More Ado About Two: Endogenous Switching, Sample Selection, Endogenous Treatment Effects and the Modified Two-Part Model
- Presenter:
Chair: Bruce Stuart; Discussant: Willard Manning Mon June 5, 2006 10:45-12:15 Room 325
Applications and theoretical assessments of the two-part model (2PM) of Duan et al. (1983) abound in the health economics, econometrics and biostatistics literatures. Mullahy (1998) shows that the conventional 2PM specification and estimator will likely be biased when used as a basis for policy analysis via estimated marginal effects or elasticities derived from the conditional mean function. At issue here is the fact that the conventional 2PM is estimated under log transformation of the outcome variable, and that so-called retransformation to express the model in untransformed conditional mean form, often requires that additional structure be imposed on the model. Mullahy (1998) shows that a modified 2PM (M2PM) which obviates retransformation is, therefore, more appropriate for policy analytic purposes. In the present paper, we derive a version of the M2PM that accommodates endogenous switching or one of its two more common incarnations – sample selection or endogenous treatment effects. There are numerous contexts in which such a model is applicable. For example, Welch et al. (1984) and Parente and Evans (1998) apply standard methods for dealing with endogenous switching to the conventional 2PM in the context of estimating the impact of health insurance on utilization and expenditure. As a by-product of the present research, we show that these rote applications of extant methods to the standard 2PM formulation will be biased. We review the 2PM and M2PM approaches and introduce the new estimator in the context of the estimation of average treatment effects. Details of the model and estimator pertaining the sample selection and full endogenous switching applications are also given. The performance of the estimator is then evaluated in the sample selection context using simulated data. We assess the accuracy and efficiency of the estimator for policy analysis relative to more conventional approaches (Heckman, 1976; Terza, 1998) which are biased in the M2PM context. The method is applied to data from the 2002 National Survey on Drug Use and Health in an analysis of the effect of drug abuse on earnings.
