Asset Accumulation, Fertility Choice and Nondegenerate Dynamics in a Small Open Economy

This paper shows that the assumption of elastic fertility choices represents an unconsidered way of introducing nondegenerate dynamics within an immortal small open economy, facing perfect capital mobility and no adjustment costs associated with capital accumulation, and having a fixed discount rate. The transient dynamics are obtained since fertility, which enters the Euler equation, renders the growth of the marginal utility of wealth strictly interconnected with wealth accumulation. The comparative dynamics are studied for two exogenous shocks: an increase in thrift, which changes fertility and capital formation permanently, and an increase in government spending, which alters fertility and capital stock temporarily.