Indeterminacy under input-specific externalities and implications for fiscal policy

In this paper, we introduce input-specific externalities in a dynamic general equilibrium model with heterogeneous households and a finance constraint (Woodford (1986)). In contrast to existing papers, average labor and capital have not a positive impact on the total productivity of factors, but respectively on labor and capital efficiencies. Focusing on not too low degrees of capital-labor substitution, we show that indeterminacy requires not only a lower bound for the elasticity of capital-labor substitution, but also an upper bound, although the returns are increasing. As a direct implication, the well known wrong slopes condition (labor demand steeper than labor supply) is neither a necessary nor a sufficient condition for indeterminacy and larger increasing returns promote sadlle-path stability when inputs are high substitutes. Using this framework, we are also able to analyze the role of variable tax rates on capital and labor income on the dynamics. In contrast to existing results, we show that tax rates decreasing with their tax base do not promote instability due to self-fulfilling expectations when capital and labor are sufficiently high substitutes, but rather have a stabilizing effect.