A framework for estimating Dynamic Stochastic General Equilibrium (DSGE) models by Bayesian methods and validation under very general information assumptions is applied to a New Keynesian model. The standard asssumption that private agents have perfect information observing all state variables including shocks, whereas the econometrician uses only observable data, is compared with both agents having the same imperfect information (II) set. We also generalise rational expectations to a behavioural composite model that allows some households and firms to form expectations adaptively. We find significant empirical support for II as an endogenous persistence mechanism, but this is dominated by that from habit and adaptive learning.