Elasticities of substitution in real business cycle models with home production

Recently, there has been considerable interest in modifying the standard real business cycle model to include home production. In this paper, we construct a simple model of home production that demonstrates the connection between the intertemporal elasticity of substitution (IES), and the elasticity of substitution between home and market consumption. Understanding this connection is important because there is much larger body of empirical evidence on the size of the IES than there is on the size of the static home-market substitution elasticity. We use this framework to shed light on the properties of a home production model with empirically plausible (lower) values of the IES. In particular, we find that such a model must display two fundamental properties in order to reproduce certain key aspects of the U.S. aggregate data: first, the steady state growth rate of technology must be the same across sectors. Second, out of steady state, shocks to technology must be sufficiently positively correlated across sectors.