Equilibrium consumption and precautionary savings in a stochastically growing economy

The derivation of a closed-form solution for consumption based on the constant elasticity utility function in the presence of stochastic labor income has proved to be intractable. This paper derives a closed-form equilibrium relationship between consumption and wealth, one that holds along a balanced growth path in a stochastic Romer endogenous growth model. By employing more general recursive preferences, we can disentangle the coefficient of relative risk aversion from the intertemporal elasticity of substitution. The effects of key structural parameters on equilibrium consumption and its tradeoff with leisure are analyzed. A significant aspect of our analysis concerns the extent to which current risk in the economy is shared between labor and capital. This plays an important role in determining the impact of risk on the economy in general, and on consumption in particular. Formal analysis is supplemented with extensive numerical simulations.