Inflation Dynamics and Inflation Uncertainty in a Model with Heterogeneous Forecasts

Recent research in macroeconomics has sought to develop a tractable form of heterogeneity in attempting to model sluggishness of response of the economy consistent with data. Sims (2003) argued that limited information processing was a promising avenue for understanding pervasive stickiness. Under his rational inattention, consumers or firms respond more slowly to the true underlying state of the economy because they are learning what the true state is. The information flow necessary to completely understand the true state of the economy is too overwhelming. In our paper, we have an endogenous ecology of expectations. Formally, we consider a model economy with a generic number of expectations formation types, represented by I. We develop a mapping from which conceptualizes the dynamics of the ecology of expectations. This mapping has a fixed point that describes a long run stationary equilibrium after an appropriate change of units. We show that a stationary equilibrium exists. We study the response differences in the dynamics of the inflation rate to changes in the mean and variance of the money supply process in economies indexed by the fraction of agents that have fully structural rational expectations. We develop small noise expansions to obtain analytical results of our economy in response to stochastic money supply processes. Lastly, we apply robust control methods, deriving conditions in which robustness leads to a temporary strong increase in the demand for money. Inflationary pressures are accordingly dampened. These results have implications for cases, like the Great Recession, in which the effects of greater model uncertainty may have played a role in keeping inflation rates low even in the face of expanding money supply