In this paper we examine the consequences of having a Central Bank whose preferences are state contingent. This has been identified in the literature as a Central Bank that is `rationally inattentive' or `constructively ambiguous'. The new feature in this paper is that we show how the private sector is likely to react. There are two possibilities: the public can form rational expectations and internalise the uncertainty about the Central Bank's preferences in full. Alternatively, and if this process of internalisation is costly, it can form a `best' guess regarding those preferences and use that. This implies an equivalence strategy applied to the preference parameters. As those parameters enter the decisions nonlinearly, a systematc error emerges. We examine the magnitude of the resulting error in ination and output, following the assumption of certainty equivalence. Under all reasonable levels of uncertainty this error turns out to be small but it involves trading a deation bias against the cost of gathering the information needed for the full rational expectations solution.