Endogenous Persistence in an Estimated DSGE Model under Imperfect Information

We provide a tool for estimating DSGE models by Bayesian Maximum-likelihood meth?ods under very general information assumptions. This framework is applied to a New Keynesian model where we compare the standard approach, that assumes an informa?tional asymmetry between private agents and the econometrician, with an assumption of informational symmetry. For the former, private agents observe all state variables including shocks, whereas the econometrician uses only data for output, inflation and interest rates. For the latter both agents have the same imperfect information set and this corresponds to what we term the ¡®informational consistency principle¡¯. We first assume rational expectations and then generalize the model to allow some households and firms to form expectations adaptively. We find that in terms of model posterior probabilities, impulse responses, second moments and autocorrelations, the assumption of informational symmetry by rational agents significantly improves the model fit. We also find qualified empirical support for the heterogenous expectations model.