Balanced-Budget Rules, Elasticity of Substitution, and Macroeconomic (In)Stability

This paper examines the relation between factor substitution and (local) stability of equilibria in a one-sector real business cycle model under balanced-budget rules. We show that under non-unitary elasticity of factor substitution, the Schmitt-Grohe-Uribe indeterminacy result can be altered. Using the two-step normalization procedure, we highlight two opposing effects of factor substitution, namely, the efficiency effect and the distribution effect, on aggregate stability. With endogenous distortionary taxes and gross substitutability between capital and labor, the existing literature overlooks the distribution effect and finds that balanced-budget rules are likely to deliver indeterminacy. However, if capital stock is relatively more abundant, a higher elasticity of substitution generates a source of stability due to the distribution effect. Our calibration shows that the distribution effect is always the dominating force.