Health care utilization and self-assessed health: specification of bivariate models using copulas

The discernment of relevant factors driving health care utilization constitutes one important research topic in health economics. This issue is frequently addressed through specification of regression models for health care use (y—often measured by number of doctor visits) including, among other covariates, a measure of self-assessed health (sah). However, the exogeneity of sah within those models has been questioned, due to the possible presence of unobservables influencing both y and sah, and because individuals’ health assessments may depend on the quantity of medical care received. This article addresses the possible simultaneity of (sah, y) by adopting a full information approach, through specification of the bivariate probability function (p.f.) of these discrete variables, conditional on a set of exogenous covariates (x). The approach is implemented with copula functions, which afford separate consideration of each variable margin and their dependence structure. The specification of the joint p.f. of (sah, y) enables estimation of several quantities of potential economic interest, namely features of the conditional p.f. of y given sah and x. The adopted models are estimated through maximum likelihood, with cross-sectional data from the Portuguese National Health Survey of 1998–1999. Estimates of the margins’ parameters do not vary much among different copula models, while, in accordance with theoretical expectations, the dependence parameter is estimated to be negative across the various joint models.