On the Stability of the Two-Sector Neoclassical Growth Model with Externalities

We study a class of two-sector neoclassical growth models, in which one sector produces consumption goods and the other sector produces the capital goods for both sectors and in which the capital-producing sector has sector-specific externalities. We show analytically that if the capital goods for the two sectors are imperfect substitutes, then 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 capital 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 for all empirically plausible specifications of the model parameters. These findings differ sharply from the standard result that if the two capital goods are <I>perfect</i> substitutes, then local indeterminacy occurs in the two-sector model for a wide range of plausible parameter values.