Multiple equilibria, expectations and the dynamics of macroeconomic models

This dissertation develops two models to study issues concerning multiple equilibria in models where expectations determine endogenous variables. The mysticism model uses an evolutionary game theory approach analyze the problem of multiple martingale solutions in models with rational expectations. This model shows conditions where agents' beliefs evolve to a single fundamental solution and conditions for expectational instability. Such instability can be the source of bubbles in an endogenous variable, and simulations help to determine conditions when such behavior occurs.; The increasing returns model examines monetary policy in the presence of increasing returns in production, which may lead to multiple equilibria. We show the existence of multiple equilibria and give conditions for expectational stability of these equilibria. We also linearize around a single equilibrium to calculate optimal policy, assuming rational expectations. Simulations, using adaptive expectations, show that if shocks are small, the policy recommendations of the linear model may be appropriate, but if shocks are large, this policy may be sub-optimal due to the presence of other equilibria. Even though there is only one stochastic element in the model, the magnitude of the variance affects optimal policy.