Elasticities of Substitution in Real Business Cycle Models with Home Production

This paper constructs a simple model of home production that demonstrates the connection between the intertemporal elasticity of substitution in market consumption (IES) and the static elasticity of substitution between home and market consumption (SES), when the utility function is additively separable over home and market consumption. Understanding this connection is important because there is a large body of empirical evidence suggesting that the IES is small, but little evidence on the size of the SES. We use our framework to shed light on the properties of a home production model with a low IES. We find that such a model must have two fundamental properties in order to match key aspects of the U.S. aggregate data. First, the steady-state growth rate of technology must be the same across sectors. Second, shocks to technology must be sufficiently positively correlated across sectors.