Macroeconomic Models with Incomplete Information and Endogenous Signals

This paper characterizes a general class of macroeconomic models with incomplete information, when the information process includes endogenous variables. I derive conditions for existence and uniqueness of equilibrium, which apply even when the model contains endogenous state variables, and I introduce an algorithm to solve the general model. As an application I consider a business cycle model with capital where firms must make inferences about aggregate shocks through the movements of endogenous prices. In this model, the central bank's policy rule determines the real effects of nominal shocks, by controlling how informative prices are about the aggregate state. The optimal policy targets acyclical inflation, which makes money neutral. Finally, I demonstrate an advantage of models with endogenous information: the noisy signals are driven by fundamental shocks, rather than ad hoc noise, so data can discipline the information structure. Accordingly, I calibrate the model using US industry-level panel data.