Expectational diversity in monetary economies
We investigate an overlapping generations monetary economy in which agents' expectations depend upon backward looking predictors of the future price level. We use discrete choice theory to model how agents select a predictor based on its past forecast error. Letting the number of available predictors tend to infinity, we obtain the large type limit of the system. Taking the large type limit dramatically reduces the number of free parameters, while maintaining the expectational diversity which we argue is necessary for constructing plausible learning-based models. The model's dynamics are strongly influenced by the intensity of choice, which measures how sensitive an agent's predictor choice is to differences in forecast errors across predictors. When the intensity of choice is low, the monetary steady state is stable. As the intensity of choice increases, two types of behavior may emerge. First, the system may undergo a saddle- node bifurcation and become explosive. Second, the system may undergo a Hopf bifurcation, in which case we document the emergence of highly irregular equilibrium price paths. The conditions under a Hopf bifurcation occurs seem economically plausible.
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