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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
    1. Alfonso Miranda, 2005. "Estimation of ordinal response models, accounting for sample selection bias," United Kingdom Stata Users' Group Meetings 2005 11, Stata Users Group.
    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.
    3. Donald S. Kenkel & Joseph V. Terza, 2001. "The effect of physician advice on alcohol consumption: count regression with an endogenous treatment effect," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(2), pages 165-184.
    4. Sophia Rabe-Hesketh & Anders Skrondal & Andrew Pickles, 2003. "Maximum likelihood estimation of generalized linear models with covariate measurement error," Stata Journal, StataCorp LP, vol. 3(4), pages 386-411, December.
    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.
    14. Wilde, Joachim, 2000. "Identification of multiple equation probit models with endogenous dummy regressors," Economics Letters, Elsevier, vol. 69(3), pages 309-312, December.
    15. Sophia Rabe-Hesketh & Anders Skrondal & Andrew Pickles, 2004. "Generalized multilevel structural equation modeling," Psychometrika, Springer;The Psychometric Society, vol. 69(2), pages 167-190, June.
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