Significant progress has been made in adapting modern macroeconomic models for use in policy analysis. Monetary economists have recently focused on determining the optimal monetary policy in New Keynesian models. This paper shows that optimal monetary policy in New Keynesian models produces a great deal of uncertainty about inflation at medium to long horizons.
We show, however, that including some weight on a price path in the monetary policy rule substantially reduces long-run inflation variability regardless of the types of nominal rigidities. The source of nominal frictions does influence the impact that a price-path target has on output stabilization. In a New Keynesian model, however, a price-path target reduces longrun inflation uncertainty by an order of magnitude more that it increases the variability of the output gap.
An important distinction between New Keynesian models and reality is the relative importance of long-run inflation uncertainty. In New Keynesian models, long-run inflation uncertainty is typically not, by itself, a source of welfare loss. Policymakers, on the other hand, closely monitor long-term interest rates because they reflect expectations about future policy. Investors pay to insure against long-run risks. Although the fundamental risk that concerns policymakers and investors may be about long-run real growth—as in Orphanides and Williams (2002), Bansal and Yaron (2004), or Ries (2005)—uncertainty about long-run inflation also matters.
Uncertainty about long-run inflation is revealed in the variability of the term structure of interest rates. Gallmeyer et al. (2007) present evidence about the volatility of yields on U.S. Treasury securities across a term structure from 1 quarter to 10 years. They report that the standard deviation of yields at the short end of the term structure, for the first 4 or 5 quarters, is about 1.9 percent at an annual rate since 1990. The standard deviation of the 10-year Treasury yield is about 1.1 percent. Using U.S. data from the indexed bond market from 1997 to 2000, McCulloch and Kochin (2000) estimate that the volatility of the inflation premium is roughly twice that of the real interest rate across the term structure. The purpose of our paper is not to model the reason why this long-run inflation uncertainty matters. Rather, it is to evaluate the relative effects of alternative monetary policy rules on uncertainty.