Stationary bubble equilibria in rational expectation models

Abstract

A linear rational expectation model with current expectations admits a unique linear stationary dynamic equilibrium only under specific restrictions on the parameter values. This paper shows that, in general, there is a multiplicity of stationary dynamic equilibria due to the existence of nonlinear stationary equilibria. These nonlinear stationary equilibria are consistent with the self-fulfilling prophecies that characterize the rational expectation equilibria, and can display speculative bubbles, volatility induced mean reversion and/or stochastic autoregressive patterns. They are also compatible with the transversality conditions when the model involves intertemporal optimization. The stationary nonlinear dynamic equilibria are economically relevant. Their analysis requires revised methods of identification for the stationary equilibrium, impulse response analysis, and estimation techniques, which are presented in this paper. Standard econometric and economic methods, which ignore the nonlinear stationary solutions provide misleading outcomes, which may affect the validity of an economic policy or portfolio strategy.