Capital-Labor Substitution, Equilibrium Indeterminacy, and the Cyclical Behavior of Labor Income

This paper examines the quantitative relationship between the elasticity of capital-labor substitution and the conditions needed for equilibrium indeterminacy (and belief-driven áuctuations) in a one-sector growth model. Our analysis employs a ìnormalizedîversion of the CES production function so that all steady-state allocations and factor income shares are held constant as the elasticity of substitution is varied. We demonstrate numerically that higher elasticities cause the threshold degree of increasing returns for indeterminacy to decline monotonically, albeit very gradually. When the elasticity of substitution is unity (the Cobb-Douglas case), our model requires increasing returns to scale of around 1.08 for indeterminacy. When the elasticity of substitution is raised to 5, which far exceeds any empirical estimate, the threshold degree of increasing returns reduces to around 1.05. We also demonstrate analytically that laborís share of income becomes pro-cyclical as the elasticity of substitution increases above unity, whereas laborís share in postwar U.S. data is countercyclical. This observation, together with other empirical evidence, indicates that the elasticity of capital-labor substitution in the U.S. economy is actually below unity.