Rational Ambiguity and Monitoring the Central Bank

In this paper we examine the consequences of having a Central Bank whose preferences are state contingent. This has variously been identified in the literature as a Central Bank that is "rationally inattentive", "risk averse", 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 internalize the uncertainty about the Bank's preferences in full. Alternatively, and particularly if the process of internalization is costly, it can form a best guess regarding those preferences. This latter case implies a strategy of certainty equivalence. We examine the magnitude of the resulting error in inflation and output if the certainty equivalence approximation is used. Under all reasonable levels of uncertainty, the error turns out to be small. In that case, the certainty equivalence strategy would be "rational". But it involves trading off accepting a deflation bias against the cost of gathering the information needed to calculate the full rational expectations solution.