Large and uncertain heterogeneity of expectations: stability of equilibrium from a policy maker standpoint

We study the dynamic behavior of heterogeneous markets with many types of agents. In particular this paper aims at studying the effects of a change in the number n of agents, who are possibly different in terms of the rule they employ to forecast, on the long-run value of a relevant state variable. On the one hand we show that a heterogeneous agents model cannot be by and large traced back to an equivalent average representative-agent model. This complicates the possibility of easily reducing large and complex models to simpler and analytically tractable ones. On the other hand, under fairly general conditions, we characterize a class of models in which the probability of convergence to the steady state becomes either one or zero as n grows. This fact has positive implications for a policy maker committed to the goal of stabilizing the economy.