Long-Run Risk Unwrapped: An Analytical Expression of the Wealth-Consumption Ratio

Abstract

We derive an analytical expression for the wealth-consumption ratio (wcr) in a representative agent model with recursive utility over consumption. Our expression assumes that the wcr is exponential affine in expected consumption growth and sets constraints on the mean-reversion of consumption growth. Our analytical expression for the wcr is practically identical to the exact numerical solution.

Keywords: wealth-consumption ratio, analytical solution, long-run risk