Formal and Informal Care: An Empirical Bayesian Analysis Using the Two-part Model

Informal care provided to the elderly by their children is proposed as a less expensive alternative to institutional long-term care. This paper explores how the elderly's consumption of medical care changes in response to changes in the informal care they receive from their children. Many earlier studies have ignored both the endogeneity of informal care and the complicated nature of health care utilization data. This paper develops a two-part model with informal care treated as an endogenous regressor and imposes exclusion restrictions on the selection process. The model is fitted using the Bayesian Markov Chain Monte Carlo (MCMC) methods, in particular the Gibbs sampler and the Metropolis-Hasting algorithm. The average treatment effects and the distributions of the treatment effects are obtained via posterior simulation. The results indicate that informal care provides a substitute for nursing home care and hospital inpatient care, but it does not affect paid home health care on average. The treatment effects are heterogeneous. The largest substitution effects occur for nursing home and hospital inpatient care at the intensive margin. The policy analysis suggests that informal care policies targeting the group that incurs the largest substitution effect may help to reduce government spending on Medicaid and Medicare.