Health Expenditure Models: a Comparison of Five Specifications Using Panel Data

In this article, we focus on the estimation of outpatient expenditures with panel data. We model the logarithm of expenditures and consider five different models. The first two models are cross section two part and sample selection models. The two-part approach appears inappropriate when moving to panel data. We therefore focus on panel data models with sample selection. Our third model is a model without lagged dependent variables, and the last two ones include such lagged variables. These two latter models differ in their assumptions on the variance of the residuals. Modeling heteroskedasticity may indeed be important to avoid the bias due to the retransformation problem. We show that lagged dependent variables are important factors of heteroskedasticity. For the models with state dependence we provide a new solution to the initial conditions problem by using generalized residuals. We establish that panel data models highly improve the correlation explained by the model in the time-series dimension without damaging the fit in the cross-section dimension. For all indicators of fit, the model with state dependence and heteroskedasticity seems to dominate the others.