A smooth mixture of Tobits model for healthcare expenditure

This paper develops a smooth mixture of Tobits (SMTobit) model for healthcare expenditure. The model is a generalization of the smoothly mixing regressions framework of Geweke and Keane (J Econometrics 2007; 138: 257–290) to the case of a Tobit‐type limited dependent variable. A Markov chain Monte Carlo algorithm with data augmentation is developed to obtain the posterior distribution of model parameters. The model is applied to the US Medicare Current Beneficiary Survey data on total medical expenditure. The results suggest that the model can capture the overall shape of the expenditure distribution very well, and also provide a good fit to a number of characteristics of the conditional (on covariates) distribution of expenditure, such as the conditional mean, variance and probability of extreme outcomes, as well as the 50th, 90th, and 95th, percentiles. We find that healthier individuals face an expenditure distribution with lower mean, variance and probability of extreme outcomes, compared with their counterparts in a worse state of health. Males have an expenditure distribution with higher mean, variance and probability of an extreme outcome, compared with their female counterparts. The results also suggest that heart and cardiovascular diseases affect the expenditure of males more than that of females. Copyright © 2011 John Wiley & Sons, Ltd.