The natural rate of interest -- the real interest rate consistent with output equaling potential -- plays an important role in both economic forecasting and monetary policy. Much of the literature has assumed that the natural rate of interest is constant. For example, the Taylor rule includes a fixed value of 2 percent. Economic theory, however, suggests that highly persistent shifts in aggregate demand or supply, such as the fiscal expansion of the 1980s and the productivity acceleration of the late 1990s, should cause the natural rate of interest to vary over time. Because neither potential output nor the natural rate of interest is directly observed, we exploit the relationship between these variables suggested by theory and jointly estimate them using the Kalman filter. We find substantial variation in the natural rate of interest over the past four decades in the United States, confirming the view that structural changes in the U.S. economy have had a significant effect on the natural rate of interest. For example, our estimates peak during the mid-sixties and the late nineties, periods of high rates of potential output growth, and decline during the productivity slowdown of the 1970s. Moreover, the fiscal expansion of the 1980s is associated with a high natural rate of interest. Our estimate of the natural rate as of the end of 2000 is 4 percent, well above estimates based on the hypothesis of a constant natural rate.