A New Keynesian Model with Diverse Beliefs

The paper explores a New Keynesian Model with diverse beliefs and studies the impact of this heterogeneity on fluctuations and monetary policy. It uses a standard model (e.g. Gali (2008), Walsh (2010) and Woodford (2003)). Aggregation is examined only for the log- linearized economy and even for this economy, aggregation problems are significant and their solutions depend upon the belief structure. Agents' beliefs are described by individual state variables and satisfy three Rationality Axioms. Belief rationality plays a key role in driving belief dynamics and mean market belief is the main tool used to solve the aggregation problems. Macro dynamics is then described by an IS curve, Phillips curve and a monetary rule similar to standard models except that mean market belief is a new force amplifying fluctuations. Due to belief heterogeneity, changes in the policy rule alter key macro-economic parameters which must be deduced from the micro equilibrium, a problem not present in a single agent economy. In addition to belief rationality agents know the equilibrium map. Diverse beliefs alter the problem faced by a central bank since a central source of fluctuations in this paper are not exogenous shocks (assumed small) but fluctuations caused by market expectations, and this alters the role of a central bank. Diverse beliefs impact response to policy due to their effect on motives to consume, supply labor etc. but market belief may support or oppose a central bank's goals. The paper draws general conclusion about efficacy of monetary rules of either contemporaneous or of expected output deviation and inflation with weights . The main conclusions are as follows. (i) Monetary policy can counter the effects of market belief by aggressive anti-inflation policy, but with cost. Large entails volatile financial markets and volatile individual consumption. Volatility of aggregate output is different from volatility of individual consumption and welfare considerations suggest that individual consumption volatility and financial market instability are at least as important goals of central bank as stability of aggregate output. The paper then shows that optimal policy outcomes require a central bank to employ moderate values of . (iii) A central bank that aims to stabilize only inflation and aggregate output can be either a one mandate bank that fights only inflation or a two mandate central bank: each can attain a different segments of the efficiency frontier. (ii) Due to diverse beliefs, the effects of ( , ) are not monotonic. (iii) As a result of (ii) the problem of output stabilization is particularly complex. Indeed, response monotonicity is a desirable property, offering a central bank feasible policy actions whose outcomes are predictable and entailing clearer policy trade-off.(iv) Both efficiency and monotonicity of output stabilization are improved if a central bank uses rules that target inflation and the causes of output volatility which are market belief and exogenous shocks, instead of output. Targeting market belief may be accomplished by targeting asset prices, which reflect market belief. As to optimal policy and "forecast-targeting" it is seen that under diverse beliefs a bank's optimal policy is not Pareto Optimal and may not even be Pareto improving. Central bank's policy does not alter agents' beliefs about state variables and under forecast targeting the private sector does not adopt the central bank's forecasts even when agents fully understand and accept the policy commitment of the bank since the bank and private sector may disagree about forecasts of endogenous variables. Hence, a bank's optimal policy may be carried out with private market opposition rather than consensus, as is the case under Rational Expectations. Also, an optimal policy relative to a bank's belief adds to privately perceived uncertainty of future bank's belief or actions even when the policy is fully understood.