Asymmetric information and rational expectations: When is it right to be "wrong"?

In this paper we examine the effects of private agents being less than fully rational in their expectations. We examine this in the context of monetary policy, where the Central Bank may have uncertain preferences either by choice or by necessity. The new feature is that we allow the public to react in two different ways. They either form rational expectations and internalize the uncertainty about the Central Bank's preferences in full; or alternatively, and if this process of internalization is costly, it forms a 'best' guess regarding those preferences. This implies a certainty equivalence strategy applied to the preference parameters. As those parameters enter the decisions non-linearly, a systematic error emerges. We examine the magnitude of the resulting error in inflation and output, following the assumption of certainty equivalence. Under all reasonable levels of uncertainty, this error turns out to be small but involves trading a deflation bias against the cost of gathering the information needed for the full information rational expectations' solution.