Empirical evidence suggests that the instrument rule describing the interest rate–setting behavior of the Federal Reserve is nonlinear. This paper shows that optimal monetary policy under parameter uncertainty can motivate this pattern. If the central bank is uncertain about the slope of the Phillips curve and follows a min–max strategy to formulate policy, the interest rate reacts more strongly to inflation when inflation is further away from target. The reason is that the worst case the central bank takes into account is endogenous and depends on the inflation rate and the output gap. As inflation increases, the worst-case perception of the Phillips curve slope becomes larger, thus requiring a stronger interest rate adjustment. Empirical evidence supports this form of nonlinearity for post-1982 U.S. data.
