Health expenditure models: A comparison 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 are two-part and sample selection cross-section models. Two-part panel data models turn out to be inappropriate for dealing with expenditures. We thus estimate sample selection models with panel data: one without a lagged dependent variable and two with a lagged dependent variable. These two latter models differ in their assumptions on the variance of the residuals. Modelling heteroscedasticity may indeed be important to avoid the bias due to the retransformation problem. We show that lagged dependent variables are important factors for heteroscedasticity. For the models with state dependence, we provide a new solution to the initial conditions problem by controlling for generalised 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 heteroscedasticity seems to dominate the others.