You Might as Well be Hung for a Sheep as a Lamb: The Loss Function of an Agent
Most of those who take macro and monetary policy decisions are agents. The worst penalty which can be applied to these agents is to sack them. Agents thus have loss functions which are bounded above. We work with a bell loss function which has this property. With additive uncertainty the certainty equivalence which holds for a quadratic loss function breaks down with a bell loss function when there are two or more targets. With multiplicative (Brainard) uncertainty policy is more conservative than in the absence of multiplicative uncertainty, but less so with the bell than the quadratic loss function.
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