A key variable for the conduct of monetary policy is the natural rate of interest -the real interest rate consistent with output equaling potential and stable inflation.Economic theory implies that the natural rate of interest varies over time and depends on the trend growth rate of output. In this paper we apply the Kalman filter to jointly estimate the natural rate of interest, potential output, and its trend growth rate, and examine the empirical relationship between these estimated unobserved series. We find substantial variation in the natural rate of interest over the past four decades in the United States. Our natural rate estimates vary about one-for-one with changes in the trend growth rate. We show that policymakers' mismeasurement of the natural rate of interest can cause a significant deterioration in macroeconomic stabilization.JEL classification: C32, E43, E52, O40.Keywords: natural rate of interest, interest rate rules, Kalman filter, trend growth, potential output, equilibrium real interest rate.

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Research and development (R&D) is a key determinant of long run productivity and welfare. A central issue is whether a decentralized economy undertakes too little or too much R&D. We develop an endogenous growth model that incorporates parametrically four important distortions to R&D: the surplus appropriability problem, knowledge spillovers, creative destruction, and congestion externalities. We show that our model is consistent with the available evidence on R&D, growth, and markups. Calibrating the model to micro and macro data, we find that the decentralized economy typically underinvests in R&D relative to what is socially optimal. The only exceptions to this conclusion occur when both the congestion externality is extremely strong and the equilibrium real interest rate is very high. These results are robust to reasonable variations in model parameters.

The federal funds rate has been at the zero lower bound for over four years, since December 2008. According to many macroeconomic models, this should have greatly reduced the effectiveness of monetary policy and increased the efficacy of fiscal policy. However, standard macroeconomic theory also implies that private-sector decisions depend on the entire path of expected future shortterm interest rates, not just the current level of the overnight rate. Thus, interest rates with a year or more to maturity are arguably more relevant for the economy, and it is unclear to what extent those yields have been constrained. In this paper, we measure the effects of the zero lower bound on interest rates of any maturity by estimating the time-varying high-frequency sensitivity of those interest rates to macroeconomic announcements relative to a benchmark period in which the zero bound was not a concern. We find that yields on Treasury securities with a year or more to maturity were surprisingly responsive to news throughout 2008-10, suggesting that monetary and fiscal policy were likely to have been about as effective as usual during this period. Only beginning in late 2011 does the sensitivity of these yields to news fall closer to zero. We offer two explanations for our findings: First, until late 2011, market participants expected the funds rate to lift off from zero within about four quarters, minimizing the effects of the zero bound on mediumand longer-term yields. Second, the Fed's unconventional policy actions seem to have helped offset the effects of the zero bound on medium-and longer-term rates.

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