In this paper we address the issue of how parameter uncertainty affects the optimal degree of central bank conservatism. The analysis is conducted in the standard macroeconomic model of a monetary policy game embedding an expectational Phillips-curve. Multiplicative "Brainard" uncertainty is added to the model. This means that the central bank's policy instrument has a stochastic impact on inflation. This type of uncertainty is particularly interesting, since it affects the credibility. We show that if the flexibility problem dominates, an increase in uncertainty reduces optimal conservatism. However, increases in uncertainty can also require increases in the optimal degree of conservatism. This happens when the central bank has a sufficiently large credibility problem. This is particularly clear in the case of the introduction of uncertainty at the margin. Furthermore, the coefficient of variation of inflation appears to contain useful information about the relative size of the credibility problem and, hence, about how incipient uncertainty can affect optimal conservatism in actual economies.
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