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in this paper we specify and estimate a structural limited dependent variable model with which we study both the health and retirement status of the elderly.Standard linear estimators, which assume that these variables are continuous, are not appropriate and categorical estimation techniques are preferred.Our model differs from previous work in that we have longitudinal data and random effects that are correlated over time for different individuals.The problem is made more complicated because there is sample truncation, which could potentially bias coefficient estimates, since approximately twenty percent of the individuals in our sample die.We outline the full information maximum likelihood estimator for such a model and implement it in our empirical analysis.With our structural estimates we analyze, among other things, the degree to which endogeneously determined health status affects the probability of retirement and how changes in social security benefits and eligibility for transfer payments modify both healthiness and the demand for leisure.
Sickles et al. (Sat,) studied this question.