Determinacy and Identification with Taylor Rules
Journal of Political Economy, Vol. 119, No. 3 (June 2011), pp. 565-615. Online Appendix B. JSTOR link, including html, pdf, and online appendix. Manuscript with Technical Appendix The technical appendix documents a few calculations. Don't miss starting on Technical Appendix page 6 a full analytical solution to the standard three equation model. I include the manuscript just so equation references in the Technical Appendix will work, the previous links to the published version are better.
Most people think Taylor rules stabilize inflation: Inflation rises, the Fed raises interest rates; this lowers “demand’’ and lowers future inflation. New-Keynesian models don’t work this way. In the models, the Fed reacts to inflation by setting interest rates in a way that ends up increasing future inflation. Inflation is “determined” as the unique initial value that doesn't set off accelerating inflation. Alas, there is nothing in economics to rule out accelerating inflation or deflation. I conclude that new-Keynesian models with Taylor rules don’t determine the price level any better than classic fixed interest rate targets. Price level determinacy requires ingredients beyond the Taylor principle, such as a non-Ricaridan fiscal regime. I survey the new-Keynesian literature to verify that no simple answer to this problem exists. All of the fixes slip in a commitment by the government to blow up the world at some point.
Even if the new-Keynesian model did work, The parameters of the Taylor rule relating interest rates to inflation and other variables are not identified. You can't measure "off equilibrium" behavior from data in an equilibrium. Thus, Taylor rule regressions cannot be used to argue that the Fed conquered inflation by moving from a "passive" to an "active" policy in the early 1980s.
The appendix uncovers an interesting mistake in the classic Obstfeld and Rogoff (1983) attempt to prune inflationary equilibria, but also shows that reversion to a price level target can do the trick. The Techical Appendix has algebra for determinacy regions and solutions of the three-equation New-Keynesian model, as well as other issues.
This article supersedes the two papers titled "Inflation Determination with Taylor Rules: A Critical Review"and "Identification with Taylor Rules: A Critical Review" (September 2007).