A simple endogenous growth model with endogenous fertility: Indeterminacy and uniqueness

Abstract

This paper studies the equilibrium dynamics and indeterminacy of equilibria in an endogenous growth model with endogenous fertility choice. We characterize the conditions that give rise to an unique equilibrium as well as multiple equilibria. Whenever there exists a unique equilibrium, it will be globally determinate; when multiple equilibria arise, indeterminacy occurs. In particular, we find that two equilibria occur - one is associated with high fertility and low growth, while the other is associated with low fertility and high growth. A parameterized example is given to assess the empirical feasibility of our results. The validity of the neo-Malthusian relation between fertility and growth is then re-examined. Finally, we study the relation between growth and welfare and compare different balanced growth equilibria in terms of their lifetime-attained utility. | Considerable literature exists upon the effect of population growth upon per capita income growth. Among the reported studies, Brander and Dowrick (1994) try to explain the large variation across countries in per capita income growth. The authors explore the possibility that even with little differences in fertility rates, different countries may experience disparate growth performances solely due to the emergence of indeterminate equilibria, which could push them into different equilibrium trajectories. The equilibrium dynamics and indeterminacy of equilibria in an endogenous growth model with endogenous fertility choice are studied. The authors characterize the conditions which give rise to a unique equilibrium as well as multiple equilibria. When a unique equilibrium exists, it will be globally determinate, and when multiple equilibria arise, indeterminacy occurs. Two equilibria were found to occur, one associated with high fertility and low growth and the other with low fertility and high growth. A parameterized example is presented to assess the empirical feasibility of results. The validity of the neo-Malthusian relation between fertility and growth is then re-examined. The authors also explore the relationship between growth and welfare, and compare different balanced growth equilibria in terms of their lifetime attained utility.