Local Indeterminacy In Continuous-Time Models: The Role Of Returns To Scale

The aim of this paper is to discuss the effect on returns to scale on the local determinacy properties of the steady state in a continuous-time two-sector economy with endogenous labor supply and sector-specific externalities. First we show that when labor is inelastic and the elasticity of intertemporal substitution in consumption is large enough, for any configuration of the returns to scale, local indeterminacy is obtained if there is a capital intensity reversal between the private and the social levels. Second, we prove that when labor is infinitely elastic, saddlepoint stability is obtained if the investment good sector has constant social returns, whereas local indeterminacy arises if the investment good sector has increasing social returns and the elasticity of intertemporal substitution in consumption admits intermediate values. Finally, our main conclusion shows that local indeterminacy requires a low elasticity of labor when the investment good has constant social returns, but requires either a low enough or a large enough elasticity of labor when the investment good has increasing social returns.