OVER THIRTY YEARS ago, in his presidential address to the American Economic Association, Milton Friedman asserted that in the long run the Phillips curve was vertical at a natural rate of unemployment that could be identified by the behavior of inflation.(1) Unemployment below the natural rate would generate accelerating inflation, and unemployment above it, accelerating deflation. Five years later the New Classical economists posed a further challenge to the stabilization orthodoxy of the day. In their models with rational expectations, not only was monetary policy unable to alter the long-term level of unemployment, it could not even contribute to stabilization around the natural rate.(2) The New Keynesian economics has shown that, even with rational expectations, small amounts of wage and price stickiness permit a stabilizing monetary policy.(3) But the idea of a natural unemployment rate that is invariant to inflation still characterizes macroeconomic modeling and informs policymaking. The familiar empirical counterpart to the theoretical natural rate is the nonaccelerating-inflation rate of unemployment, or NAIRU. Phillips curves embodying a NAIRU are estimated using lagged inflation as a proxy for inflationary expectations. NAIRU models appear in most textbooks, and estimates of the NAIRU--which is assumed to be relatively constant--are widely used by economic forecasters, policy analysts, and policymakers. However, the inadequacy of such models has been demonstrated forcefully in recent years, as low and stable rates of inflation have coexisted with a wide range of unemployment rates. If there were a single, relatively constant natural rate, we should have seen inflation slowing significantly when unemployment was above that rate, and rising when it was below. Instead, the inflation rate has remained fairly steady, with annual inflation as measured by the urban consumer price index (CPI-U) ranging from 1.6 to 3.0 percent since 1992, while the unemployment rate has ranged from 6.8 to 3.9 percent. In this paper we present a model that can accommodate relatively constant inflation over a wide range of unemployment rates. Another motivation is a recent finding by William Brainard and George Perry.(4) Estimating a Phillips curve in which all the parameters are allowed to vary over time, they find that the coefficient on the proxy for expected inflation in the Phillips curve has changed considerably, while other parameters of that model have been relatively constant. In particular, Brainard and Perry found that the coefficient on expected inflation was initially low in the 1950s and 1960s, grew in the 1970s, and has fallen since then. The model we present can explain both why the coefficient on expected inflation might be expected to change over time and, to some extent, the time pattern of changes observed by Brainard and Perry. Our paper also allows an interpretation of the findings of Robert King arm Mark Watson and of Ray Fair.(5) Both find a long-run trade-off between inflation and unemployment. In addition, King and Watson find that the amount of inflation that must be tolerated to obtain a given reduction of unemployment rose considerably after 1970. Our model allows a trade-off, but only at low rates of inflation such as those that prevailed in the 1950s, 1960s, and 1990s. At higher rates of inflation, the trade-off is reduced, and at high enough rates of inflation, it disappears. Much of the empirical controversy surrounding the relationship between inflation and unemployment has focused on how people form expectations. This may be neither the most important theoretical nor the most important empirical issue. Instead, this paper suggests that it is not how people form expectations but how they use them--and even whether they use them at all--that is the issue. Economists typically assume that economic agents make the best possible use of the information available to them. But psychologists who study how people make decisions have a different view. …