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

By Adam, Klaus; Billi, Roberto M. | Journal of Money, Credit & Banking, October 2006 | Go to article overview

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


Adam, Klaus, Billi, Roberto M., Journal of Money, Credit & Banking


THE LOW LEVELS OF NOMINAL interest rates experienced over the last years in major world economies has generated considerable interest in how monetary policy should be conducted in the presence of a zero lower bound on nominal interest rates. Nevertheless, there exists no rigorous treatment of the optimal policy design problem under the standard conditions of uncertainty and rational expectations. Intuition on how monetary policy should be conducted had to be built from models without bound (e.g., Clarida, Gali, and Gertler, 1999, Woodford, 2003) or from models with the bound but either deterministic (e.g., Jung, Teranishi, and Watanabe, 2005, Eggertsson and Woodford, 2003) or with backward-looking expectations (e.g., Kato and Nishiyama 2005).

This paper studies optimal monetary policy under commitment in a stochastic and forward-looking New Keynesian model along the lines of Clarida, Gali, and Gertler (1999) and Woodford (2003), but takes explicitly into account that nominal interest rates cannot be set to negative values. (1)

In our model the lower bound on nominal interest rates will occasionally be reached due to adverse shocks hitting the economy. (2) As a result, we are able to study how monetary policy should be conducted when interest rates are still positive, but there is the possibility of reaching the lower bound in the near future. In addition, having a fully stochastic setup allows us to calibrate the model to the U.S. economy and to assess the quantitative implications of the zero lower bound on nominal interest rates.

Two qualitatively new features of optimal policy emerge from our analysis.

First, we find that nominal interest rates may have to be lowered more aggressively in response to shocks than what is instead suggested by a model without lower bound. Such "preemptive" easing of nominal rates is optimal because agents anticipate the possibility of shocks leading to zero nominal rates in the future and reduce already today their output and inflation expectations correspondingly. (3) Such expectations end up amplifying the adverse effects of shocks and thereby trigger a stronger policy response. A similar finding for backward-looking models is reported by Kato and Nishiyama (2005) and Orphanides and Wieland (2000).

Second, the presence of shocks that lead to zero nominal rates alters also the optimal policy response to non-binding shocks. This occurs because the policymaker cannot affect the average real interest rate in any stationary equilibrium and, therefore, faces a "global" policy constraint. The inability to lower nominal and real interest rates as much as desired requires that optimal policy increases rates less (or lowers rates more) in response to non-binding shocks, compared to the policy that would instead be optimal in the absence of the lower bound.

There are also a number of quantitative results regarding optimal monetary policy for the U.S. economy emerging from this analysis.

First, the zero lower bound appears inessential in dealing with mark-up shocks, i.e., variations over time in the degree of monopolistic competition between firms. (4) More precisely, the empirical magnitude of mark-up shocks observable in the U.S. economy for the period 1983-2002 is too small for the lower bound on nominal rates to be reached. This would remain the case even if the true variance of markup shocks were threefold above our estimated value.

Second, the shocks to the "natural" real rate of interest may cause zero nominal rates, but this happens relatively infrequently and is a feature of optimal policy. (5) Based on our estimates for the 1983-2002 period, in the U.S. economy the bound would be reached on average one quarter every 17 years under optimal policy. Once zero nominal interest rates are observed, they are expected to endure not more than one to two quarters. Moreover, the average welfare losses entailed by the zero lower bound seem to be rather small. …

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