Intertemporal substitution in consumption, labor supply elasticity and sunspot fluctuations in continuous-time models

The aim of this paper is to discuss the roles of the elasticity of intertemporal substitution in consumption and the elasticity of the labor supply on the local determinacy properties of the steady state in a two-sector economy with constant elasticity of substitution technologies and sector-specific externalities. Our main results provide necessary and sufficient conditions for local indeterminacy. First, we show that the consumption good sector needs to be capital intensive at the private level and labor intensive at the social level. Second, we prove that under this capital intensity configuration, the existence of sunspot fluctuations is obtained if and only if the elasticity of intertemporal substitution in consumption is large enough but the elasticity of the labor supply is low enough. In particular, we will show on the one hand that when the labor supply is infinitely elastic, the steady state is always saddle-point stable, and on the other hand that when the elasticity of intertemporal substitution in consumption is infinite, labor does not have any influence on the local stability properties of the equilibrium path.