Optimal discretionary monetary policy under persistent-transitory confusion over cost shock

In this study, I model the debated statements of Federal Reserve regarding transitory inflation in New Keynesian context and imperfect information about cost shock, where it is formulated as sum of unobserved persistent and transitory components. Specifically, I consider the case, in which policy maker and private agents are uninformed about the components and subject to a gradual recognition from observation using a Kalman filter. Policy maker solves the inference problem to learn the components, and, in turn, private agents rely on central bank speeches to learn policy maker’s inferences. Then, based on policy maker’s estimation, private agent’s problem and, so New Keynesian relations are formulated. The responses with filtered variables incorporate progressive learning. In particular, when the true realization of the shock and its perception is persistent, the increase (decline) in inflation (output), therefore in interest rate is less compared to that of perfect information responses, creating a relatively desirable outcome for the policy maker. If instead shock is perceived as transitory and communicated as such, which was the case in Fed’s statements, the response of inflation, hence the required policy response is significantly more pronounced. This leads me to conclude that it may not be the best response to announce that shock is transitory while it is not the case. Then, I continue studying welfare loss under discretionary policy when the estimation and the actual realization is persistent. I find that loss under imperfect information with an inferred persistent shock is smaller relative to that of perfect information when variance of the noise increases, and shock becomes less persistent. Lastly, I extend the model by introducing a signal on transitory component.