Capital-Labor Substitution and Equilibrium Indeterminacy

Empirical evidence indicates that the elasticity of capital-labor substitution for the aggregate U.S. economy is below unity. In contrast, the existing indeterminacy literature has mostly restricted attention to a Cobb-Douglas production function which imposes a substitution elasticity exactly equal to unity. This paper examines the quantitative relationship between capital-labor substitution and the conditions needed for equilibrium indeterminacy (and belief-driven fluctuations) in a one-sector growth model. With variable capital utilization, the substitution elasticity has little quantitative impact on the minimum degree of increasing returns needed for indeterminacy. However, when capital utilization is constant, a below-unity substitution elasticity sharply raises the minimum degree of increasing returns. In this version of the model, lower substitution elasticities impose a higher adjustment cost on labor hours that cannot be mitigated by shifts in the capital utilization rate. Overall, our results show that empirically-plausible departures from the Cobb-Douglas specification can make indeterminacy more difficult to achieve.