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.

Gary Becker and Kevin Murphy (1988) present a theoretical model of rational addiction that requires information on past, present and future prices. They do not study illegal drugs empirically in this and their related papers. A major data source is the annual survey of high school seniors (HSS), also known as Monitoring the Future. This work is summarized in L. Johnston et al. (1988). They find a growing use of drugs (measured by monthly, annual, and lifetime prevalence) over time, and differences by region and sex. Cocaine use showed marked increases from 1976, though this levelled off from 1986 to 1987. They often rely on cross-tabs that leaves many variables uncontrolled and the results subject to omitted variable bias. J. Bachman et al. (1984) use ordinary least squares (OLS) regressions in which the drug use in the three years post-high school is related to various characteristics such as living arrangements. While an improvement over cross-tabs, OLS applied to categorical dependent variables yields inefficient estimates (see M. Nerlove and S. Press, 1973). Johnston et al. used follow-up surveys of a subsample drawn from each cohort. They find the use of some drugs decline at older ages, say 35, though they do not determine if the heavy users have died, dropped of the sample, or have been rehabilitated.' The HSS's initial restriction to high school seniors removes about 30 percent of the population who drop of high school perhaps because of taking drugs. Studies based on the National Institute of Drug Abuse (NIDA) sample of people 12 and older show some heavy drug use of people less than 17 years old. (See J. D. Miller et al., 1982, and NIDA, 1985.) Richard Clayton (1985) using the 1980 HSS presents univariate regressions that shows the frequency of use of cocaine is positively related to lifetime marijuana use and days of school in the past month, but negatively related to high school grade point average. H. Abelson and Miller (1985), using the NIDA surveys covering 1974-82, show differences in the percentage using cocaine by education and race-for lifetime, 12 months, and last month measures. They find strong trends. D. Kandel (1980) presents a recent survey of drinking and drug use among youth. People in their late 30's mature out of heroin use rather than die.

N recent years a great deal of research has been directed to the modelling and measurement of technical and allocative efficiency in production. With few exceptions this research has been restricted to single-product firms.' However, recent developments in duality theory have facilitated the extension of this research to multi-product firms. The main purpose of this paper is to develop a model of the multiproduct firm in which the possibilities of both technical and allocative inefficiency are incorporated in an econometrically useful way. The first model we develop includes a nonneutral2 type of technical inefficiency and three distinguishable types of allocative inefficiency-output mix, input mix, and scale. Each type of inefficiency is costly to the firm, in the sense that each causes a reduction in profit beneath the maximum value attainable under full efficiency. The cost of each type of inefficiency depends on the magnitude of the inefficiency and the structure of the underlying production technology. In the second model we develop, technical inefficiency remains nonneutral, but allocative inefficiency is not generally decomposable into output mix, input mix and scale components. However, both technical and allocative inefficiency remain costly to the firm, the cost of each type of inefficiency depending on its magnitude and the structure of the underlying production technology. We model the technology of a competitive profit maximizing multi-product firm with the dual profit function. This enables us to use Hotelling's Lemma to generate a system of profit maximizing output supply and input demand equations. These equations are then modified to allow for the possibility of technical and three types of allocative inefficiency. A virtue of using the profit function to represent production technology is that it permits a straightforward comparison of maximum profit under full efficiency with actual profit, and with the profit that would result from any combination of the four types of inefficiency. This enables us to allocate the cost of inefficiency to each of four components. Our model of inefficiency is parametric, and is embedded in a Generalized Leontief profit function, although any flexible specification of the profit function can be used. The model is developed in sections II-IV. Estimation of the model is considered in section V. An empirical example designed to illustrate the workings of the model is discussed in section VI. Section VII concludes.

Full-information maximum likelihood is used to estimate union wage, hours, and earnings markups. Construction union wage markups are positive (58.2% at the sample means). Since union hours markups are negative (-4.0%) for most demographic groups, union earnings markups (51.1%) are smaller than the wage markups. All exogenous variables are allowed to interact with the endogenous union dummy variable, which allows us to test whether markups vary across demographic groups, whether increased local unionization has a positive spillover effect in the nonunion sector, and whether increased local unemployment equally affects wages and hours in increased local unemployment equally affects wages and hours in the two sectors.

Keun Huh, Robin C. Sickles, Estimation of the Duration Model by Nonparametric Maximum Likelihood, Maximum Penalized Likelihood, and Probability Simulators, The Review of Economics and Statistics, Vol. 76, No. 4 (Nov., 1994), pp. 683-694

Robert A. Pollak, Robin C. Sickles, Terence J. Wales, The CES-Translog: Specification and Estimation of a New Cost Function, The Review of Economics and Statistics, Vol. 66, No. 4 (Nov., 1984), pp. 602-607