Infantile mortality and fertility decisions in a stochastic environment

We analyze the effect of stochastic survival of children on fertility decision in a dynastic utility model where saving, so to speak, can only be made through having children, the number of which is an endogenous decision to the household. In our stochastic framework where the rate of population change undergoes a process of Brownian motion, the probability distribution of the steady state is well determined, and saving via the number of offsprings incorporates a precautionary component. Any health care assistance proposed to reduce the variance of the Brownian process, for example, to reduce the risk of premature infantile mortality, would have a negative effect on the fertility rate and a positive effect on the per capita consumption in the long run.