The Zero Bound on Interest Rates and Optimal Monetary Policy

The paper asks whether expanding the monetary base (“quantitative easing”) gives a central bank an additional policy instrument once the short-term nominal rate is stuck at zero, and how the existence of the zero lower bound (ZLB) should change the design of optimal monetary policy. These questions were motivated by Japan’s near-zero call rate since the late 1990s and the US federal funds rate’s approach to 1% at the time of writing. The authors describe their analysis as a development of key themes in Krugman’s (1998) treatment of the same topic, but replace his one-period flexible-price model with a fully dynamic, staggered-price (Calvo) model. The richer dynamics matter because they let a real disturbance keep output below potential for years and let the authors analyze the form that an optimal policy commitment should take, not just whether a temporary inflation promise is desirable in principle.

The model is a discrete-time New Keynesian general-equilibrium economy: a representative household with money in the utility function (non-separable from consumption, with a satiation level so the ZLB can be reached), monopolistic competition, Calvo (1983) staggered price-setting with a fraction of prices left unchanged each period, complete financial markets, and a central-bank balance sheet that can hold any of several assets with arbitrary state-contingent returns. For the optimal-policy analysis the model is log-linearized around a zero-inflation steady state into a forward-looking IS relation (the output gap depends on the expected future output gap and the gap between the real interest rate and the “natural” (Wicksellian) rate of interest) and a forward-looking New Keynesian Phillips curve (inflation depends on the output gap and expected future inflation), subject to the constraint that the nominal interest rate cannot go below zero. The zero bound binds precisely when the natural rate of interest falls sufficiently negative — in the paper’s calibrated illustration, quarterly with intertemporal elasticity sigma=0.5, Phillips-curve slope kappa=0.02, discount factor beta=0.99 (implying a 4%-a-year long-run real rate), the natural rate drops to -2% a year in period 0 and reverts to steady state with probability 0.1 each quarter, so it is expected to stay negative for roughly ten quarters.

No — the paper proves an irrelevance proposition: 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, and the debt-composition rule, provided these operations do not change expectations about the future conduct of monetary or fiscal policy. The intuition is that in a complete-markets, representative-household setting, the marginal utility of income to the household in a given state depends on its consumption in that state, not on the aggregate payoff of its portfolio, so changing the composition of assets the public holds (e.g., buying long bonds with reserves) does not change state-contingent consumption — the classic mean-variance portfolio-balance channel is absent. The authors describe this as being “in the spirit of” Wallace’s (1981) irrelevance proposition for open-market operations. Critically, the authors do not claim QE is “necessarily pointless”: the result rests on complete markets, no borrowing limits, a representative household, and unchanged expectations about future policy and the path of total government liabilities. A permanent base expansion or a “helicopter drop” that changes fiscal policy is not covered by the proposition and can have real effects — precisely because it changes expectations, which the authors argue reconciles their result with the apparent contrast to Auerbach-Obstfeld (2003). They acknowledge that real-world frictions such as heterogeneous investor clienteles (citing Clouse et al. 2003) could give QE some effect, but argue it “seems unlikely that they should be large,” and that even such effects would operate through signaling of future policy rather than mechanical portfolio rebalancing.

Under a strict zero-inflation target, the calibrated model produces a 14% output gap and 10% annual deflation once the natural rate turns negative, because the central bank cannot deliver the negative real rate the Euler equation calls for, and the resulting expectation of continued negative rates and deflation feeds back to deepen the slump. A strict inflation target requires setting the nominal rate equal to the natural rate plus the inflation target, which is infeasible whenever the natural rate is below minus the target. Raising the constant inflation target helps — a 2% target can accommodate a -2% natural rate by delivering the needed -2% real rate exactly at the zero bound (the Phelps/Summers/Fischer/Krugman argument for a positive inflation buffer) — but at the cost of distortions from steady inflation in normal times, and an intermediate 1% target still leaves about a 7% output gap and 4% annual deflation when the trap binds. The authors conclude that “no such [constant-target] solution allows a complete solution of the problem.”

Minimizing the expected discounted sum of a quadratic loss in inflation and the output gap, subject to the IS and Phillips-curve relations and the zero bound, yields first-order conditions containing lagged Lagrange multipliers — meaning the optimal policy is history-dependent rather than purely forward-looking. In the calibrated illustration where the natural rate is negative for 15 quarters, the optimal commitment holds the nominal rate at zero for five additional quarters beyond the point the natural rate itself turns positive again, versus an immediate return to the steady-state rate under a purely forward-looking (including strict zero-inflation-targeting) policy. The mechanism is that committing to an output boom and above-target inflation once the trap ends stimulates current demand and reduces current deflation while the economy is still in the trap, because the forward-looking IS and Phillips-curve relations make current outcomes depend on the entire expected future path of real rates and inflation — this is the Krugman “manage expectations” channel, but operating through the whole expected future path rather than a single future inflation target. Unlike a constant positive-inflation target, which implies an ever-rising price level, the optimal commitment ultimately stabilizes the price level. A purely forward-looking policy, including strict inflation targeting, is strictly suboptimal.

The optimum is implementable as a targeting rule written in terms of a “gap-adjusted” price index (the price level plus the output gap scaled by the ratio of the output-gap weight to the Phillips-curve slope): the central bank sets the interest rate to hit a target path for this index when feasible, and sets it to zero otherwise, updating next period’s target upward whenever the zero bound forces an undershoot. This rule requires the central bank to observe only the price level and the output gap — no estimate of the natural rate of interest is needed, which the authors note makes it “robustly optimal” in the sense of Giannoni and Woodford (2003). In a calibrated welfare comparison (expected discounted loss expressed as a percentage of the loss under a strict zero-inflation target, normalized to 100), a strict 1% inflation target scores 24.1 and a strict 2% target scores 32, while a simpler constant gap-adjusted price-level target scores just 0.0725 and the fully optimal history-dependent rule scores 0.036 — the authors describe the two price-level-based rules as “vastly superior” to any strict inflation target. The simpler constant price-level target is not fully optimal at the zero bound but captures most of the gain because a price-level target automatically commits the bank to undo any deflation with later inflation, a built-in stabilizer that inflation targeting lacks. By contrast, an equivalent-away-from-the-bound rule written in inflation terms performs worse than even strict zero-inflation targeting at the bound, because it mandates deflation during the recovery’s output growth — leading the authors to stress that “it is crucial to communicate that the government is committed to a long-run price-level target.”

Under the optimal targeting rule, an increased assessment of the probability that the zero bound will bind in the future does not, by itself, justify raising the price-level target pre-emptively — only realized shortfalls against the current target do. However, once a future negative-natural-rate shock is actually anticipated with certainty (e.g., known to arrive four quarters ahead), optimal policy drives the nominal rate to zero even before the natural rate itself turns negative, because the anticipated future decline already causes current price and output declines that undershoot the target today. The authors caution that this anticipation result “depend[s] on a relatively special feature” of their model — that the target variables are purely forward-looking — so it should not be read as a fully general result.

Yes — the model’s Euler, money-demand, and pricing relations are consistent with a self-fulfilling perpetual deflation in which the price level falls forever and the zero bound binds forever even though the natural rate is non-negative, and the commitment to a non-decreasing price-level target does not by itself rule this out. Excluding it requires pairing the monetary commitment with a fiscal commitment that prevents the nominal value of government liabilities from contracting at the rate the transversality condition would otherwise require — for example, a Ricardian or balanced-budget-type fiscal rule (citing Benhabib-Schmitt-Grohé-Uribe 2001 and Schmitt-Grohé-Uribe 2000), or a central-bank commitment never to contract the monetary base together with a non-negative-asymptotic-present-value commitment on public debt.

The paper’s central contribution is to identify management of expectations about the future path of short-term interest rates — not the current short rate, and not the size or composition of the central bank’s balance sheet — as the decisive lever at the zero bound, best implemented as a history-dependent price-level target; this became the theoretical foundation later invoked for forward guidance, and a theoretical foil to the portfolio-balance rationale for QE. The results carry several explicit scope conditions the authors flag themselves: the irrelevance proposition rests on complete markets, a representative household, no borrowing limits, and unchanged policy expectations, and would not necessarily survive investor-clientele frictions (though the authors judge any resulting QE effect “unlikely” to be large); the optimal-policy results use a log-linear approximation valid only for “small enough” disturbances, and the calibration (sigma=0.5, kappa=0.02) was deliberately chosen with a modest interest sensitivity “so as not to exaggerate” the output contraction; the model abstracts from capital, from endogenous state-contingent fiscal stabilization policy, and from monetary frictions in the welfare criterion; and the quantitative results are specific to the particular two-state Markov process assumed for the natural rate (though the targeting rule itself is claimed optimal regardless of that process).