Michael Woodford | Macro Paper Warehouse

Fiscal Requirements for Price Stability

Woodford argues that commitment to a sound monetary policy rule, such as a Taylor rule, cannot by itself guarantee price stability, because Ricardian equivalence fails to make fiscal policy irrelevant to inflation whenever the fiscal regime is “non-Ricardian” – illustrated by the U.S. bond-price-support regime of the 1940s – and he proposes pairing a Taylor rule with a fiscal commitment to nominal-deficit targeting to secure both existence and uniqueness of a low-inflation equilibrium. Against the “increasingly widely accepted” view that monetary policy can be separated from fiscal policy in the pursuit of inflation targets, Woodford argues that this separation rests on two theses – that fiscal policy is inconsequential for inflation, and that monetary policy has little fiscal effect – neither of which holds generally, and for related reasons. He shows, through an analysis of the government’s intertemporal budget constraint, that “fiscal dominance” over the price level does not require the textbook mechanism of seignorage targets forced onto an accommodating central bank; the U.S. bond-price-support regime of 1942-1951, in which the Fed defended fixed prices for Treasury bills and bonds (even selling billions of dollars of bond holdings in 1949 to hold the line), shows fiscal considerations shaping monetary policy and price-level outcomes directly. The paper’s theoretical core is a precise definition of “Ricardian” fiscal policy – one that automatically adjusts future surpluses to satisfy the government’s present-value budget constraint regardless of the price-level path – and the demonstration that policies failing this property (“non-Ricardian”) turn the government’s budget constraint itself into an equilibrium condition that helps determine the price level, independent of monetary policy. Following Loyo’s (1999) analysis of Brazilian hyperinflation, Woodford shows that a central bank’s commitment to an anti-inflationary Taylor rule, if combined with non-Ricardian fiscal expectations inconsistent with the rule’s implicit inflation target, can produce not price stability but an explosive inflationary or deflationary spiral, and that even under Ricardian-consistent fiscal policy a Taylor rule alone may fail to exclude self-fulfilling deflationary equilibria. Woodford’s proposed solution is to pair a Taylor rule with a fiscal-policy commitment to targeting the nominal government budget deficit, which is locally Ricardian (so it does not frustrate the monetary rule) while also placing a floor under the nominal value of government liabilities that helps rule out the deflationary alternative equilibria.

Monetary Policy in a World Without Money

Against fears that electronic money will erode central banks’ monopoly over a monetary base and so undermine their power to control inflation, Woodford argues that monetary policy works through control of a short-term nominal interest rate, not through a stable link between the size of the monetary base and nominal spending, and that even a complete disappearance of demand for central-bank money would leave interest-rate control – and hence price-level control – intact, especially under the “channel” systems already used in Canada, Australia and New Zealand. Responding directly to alarmed essays by Benjamin Friedman and Mervyn King about the “New Economy” threat to central banking, Woodford identifies three misconceptions in the conventional quantity-theoretic worry: that monetary control requires a stable relationship between the monetary base and nominal spending, that the transactional use of currency is essential to the transmission mechanism, and that a central bank must be able to ration bank reserves (creating a scarcity-driven interest-rate spread) in order to move interest rates. Drawing on the theoretical “cashless limit” of his own earlier work, Woodford shows that as the demand for base money used in transactions shrinks toward zero, the price-level path implied by a given interest-rate policy is essentially unaffected, so long as the central bank retains some ability to vary the spread between the return on base money and other assets; and he shows that even where that ability itself might be lost, a central bank can still control short-term rates directly by varying the interest paid on its own liabilities – a method already implemented in the “channel” or “corridor” systems used by Canada, Australia, and New Zealand, in which standing lending and deposit facilities bracket a target rate so tightly that only trivial quantities of reserves need change hands. Only in the extreme and, in his view, implausible case of a “fully frictionless economy” in which demand for every component of the monetary base collapses to exactly zero at any positive interest-rate differential would today’s methods genuinely fail – and even there, Woodford argues, the central bank’s continuing role in defining the unit of account used in contracts would preserve its influence over the exchange value of its currency, so long as anyone continues to contract in it.

Price-Level Determinacy Without Control of a Monetary Aggregate

Woodford shows that the price level remains determinate even under two forms of radical money-supply endogeneity long thought to destroy monetary control – a central-bank interest-rate peg and unrestricted private (“free banking”) issuance of money substitutes – once one recognizes that the government’s intertemporal budget constraint, not the quantity-theoretic money-demand equation, is what pins down the price level under a “fiscal theory of the price level.” Woodford argues the quantity-theoretic tradition’s requirement that a central bank control a monetary aggregate to ensure price-level determinacy relies on an incomplete accounting of equilibrium conditions. Working in a Sidrauski-Brock representative-household monetary model, he derives, alongside the familiar money-demand (“LM”) equation, a second necessary equilibrium condition equating the real value of net government liabilities to the discounted present value of current and future primary budget surpluses, plus the interest saved on monetary liabilities. This fiscal condition lacks the homogeneity property that makes the quantity-theoretic account depend only on the ratio of money to prices, so it can determine a unique price-level path on its own whenever the fiscal regime is “non-Ricardian” – that is, whenever the government’s budget is not automatically adjusted to guarantee its own present-value balance regardless of the price path. Woodford first shows an “irrelevance proposition”: under a Ricardian-consistent fiscal rule, changes in the path of the money supply, holding the government’s fiscal position fixed, have no effect on the equilibrium price level at the date of the change, since the fiscal equation is unaffected. He then applies this reasoning to two harder cases. Under a pure interest-rate peg – the classic case Sargent-Wallace-style analyses treat as generating indeterminacy – the fiscal condition alone yields a unique positive price-level path given the paths of government purchases, tax revenue, and net liabilities. And under a “free banking” extension in which unregulated intermediaries issue interest-bearing deposits that perfectly substitute for the monetary base (subject only to an intermediation cost), the same fiscal condition continues to pin down a unique price path, so unrestricted private money creation “need pose no threat” to price-level determinacy. Woodford concludes that money-supply variations matter for the price level, under either regime, only insofar as they affect the government’s fiscal position through seignorage – not through any independent quantity-theoretic channel – so central banks need not resist interest-rate targeting or financial deregulation on determinacy grounds.

Simple Analytics of the Government Expenditure Multiplier

This paper works through a sequence of deliberately simple, analytically solvable New Keynesian models to isolate what actually determines the size of the government-spending multiplier, arguing that “the size of the multiplier depends crucially on the monetary policy response” rather than on any single structural feature of the economy. In a flexible-price neoclassical benchmark, the multiplier is necessarily below 1, since higher government purchases always crowd out some private expenditure. With sticky prices or wages, the multiplier instead depends entirely on how monetary policy responds: it equals exactly 1 if the central bank holds the real interest rate constant regardless of the fiscal shock (the same answer as the textbook “IS curve” calculation), falls below 1 – potentially even below the neoclassical benchmark – under a conventional Taylor rule that raises real rates in response to the resulting inflation and output gap, and rises well above 1 when the policy rate is constrained by the zero lower bound (ZLB), because fiscal expansion then raises expected inflation without any offsetting rise in the nominal rate, pushing real rates down and crowding in private spending. This last result, however, depends critically on the spending increase being expected to end when the ZLB episode ends: spending that is expected to persist into the post-crisis, Taylor-rule-governed period feeds back to reduce – and can even reverse the sign of – the multiplier during the crisis itself. The paper also shows that a large multiplier does not automatically imply a large welfare gain: because government purchases divert real resources from other uses, even at the ZLB the welfare-optimal fiscal expansion is generally only a fraction of what would be needed to fully close the output gap, growing toward (but not reaching) full output-gap-closing stimulus only as the expected duration of the financial disturbance grows large. Away from the ZLB, the paper argues that output-gap stabilization is more efficiently left to monetary policy, with government purchases chosen instead according to their own cost-benefit merits.

The Central-Bank Balance Sheet as an Instrument of Monetary Policy

This paper extends a standard New Keynesian model to give the central bank’s balance sheet a genuine role in equilibrium determination, motivated by the dramatic growth and compositional change of the Federal Reserve’s balance sheet after 2008. The authors distinguish three separately controllable dimensions of monetary policy: the operating target for the short-term policy rate; the supply of reserves (equivalently, the overall size of the balance sheet, together with the interest rate paid on reserves); and the composition of the central bank’s asset portfolio (equivalently, the scale of “credit policy,” or targeted purchases of illiquid or risky private assets). They first show that under two idealized conditions – that all assets are valued only for their pecuniary returns, and that all investors can trade them at the same prices – both the size and the composition of the central bank’s balance sheet are irrelevant for equilibrium prices and quantities, a Modigliani-Miller-style result generalizing Wallace (1981): private investors simply undo any central-bank portfolio reshuffling with offsetting trades of their own, because their exposure to the underlying risks, and hence their state-contingent tax liabilities, is unaffected. To make balance-sheet policy meaningful, the authors build a model with heterogeneous “borrower” and “saver” households who must transact through imperfectly competitive financial intermediaries, so that a market-determined credit spread between borrowing and saving rates matters for aggregate demand and (through a generalized New Keynesian Phillips curve) for inflation, and they allow central-bank reserves to supply transactions services not perfectly substitutable with other assets. Within this model, they derive three main results. First, optimal reserve-supply policy requires satiating intermediaries with reserves at all times, which is equivalent to setting the interest rate paid on reserves equal to the operating target for the policy rate – a rule that, once adopted, removes any need for separate deliberation over a reserve-quantity target, and that implies “quantitative easing” in the strict sense (expanding reserves via purchases of safe government debt, without otherwise changing central-bank asset composition or expected future interest-rate policy) is irrelevant for output and inflation, even when the zero lower bound binds; the authors note this generalizes the corresponding irrelevance result in Eggertsson and Woodford (2003) and argue it is consistent with the Bank of Japan’s 2001-2006 quantitative-easing experience, during which nominal GDP failed to rise despite a near-75-percent increase in the monetary base. Second, targeted purchases of illiquid or risky private assets – “credit easing” – are not subject to this irrelevance result once private financial intermediation is imperfect, and a numerical exercise calibrated to U.S. data shows such purchases can lower equilibrium credit spreads and raise welfare, particularly when the zero lower bound prevents the policy rate from falling as far as would otherwise be optimal; but the authors caution that the size of an observed increase in credit spreads is not by itself sufficient information to judge how much credit policy is warranted, because different underlying financial disturbances (a rise in intermediaries’ resource costs versus a rise in expected loan losses) call for different optimal scales and durations of central-bank lending even when they produce similar spread paths. Third, because the interest rate on reserves can be freely adjusted, decisions about the size and composition of the balance sheet are, in the model, entirely separable from interest-rate policy: a central bank can maintain a large or unconventional balance sheet while still hitting its interest-rate target and inflation goal, which implies that the timing of “exit” from unconventional asset holdings need not be mechanically tied to the timing of policy-rate increases, and should instead be governed by conditions specific to the markets for the assets in question.

The Taylor Rule and Optimal Monetary Policy

Evaluating Taylor’s interest-rate rule against an explicit optimizing New Keynesian model built from a forward-looking IS equation and an expectations-augmented Phillips curve, this paper asks how closely the rule resembles genuinely optimal policy. It first shows that the Taylor rule’s feedback from inflation and the output gap satisfies a general determinacy condition – which the paper names the “Taylor principle”: a sustained k-percent rise in inflation must eventually raise the nominal rate by more than k percent – and that this same condition also secures “expectational stability” under adaptive learning, resolving both the classic Sargent-Wallace indeterminacy critique and the Wicksellian self-fulfilling-inflation-spiral critique of interest-rate rules, since those classic results assume an exogenous interest-rate path rather than feedback from economic conditions. The paper then shows the rule’s twin goals of inflation and output-gap stabilization have a welfare-theoretic basis: a second-order approximation to household utility yields a loss function in squared inflation (reflecting Calvo-pricing price dispersion) and the squared output gap relative to the natural rate, implying an optimal long-run inflation target of zero (not Taylor’s two percent) and an output-gap concept tied to the natural, not simply trend, level of output – with evidence (via Sbordone’s use of real unit labor cost) that this welfare-relevant output gap can differ sharply, even in correlation sign, from simple detrended output. Its central critique concerns the rule’s constant intercept: full optimality requires the intercept to move one-for-one with the time-varying Wicksellian natural rate of interest, whereas Taylor’s classic formulation assumes a fixed real-rate estimate (two percent), so that failing to track the natural rate leaves inflation and the output gap fluctuating regardless of how large the feedback coefficients are. The paper closes by noting that once inefficient variation in the natural rate, the zero lower bound, or a distaste for interest-rate volatility are admitted, full stabilization of inflation and the output gap is no longer optimal, and cites companion work characterizing the resulting more complex optimal responses.

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.