Zero-inflated endogenous count in censored model: Effects of informal family care on formal health care

If informal family health care is a substitute for formal health care, then there is a scope to reduce formal health care cost by promoting informal family health care. With the use of Korean data for the elderly, this paper estimates the effects of informal family health care on formal health care, where the former is measured by the number of caregivers and the latter is measured by the formal health care expenditure. This task, however, poses a number of difficulties. The first is that the number of the family caregivers is an endogenous count regressor. The second is that there are too many zeros in the count (85%). The third is that the response variable also has a nontrivial proportion of zeros (14%). This paper overcomes these problems by combining 'control function approach', 'zero-inflated' counts, and a semiparametric estimator for censored models. The resulting procedure avoids strong parametric assumptions and behaves well computationally. Our main empirical finding is that informal family health care has a large substitute effect for diabetics and that there are also weak evidences that informal family health care has substitute effects for high blood pressure and mental diseases.