Health externalities to labor productivity and optimal policies with endogenous fertility, labor, and longevity

We study the optimal health subsidy in a dynastic model of altruistic middle-aged and old agents who choose health spending, savings, inter-vivos transfers, and the number of children. Health spending enhances labor productivity and longevity, but firms cannot observe individuals' health spending. This causes health externalities on labor productivity. We show that the externalities reduce health spending, labor productivity, and longevity but may indirectly increase savings and decrease fertility from the first-best levels. Public or employer-based health subsidies increase health spending to an age-dependent level, but these subsidies to old agents also increase their transfers to middle-aged agents (the transfer cost of childrearing). Age-specific labor-income taxes decrease age-specific health spending and the (time and transfer) costs of childrearing. The decentralization of the social optimum thus requires appropriate age-specific public or employer-based health subsidies and age-specific labor-income taxes to an extent that is increasing with the degree of the health externalities.