Determinacy with Capital Adjustment Costs and Sector-Specific Externalities

This Paper explores the stability properties of the steady state in the standard two-sector real business cycle model with a sector-specific externality in the capital-producing sector. When the steady state is stable then equilibrium is indeterminate and stable sunspots are possible. We find that capital adjustment costs of any size preclude stable sunspots 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 the existence of stable sunspots is an upward-sloping labour demand curve in the capital-producing sector, which in turn requires an implausibly strong externality. This result contrasts sharply with the standard result that when we abstract from capital adjustment costs, stable sunspots occur in the two-sector model for a wide range of plausible parameter values.