Indeterminacy and Endogenous Fluctuations with Arbitrarily Small Externalities

Abstract

In this paper we study the occurrence of local indeterminacy, endogenous fluctuations, and bifurcations in a simple non-monetary 2-period overlapping generations economy (in which people do not consume when young) with capital-labor substitution, elastic labor supply, and productive externalities. We show that, in contrast with the local dynamics generated by many one-sector models of capital accumulation studied in the current literature, local indeterminacy and, therefore, stationary stochastic equilibria driven by self-fulfilling beliefs (sunspots), as well as multiple stationary equilibria, are pervasive phenomena when the elasticity of input substitution is large and when the size of externalities is arbitrarily small. We also demonstrate that, when externalities are arbitrarily small, the Cobb–Douglas production function, often used for its analytical tractability in many models, is structurally unstable: it is always associated with uniqueness of the steady-state, but any small perturbation of the elasticity of input substitution leads to the existence of two stationary equilibria, which may be close to each other, with the consequence that the dynamics may be qualitatively very different from those originated in the unit elasticity case. Journal of Economic Literature Classification Numbers: E32, C62.