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This paper dreives optimal monetary policy rules in setups where certainty equivalence does not hold because either central bank preferences are not quadratic, and/or the aggregate supply relation is nonlinear. Analytical results show that these features lead to sign and size aymmetries, and nonlinearities in the policy rule. Reduced-form estimates indicate that US monetary policy can be characterized by a nonlinear policy rule after 1983, but not before 1979. This finding is consistent withdoi:10.2202/1558-3708.1155 fatcat:zh7yxmzdofbtdgrte5nlcofzja