Modeling diverse expectations in an aggregated New Keynesian Model

We explore a New Keynesian Model with diverse beliefs and study the aggregation problems in the log-linearized economy. We show the solution of these problems depend upon the belief structure. Agents' beliefs are described by individual state variables and satisfy three Rationality Axioms, leading to the emergence of an aggregate state variable named "mean market state of belief." In equilibrium, endogenous variables are functions of mean market belief and this state variable is the tool used to solve the aggregation problems.Diverse beliefs alter the problem faced by a central bank since the source of fluctuations is not only exogenous shocks but also market expectations. Due to diverse beliefs the effects of policy instruments are not monotonic and the trade-off between inflation and output volatilities is complex. Also, monetary policy can counter the effects of market belief by aggressive anti-inflation policy but at the cost of increased volatility of financial markets and individual consumption.