The Zero Bound on Interest Rates and Optimal Monetary Policy

This 2003 Brookings Papers on Economic Activity article by Gauti Eggertsson and Michael Woodford builds a fully dynamic New Keynesian general-equilibrium model — Calvo (1983) staggered pricing, money in the utility function with a satiation level so the zero lower bound (ZLB) can actually bind, complete financial markets, and a central bank balance sheet that can hold any of several assets with arbitrary state-contingent returns — to ask two questions raised by Japan’s near-zero call rate and the US funds rate’s approach to 1%: does expanding the monetary base (quantitative easing) give a central bank an additional policy instrument once the short rate is stuck at zero, and how should optimal monetary policy be redesigned when the ZLB can bind? It is framed as a dynamic extension of Krugman’s (1998) one-period flexible-price treatment of the same problem. The paper is a theory paper; all quantitative results below are model propositions or numerical illustrations from a calibrated log-linearized model (quarterly, relative-risk-aversion-type intertemporal elasticity sigma=0.5, Phillips-curve slope kappa=0.02, discount factor beta=0.99, long-run real rate 4% a year), not empirical estimates, and depend on that calibration. First, the authors prove an irrelevance proposition: with complete markets, a representative household, and no change in expectations about future monetary or fiscal policy, the equilibrium paths of prices, output, the interest rate, and total government liabilities are independent of the central bank’s base-supply rule, its portfolio-composition rule, or the debt-composition rule — so open-market purchases of long-term bonds or other assets, on their own, have no effect (a result in the spirit of Wallace 1981), and any real-world effect of QE must run through the way such operations change expectations about future policy rather than through mechanical portfolio-balance channels. Second, they show the ZLB is a genuine binding constraint: under a strict zero-inflation target, when the natural rate of interest falls to -2% a year and is expected to stay negative for about ten quarters, the calibrated model produces a 14% output gap and 10% annual deflation, and even a positive constant inflation target only partially mitigates this (a 1% target still leaves roughly a 7% output gap and 4% annual deflation when the trap binds). Third, and centrally, they show that optimal policy — minimizing a quadratic loss in inflation and the output gap subject to the New Keynesian IS and Phillips-curve relations and the ZLB — is history-dependent: it commits the central bank to engineer a future output boom and above-target inflation once the natural rate turns positive again, and to hold the nominal rate at zero for longer than a purely forward-looking (including strict inflation-targeting) policy would — five additional quarters beyond the point the natural rate itself turns positive, in their illustrative 15-quarter trap. Fourth, they show this optimal commitment is implementable as a history-dependent price-level targeting rule expressed in a gap-adjusted price index, requires no estimate of the natural rate, and dramatically dominates any strict inflation target in a calibrated welfare comparison (expected discounted loss relative to a strict zero-inflation target normalized to 100: strict 1% target 24.1, strict 2% target 32, a simple constant gap-adjusted price-level target 0.0725, the fully optimal history-dependent rule 0.036); a simpler constant price-level target captures most of this gain because it automatically commits to undoing deflation with later inflation, while a rule written in inflation terms performs worse than even strict zero-inflation targeting because it mandates deflation during the recovery. Finally, the paper shows optimal policy responds to anticipated future ZLB episodes (driving the nominal rate to zero even before the natural rate turns negative once a future shock is foreseen) but not to a mere increase in the assessed probability of a future binding ZLB, and discusses how a self-fulfilling permanent deflationary trap — which the model does not otherwise rule out — must be excluded by pairing the price-level commitment with a fiscal or base-supply commitment that prevents the nominal value of government liabilities from contracting without bound.

Gauti B. Eggertsson | Macro Paper Warehouse

The Zero Bound on Interest Rates and Optimal Monetary Policy