Optimal investment in health when lifetime is stochastic, or, rational agents do not often follow health recommendations

Abstract There exists considerable evidence that people do not often follow the health recommendations issued by health authorities. It might be tempting to think that not following health recommendations is a sign of irrationality and that behavioral considerations are required in order to explain such behavior. Despite this temptation, and using a general health‐capital model which accounts for the consumption of many goods, a stock of health and investment in it, as well as an agent's random lifetime and accumulation of wealth, it is shown that such seemingly irrational decisions are in fact consistent with rational, forward‐looking, decision making. Moreover, it is shown, among other things, that the prototypical assumptions employed in the literature imply that rational agents invest more in their health at each point in time than that which minimizes the conditional probability of dying at that point in time, and thus lack sufficient explanatory reach.