In most of the models we have analysed so far we have concentrated on unique steady states and unique convergent paths towards 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 so called fundamental solutions, which, with few exceptions, such as in the Samuelson and Diamond overlapping generations models, or the Calvo public debt model, were unique and characterized by the saddle point property.
In this chapter we shall focus on solutions other than the fundamental solution, and we shall delve deeper into models in which there are multiple equilibria.
We start with the analysis of bubbles in linear first order rational expectations models, and then move on to non-linear dynamic models with multiple equilibria and sunspots.
Bubbles refer to non fundamental 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, and can in many cases be ruled out by appropriate transversality conditions. In inherently unstable models, that 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.
Compared to the properties of models with a unique steady state, non-linear 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 a sunspot equilibria, developed by Shell [1977] and Cass and Shell [1983]. This refers to equilibriia influenced by extrinsic belief shocks in a general equilibrium setting. Sunspot equilibria can be constructed by randomizing over multiple equilibria, and require deviations from the Arrow Debreu structure of complete markets, such as those occurring in overlapping generations models or models with externalities, informational asymmetries, increasing returns to scale and money.
In the remainder of this chapter we provide a number of examples of models with bubbles, multiple equilibria and sunspots, focusing on models of financial and money markets.
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Dynamic Macroeconomics 