. Alfonso Miranda, 2004. "FIML estimation of an endogenous switching model for count data," Stata Journal, StataCorp LP, vol. 4(1), pages 40-49, March.
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    5. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-959, July.
    6. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    7. Massimiliano Bratti & Alfonso Miranda, 2010. "Non‐pecuniary returns to higher education: the effect on smoking intensity in the UK," Health Economics, John Wiley & Sons, Ltd., vol. 19(8), pages 906-920, August.
    8. Terza, Joseph V., 1998. "Estimating count data models with endogenous switching: Sample selection and endogenous treatment effects," Journal of Econometrics, Elsevier, vol. 84(1), pages 129-154, May.
    9. Sophia Rabe-Hesketh, 2002. "Multilevel selection models using gllamm," Dutch-German Stata Users' Group Meetings 2002 1, Stata Users Group.
    10. Francis Vella, 1998. "Estimating Models with Sample Selection Bias: A Survey," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 127-169.
    11. Rabe-Hesketh, Sophia & Skrondal, Anders & Pickles, Andrew, 2005. "Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects," Journal of Econometrics, Elsevier, vol. 128(2), pages 301-323, October.
    12. Sophia Rabe-Hesketh & Anders Skrondal & Andrew Pickles, 2002. "Reliable estimation of generalized linear mixed models using adaptive quadrature," Stata Journal, StataCorp LP, vol. 2(1), pages 1-21, February.
    13. Van de Ven, Wynand P. M. M. & Van Praag, Bernard M. S., 1981. "The demand for deductibles in private health insurance : A probit model with sample selection," Journal of Econometrics, Elsevier, vol. 17(2), pages 229-252, November.
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