Recursive utility, endogenous growth, and the welfare cost of volatility

Abstract

This paper proposes a measure of the welfare cost of volatility derived from a stochastic endogenous growth model extended to the case of a recursive utility function which disentangles risk aversion from intertemporal elasticity of substitution. The measure of the welfare cost of volatility takes into account not only the direct effect of volatility on expected utility but also the link between volatility and growth. It thus encompasses a direct welfare cost of fluctuations and a welfare cost due to the endogeneity of the consumption. We obtain a closed form solution for these two costs and show that the total welfare cost of volatility increases with both the risk aversion and the intertemporal elasticity of substitution. For plausible values of the agent's preference parameters, the cost of volatility may be greater than measures based on an exogenous process for consumption. However, when applied to the US economy, our measure shows little differences compared with the one derived under the assumption that the consumption process is exogenous. Yet, we show that this may not be the case for more volatile economies.