Working Paper

Capital-Labor Substitution and Equilibrium Indeterminacy

Abstract: 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.

JEL Classification: E30; E32;

https://doi.org/10.24148/wp2008-06

Bibliographic Information

Provider: Federal Reserve Bank of San Francisco

Part of Series: Working Paper Series

Publication Date: 2009-06-01

Number: 2008-06

Note: PDF date: June 24, 2009.