On the stability of the two-sector neoclassical growth model with externalities

We study a class of two-sector growth models with sector-specific externalities, in which one sector produces consumption and the other sector produces investment. The novelty is that investment allocated to the consumption sector is an imperfect substitute for investment allocated to the investment sector. We show analytically that in this case local indeterminacy near the steady state is impossible for every empirically plausible specification of the model parameters. More specifically, we show that a necessary condition for local indeterminacy is an upward-sloping aggregate labor demand curve in the investment sector, which requires a counterfactual strength of the externality. We show numerically that an elasticity of substitution of plausible size implies determinacy near the steady state. These findings differ sharply from the standard result for two-sector models that if the investments allocated to the two sectors are perfect substitutes, then local indeterminacy occurs for a wide range of plausible parameter values.