Optimal Monetary Policy under Commitment with a Zero Bound on Nominal Interest Rates

By Klaus Adam and Roberto M. Billi
First version: March 24, 2003
This version: October 1, 2005
RWP 05-07
Research Division 
Federal Reserve Bank of Kansas City 

Abstract

      We determine optimal monetary policy under commitment in a forward-looking New Keynesian model when nominal interest rates are bounded below by zero. The lower bound represents an occasionally binding constraint that causes the model and optimal policy to be nonlinear. A calibration to the U.S. economy suggests that policy should reduce nominal interest rates more aggressively than suggested by a model without lower bound. Rational agents anticipate the possibility of reaching the lower bound in the future and this amplifies the effects of adverse shocks well before the bound is reached. While the empirical magnitude of U.S. mark-up shocks seems too small to entail zero nominal interest rates, shocks affecting the natural real interest rate plausibly lead to a binding lower bound. Under optimal policy, however, this occurs quite infrequently and does not imply positive average inflation rates in equilibrium. Interestingly, the presence of binding real rate shocks alters the policy response to (non-binding) mark-up shocks.

Keywords: nonlinear optimal policy, zero interest rate bound, commitment, liquidity trap, New Keynesian

JEL classification: C63, E31, E52

*Klaus Adam is a senior economist at the European Central Bank and Roberto Billi is an economist at the Federal Reserve Bank of Kansas City. This paper is forthcoming in the “Journal of Money, Credit, and Banking.” Thanks go to an anonymous referee, Kosuke Aoki, Ben Bernanke, Joachim Keller, Albert Marcet, Ramon Marimon, Athanasios Orphanides, Lars Svensson, Volker Wieland, Mike Woodford, and seminar participants at the Tilburg University, Cambridge University, Pompeu Fabra, University of Dortmund, University of Munich, Goether University Frankfurt, and the CEPR-INSEAD conference on “Monetary Policy Effectiveness: Theory, Evidence, Challenges” for helpful comments and discussions. Errors remain ours. The views expressed herein are solely those of the authors and do not necessarily reflect the views of the European Central Bank, the Federal Reserve Bank of Kansas City or the Federal Reserve System.

Adam email: Klaus.Adam@ecb.int
Billi email: Roberto.Billi@kc.frb.org

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