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

Abstract

This Paper explores the local stability properties of the steady state in the two-sector neo-classical growth model with sector-specific externalities. We show analytically that capital adjustment costs of any size preclude local indeterminacy nearby the steady state for every empirically plausible specification of the model parameters. More specifically, we show that when capital adjustment costs of any size are considered, a necessary condition for local indeterminacy is an upward-sloping labour demand curve in the capital-producing sector, which in turn requires an implausibly strong externality. We show numerically that capital adjustment costs of plausible size imply determinacy nearby the steady state for empirically plausible specifications of the other model parameters. These findings contrast sharply with the previous finding that local indeterminacy occurs in the two-sector model for a wide range of plausible parameter values when capital adjustment costs are abstracted from.

Keywords: Capital adjustment costs, determinacy, externality, local indeterminacy, stability

JEL Classification: E00, E30