Core inflation in the United States declined from the end of 1995 through the end of 1999 and has remained modest thereafter despite persistent above-trend growth and a decline in the unemployment rate to a level well below earlier estimates of the non-accelerating-inflation rate of unemployment (NAIRU). 1 These developments have had at least two implications for the conduct of monetary policy. First, policymakers (at least those that have continued to rely on the NAIRU framework) have had to

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... date their estimates of the NAIRU as they have decided how much to adjust the federal funds rate in response to realizations in inflation and unemployment. Second, policymakers have had to adjust the conduct of monetary policy to take into account the heightened uncertainty about the NAIRU. Although a standard result in the literature on monetary policy under uncertainty is that of certainty-equivalence, a recent strand of this literature has focused on signal extraction in the estimation stage of the policymakers' problem. This part of the literature suggests that policymakers should attenuate their response to changes in the observed unemployment rate when they are more uncertain about the NAIRU and, at the same time, respond more aggressively to movements in the inflation rate (Swanson, 2000a ). In addition, Meyer (1999) has suggested that episodes of heightened uncertainty about the NAIRU may also warrant a nonlinear policy response to changes in the unemployment rate. Specifically, he has suggested that in such circumstances, policymakers: (i) initially attenuate their response to changes in the unemployment rate, but (ii) return to a more aggressive policy response when the unemployment rate falls far enough that policymakers regain confidence that it lies below the NAIRU. This paper is an attempt to formalize such a nonlinear policy rule and test its performance when there is heightened uncertainty about the NAIRU. I. Optimal Nonlinear Policy To illustrate the basic point of the paper without introducing unnecessary complications, we use a simple backward-looking model (in simulations we also consider models with richer dynamics and rational expectations). This model consists of an "IS" type equation relating the lagged real interest rate r t Ϫ 1 to unemployment u t , and a short-run Phillips curve that determines inflation t : where r*, , ␣, and ␤ are known parameters, t and t are stochastic disturbances, and u* denotes the NAIRU. Policymakers never observe u* directly but must infer it from observations of u and . We maintain the standard assumption that policymakers' preferences are quadratic over inflation and unemployment gaps. Optimal policy in this standard linear-quadratic model is then given by (3) r t ϭ r* ϩ a͑ t Ϫ *͒ Ϫ b͑u t Ϫ E t u*͒ where we assume that policymakers control the real interest rate r t . This policy displays the usual property of certainty-equivalence: interest * Meyer and Swanson: Federal Reserve Board, 20th and Constitution Ave., N.W.,