In most of the models analyzed so far, we have concentrated on unique steady states and unique convergent paths toward the steady state.
In both the deterministic models with perfect foresight (such as the ones in the chapters on economic growth) and the stochastic models with rational expectations (such as the ones in the chapters on aggregate fluctuations), we have focused on the fundamental solutions.
With few exceptions,1 the solutions were unique and were characterized by the saddle point property.In this chapter, we focus on solutions other than the fundamental solution, and we delve deeper into models in which there are multiple equilibria.
Let us start with the analysis of bubbles in linear first-order rational expectations models, and then move on to nonlinear dynamic models with multiple equilibria, self-fulfilling prophecies, and sunspots.
Bubbles refer to nonfundamental solutions in rational expectations models, and can even arise in linear models with a unique equilibrium based on fundamentals. In models characterized by the saddle point property, bubbles result in explosive solutions, which in many cases can be ruled out by appropriate transversality conditions. In inherently unstable models which are not characterized by the saddle point property, there are multiple adjustments paths. In such models, bubbles are not explosive and can thus be stabilizing.2
Compared to the properties of models with a unique steady state, nonlinear dynamic models possessing multiple equilibria provide a different account of the growth process, the propagation mechanism of business cycles, and the monetary transmission mechanism. Closely related to multiple equilibria in such models is the concept of sunspot equilibria, developed by Shell [1977] and Cass and Shell [1983]. This refers to equilibria influenced by extrinsic belief shocks in a general equilibrium setting. Sunspot equilibria can be constructed by randomizing over multiple equilibria. They require deviations from the Arrow-Debreu structure of complete markets, such as those occurring in overlapping generations (OLG) models or models with externalities, informational asymmetries, increasing returns to scale, and money.3
In the remainder of this chapter, we explore examples of models with bubbles, multiple equilibria, self-fulfilling prophecies, and sunspots, focusing on models of financial markets and general equilibrium models with money.
22.1