conventional and unconventional monetary policy reserve bank of st.louis r evi w july /august 2 01...

FEDERAL RESERVE BANK OF ST. LOUIS REVIEW JULY/AUGUST 2010 229

Conventional and Unconventional Monetary Policy

Vasco Cúrdia and Michael Woodford

The authors extend a standard New Keynesian model to incorporate heterogeneity in spendingopportunities and two sources of (potentially time-varying) credit spreads and to allow a role forthe central bank’s balance sheet in equilibrium determination. They use the model to investigatethe implications of imperfect financial intermediation for familiar monetary policy prescriptions,and to consider additional dimensions of central bank policy—variations in the size and composi-tion of the central bank’s balance sheet and payment of interest on reserves—alongside the tradi-tional question of the proper choice of setting an operating target for an overnight policy rate. Theauthors also give particular attention to the special problems that arise when the policy rate reachesthe zero lower bound. They show that it is possible within a single unified framework to identifythe criteria for policy to be optimal along each dimension. The suggested policy prescriptions applyequally well when financial markets work efficiently as when they are substantially disrupted andinterest rate policy is constrained by the zero lower bound. (JEL E44, E52)

Federal Reserve Bank of St. Louis Review, July/August 2010, 92(4), pp. 229-64.

inflation and real GDP alone, such as the Taylor(1993) rule or common accounts of “flexibleinflation targeting” (Svensson, 1997), may beinadequate to circumstances of the kind recentlyfaced.1 As a further, more-specific question, howshould a central bank’s interest rate policy beaffected by the observation that other key interestrates no longer co-move with the policy rate (thefederal funds rate in the case of the United States)in the way they typically have in the past? Thedramatically different behavior of the LIBOR-OISspread, shown in Figure 1, since August 2007, hasdrawn particular comment. Indeed, John Taylor

T he recent global financial crisis hasconfronted central banks with a num-ber of questions beyond the scope ofmany conventional accounts of the

theory of monetary policy. For example, do pro-jections of the paths of inflation and of aggregatereal activity under some contemplated path forpolicy provide a sufficient basis for monetarypolicy decisions, or must financial conditionsbe given independent weight in such delibera-tions? That the Fed began aggressively cuttingits target for the federal funds rate in late 2007and early 2008, while inflation was arguablyincreasing and real GDP was not yet known to becontracting—and has nonetheless often been criti-cized as responding too slowly in this period—suggests that familiar prescriptions that focus on

1 See Mishkin (2008) for discussion of some of the considerationsbehind the Fed’s relatively aggressive rate cuts in the early part ofthe crisis.

Vasco Cúrdia is an economist at the Federal Reserve Bank of New York. Michael Woodford is a professor in the department of economics atColumbia University. The authors thank Michele Boldrin, Gauti Eggertsson, Marvin Goodfriend, Jamie McAndrews, John Taylor, and KazuoUeda for helpful discussions; Neil Mehrotra, Ging Cee Ng, and Luminita Stevens for research assistance; and the National Science Foundationfor research support of the second author.

© 2010, The Federal Reserve Bank of St. Louis. The views expressed in this article are those of the author(s) and do not necessarily reflect theviews of the Federal Reserve System, the Board of Governors, the Federal Reserve Bank of New York or the regional Federal Reserve Banks.Articles may be reprinted, reproduced, published, distributed, displayed, and transmitted in their entirety if copyright notice, author name(s),and full citation are included. Abstracts, synopses, and other derivative works may be made only with prior written permission of the FederalReserve Bank of St. Louis.

himself (Taylor, 2008) has suggested that move-ments in this spread should be taken into accountin an extension of his famous rule.

In addition to such new questions about traditional interest rate policy, the very focus oninterest rate policy as the central question aboutmonetary policy has been called into question.The explosive growth of base money in the UnitedStates since September 2008 (shown in Figure 2)has led many commentators to suggest that themain instrument of U.S. monetary policy haschanged from an interest rate policy to one oftendescribed as “quantitative easing.” Does it makesense to regard the supply of bank reserves (orperhaps the monetary base) as an alternative orsuperior operating target for monetary policy?Does this (as some would argue) become the onlyimportant monetary policy decision once the

overnight rate (the federal funds rate) has reachedthe zero lower bound, as it effectively has in theUnited States since December 2008 (Figure 3)?And now that the Federal Reserve has legal author-ization to pay interest on reserves (under theEmergency Economic Stabilization Act of 2008),how should this additional potential dimensionof policy be used?

The past two years have also seen dramaticdevelopments in the composition of the asset sideof the Fed’s balance sheet (Figure 4). Whereas theFed had largely held Treasury securities on itsbalance sheet before the fall of 2007, other kindsof assets—including both a variety of new “liquid-ity facilities” and new programs under which theFed has essentially become a direct lender to cer-tain sectors of the economy—have rapidly grownin importance. How to manage these programs has

Cúrdia and Woodford

230 JULY/AUGUST 2010 FEDERAL RESERVE BANK OF ST. LOUIS REVIEW

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Spread Between the U.S. Dollar LIBOR Rate and the Corresponding OIS Rate

SOURCE: Bloomberg.

occupied much of the attention of policymakersrecently. How should one think about the aims ofthese programs and the relation of this new com-ponent of Fed policy to traditional interest ratepolicy? Is Federal Reserve credit policy a substi-tute for interest rate policy, or should it have dif-ferent goals from those of interest rate policy?

These are clearly questions that a theory ofmonetary policy adequate to our present circum-stances must address. Yet, not only these questionsreceived relatively little attention until recently,but the very models commonly used to evaluatethe effects of alternative prescriptions for mone-tary policy have little to say about them. ManyNew Keynesian (NK) models abstract entirelyfrom the role of financial intermediation in theeconomy (by assuming a representative house-hold) or assume perfect risk-sharing (to facilitateaggregation), so that the consequences of financial

disruptions cannot be addressed. Many modelsinclude only a single interest rate (or only a singleinterest rate of a given maturity, with long ratestied to short rates through a no-arbitrage condi-tion) and hence cannot say anything about theproper response to changes in spreads. And manymodels abstract entirely from the balance sheetof the central bank, so that questions about theadditional dimensions of policy resulting fromthe possibility of varying the size and composi-tion of the balance sheet cannot be addressed.2



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2 In a representative-household model, abstraction from the role ofthe central bank’s balance sheet in equilibrium determination isrelatively innocuous; in particular, Eggertsson and Woodford (2003)show that introducing both a large range of possible choices aboutthe composition of the balance sheet and transactions frictions thataccord a special role to central bank liabilities need not imply anyadditional channels through which monetary policy can affect theeconomy when the zero lower bound is reached. However, we wishto reconsider this question in a framework where financial inter-mediation is both essential and costly.

The aim of the research summarized here3 isto show how such issues can be addressed in adynamic stochastic general equilibrium (DSGE)framework. We extend a basic NK model in direc-tions that are crucial for analysis of the questionsjust posed: We introduce (i) nontrivial heterogene-ity in spending opportunities, so that financialintermediation matters for the allocation ofresources; (ii) imperfections in private financialintermediation and the possibility of disruptionsto the efficiency of intermediation for reasonstaken here as exogenous; and (iii) additionaldimensions of central bank policy, by explicitlyconsidering the role of the central bank’s balancesheet in equilibrium determination and by allow-

ing central bank liabilities to supply transactionsservices. Unlike some other recent approaches tothe introduction of financial intermediation intoNK DSGE models4—which arguably includesome features that allow for greater quantitativerealism—our aim has been to develop a modelthat departs from a standard (representative-household) model in only the most minimal waysnecessary to address the issues raised above. Inthis way, we can nest the standard (and extensivelystudied) model as a special case of our model sothat the sources of our results and the precisesignificance of the new model elements intro-duced can be more clearly understood.



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NOTE: Beginning with December 2008, the target rate is replaced with a target bank of 0 to 25 basis points.


3 This paper summarizes results that are explained in greater detailin Cúrdia and Woodford (2009a, 2009b, 2010).

4 This has been a very active literature of late. See, for example,Christiano, Motto, and Rostagno (2007), Faia and Monacelli (2007),Gerali et al. (2008), and Gertler and Karadi (2009).

1. A MODEL WITH MULTIPLEDIMENSIONS OF MONETARYPOLICY

Here we sketch the key elements of our model,which extends the model introduced in Cúrdiaand Woodford (2009a), to introduce the additionaldimensions of policy associated with the centralbank’s balance sheet. (See this earlier paper, espe-cially its technical appendix, for more details.)We stress the similarity between the model devel-oped there and the basic NK model and show howthe standard model is recovered as a special caseof the extended model.

1.1 Heterogeneity and the AllocativeConsequences of Credit Spreads

Our model is a relatively simple generalizationof the basic NK model used by Goodfriend andKing (1997), Clarida, Gali, and Gertler (1999),Woodford (2003), and others to analyze optimalmonetary policy. The model is still highly stylizedin many respects; for example, we abstract fromthe distinction between the household and firmsectors of the economy and instead treat all privateexpenditure as the expenditure of infinitely livedhousehold-firms. Similarly, we abstract from theconsequences of investment spending for theevolution of the economy’s productive capacity,



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instead treating all private expenditure as if itwere nondurable consumer expenditure (yieldingimmediate utility at a diminishing marginal rate).

We depart from the assumption of a represen-tative household in the standard model by suppos-ing that households differ in their preferences.Each household i seeks to maximize a discountedintertemporal objective of the form

(1)

where τ i b,s indicates the household’s “type”in period t. Here ubc;ξ and usc;ξ are two differ-ent period utility functions, each of which mayalso be shifted by the vector of aggregate tasteshocks, ξt and ν bh;ξ and ν sh;ξ are correspond-ingly two different functions indicating the perioddisutility from working for the two types. As inthe basic NK model, there is assumed to be a con-tinuum of differentiated goods, each producedby a monopolistically competitive supplier; cti is a Dixit-Stiglitz aggregator of the household’spurchases of these differentiated goods. Thehousehold similarly supplies a continuum ofdifferent types of specialized labor, indexed by j,that are hired by firms in different sectors of theeconomy; the additively separable disutility ofwork, ντh;ξ , is the same for each type of labor,though it depends on the household’s type andthe common taste shock.

Each agent’s type, τ ti, evolves as an inde-pendent two-state Markov chain. Specifically, weassume that each period, with probability 1 – δ(for some 0 ≤ δ < 1), an event occurs that resultsin a new type for the household being drawn;otherwise it remains the same as in the previousperiod. When a new type is drawn, it is b withprobability πb and swith probability πs, where 0 < πb,πs < 1, πb + πs +1. (Hence the populationfractions of the two types are constant at all timesand equal to πτ for each type τ .) We assume more-over that ucbc;ξ > ucsc;ξ when expenditure, c,falls in the range of values that occur in equilib-rium. (See Figure 5, where these functions aregraphed in the case of the calibration, which showsthe functions ucbc and ucsc used in the numeri-cal work reported here.) Hence a change in ahousehold’s type changes its relative impatience

E u c i v h j it

t

it t

it t

t t0

00

1β ξ ξτ τ

=

∞ ( ) ( )∑ ∫( )( ) − ( )( ); ; ; ddj

,

to consume, given the aggregate state ξt; in addi-tion, each household’s current impatience toconsume depends on the aggregate state ξt. Wealso assume that the marginal utility of additionalexpenditure diminishes at different rates for thetwo household types (see Figure 5); type b house-holds (who are borrowers in equilibrium) have amarginal utility that varies less with the currentlevel of expenditure, resulting in a greater degreeof intertemporal substitution of their expendituresin response to interest rate changes. Finally, thetwo types are also assumed to differ in the marginaldisutility of working a given number of hours;this difference is calibrated so that the two typeschoose to work the same number of hours in steadystate, despite their differing marginal utilities ofincome. For simplicity, the elasticities of laborsupply of the two types are not assumed to differ.

The coexistence of the two types with differ-ing impatience to consume creates a social func-tion for financial intermediation. In the presentmodel, as in the basic NK model, all output isconsumed either by households or by the govern-ment; hence intermediation serves an allocativefunction only to the extent that there are reasonsfor the intertemporal marginal rates of substitutionof households to differ in the absence of financialflows. The present model reduces to the standardrepresentative-household model in the case thatone assumes that ubc;ξ = usc;ξ and ν bh;ξ =ν sh;ξ .

We assume the following: that householdsgenerally are able to spend an amount differentfrom their current income only by depositingfunds with or borrowing from financial interme-diaries; that the same nominal interest rate it

d isavailable to all savers; and that a (possibly) differ-ent nominal interest it

b is available to all borrow-ers,5 independent of the quantities that a givenhousehold chooses to save or to borrow. For sim-plicity, we also assume that only one-period risk-less nominal contracts with the intermediary arepossible for either savers and borrowers. Theassumption that households cannot engage infinancial contracting other than through the inter-



5 Here “savers” and “borrowers” identify households according towhether they choose to save or borrow and not according to theirtype.

mediary sector represents one of the key financialfrictions. We also allow households to hold one-period riskless nominal government debt. But,because government debt and deposits with inter-mediaries are perfect substitutes as investments,households must pay the same interest rate it

d inequilibrium and their decision problem is thesame as the case in which they have only onedecision about how much to deposit with or bor-row from intermediaries.

Aggregation is simplified by assuming thathouseholds are able to sign state-contingent con-tracts with one another, through which they mayinsure one another against both aggregate risk andthe idiosyncratic risk associated with a house-hold’s random draw of its type, but also assumingthat households are only intermittently able toreceive transfers from the insurance agency;

between these infrequent occasions when ahousehold has access to the insurance agency, it can only save or borrow through the financialintermediary sector mentioned previously. Theassumption that households are eventually ableto make transfers to one another in accordancewith an insurance contract signed earlier meansthat they continue to have identical expectationsregarding their marginal utilities of income farenough in the future, regardless of their differingtype histories.

It then turns out that in equilibrium, the mar-ginal utility of a given household at any point intime depends only on its type τ ti at that time;hence the entire distribution of marginal utilitiesof income at any time can be summarized by twostate variables, λtb and λts, indicating the marginalutilities of each of the two household types. The



0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

1

2

3

4

5

ubc(c)

usc(c)

c−bc−s

λ−b

λ−s

Figure 5

Marginal Utilities of Consumption for Two Household Types

NOTE: The values of c–s and c–b indicate steady-state consumption levels of the two types, and λ–s and λ–b their corresponding steady-state marginal utilities.

expenditure level of type τ is also the same for allhouseholds of that type and can be obtained byinverting the marginal-utility functions (graphedin Figure 5) to yield an expenditure demand func-tion cτλ;ξt for each type. Aggregate demand Ytfor the Dixit-Stiglitz composite good can then bewritten as

(2)

where Gt indicates the (exogenous) level of gov-ernment purchases, and Ξt indicates resourcesconsumed by intermediaries (the sum of twocomponents, Xit

p representing costs of the privateintermediaries and Ξtcb representing costs of cen-tral bank activities, each discussed further below).Thus the effects of financial conditions on aggre-gate demand can be summarized by tracking the evolution of the two state variables λtτ. Themarginal-utility ratio Ωt λtb/λts ≥ 1 provides animportant measure of the inefficiency of the allo-cation of expenditure owing to imperfect financialintermediation—since, in the case of frictionlessfinancial markets, we would have Ωt = 1 at alltimes.

In the presence of heterogeneity, instead of asingle Euler equation each period relating the pathof the marginal utility of income of the represen-tative household to the model’s single interest rate,we have two Euler equations each period, onefor each household type and each involving adifferent interest rate: it

b for type b households(who choose to borrow in equilibrium) and it

d fortype s households (who choose to save). If we log-linearize these Euler equations,6 and combinethem with a log-linearized version of (2), we obtaina structural relation of the form

(3)

generalizing the “intertemporal IS relation” ofthe basic NK model. Here Yt logYt/Y

– measures

Y c c Gt bb

tb

t ss

ts

t t t= + + +( ) ( )π λ ξ π λ ξ; ; ,Ξ

ˆ ˆ ˆ

ˆ

Y ı E E Y E g

E

t tavg

t t t t t t

t t

= − −( ) + −

− −

+ + +

+

σ π 1 1 1

1

∆

∆Ξ σσ σ ψs s Et t tΩ Ω ΩΩ Ωˆ ˆ+ +( ) +1,

the percentage deviation of aggregate output fromits steady-state level;

is the average of the interest rates that are rele-vant (at the margin) for all of the savers andborrowers in the economy, where we define ît

τ log1+ itτ/1 + ı–τ for τ b,d;7 gt is a compos-

ite “autonomous expenditure” disturbance as inWoodford (2003, pp. 80, 249), taking account ofexogenous fluctuations in Gt, as well as exogenousvariation in the spending opportunities facing thetwo types of households (reflected in the depend-ence of the functions uτc;ξt on the state vectorξt); Ξt Ξt – Ξ–/Y– measures departures of thequantity of resources consumed by the inter-mediary sector from its steady-state level8; andΩt logΩt/Ω

– measures the gap between themarginal utilities of the two household types.

Note that the first four terms on the right-handside of (3) are exactly as in the basic NK model,except for these differences: (i) instead of “the”interest rate we have an average interest rate; (ii)σ– is no longer the intertemporal elasticity of sub-stitution for the representative household, butinstead a weighted average of the correspondingparameters for the two types; and (iii) the compos-ite disturbance, gt, similarly averages the changesin spending opportunities for the two types. Thecrucial differences are the presence of the newterms involving Ξt and Ωt , which exist only in thecase of financial frictions. The sign of the coeffi-cient sΩ depends on the asymmetry of the degreesof interest sensitivity of expenditure by the twotypes; in the case shown in Figure 5 (which weregard as the empirically relevant case), sΩ > 0because the intertemporal elasticity of expendi-ture is higher for type b.9 In this case, a largervalue of Ωt reduces aggregate demand for givenexpectations about the forward path of average

ˆ ˆ ˆı ı ıtavg

b tb

s td≡ +π π

6 Here and in the case of all other log-linearizations discussed below,we log-linearize around a deterministic steady state in which theinflation rate is zero and aggregate output is constant.



7 One can show that, for a log-linear approximation, the averagemarginal utility of income in the population depends only on theexpected path of this particular average of the interest rates in theeconomy.

8 We adopt this notation so that Ξt is defined even when the modelis parameterized so that Ξ– = 0.

9 In our calibration, ψΩ is a small negative quantity, but because itis small its sign is not of great importance.

real interest rates; this can be thought of as rep-resenting “financial headwinds” of a kind some-times discussed within the Federal Reserve system.10

Log-linearization of the two Euler equationsalso implies that

(4)

where ωt îtb – ît

d is the short-term credit spreadand δ is a coefficient satisfying 0 < δ <1. Thus themarginal-utility gap, Ωt , is a forward-looking mov-ing average of the expected path of the short-termcredit spread. Alternatively, we can view Ωtitself as a credit spread, a positive multiple of thespread between two long-term yields,

for τ b,d. Hence the terms in (3) involving Ωtindicate that variations in credit spreads are rele-vant to aggregate demand. Credit spreads are alsorelevant to the relation between the path of thepolicy rate11 and aggregate expenditure becauseof the identity

(5)

connecting the policy rate to the interest rate thatappears in (3). Under an assumption of Calvo-style staggered price adjustment, we similarlyobtain an aggregate supply relation that is onlyslightly different from the “NK Phillips curve” ofthe representative-household model. Specifically,we obtain

(6)

where Ytn (the “natural rate of output”) is a com-

posite exogenous disturbance that depends ontechnology, preferences, and government pur-chases; ut (the “cost-push shock”) is another com-

ˆ ˆ ˆ ˆΩ Ωt t t tE= + +ω δ 1,

r E ıtj

jt t j

τ τδ δ≡ −( )−

=

∞

+∑11

0

ˆ ˆ ˆ

ˆ ˆ ˆı ıtavg

td

b t= + π ω

π κ β π κ κt t tn

t t t t tY Y E u= −( ) + + + −+ˆ ˆ ˆ ˆ

1 Ω ΞΩ Ξ ,

posite exogenous disturbance that depends onvariations in distorting taxes and in the degree ofmarket power in labor or product markets; andthe coefficients satisfy κ, κΞ > 0 and, in the casethat we regard as realistic, κΩ > 0 as well. Here thefirst three terms on the right-hand side are iden-tical to those of the standard “NK Phillips curve,”subject to similar comments as above about thedependence of κ on a weighted average of theintertemporal elasticities of substitution of the twotypes and the dependence of Yt

n on a weightedaverage of the preference shocks of the two types;the final two terms appear only as a result of creditfrictions. We note in particular that increases incredit spreads shift both the aggregate-supplyand aggregate-demand relations in our model.

In the presence of heterogeneity, householdbehavior results in one further structural equationthat has no analog in the representative-householdmodel. This is a law of motion for bt , the per capitalevel of private borrowing, which depends on thefluctuations in the levels of expenditure of thetwo types and, hence, on the fluctuations in bothmarginal utilities λtτ. Details of this additionalrelationship are provided in Cúrdia and Woodford(2009a). We also suppose that the governmentissues one-period riskless nominal debt, the realvalue of which at the end of period t is denotedbtg. We treat bt

g as an exogenous process; this isone of three independent fiscal disturbances thatwe allow for.12 We suppose that government debtcan be held either by saving households or by thecentral bank,13 and in equilibrium we supposethat at least part of the public debt is always heldby households. Since government debt is a perfectsubstitute for deposits with the intermediaries inour model, from the standpoint of saving house-holds, in equilibrium the yield on governmentdebt must always equal it

d, the competitive interestrate on deposits.



10 See, for example, the reference by Alan Greenspan (1997) to theU.S. economy in the early 1990s as “trying to advance in the faceof fifty-mile-an-hour headwinds,” owing to “severe credit con-straint.” The point of the metaphor was that under such conditions,a given reduction in the federal funds rate stimulated less expen-diture than it ordinarily would have.

11 The identification of itd with the policy rate is discussed below in

Section 1.3.

12 The other two disturbances are exogenous variations in governmentpurchases, Gt, of the composite good and exogenous variations ina proportional sales tax rate.

13 We could also allow intermediaries to hold government debt, butthey will choose not to as long as it

b > itd, as is always true in the

equilibria that we consider.

1.2 Financial Intermediaries

We assume an intermediary sector made upof identical, perfectly competitive firms. Inter -mediaries take deposits on which they promiseto pay a riskless nominal return, it

d, one-periodlater, and make one-period loans on which theydemand a nominal interest rate it

b. An intermedi-ary also chooses a quantity of reserves, Mt, to holdat the central bank, on which it will receive anominal interest yield it

m. Each intermediary takesas given all three of these interest rates. We assumethat arbitrage by intermediaries need not eliminatethe spread between it

b and itd for either of two rea-

sons: (i) Resources are used in the process of loanorigination or (ii) intermediaries may be unableto tell the difference between good borrowers(who will repay their loans the next period) andbad borrowers (who will be able to disappear with-out having to pay) and as a consequence may haveto charge a higher interest rate to good and badborrowers alike.

We suppose that origination of good loans inreal quantity Lt requires an intermediary to alsooriginate bad loans in quantity χtLt , where χt′,χt′′ ≥ 0, and the function χtL may shift fromperiod to period for exogenous reasons. (Whilethe intermediary is assumed to be unable to dis-criminate between good and bad loans, it is ableto predict the fraction of loans that will be bad inthe case of any given scale of its lending activity.)This scale of operations also requires the inter-mediary to consume real resources Ξt

pLt ;mt inthe period in which the loans are originated,where mt Mt/Pt , and Ξt

pL;m is a convex func-tion of its two arguments, with ΞpLt ≥ 0, Ξpmt ≤ 0,ΞpLmt ≤ 0. We further suppose that for any scale ofoperations, L, there exists a finite satiation levelof reserve balances, m–tL, defined as the lowestvalue of m for which ΞpmtL;m = 0. (Our convexityand sign assumptions then imply that ΞpmtL;m = 0for all m > m–tL.) We assume the existence of afinite satiation level of reserves for an equilibriumto be possible in which the policy rate is drivento zero, a situation of considerable practical rele-vance at present.

Given an intermediary’s choice of its scale oflending operations, Lt , and reserve balances, mt ,

to hold, we assume that it acquires real deposits,dt , in the maximum quantity that it can repay(with interest at the competitive rate) from theanticipated returns on its assets (taking intoaccount the anticipated losses on bad loans). Thusit chooses dt such that

The deposits that it does not use to finance eitherloans or the acquisition of reserve balances,

are distributed as earnings to its shareholders.The intermediary chooses Lt and mt each periodto maximize these earnings, given it

d,itb,it

m. Thisimplies that Lt and mt must satisfy the first-orderconditions:

(7)

(8)

Equation (7) can be viewed as determining theequilibrium credit spread, ωt , as a functionωtLt ;mt of the aggregate volume of private creditand the real supply of reserves.14 As indicatedabove, a positive credit spread exists in equilib-rium to the extent that Ξt

pL;m, χtL , or both areincreasing in L. Equation (8) similarly indicateshow the equilibrium differential δ tm between theinterest paid on deposits and that paid on reservesat the central bank is determined by the same twoaggregate quantities.

In addition to these two equilibrium condi-tions that determine the two interest rate spreadsin the model, the absolute level of (real) interestrates must be such that the supply and demandfor credit are equal. Market clearing in the creditmarket requires that

(9)

1 1 1+( ) = +( ) + +( )i d i L i mtd

t tb

t tm

t .

d m L L L mt t t t t tp

t t− − − −( ) ( )χ Ξ ; ,

ΞLtp

t t Lt t ttb

td

tdL m L

i ii

; ,( ) ( )+ = ≡−+

χ ω1

− = ≡−+

( )Ξmtp

t t tm t

dtm

tdL m

i ii

; .δ1

b L Lt t tcb= + ,

14 Note that in terms of this definition of the credit spread, ωt, thepreviously defined deviation corresponds to ωt log1 + ωt/1 + ω

–.



where Ltcb represents real lending to the private

sector by the central bank, as discussed next.

1.3 The Central Bank and Interest RateDetermination

In our model, the central bank’s liabilitiesconsist of the reserves, Mt , (which also constitutethe monetary base) on which it pays interest atthe rate it

m. These liabilities in turn fund the cen-tral bank’s holdings of government debt and anylending by the central bank to type b households.We let Lt

cb denote the real quantity of lending bythe central bank to the private sector; the centralbank’s holdings of government debt are then givenby the residual mt – Lt

cb. We can treat mt (or Mt )and Lt

cb as the bank’s choice variables, subject tothe following constraints:

(10)

It is also necessary that the central bank’s choicesof these two variables also satisfy the bound

where btg is the total outstanding real public debt,

so that a positive quantity of public debt remainsin the portfolios of households. In the calculationsbelow, however, we assume that this last con-straint is never binding. (We confirm this in ournumerical examples.)

We assume that central bank extension ofcredit other than through open-market purchasesof Treasury securities consumes real resources,just as in the case of private intermediaries, andrepresent this resource cost by a function ΞcbLtcb,discussed further in Section 4, which is increasingand at least weakly convex, with Ξcb′0 > 0.

The central bank has one further independentchoice to make each period, which is the rate ofinterest it

m to pay on reserves. We assume that ifthe central bank lends to the private sector, it sim-ply chooses the amount that it is willing to lendand auctions these funds, so that in equilibriumit charges the same interest rate it

b on its lendingthat private intermediaries do; this is thereforenot an additional choice variable for the centralbank. Similarly, the central bank receives the

0 ≤ ≤L mtcb

t .

m L bt tcb

tg< + ,

market-determined yield itd on its holdings of

government debt. The interest rate it

d at which intermediariesare able to fund themselves is determined eachperiod by the joint inequalities

(11)

(12)

together with the “complementary slackness”condition that at least one of these—(11) and/or(12)—must hold with equality each period; heremtdL,δm is the demand for reserves defined by (8),

defined to equal the satiation level m–tL in thecase that δm = 0. (Condition (11) may hold onlyas an inequality, as intermediaries will be willingto hold reserves beyond the satiation level as longas the opportunity cost, δ tm, is zero.) We identifythe rate it

d at which intermediaries fund themselveswith the central bank’s policy rate (e.g., the federalfunds rate in the case of the United States).

The central bank can influence the policyrate through two channels: its control of the sup-ply of reserves and its control of the interest ratepaid on them. By varying mt , the central bank canchange the equilibrium differential, δ tm, deter-mined as the solution to (11) and (12). And byvarying it

m, it can change the level of the policyrate, it

d, that corresponds to a given differential.Through appropriate adjustment on both margins,the central bank can control it

d and itm separately

(subject to the constraint that itm cannot exceed

itd). We also assume that for institutional reasons,it is not possible for the central bank to pay a nega-tive interest rate on reserves. (We may supposethat intermediaries have the option of holdingcurrency, earning zero interest, as a substitutefor reserves, and that the second argument of theresource cost function, Ξt

pb;m, is actually thesum of reserve balances at the central bank plusvault cash.) Hence the central bank’s choice ofthese variables is subject to the constraints

(13)

In our model, there are thus three independentdimensions along which central bank policy can

m m Lt td

t tm≥ ( ), ,δ

δtm ≥ 0,

0 ≤ ≤i itm

td .



be varied: the quantity of reserves, Mt , that aresupplied; the interest rate it

m paid on thosereserves; and the breakdown of central bank assetsbetween government debt and lending Lt

cb to theprivate sector. Alternatively, we can specify thesethree independent dimensions as (i) interest ratepolicy, the central bank’s choice of an operatingtarget for the policy rate, it

d; (ii) reserve-supplypolicy, the choice of Mt , which in turn impliesa unique rate of interest it

m that must be paid onreserves for the reserve-supply policy to be con-sistent with the bank’s target for the policy rate15;and (iii) credit policy, the central bank’s choiceof the quantity of funds Lt

cb to lend to the privatesector. We prefer this last identification of thethree dimensions of policy because in this caseour first dimension (interest rate policy) corre-sponds to the sole dimension of policy empha-sized in many conventional analyses of optimalmonetary policy; the first two are additionaldimensions of policy introduced by our extensionof the basic NK model.16 Changes in central bankpolicy along each of these dimensions has conse-quences for the bank’s cash flow, but we abstractfrom any constraint on the joint choice of thethree variables associated with cash-flow con-cerns. (We assume that seignorage revenues aresimply turned over to the Treasury, where theironly effect is to change the size of lump-sumtransfers to the households.)

Given that central bank policy can be inde-pendently varied along each of these three dimen-sions, we can independently discuss the criteria forpolicy to be optimal along each dimension. Below,we take up each of the three dimensions in turn.

1.4 The Welfare Objective

In considering optimal policy, we take theobjective of policy to be the maximization ofaverage expected utility. Thus we can expressthe objective as maximization of

(14)

where the welfare contribution, Ut , each periodweights the period utility of each of the two typesby their respective population fractions at eachpoint in time. As shown in Cúrdia and Woodford(2009a),17 this can be written as

(15)

Here ∆t is an index of price dispersion in period t,taking its minimum possible value of 1 when theprices of all goods are identical; for any given totalquantity Yt of the composite good that must beproduced, the total disutility of working indicatedin (1) is greater the more dispersed are prices, asthis implies a correspondingly less uniform (andhence less efficient) composition of output.

The total disutility of working is also a decreas-ing function of Ωt , since a larger gap between themarginal utilities of the two types implies a less-efficient division of labor effort between the twotypes. The average utility from consumption issmaller, for given aggregate output Yt , the largeris Ξt , since only resources Yt – Gt – Ξt are con-sumed by households. And the average utilityfrom consumption is also decreasing in Ωt , sincea larger marginal-utility gap implies a less-efficientdivision of expenditure between the two types.Thus the derived utility U. is a concave functionof Yt that reaches an interior maximum for givenvalues of the other arguments, and a monotoni-cally decreasing function of Ωt , Ξt , and ∆t . The

E Utt t

t t0

0

0

β −

=

∞

∑ t ,

U U Yt t t t t t= ( ), , , ; .Ω Ξ ∆ ξ

15 We might choose to call the second dimension “variation in theinterest rate paid on reserves,” which would correspond to some-thing that the Board of Governors makes an explicit decision aboutunder current U.S. institutional arrangements, as is also true atmost other central banks. But describing the second dimension ofpolicy as “reserve-supply policy” allows us to address the questionof the value of “quantitative easing” under this heading as well.

16 Goodfriend (2009) similarly describes central bank policy as involv-ing three independent dimensions. These correspond to our firstthree dimensions, but he calls the first dimension (the quantity ofreserves, or base money) “monetary policy.” We believe that thisdoes not correspond to standard usage of the term “monetary policy,”since the traditional focus of Federal Open Market Committee(FOMC) deliberations about monetary policy has been the choiceof an operating target for the policy rate, as is generally the casefor central banks. Reis (2009) also distinguishes among the threedimensions of policy in terms similar to ours.



17 Cúrdia and Woodford (2009a) analyze a special case of the presentmodel in which central bank lending and the role of central bankliabilities in reducing the transactions costs of intermediaries areabstracted from. However, the form of the welfare measure (15)depends only on the nature of the heterogeneity in our model, andthe assumed existence of a credit spread and of resources consumedby the intermediary sector; the functions that determine how Ωtand Ξt are endogenously determined are irrelevant for this calcula-tion, and those are the only parts of the model that are generalizedin this paper. Hence the form of the welfare objective in terms ofthese variables remains the same.

dependence of U. on Yt and ∆t is the same as inthe representative-household model of Benignoand Woodford (2005), while the dependence onΩt and Ξt indicates new distortions resultingfrom the credit frictions in our model.

As in Benigno and Woodford, the assumptionof Calvo-style price adjustment implies that theindex of price dispersion evolves according to alaw of motion of the form

where for a given value of ∆t–1, h∆t–1,. has aninterior minimum at an inflation rate that is nearzero when ∆t–1 is near 1. Thus for given paths ofthe variables Ωt,Ξt welfare is maximized by trying(to the extent possible) to simultaneously keepaggregate output near the (time-varying) level thatmaximizes U and inflation near the (always low)level that minimizes price dispersion. Hence ourmodel continues to justify concerns about outputand inflation stabilization common to the NK lit-erature. However, it also implies that welfare canbe increased by reducing credit spreads and thereal resources consumed in financial intermedia-tion. These latter concerns make the effects ofpolicy on the evolution of aggregate credit andon the supply of bank reserves also relevant tomonetary policy deliberations. We now turn tothe question of how each of the three dimensionsof central bank policy can effect these severalobjectives.

2. OPTIMAL POLICY: THE SUPPLYOF RESERVES

We shall first consider optimal policy withregard to the supply of reserves, taking as given(for now) the way in which the central bankchooses its operating target for the policy rate, it

d

and the state-contingent level of central bank lend-ing to the private sector, Lt

cb. Under fairly weakassumptions, we obtain a very simple result:Optimal policy requires that intermediaries besatiated in reserves, that is, that Mt/Pt ≥ m–tLt atall times.

For levels of reserves below the satiation point,an increase in the supply of reserves has two

∆ ∆t t th= ( )−1, ,π

effects relevant for welfare: The resource cost offinancial intermediation, Ξt

p, is reduced (for a givenlevel of lending by the intermediary sector), andthe credit spread, ωt , is reduced (again, for a givenlevel of lending) as a consequence of (7). Each ofthese effects raises the value of the objective in(14); note that the reductions in credit spreadsincrease welfare because of their effect on the pathof the marginal-utility gap, Ωt, as a consequenceof (4). Hence an increase in the supply of reservesis unambiguously desirable in any period in whichthey remain below the satiation level.18 Oncereserves are at or above the satiation level, how-ever, further increases reduce neither the resourcecosts of intermediaries nor equilibrium creditspreads (as in this case, Ξpmt = Ξ

pLmt = 0), so there

would be no further improvement in welfare.Hence policy is optimal along this dimension ifand only if Mt/Pt ≥ m–tLt at all times,19 so that

(16)

This is just another example in which thefamiliar Friedman rule for “the optimum quantityof money” (Friedman, 1969) applies. Note, how-ever, that our result has no consequences forinterest rate policy. While the Friedman rule issometimes taken to imply a strong result aboutthe optimal control of short-term nominal interestrates—namely, that the nominal interest rateshould equal zero at all times—the efficiencycondition (16), together with the equilibriumrelation (8), implies only that the interest ratedifferential, δ tm, should equal zero at all times.With zero interest on reserves, this would alsorequire that it

d = 0 at all times; but given that thecentral bank is free to set any level of interest onreserves consistent with (13), the efficiency con-dition (16) actually implies no restriction on eitherthe average level or the degree of state-contingencyof the central bank’s target for the policy rate, it

d.

Ξmtp

t tL m; .( ) = 0



18 The discussion here assumes that the upper bound in (10) is not abinding constraint. But if that constraint does bind, then an increasein the supply of reserves relaxes the constraint, and this too increaseswelfare, so that the conclusion in the text is unchanged.

19 To be more precise, policy is optimal if and only if (16) is satisfiedand the upper bound in (10) does not bind. Both conditions willbe satisfied by any quantity of reserves above some finite level.

2.1 Is a Reserve-Supply Target Needed?

Our result about the importance of ensuringan adequate supply of reserves might suggest thatthe question of the correct target level of reservesat each point in time should receive the samedegree of attention at meetings of the FOMC asthe question of the correct operating target forthe federal funds rate. But deliberations of thatkind are not needed to ensure fulfillment of theoptimality criterion (16); the efficiency conditioncan alternatively be stated (using (8)) as requiringthat it

d = itm at all times. Reserves should be sup-

plied to the point at which the policy rate falls tothe level of the interest rate paid on reserves, or,in a formulation that is more to the point, interestshould be paid on reserves at the central bank’starget for the policy rate.

Given a rule for setting an operating targetfor it

d (discussed in the next section), itm should

be chosen each period in accordance with thesimple rule

(17)

When the central bank implements its target forthe policy rate through open-market operations,it will automatically have to adjust the supply ofreserves to satisfy (16). But this does not requirea central bank’s monetary policy committee (theFOMC in the case of the United States) to delib-erate about an appropriate target for reserves ateach meeting; once the target for the policy rate ischosen (and the interest rate to be paid on reservesis determined by that, through condition (17)),the quantity of reserves that must be supplied toimplement the target can be determined by thebank staff in charge of carrying out the necessaryinterventions (the Trading Desk at the New YorkFed in the case of the United States), on the basisof a more frequent monitoring of market condi-tions than is possible for the monetary policycommittee.

One obvious way to ensure that the efficiencycondition (17) is satisfied is to adopt a routinepractice of automatically paying interest onreserves at a rate that is tied to the current operat-ing target for the policy rate. This is already thepractice of many central banks outside the United

i itm

td= .

States. At some of those banks, the fixed spreadbetween the target for the policy rate and the ratepaid on overnight balances at the central bank isquite small: for example, 25 basis points in thecase of the Bank of Canada; in the case of NewZealand, the interest rate paid on overnight bal-ances is the policy rate itself. There are possiblearguments (relating to considerations not reflectedin our simple model) why the optimal spreadmight be larger than zero, but it is likely in anyevent to be desirable to maintain a constant smallspread rather than treat the question of the interestrate to be paid on reserves as a separate, discre-tionary policy decision to be made at each policycommittee meeting. Apart from the efficiencygains modeled here, such a system should alsohelp to facilitate the central bank’s control of thepolicy rate (Goodfriend, 2002, and Woodford,2003, Chap. 1, Sec. 3).

2.2 Is There a Role for “QuantitativeEasing”?

While our analysis implies that it is desirableto ensure that the supply of reserves never fallsbelow a certain lower bound, m–tLt it also impliesthat there is no benefit from supplying reservesbeyond that level. There is, however, one impor-tant exception to this assertion: It can be desirableto supply reserves beyond the satiation level ifthis is necessary to make the optimal quantity ofcentral bank lending to the private sector, Lt

cb,consistent with (10). This qualification is impor-tant when considering the desirability of the mas-sive expansion in the supply of reserves by theFed since September 2008, as shown in Figure 2.The increase in reserves (shown in Figure 4)occurred only after the Fed expanded the vari-ous newly created liquidity and credit facilitiesbeyond the scale that could be financed simplyby reducing its holdings of Treasury securities(as had been its policy over the previous year).20

Some have argued, instead, that further expan-sion of the supply of reserves beyond the level

20 Bernanke (2009) distinguishes between the Federal Reserve policyof “credit easing” and the type of “quantitative easing” practicedby the Bank of Japan earlier in the decade, essentially on thisground.



needed to bring the policy rate down to the levelof the rate of interest paid on reserves is an impor-tant additional policy tool in its own right—oneof particular value precisely when a central bankis no longer able to further reduce its operatingtarget for the policy rate, owing to the zero lowerbound (as at present in the United States andmany other countries). It is sometimes proposedthat when the zero lower bound is reached, it isdesirable for a central bank’s policy committeeto shift from deliberations, about an interest ratetarget to a target for the supply of bank reserves,as under the Bank of Japan’s policy of “quantita-tive easing” during the period between March2001 and March 2006.

Our model provides no support for the viewthat such a policy should be effective in stimu-lating aggregate demand. Indeed, it is possible tostate an irrelevance proposition for quantitativeeasing in the context of our model. Let the threedimensions of central bank policy be describedby functions that specify the operating target forthe policy rate, the supply of reserves, the inter-est rate to be paid on reserves, and the quantityof central bank credit as functions of macroeco-nomic conditions. For the sake of concreteness,we may suppose that each of these variables is tobe determined by a Taylor-type rule,

where the functions are such that constraints in(10) through (13) are satisfied for all values ofthe arguments. (Here the vector of exogenousdisturbances, ξt , on which the reaction functionsmay depend, includes the exogenous factors thatshift the function Ξt

pL;m.) Then our result is that,given the three functions φ id., φ im., and φL.,the set of processes πt ,Yt ,Lt ,bt , itd, itb,Ωt,∆t thatconstitute possible rational expectations equilib-ria is the same independent of the choice of thefunction φm. as long as the specification of φm.is consistent with the other three functions (inthe sense that (10) and (11) are necessarily satis-

i

i

Y L

M P Y L

td

tm

idt t t t

t tm

t t t t

= ( )= ( )

φ π ξ

φ π ξ

, , ; ,

, , ; ,

== ( )= ( )

φ π ξ

φ π ξ

imt t t t

Lt t t tt

cb

Y L

Y LL

, , ; ,

, , ; ,

fied and that (11) holds with equality in all caseswhere (12) is a strict inequality).21

Of course, the stipulation that φm. be con-sistent with the other functions uniquely deter-mines what the function must be for all values ofthe arguments for which the functions id. andim. imply that δ tm > 0. However, the class of poli-cies considered allows for an arbitrary degree ofexpansion of reserves beyond the satiation levelin the region where those functions imply thatδ tm = 0, and in particular, for an arbitrary degreeof quantitative easing when the zero bound isreached (i.e., when it

d = itm = 0). The class of poli-

cies considered includes the popular proposalunder which the quantity of excess reserves shoulddepend on the degree to which a standard Taylorrule (unconstrained by the zero bound) would callfor a negative policy rate. Our result implies thatthere should be no benefits from such policies.

Our result might seem to be contradicted bythe analysis of Auerbach and Obstfeld (2005), inwhich an open market operation that expands themoney supply is found to stimulate real activityeven when the economy is at the zero bound atthe time of the monetary expansion. But theirthought experiment does not correspond to purequantitative easing of the kind contemplated inthe above proposition—because they specifymonetary policy in terms of a path for the moneysupply and the policy change that they consideris one that permanently increases the money sup-ply, so that it remains higher after the economyhas exited from the “liquidity trap” in which thezero bound is temporarily binding. The contem-plated policy change is therefore not consistentwith an unchanged reaction function φ id. forthe policy rate, and the effects of the interven-tion can be understood to be the consequencesof the commitment to a different future interestrate policy.

Our result implies only that quantitative eas-ing should be irrelevant under two conditions:when (i) an increase in reserves finances anincrease in central bank holdings of Treasurysecurities, rather than an increase in central bank



21 This result generalizes the irrelevance result for quantitative easingin Eggertsson and Woodford (2003) to a model with heterogeneityand credit frictions.

lending to the private sector, and (ii) policyimplies no change in the way that people shouldexpect future interest rate policy to be conducted.

Our model does allow for real effects of anincrease in central bank lending, Lt

cb, financed byan increase in the supply of reserves, if private-sector financial intermediation is inefficient22;but the real effects of the increased central banklending in that case are the same whether thelending is financed by an increase in the supplyof reserves or by a reduction in central bank hold-ings of Treasury securities. Our model also allowsfor real effects of an announcement that interestrate policy in the future will be different, as whena central bank commits itself not to return imme-diately to its usual Taylor rule as soon as the zerobound ceases to bind, but promises instead tomaintain policy accommodation for some timeafter it would become possible to comply withthe Taylor rule (as discussed in the next section).But such a promise (if credible and correctlyunderstood by the private sector) should increaseoutput and prevent deflation to the same extenteven if it implies no change in policy during theperiod when the zero lower bound binds.

While our definition of quantitative easingmay seem narrow, the policy of the Bank of Japanduring the period 2001-06 fits our definition fairlyclosely. The Bank of Japan’s policy involved theadoption of a series of progressively higher quan-titative targets for the supply of reserves. The aimof the policy was understood to be to increasethe monetary base, rather than to allow the Bankof Japan to acquire any particular type of assets.The assets purchased were almost entirelyJapanese government bonds, since credit alloca-tion to malfunctioning markets was not a goal.There was no suggestion that the targets of policyafter the end of the zero-interest-rate period wouldbe any different from before. There was no com-mitment to maintain the increased quantity ofbase money in circulation permanently; and,

indeed, once it was judged time to end the zero-interest-rate policy, the supply of reserves wasrapidly contracted again (Figure 6).

Our theory suggests that expansion of thesupply of reserves under such circumstancesshould have little effect on aggregate demand,and this seems to have been the case. For example,as is also shown in Figure 6, despite an increasein the monetary base of 60 percent during thefirst two years of the quantitative easing policy,and an eventual increase of nearly 75 percent,nominal GDP never increased at all (relative toits March 2001 level) during the entire five yearsof the policy.23

3. OPTIMAL POLICY: INTERESTRATE POLICY

We turn now to a second dimension of policy,the approach taken by the central bank in deter-mining its operating target for the policy rate(the federal funds rate in the case of the FederalReserve). In this section, we take for granted thatreserve-supply policy is being conducted in theway recommended in the previous section, thatis, that the rate of interest on reserves will satisfy(17) at all times. In this case, we can replace thefunction Ξt

pLt ;mtwith

and the function ωtLt ;mt, defined by the left-hand side of (7), with

since there will be satiation in reserves at alltimes.24 Using these functions to specify the

Ξ Ξtp

t tp

t t tL L m L( ) ( )( )≡ ;

ω ωt t t t t tL L m L( ) ( )( )≡ ; ,

22 This result differs from that obtained in Eggertsson and Woodford(2003), where changes in the composition of the assets on thecentral bank’s balance sheet are also shown to be irrelevant. Thatstronger result depends on the assumption of a representativehousehold (as in Eggertsson and Woodford) or, alternatively, friction-less financial intermediation.



23 As indicated in Figure 6, over the first two years of the quantitative-easing policy, nominal GDP fell by more than 4 percent, despiteextremely rapid growth of base money. While nominal GDP recov-ered thereafter, it remained below its 2001:Q1 level over the entireperiod until 2006:Q4, three quarters after the official end of quan-titative easing, by which time the monetary base had been reducedagain by more than 20 percent. Moreover, even if the growth ofnominal GDP after 2003:Q1 is regarded as a delayed effect of thegrowth in the monetary base two years earlier, this delayed nominalGDP growth was quite modest relative to the size of the expansionin base money.

24 Even if at some times mt exceeds m–tLt, this will not affect the

values of Ξpt or ωt.

equilibrium evolution of Ξtp and ωt as functions

of the evolution of aggregate private credit, wecan then write the equilibrium conditions of themodel without any reference to the quantity ofreserves or to the interest rate paid on reserves.We shall also take as given the state-contingentevolution of central bank lending Lt

cb, and askhow the central bank’s target for the policy rateshould be adjusted in response to shocks to theeconomy. In this case the problem considered isof the form considered in Cúrdia and Woodford(2009a).

As in a representative-household model withno financial frictions, a consideration of optimalinterest rate policy requires taking into account

the desired evolution of aggregate output and ofinflation (which affects the objective (14) becauseof the consequences of inflation for the evolutionof the price dispersion index, ∆t), given the trade-off between variations in these two variablesimplied by the aggregate-supply relation. Whileour model implies that, in the presence of creditfrictions, interest rate policy also has consequencesfor the evolution of Ξt and Ωt (which are alsoarguments of (15)), owing to its effects on thevolume of lending by the intermediary sector,the most important effects are the effects on thepaths of output and inflation. The way in whichthe paths of output and inflation matter for wel-fare are essentially the same as in a model with-



Trillion Yen

600

500

400

300

200

100

0

Trillion Yen

120

105

90

75

60

30

0

45

15Nominal GDP (left axis)

Monetary Base (right axis)

1990

:Q1

1990

:Q4

1991

:Q3

1992

:Q2

1993

:Q1

1993

:Q4

1994

:Q3

1995

:Q2

1996

:Q1

1996

:Q4

1997

:Q3

1998

:Q2

1999

:Q1

1999

:Q4

2000

:Q3

2001

:Q2

2002

:Q1

2002

:Q4

2003

:Q3

2004

:Q2

2005

:Q1

2005

:Q4

2006

:Q3

2007

:Q2

2008

:Q1

2008

:Q4

Figure 6

The Monetary Base and Nominal GDP for Japan 1990-2009 (seasonally adjusted)

NOTE: The shaded region shows the period of “quantitative easing,” from March 2001 through March 2006.

SOURCE: International Monetary Fund International Financial Statistics and Bank of Japan.

out financial frictions, and the nature of theaggregate-supply tradeoff indicated by (6) remainsthe same as well, with credit frictions appearingmainly as a source of additional shift terms (likethe “cost-push shocks” emphasized in treatmentssuch as those of Clarida, Gali, and Gertler, 1999).Hence some of the important conclusions of thestandard literature continue to apply, at leastapproximately, even in an environment wherecredit frictions are nontrivial and time varying.

3.1 The Robustness of Flexible Inflation(or Price-Level) Targeting

Benigno and Woodford (2005) show that inthe representative-household version of ourmodel, optimal interest rate policy can be char-acterized by the requirement that interest rates beadjusted so that a certain target criterion is satis-fied each period.25 To a log-linear approximation,the optimal target criterion can be expressed as

(18)

regardless of the degree of steady-state distortionsdue to market power or distorting taxes, where xt Yt – Yt*, Yt* is a function of the exogenousdisturbances to preferences, technology, fiscalpolicy, and markups,26 and φ is a positive coeffi-cient. This can be viewed as a form of “flexibleinflation targeting” in the sense of Svensson(1997): The acceptable near-term inflation pro-jection should be adjusted by an amount propor-tional to the projected change in the output gap.(Farther in the future, there will never be contin-uing forecastable changes in the output gap; sothe criterion will always require that the projectedpath of inflation a few years in the future willequal an unchanging long-run target value, hereequal to zero.)

π φt t tx x+ −( ) =−1 0,

The optimal target criterion in the representative-household model can alternativelybe expressed in the form

(19)

where pt is the log of the general price index attime t. (Note that (18) simply states that the firstdifference of pt should be zero each period, sothat ptmust never be allowed to change.) This isan output gap–adjusted price-level target, or thecommitment to a rule of the form in (19), whichis an example of what Hall (1984) calls an “elasticprice standard.” If the target criterion can be ful-filled precisely each period, the two target criteriaare equivalent; but if it is not always possible forthe central bank to satisfy the target criterion (aswhen the zero lower bound is reached, discussedbelow), the two commitments are no longer equiv-alent. In this case, there are actually advantages tothe price-level formulation, as we discuss below.

Cúrdia and Woodford (2009a) show that in aspecial limiting case, the target criterion (18) oralternatively, (19)—continues to be necessary andsufficient for the optimality of interest rate policy,even in the model with heterogeneity and creditfrictions. This is the special case in which steady-state distortions (including the steady-state creditspread ω–) are negligible, though we allow forshocks that temporarily increase credit spreadsrelative to the steady-state level. Real resourcesused in financial intermediation are negligible(so that the shocks that increase credit spreadsare purely due to an increase in the perceivedfraction of bad loans), and the time-varying frac-tion of bad loans is independent of intermediaries’scale of operations. In this case, there are no vari-ations in Ξt and the fluctuations in Ωt are essen-tially exogenous, so that the welfare-relevant effectsof interest rate policy relate only to its effects onoutput and inflation, as in a model without creditfrictions; and the additional terms in the aggregate-supply tradeoff (6) are purely exogenous distur-bance terms, so that the derivation of the optimaltarget criterion proceeds as in the representative-household model.

More generally, the target criterion (18) willnot correspond precisely to optimal policy; butour numerical investigations of calibrated models

p p x pt t t≡ + =φ *,

25 For further discussion of targeting regimes as an approach to theconduct of monetary policy, see Svensson (1997 and 2005),Svensson and Woodford (2005), or Woodford (2007).

26 In the case that the steady-state level of output under flexible prices(or with zero inflation) is efficient, Yt* corresponds to variationsin the efficient level of output. When the steady-state level of out-put under flexible prices is not efficient, the two concepts differsomewhat; for the more general definition of Yt*, and discussion ofits relation to the efficient level of output and to the flexible-priceequilibrium level of output, see Woodford (2009, section 2).



suggest that it can easily continue to provide areasonably good approximation to the optimalRamsey policy, making the prescription of “flexibleinflation targeting” still a useful practical rule ofthumb. Figures 7 through 10 illustrate this, forone illustrative calibration of our model, nowallowing both Ξt

p and ωt to vary endogenously withthe volume of private lending.27 Each figure plotsthe impulse responses (under a log-linear approxi-mation to the model dynamics) of several of theendogenous variables to a particular type of exoge-nous disturbance, under each of four differentpossible specifications of monetary policy: (i) asimple “Taylor rule” using the coefficients pro-posed by Taylor (1993); (ii) a “strict inflation-targeting” regime, under which interest rate policyis used to ensure that inflation never deviatesfrom its target level (zero) in response to anydisturbance; (iii) a “flexible inflation-targeting”regime, under which interest rate policy ensuresthat (18) holds each period; and (iv) a fully opti-mal policy (the solution to the Ramsey policyproblem).

In each of the cases shown (as well as for alarge number of other types of disturbances thatwe have considered), the “flexible inflation-targeting” regime remains a good approximationto the fully optimal policy, even if it is no longerprecisely the optimal policy. Both types of infla-tion-targeting regimes are closer to the optimalpolicy than is the Taylor rule, which mechanicallyresponds to observed variations in real activitywithout taking account of the types of disturbances

responsible for those variations.28 (The Taylor ruletightens policy too much in response to increasesin output resulting from productivity growth orincreased government purchases, while it doesnot tighten enough in the case of the wage-markupshock, which causes output to fall even as infla-tion increases.) But especially in the case of thewage-markup shock and the shock to governmentpurchases, the flexible inflation target providesa better approximation to optimal policy thanwould a strict inflation target.

The target criterion (18) continues to providea good approximation to optimal policy in thecase of a “purely financial” disturbance as well,even though such disturbances are not allowed forin the analysis of Benigno and Woodford (2005).Figure 10 shows the impulse responses to anexogenous increase in the function χtL , corre-sponding to an increase in the fraction of loansexpected to be bad loans, that then gradually shiftsback to its steady-state value. Such a shock tem-porarily shifts up the value of ω–tL for any valueof L and so represents a contraction of the loansupply for reasons internal to the financial sector.In equilibrium, such a disturbance results bothin a contraction of private lending (and hence inequilibrium borrowing bt, as shown in the bottom-left panel) and in an increase in the equilibriumcredit spread, ωt (as shown in the middle-rightpanel). If the central bank follows the Taylor rule,such a shock results in both an output contractionand deflation, but an optimal policy would allowlittle of either to occur.29 Again, the flexible



27 The calibration is discussed further in Cúrdia and Woodford (2009a).The model parameters that are shared with the representative-household version of the model are calibrated as in Woodford (2003,Chap. 6), on the basis of the empirical estimates of Rotemberg andWoodford (1997). The degree of heterogeneity of the consumptionpreferences of the two types is as shown in Figure 5, while thedisutility of labor is the same for the two types, except for a multi-plicative factor chosen so that in steady state the two types workthe same amount. The steady-state credit spread is calibrated toequal 2 percent per annum, as in Mehra, Piguillem, and Prescott(2008), and is attributed entirely to the marginal resource cost ofprivate financial intermediation, to make the endogeneity of Ξt asgreat as possible given the average size of the spread. A highly con-vex function Ξ–pL is also assumed in the numerical results presentedhere, to make the endogeneity of the credit spread as great as pos-sible. If we assume a less convex function for Ξ–pL or that a smallerfraction of the steady-state credit spread is due to real resourcecosts, then the special case in which equation (18) is optimal is aneven better approximation than in the case shown in the figures.

28 Here we assume a rule in which the intercept term representingthe equilibrium real funds rate is a constant, and the output gap isdefined as output relative to a deterministic trend, as in Taylor(1993). A more sophisticated variant, in which the intercept varieswith variations in the “natural rate of interest,” and the outputgap is defined relative to variations in the “natural rate of output”(defined as in equation (6)), provides a better approximation tooptimal policy, but still less close an approximation than thatprovided by the flexible inflation-targeting rule. The responses toexogenous disturbances under the more sophisticated form ofTaylor rule are discussed in Cúrdia and Woodford (2009b).

29 Interestingly, the optimal policy does not involve a much larger cutin the policy rate than occurs under the Taylor rule. The differenceis that under the Taylor rule, the central bank is unwilling to cutthe policy except to the extent that this can be justified by a fall ininflation or output, and so in equilibrium those must occur; underthe optimal policy, the central bank is willing to cut the policy ratewithout requiring inflation or output to decline, and in equilibriumthey do not.

inflation-targeting regime provides a reasonableapproximation to what would happen under anoptimal policy commitment. (We obtain a verysimilar figure in the case in which the disturbanceis instead an exogenous increase in the marginalresource cost of private financial intermediation.)

These results provide an answer to one of thequestions posed in the introduction: Does keep-ing track of the projected paths of inflation andoutput alone provide a sufficient basis for judg-ments about whether monetary policy (by whichinterest rate policy is here intended) remains ontrack, even during times of financial turmoil?

Our results suggest that, while the target criterion(18) involving only the projected paths of inflationand the output gap is not complex enough toconstitute a fully optimal policy in our extendedmodel, ensuring that (18) holds at all times wouldin fact ensure that policy is not too different froma fully optimal policy commitment—not only inan environment in which financial intermediationis imperfect, but even when the main disturbancesto the economy originate in the financial sector andimply large increases in the size of credit spreads.

It is important to note, however, that ourresults do not imply that there is no need for a



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SOURCE: Cúrdia and Woodford (2009a).

central bank to monitor or respond to financialconditions. Under the targeting regime recom-mended here, it is necessary to keep track of thevarious exogenous disturbances affecting theeconomy, to correctly forecast the evolution ofinflation and output under alternative paths forthe policy rate—and this includes keeping trackof financial disturbances, when these are impor-tant. The simple Taylor rule, which does notrequire the central bank to use information aboutany variables other than inflation and real GDP,would not be an adequate guide to policy.

3.2 A Spread-Adjusted Taylor Rule?

Might a Taylor rule instead be a sufficientbasis for setting interest rate policy if the standardTaylor rule is augmented, as proposed by Taylor(2008), by an adjustment for observed variationsin a credit spread, such as one of the LIBOR-OISspreads shown in Figure 1? For the kind of dis-turbance considered in Figure 10, this type ofadjustment would allow the policy rate to be cutby more than a full percentage point even in theabsence of any decline in inflation or output—which is exactly what is necessary to the allow



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Impulse Responses to a 1 Percent Increase in the Wage Markup, Under Four AlternativeMonetary Policies


the kind of equilibrium responses associatedwith the optimal policy commitment.

Cúrdia and Woodford (2009b) consider modi-fied Taylor rules of this kind in the context of thesame calibrated structural model used in Figures 7through 10. While they find that the type of spreadadjustment proposed by Taylor (2008) would bebeneficial under some circumstances—such asthe type of disturbance considered in Figure 10—the desirable degree of adjustment (and evensometimes the sign of the adjustment) of the policyrate in response to a change in credit spreads isnot independent of the nature of the disturbance

that causes spreads to change. Even in the caseof “purely financial” disturbances, like the kindconsidered in Figure 10, the optimal degree ofresponse to changes in the credit spread dependson the degree of anticipated persistence of thedisturbance.

In fact, the targeting regime that we proposeabove automatically involves a spread adjustmentof the general type proposed by Taylor (2008).Given that a change in the credit spread (and inthe anticipated future path of credit spreads,which determines the marginal-utility gap, Ωt ,because of (4)) affects aggregate demand for any



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Impulse Responses to a 1 Percent Increase in Gt Equal to 1 Percent of Steady-State Output,Under Four Alternative Monetary Policies


given anticipated path of the policy rate—bothbecause of the difference between it

avg and thepolicy rate indicated in (5) and because of the Ωt

terms in (3)—the consequences of a given path ofthe policy rate for the inflation and output pro-jections will be different when the path of creditspreads changes, and so the path for the policyrate required to produce projections that conformto the target criterion will be different. Since largercredit spreads (now and in the future) reduceaggregate demand leading to lower inflation, thepolicy rate will generally need to be reduced tooffset this effect.

Moreover, we believe that the targetingapproach represents a conceptually superiorway of introducing these considerations intodecisions about interest rate policy. The Taylor(2008) proposal requires that one specify whichparticular measure of credit spreads will be takeninto account in the modified reaction function.(Taylor has proposed one very specific spread—the LIBOR-OIS spread.) But in fact central banksmonitor many different credit spreads; and whilein our highly stylized model there is only a singlecredit spread, a more empirically realistic modelwould have to include several (as indeed the



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Figure 10

Impulse Responses to a Shift in the Function χt(L) that Triples the Size of ω–t(L) for Each Value of L,Under Four Alternative Monetary Policies


FRB/U.S. model already does). Under our pro-posed targeting regime, each of these would berelevant to setting interest rate policy: Variationsin each of the different spreads would be takeninto account to the extent that they enter the equa-tions of the model used to project the paths ofinflation and output. Furthermore, under thetargeting approach, the adjustment of the policyrate would not have to be a mechanical (and purelycontemporaneous) function of the change in thecredit spread; instead, one would automaticallyrespond differently depending on the nature of thedisturbance and would respond also to changesin the expected future path of spreads as well asto the current spread.

3.3 Policy When the Zero Lower BoundIs Reached

In the discussion above (and in the simula-tions in Figures 7 through 10), it is assumed thatthe zero lower bound on the policy rate is neverreached, and our theoretical model implies thatit should not be reached, in the case of smallenough shocks. But it is theoretically possiblefor it to bind in the case of large-enough shocksof certain types, and recent events in the UnitedStates and elsewhere have shown that one cannotpresume that the constraint will never bind inpractice. (As a practical matter, it seems that it ismost likely to bind following severe disruptionsof the financial sector, as in the case of the GreatDepression, in Japan during the 1990s, and atpresent.)

When the zero bound is a binding constraint,it may not be possible for the central bank to useinterest rate policy to ensure fulfillment of thetarget criterion (19) in all periods. Does this affectthe validity of our recommendation of this policy?Although it may not be possible to fulfill the targetcriterion at all times, that does not in itself implythat it is not desirable to adjust interest rate policyto fulfill the criterion when it can be satisfied.Also, nothing here implies that, when policy-makers deliberate interest rate policy, they shouldforgo the question of whether there exists aninterest rate path that would satisfy the targetcriterion.

But the fact that the lower bound is sometimesa binding constraint also has consequences forthe appropriate policy target even under certaincircumstances when the zero lower bound wouldnot prevent one from achieving the target criterion(18). The reason is that the severity of the distor-tions during the period when the lower bound isbinding should depend on the way in whichpolicy is expected to be conducted after the con-straint ceases to bind. Hence, the policy that acentral bank should commit to follow in such aperiod should be chosen with a view to the con-sequences of the anticipation of that policy duringthe period when the zero bound binds.

Eggertsson and Woodford (2003) analyze thisissue in a model that is equivalent to a specialcase of the model considered here. Let us againconsider the special case (mentioned in Section3.1) in which there are no steady-state distortions,no resources are used in financial intermediation,and the fraction of bad loans is independent ofthe scale of lending. Because in this case both thecredit spread and the marginal-utility gap evolveexogenously, a second-order Taylor series approxi-mation to the objective function (14), expandingaround the optimal (zero-inflation) steady state,is exactly the same quadratic function of inflationand the output gap as in the case of a representa-tive-household model (the case considered byEggertsson and Woodford). The “intertemporal ISrelation” (3) and the aggregate-supply relation (6)are also identical to those of the representative-household model, except for the presence ofadditional additive disturbance terms involvingωt and Ωt .

The optimal policy problem—which can bestated as the choice of processes for inflation,output, and the policy rate consistent with (3),(6), and (13) each period to maximize the welfaremeasure written in terms of output and infla-tion—is of the same form as the one analyzed byEggertsson and Woodford (2003), except withadditional possible interpretations of the exoge-nous disturbance terms. In particular, the exten-sion of the model to incorporate credit frictionsprovides a more empirically realistic interpretationof the disturbance hypothesized by Eggertsson andWoodford (2003), which makes the real policy



rate needed to maintain a constant zero outputgap temporarily negative. Rather than postulatea sudden, temporary disappearance of real spend-ing opportunities or a temporary reduction in therate of time preference, we can instead attributethe situation to a temporary increase in creditspreads as a result of disruption of the financialsector.

Eggertsson and Woodford (2003) show that itcan be a serious mistake for a central bank to beexpected to return immediately to the pursuit ofits normal policy target as soon as the zero boundno longer prevents it from hitting that target. Forexample, Figure 11 (reproduced from their paper)compares the dynamic paths of the policy rate,the inflation rate, and aggregate output under two



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Equilibrium Responses of the Policy Rate, Inflation, and the Output Gap, Under Two AlternativeMonetary Policies

NOTE: The figure represents equilibrium responses when the expected probability of loan default exogenously increases beginningin quarter zero and ending in quarter 15.

SOURCE: Eggertsson and Woodford (2003).

alternative monetary policies in the case of a realdisturbance (here interpreted as an exogenousincrease in the probability that loans are bad,requiring intermediaries to increase the creditspread by several percentage points) that beginsin period zero and lasts for 15 quarters, beforereal fundamentals permanently return to theiroriginal (“normal”) state.

In this case, if the financial disturbance werenever to occur, optimal policy would involvemaintaining a zero inflation rate, as this wouldalso imply a zero output gap in every period. Afterthe disturbance dissipates, one of the feasible poli-cies is an immediate return to this zero-inflationsteady state (under the parameterization assumedin the figure, this involves a nominal interest rateof 4 percent), and this is optimal from the pointof view of welfare in all periods after the financialdisturbance dissipates. It is not, however, possibleto maintain the zero-inflation steady state at alltimes, because during the financial disturbancethis would require the policy rate to equal –2 per-cent, which would violate the zero lower bound.

One of the policies considered in Figure 10(dashed lines) is strict (forward-looking) inflationtargeting: The central bank uses interest rate pol-icy to maintain a zero inflation rate whenever itis not prevented by the zero lower bound on thepolicy rate. When undershooting the inflationtarget cannot be avoided, the policy rate is main-tained at the lower bound. The other policy (solidlines) is the optimal Ramsey policy, when the zerolower bound is included among the constraintson the set of possible equilibria. The forward-looking inflation-targeting policy is clearly muchworse, as it involves both a much more severeoutput contraction and much more severe defla-tion during the period when the zero bound con-strains policy.

The problem with the forward-looking infla-tion-targeting policy is that because the centralbank simply targets zero inflation from the timethat it again becomes possible to do so, all of thedeflation that occurs while the zero bound bindsis fully accommodated by the subsequent policy:The central bank continues to maintain the pricelevel at whatever level it has fallen to. This resultsin expected deflation during the entire period of

the financial disturbance, for deflation will con-tinue as long as the financial disruption continues,while no inflation will be allowed even if thedisturbance dissipates; this expected deflationmakes the zero bound on nominal interest ratesa higher lower bound on the real policy rate, mak-ing the contraction and deflation worse, givingpeople reason to expect more deflation as long asthe disruption continues, and so on in a viciouscircle.

The outcome would be even worse if thecentral bank were to seek to achieve the targetcriterion (18) each period as soon as it becomespossible to do so. This is because, once creditspreads contract again, this policy would requirethe central bank to target negative inflation and/ora negative output gap (even though zero inflationand a zero output gap would now be achievable),simply because there had been a large negativeoutput gap in the recent past (when the zerobound was a binding constraint); but the expec-tation of such policy would make the output con-traction while the zero bound constrained policyeven more severe (justifying even tighter policyimmediately following the “exit” from the “liquid-ity trap,” and so on).

Under the optimal policy, there is instead acommitment to maintain accommodative condi-tions for a brief interval, even though the reduc-tion in credit spreads means that this level for thepolicy rate is now expansionary, leading to a mildboom and temporary inflation above the long-runtarget level (of zero). The expectation that thiswill occur during the “exit” from the trap resultsin much less contraction of economic activityand much less deflation, because it makes theperceived real rate of interest lower at all timeswhile the policy rate is at zero (given that thereis in each period some probability that creditspreads will shrink again in the next period, allow-ing mild inflation to occur). This expectationresults in less deflation and higher real activitywhile the lower bound binds; and the expectationthat continuation of the financial stress will haveless drastic consequences is itself a substantialfactor in making those consequences much lessdrastic—in a “virtuous circle” that exactly reversesthe logic of our analysis above.



While our analysis implies that it is desirablefor people to be able to expect that the “exit” fromthe trap will involve mild inflation, it does notfollow that the possibility of occasionally hittingthe zero lower bound on the policy rate is a rea-son to aim for a substantial positive rate of infla-tion at all times (as proposed by Summers, 1991)simply to ensure that a zero nominal interest ratewill always mean a sufficiently negative value ofthe real policy rate. To the extent that a history-dependent inflation target of the kind called forin Eggertsson and Woodford (2003) can be madecredible and understood by the public, it sufficesthat the central bank be committed to bringingabout a temporarily higher rate of inflation onlyon the particular occasions when the zero lowerbound has bound in the recent past, and not allof the time.30

This analysis implies that a commitment tomaintain policy accommodation can play animportant role in mitigating the effects of the zerolower bound on interest rates. One might reason-ably ask for what length of time it is sensible tocommit to keep rates low, and in particularwhether it is really prudent to make any lengthycommitment when it is hard for a central bank tobe certain that recovery may not come muchsooner than anticipated. The answer is that thebest way to formulate such a commitment is notin terms of a period of time that can be identifiedwith certainty in advance, but rather in terms oftargets that must be met for the removal of policyaccommodation to be appropriate.

In fact, Eggertsson and Woodford (2003) showthat in the representative-household model (andhence similarly in the special case describedabove), optimal policy can be precisely described,regardless of the nature of the exogenous distur-bances,31 by a target criterion involving onlythe path of the output gap–adjusted price level

defined in (18). Under the optimal rule, the centralbank has a target each period for pt that dependsonly on the economy’s history through period t–1and must use interest rate policy to achieve thetarget, if this is possible without violation of thezero lower bound; if the target is undershot evenwith a zero policy rate, the policy rate is at anyrate reduced to zero—and the target for pt–1 isincreased in proportion to the degree of under-shooting. In periods when the zero bound doesnot bind, the target for the gap-adjusted price levelis not adjusted, and the target criterion is the sameas the one discussed in Section 3.1.

Actually, the adjustments of the target are notof great importance, even when the zero bounddoes bind: Eggertsson and Woodford (2003) showthat almost all of the improvement in stabilizationachievable under the optimal policy commitmentcan be obtained by simply committing to a targetcriterion of the form in (19) with a constant targetp*. The crucial feature of the optimal policy isthat the target for ptmust not be allowed to fallas a result of having undershot the target in pastperiods. Hence one of the approximate character-izations of optimal policy proposed in Section 3.1continues to provide a good approximation tooptimal policy even when the zero lower boundsometimes binds: It is simply important that thecommitment be to the level form of the target cri-terion (19) rather than to the growth rate form (18).

4. OPTIMAL POLICY: CREDITPOLICY

We turn now to the final of our three inde-pendent dimensions of central bank policy,namely, adjustment of the composition of the assetside of the central bank’s balance sheet, taking asgiven the overall size of the balance sheet (deter-



30 Eggertsson and Woodford (2003) compare the welfare levels associ-ated with alternative constant inflation targets and find that theexistence of an occasionally binding zero lower bound does indeedmake the optimal inflation target higher than it would otherwisebe, if one must choose from among this very restrictive class of poli-cies. But they show that even the best policy in that class involvesmuch larger average distortions than a price-level targeting policy,even though a price-level targeting policy implies a long-run averageinflation rate of zero.

31 Their analysis allows for both exogenous variations in the “naturalrate of interest” (which means an additive exogenous term in theintertemporal IS relation) and in the “cost-push” term (which meansan additive exogenous term in the Phillips-curve tradeoff), evolv-ing according to arbitrary stochastic processes. Since the effectsof the financial frictions in (3) and (6) are to add additional termsinvolving Ωt that can be viewed as a combination of these two typesof shifts, the optimal target criterion derived by Eggertsson andWoodford (2003) continues to apply—under the special assump-tions stated above—even in the presence of time-varying creditfrictions.

mined by the reserve-supply decision discussedin Section 2). According to the traditional doctrineof “Treasuries only,” the central bank should notvary the composition of its balance sheet as apolicy tool. Instead, it should avoid both balance-sheet risk and the danger of politicization by hold-ing only (essentially riskless) Treasury securitiesat all times, while varying the size of its balancesheet to achieve its stabilization goals for theaggregate economy.32

Apart from these prudential concerns, if pri-vate financial markets can be relied on to allocatecapital efficiently, it is hard to argue that therewould be any substantial value to allowing thecentral bank this additional dimension of policy.Eggertsson and Woodford (2003) present a formalirrelevance proposition in the context of a repre-sentative-household general-equilibrium model.In their model, the assets purchased by the centralbank have no consequences for the equilibriumevolution of output, inflation, or asset prices—and this is true regardless of whether the centralbank purchases long-term or short-term assets,nominal or real assets, riskless or risky assets, andso on. In addition, even in a model with hetero-geneity of the kind considered here, the compo-sition of the central bank’s balance sheet wouldbe irrelevant if we were to assume frictionlessprivate financial intermediation, since privateintermediaries would be willing to adjust theirportfolios to perfectly offset any changes in theportfolio of the central bank.

This irrelevance result does not hold, how-ever, in the presence of credit frictions of the kindassumed in Section 1; so we can also considerthe optimal use of this additional dimension ofpolicy if we are willing to suppose that the pru-dential arguments against the central bank’sinvolvement in the allocation of credit shouldnot be determinative, at least in the case of suffi-ciently severe financial disruptions. In our model,an increase in Lt

cb can improve welfare on twogrounds: For a given volume of private borrowing,bt an increase in Lt

cb allows the volume of privatelending, Lt, to fall, which should reduce both the

resources Ξtp consumed by the intermediary sector

and the equilibrium credit spread, ωt (due toequilibrium (7)). Under plausible conditions, ourmodel implies both a positive shadow value ϕΞ,tof reductions in Ξt (the Lagrange multiplier associ-ated with the resource constraint (2)) and a posi-tive shadow value ϕω,t of reductions in ωt (theLagrange multiplier associated with the constraint(4)); hence an increase in Lt

cb should be desirableon both grounds.

In the absence of any assumed cost of centralbank credit policy, one can easily obtain the resultthat it is always optimal for the central bank tolend an amount sufficient to allow an equilib-rium with Lt = 0; that is, the central bank shouldsubstitute for private credit markets altogether.Of course, we do not regard this as a realisticconclusion. As a simple way of introducing intoour calculations the fact that the central bank isunlikely to have a comparative advantage at theactivity of credit allocation under normal circum-stances, we assume that central bank lending con-sumes real resources in a quantity ΞcbLtcb, byanalogy with our assumption that real resources,Ξ tp, are consumed by private intermediaries. The

function ΞcbL is assumed to be increasing andat least weakly convex; in particular, we assumethat Ξcb′0 > 0 so that there is a positive marginalresource cost of this activity, even when the cen-tral bank starts from a balance sheet made upentirely of Treasury securities.

4.1 When Is Active Credit Policy Justified?

The first-order conditions for optimal choiceof Lt

cb then become

(20)

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32 See Goodfriend (2009) for a discussion of this view and a warningabout the dangers of departing from it.



ing constant the value of total borrowing, bt; thesecond expression in square brackets is the par-tial derivative of ωtwith respect to Lt

cb under thesame assumption.)

A “Treasuries only” policy is optimal in theevent of a corner solution, in which (20) is aninequality, as will be the case if Ξcb′0 is largeenough. In our view, it is probably most reason-able to calibrate the model so that this is true insteady state. Then not only will the optimal pol-icy involve “Treasuries only” in the steady state,but (assuming that the inequality is strict at thesteady state) this will continue to be true in thecase of any stochastic disturbances that are smallenough. However, it will remain possible for theoptimal policy to require Lt

cb > 0 in the case ofcertain large-enough disturbances. This is espe-cially likely to be true in the case of large-enoughdisruptions of the financial sector of a type thatincrease the marginal resource cost of private inter-mediation (the value of Ξ–p′ ) and/or the degree towhich increases in private credit require a largercredit spread (the value of ω–′).

However, not all “purely financial” distur-bances—by which we mean exogenous shifts inthe functions Ξ–t

pL or χtL of a type that increasethe equilibrium credit spread ω–tL for a givenvolume of private credit—are equally likely tojustify an active central bank credit policy on thegrounds just mentioned.33 To illustrate this, let usconsider four different possible purely financialdisturbances, each of which will be assumed toincrease the value of ω–tL

– by the same numberof percentage points. Here, by an additive shock,we mean one that translates the schedule ω–tLvertically by a constant amount; a multiplicativeshock will instead multiply the entire scheduleω–tL by some constant factor greater than 1. Weshall also distinguish between disturbances thatchange the function Ξ–tL (“Ξ shocks”) and distur-bances that change the function χtL (“χ shocks”).Thus a “multiplicative χ shock” is a change in the

function χtL; as a consequence, of which theschedule ω–tL is multiplied by a factor greaterthan 1 for all values of L, and so on.

With the model calibrated as in the numericalexercises in Figures 7 through 10, Figure 12 plotsthe dynamic response of the sum of the three posi-tive terms on the left-hand side of (20) to each ofthese four types of purely financial disturbances.In these simulations, both interest rate policy andreserve-supply policy are assumed to be optimal,as discussed in Sections 2 and 3. We assume ineach case that there is no central bank lending tothe private sector in the equilibrium being com-puted, but we ask (in the equilibrium computedunder this assumption) what the smallest valueof Ξcb′0 is at each point in time, for which thiswould be consistent with the first-order condition(21). (Thus an increase in the quantity plottedmeans that the marginal benefit of central bankcredit policy is increased, even if in our calcula-tions no central bank lending actually occurs.)We divide the sum of the three terms by the valueof ϕΞ,t, so that the quantity plotted is preciselythe threshold value of Ξcb′0, expressed in termsof an interest rate spread. (Since it is an interestrate spread, we multiply by 4 so that the quantityon the vertical axis of the figure is in units of per-centage points per annum.) In the figure, each ofthe four disturbances is of a size that increases thevalue of ω–tL

– by 4 percentage points per annum(i.e., from 2.0 percent to 6.0 percent).

In the absence of any disturbances, the steady-state value of this quantity is a little less than 3.5percentage points per annum. This means that amarginal resource cost of central bank loan origi-nation of 3.5 percent or higher will suffice to jus-tify our proposal above—that in the steady statethe optimal quantity of central bank credit iszero.34 Let us suppose that Ξcb′0 is equal to 4.0percent. Then in the absence of shocks, a cornersolution with Treasuries only is optimal. How -ever, either a “multiplicative Ξ shock” or an“additive Ξ shock” of the size assumed would



33 Our result here is quite different from that in Section 3, where theconsequence of a “purely financial” disturbance for optimal interestrate policy, taking as given the path of central bank lending to theprivate sector, depends (to a first approximation) only on the size ofthe shift in ω–tL

–, which is why we do not bother to show the opti-mal responses to more than one type of purely financial disturbance.

34 Note that this quantity is well above the marginal resource cost ofprivate lending in the steady state, which we have calibrated at2.0 percent per annum because our baseline calibration implies arelatively inelastic private supply of credit: ω–tL is steeply increas-ing with L.

cause condition (21) to be violated in the case ofa corner solution; hence optimal policy wouldrequire a positive quantity of central bank lend-ing. (In the case of the “multiplicative Ξ shock,”this would be true even if Ξcb′0 were equal to5.0 percentage points.)

On the other hand, even in the case of the“multiplicative Ξ shock,” the threshold requiredto justify a corner solution is only above 4 percentin the quarter of the shock and the quarter imme-diately following it—despite the fact that in ournumerical experiment the disturbance is assumedto have an autocorrelation coefficient of 0.9, sothat the shift in the ω–tL schedule is still 65 per-cent of its initial magnitude a year later. This sug-gests that, even in the case of those disturbancesfor which the welfare benefits of central bank

credit policy are greatest, departure from the cor-ner solution is likely to be justified only for a rel-atively brief period of time.

4.2 An Example with Active Credit Policy

As an example of how optimal credit policycan, under some circumstances, substantiallyalter the economy’s response to a financial dis-ruption, Figure 13 considers the optimal responseto a “multiplicative Ξ shock,” under a calibrationin which Ξcb′0 is assumed to be low enough sothat even in the steady state a corner solution isnot optimal.35 (While this is not the case that weregard as most realistic, it simplifies the calcula-



4 8 12 16 20

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Additive χ

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Figure 12

Response of the Critical Threshold Value of Ξcb′(0) for a Corner Solution, Under Four “PurelyFinancial” Disturbances

NOTE: For each disturbance, ω–t(L–) increases by 4 percentage points.

35 This alternative calibration is chosen to imply that in the steadystate, only 5 percent of total credit, bt, is supplied by the central bank.

tions reported in Figure 13, since it implies thatconstraint (21) never binds. We leave for futurework analysis of the more interesting case, inwhich (21) binds in some periods and not inothers.) The figure plots the impulse responsesunder two alternative assumptions about policy:With credit, central bank policy is optimal alongall three dimensions (and Lt

cb varies over time);with no credit, Lt

cb is constrained to equal thesteady-state value L

–cb at all times,36 while interest-rate policy and reserve-supply policy are optimal.

In addition to the responses of the five vari-ables plotted in Figures 7 through 10, Figure 13also plots the response of an additional variable,Lˆtcb, indicating the deviation of central bank

credit from its steady-state value, expressed as afraction of total steady-state credit, b

–(in percent-

age points).Under an optimal use of credit policy, central

bank lending to the private-sector increases sub-stantially in response to the financial disturbance(central bank lending increases from 5 percent oftotal credit to a little over 9 percent). As a result,the large increase in the credit spread that wouldotherwise occur as a result of the shock is essen-



−0.4

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Figure 13

Impulse Responses to a Shift in Ξ– t(L) that Triples the Size of ω–t(L) for Each Value of L, UnderOptimal Interest Rate Policy and Two Alternative Assumptions About Credit Policy

36 We impose the constraint that Ltcbmust equal L–cb, rather than zero,

in the no-credit case, so that the steady state is the same underboth policies.

tially prevented from occurring (so that the creditspread remains close to its steady-state level of2.0 percent per annum). As a further consequence,it is not necessary under this policy to cut thepolicy rate sharply, as would otherwise berequired by an optimal interest rate policy. Thesubstantial contraction of credit that would oth-erwise occur (an eventual contraction of aggre-gate credit by more than 2 percent a year afterthe shock) is largely avoided, and the modesteffects on output and inflation that would occureven under an optimal interest rate policy in theabsence of an active credit policy are also largelyavoided.

This example indicates that, under at leastsome circumstances, our model would supporta fairly aggressive use of active credit policy forstabilization purposes. We must caution, how-ever, that these results are quite dependent uponassumptions about the nature of the financial dis-turbance. It is equally possible to conclude thatcentral bank credit should be contracted (assum-ing that it would be positive to begin with) inresponse to a disturbance that increases creditspreads. If the only form of purely financial dis-turbance is an “additive χ disturbance,” and weassume that ΞcbLcb is a linear function, then noneof the functions Ξ–p′L, Ξ–p′′L, or χ ′L is timevarying and Ξcb′ is a constant. In this case, therequirement that (20) hold with equality deter-mines the volume of private credit, Lt, as a time-invariant function of ϕω,t/ϕΞ,t. In the case of adisturbance that increases the credit spread, theresulting decline in credit demand, bt, means that,for credit supply Lt to be stabilized, Lt

cb wouldhave to contract; so unless ϕω,t/ϕΞ,t changes tosuch an extent that the value of Lt consistent with(20) falls as much as bt does,37 it is optimal forLtcb to contract (as Figure 12 would also suggest).In a case of this kind, active credit policy wouldactually cause credit to contract by more (andcredit spreads to increase by more) than theywould if the supply of central bank credit didnot respond to the shock.

4.3 Segmented Credit Markets

In the simple model expounded above, thereis a single credit market and single borrowingrate, it

b, charged for loans in this market. Our dis-cussion of central bank credit policy has corre-spondingly simply referred to the optimal quantityof central bank lending to the private sector over-all, as if the allocation of this credit is not an issue.In reality, of course, there are many distinct creditmarkets and many different parties to which thecentral bank might consider lending. Moreover,since there is only a potential case to be made forcentral bank credit policy when private financialmarkets are severely impaired, it does not makesense to assume efficient allocation of credit amongdifferent classes of borrowers by the private sector,so that only the total credit extended by the centralbank would matter. Our simple discussion herehas sought merely to clarify the connection thatexists, in principle, between decisions about creditpolicy and the other dimensions of credit policy.An analysis of credit policy that could actually beused as a basis for credit policy decisions wouldinstead need to allow for multiple credit markets,with imperfect arbitrage between them.

We do not here attempt an extension of ourmodel in that direction. (A simple extensionwould be to allow for multiple types of “type b”households, each only able to borrow in a partic-ular market with its own borrowing rate andmarket-specific frictions for the intermediarieslending in each of these markets.) We shall simplynote that in such an extension there would be adistinct first-order condition, analogous to con-ditions (20) and (21), for each of the segmentedcredit markets. There would be no reason toassume that the question of whether active creditpolicy is justified should have a single answer ata given point in time: Lending might be justifiedin one or two specific markets while the cornersolution remained optimal in the other markets.

The conditions that should be appealed to inorder to justify central bank lending are moremicroeconomic than macroeconomic: They relateto the severity of the distortions that have arisenin particular markets and to the costs of interven-tion in those particular markets, rather than to

37 Our numerical experiments indicate that this can easily fail to bethe case.



aggregate conditions. Thus the main determinantsof whether central bank credit policy is justified—when it is justifiable to initiate active policy andwhen it would be correct to phase out such pro-grams—should not be questions such as whetherthe zero lower bound on interest rate policy bindsor whether the central bank continues to under-shoot the level of real GDP that it would like toattain. While aggregate conditions will be onefactor that affects the shadow value of marginalreductions in the size of credit spreads (repre-sented by the multiplier ϕω,t in (20)), the value ofthis multiplier will likely be different for differentmarkets and the main determinants of variationsin it are likely to be market specific. This willapply even more to the other variables that enterinto the first-order condition (20).

Hence it would be a mistake to think of creditpolicy as a substitute for interest rate policy, analternative tool that can be used to achieve thesame goals and that should be used to achieve thecentral bank’s target criterion for inflation andthe output gap when interest rate policy alone isunable to. Such a concept would be dangerous fortwo reasons. On the one hand, it would directattention away from the most relevant costs andbenefits when thinking about the appropriatescale, timing, and allocation of active credit policy.And on the other hand, it could also allow thecentral bank to avoid recognition of the extent towhich the correct target criterion for interest ratepolicy needs to be modified as a result of the zerolower bound—in particular, to avoid the challengeof shaping expectations about interest rate policyafter the lower bound ceases to bind, on theground that credit policy (or “quantitative easing”)should allow the bank’s usual target criterion tobe achieved continuously, without any need forsignaling about unconventional future interestrate policy as compensation for past target misses.

CONCLUSIONSWe have shown that a canonical New

Keynesian model of the monetary transmissionmechanism can be extended in a fairly simpleway to allow analysis of additional dimensions

of central bank policy that have been at centerstage during the recent global financial crisis—variations in the size and composition of thecentral bank balance sheet and in the interestrate paid on reserves—alongside the traditionalmonetary policy issue of the choice of an operatingtarget for the federal funds rate (or some similarovernight inter-bank rate elsewhere). We have alsoconsidered the consequences for monetary policyanalysis both of nonzero credit spreads all of thetime and of financial disruptions that greatlyincrease the size of those spreads for a period oftime; we have also considered the consequencesof the fact the zero lower bound for short-termnominal interest rates is sometimes a bindingconstraint on interest rate policy.

One of our most important conclusions is thatthese issues can be addressed in a framework thatrepresents a straightforward extension of the kindof model often used for monetary policy analysisin the past. This allows both the considerationsemphasized in the traditional literature and themore novel considerations brought to the fore byrecent events to be taken into account, within asingle coherent framework. This integration isparticularly important, in our view, for clear think-ing about the way in which the transition fromthe current emergency policy regime to a morecustomary policy framework should be handledas financial conditions normalize. Because of theimportance of expectations regarding future policyin determining market outcomes now, we believethat clarity about “exit strategy” is important forthe success of policy even during periods ofsevere disruption of financial markets.

Another important implication of our modelis that interest rate policy should continue to bea central focus of monetary policy deliberations,despite the existence of the other dimensions ofpolicy discussed here, and despite the existenceof time-varying credit frictions that complicatethe relationship between the central bank’s policyrate and financial conditions more broadly. Whilewelfare can also be affected by reserve-supplypolicy, we argue that this dimension of policyshould be determined by a simple principle thatdoes not require any discretionary adjustmentsin light of changing economic conditions: Inter -



mediaries should be satiated in reserves at alltimes, by maintaining an interest rate on reservesat or close to the current target for the policy rate.

And while welfare can similarly be affectedby central bank credit policy, to the extent thatnontrivial credit frictions exist, we nonethelessbelieve that under normal circumstances a cornersolution (“Treasuries only”) is likely to representthe optimal composition of the central bank bal-ance sheet. Decisions about active credit policythen will be necessary only under relativelyunusual circumstances, and it will be desirableto phase out special credit programs relativelyrapidly after the disturbances that have justifiedtheir introduction. We thus do not anticipate thatit should be necessary to routinely make state-contingent adjustments of central bank policyalong multiple dimensions, even if recent eventssuggest that it is desirable for central banks to havethe power to act along additional dimensionsunder sufficiently exigent circumstances.

Finally, our results suggest that the traditionalemphasis in interest rate policy deliberations onthe consequences of monetary policy for the pro-jected evolution of inflation and aggregate realactivity is not mistaken, even taking into accountthe consequences for the monetary transmissionmechanism of time-varying credit frictions. Atleast in the context of the simple model of creditfrictions proposed here, optimal interest ratepolicy can be characterized to a reasonable degreeof approximation by a target criterion that involves

the paths of inflation and of an appropriatelydefined output gap, but no other endogenoustarget variables. This does not mean that centralbanks should remain indifferent toward changesin financial conditions; to the contrary, creditspreads (and perhaps other measures of financialmarket distortions as well) should be closelymonitored and taken into account in judging theforward path of interest rate policy necessary forconformity with the target criterion. However,financial variables need not be taken themselvesas targets of monetary policy.

The main respect in which the appropriatetarget criterion for interest rate policy should bemodified to take account of the possibility of finan-cial disruptions is by aiming at a target path forthe price level (ideally, for an output gap–adjustedprice level), rather than for a target rate of inflationlooking forward, as a forward-looking inflationtarget accommodates a permanent decline in theprice level after a period of one-sided target missesdue to a binding zero lower bound on interestrates. Our analysis implies that a credible com-mitment to the right kind of “exit strategy” shouldsubstantially improve the ability of monetarypolicy to deal with the unusual challenges posedby a binding zero lower bound during a deep finan-cial crisis; and, to the extent that this is true, thedevelopment of an integrated framework for policydeliberations, suitable both for crisis periods andfor more normal times, is a matter of considerableurgency for the world’s central banks.



REFERENCESAuerbach, Alan J. and Obstfeld, Maurice. “The Case for Open-Market Purchases in a Liquidity Trap.” AmericanEconomic Review, March 2005, 95(10), pp. 110-37.

Benigno, Pierpaolo and Woodford, Michael. “Inflation Stabilization and Welfare: The Case of a Distorted SteadyState.” Journal of the European Economic Association, December 2005, 3(6), pp. 1185-236.

Bernanke, Ben S. “The Crisis and the Policy Response.” Stamp Lecture, London School of Economics, January 13,2009; www.federalreserve.gov/newsevents/speech/bernanke20090113a.htm.

Christiano, Lawrence J.; Motto, Roberto and Rostagno, Massimo. “Financial Factors in Business Cycles.”Unpublished manuscript, Northwestern University, November 2007.

Clarida, Richard H.; Gali, Jordi and Gertler, Mark. “The Science of Monetary Policy: A New Keynesian Perspective.”Journal of Economic Literature, December 1999, 37(4), pp. 1661-707.

Cúrdia, Vasco and Woodford, Michael. “Credit Frictions and Optimal Monetary Policy.” Unpublished manuscript,Federal Reserve Bank of New York, July 2009a.

Cúrdia, Vasco and Woodford, Michael. “Credit Spreads and Monetary Policy.” NBER Working Paper 15289,National Bureau of Economic Research, August 2009b; www.nber.org/papers/w15289.pdf.

Cúrdia, Vasco and Woodford, Michael. “The Central-Bank Balance Sheet as an Instrument of Monetary Policy.”Unpublished manuscript, Federal Reserve Bank of New York, April 2010.

Eggertsson, Gauti B. and Woodford, Michael. “The Zero Bound on Interest Rates and Optimal Monetary Policy.”Brookings Papers on Economic Activity, 2003, 1(34), pp. 139-211.

Faia, Ester and Monacelli,Tommaso. “Optimal Interest Rate Rules, Asset Prices, and Credit Frictions.” Journalof Economic Dynamics and Control, October 2007, 31(10), pp. 3228-54.

Friedman, Milton. “The Optimum Quantity of Money,” in Milton Friedman, ed., The Optimum Quantity ofMoney and Other Essays. Chicago: Aldine, 1969, pp. 1-50.

Gerali, Andrea; Neri, Stefano; Sessa, Luca and Signoretti, Federico M. “Credit and Banking in a DSGE Model.”Unpublished manuscript, Bank of Italy, June 2008.

Gertler, Mark and Karadi, Peter. “A Model of Unconventional Monetary Policy.” Unpublished manuscript,New York University, April 2009.

Goodfriend, Marvin. “Interest on Reserves and Monetary Policy.” Federal Reserve Bank of New York EconomicPolicy Review, May 2002, 8(1), pp. 77-84; www.newyorkfed.org/research/epr/02v08n1/0205good.pdf.

Goodfriend, Marvin, “Central Banking in the Credit Turmoil: An Assessment of Federal Reserve Practice.”Unpublished manuscript, Carnegie-Mellon University, May 2009.

Goodfriend, Marvin and King, Robert G. “The New Neoclassical Synthesis and the Role of Monetary Policy,”in B. Bernanke and J. Rotemberg, eds., NBER Macroeconomics Annual 1997. Volume 12. Cambridge, MA:MIT Press, 1997, pp. 231-96.

Greenspan, Alan. “Performance of the U.S. Economy.” Testimony before the Committee on the Budget, U.S.Senate, January 21, 1997.

Hall, Robert E. “Monetary Strategy with an Elastic Price Standard,” in Price Stability and Public Policy.Federal Reserve Bank of Kansas City, 1984; www.kansascityfed.org/publicat/sympos/1984/S84HALL.PDF.

Mehra, Rajnish; Piguillem, Facundo and Prescott, Edward C. “Intermediated Quantities and Returns.” ResearchDepartment Staff Report 405, Federal Reserve Bank of Minneapolis, August 2008 version; www.minneapolisfed.org/publications_papers/pub_display.cfm?id=1115.



Mishkin, Frederic S. “Monetary Policy Flexibility, Risk Management and Financial Disruptions.” Speech at theFederal Reserve Bank of New York, January 11, 2008;www.federalreserve.gov/newsevents/speech/mishkin20080111a.htm.

Reis, Ricardo. “Interpreting the Unconventional U.S. Monetary Policy of 2007-09.” Unpublished Manuscript,Columbia University, August 2009.

Rotemberg, Julio J. and Woodford, Michael. “An Optimization-Based Econometric Framework for the Evaluationof Monetary Policy,” in B. Bernanke and J. Rotemberg, eds., NBER Macroeconomics Annual 1997. Volume 12.Cambridge, MA: MIT Press, 1997, pp. 297-346.

Summers, Lawrence. “How Should Long-Term Monetary Policy Be Determined? ” Journal of Money, Credit, andBanking, August 1991, 23(3 Part 2), pp. 625-31.

Svensson, Lars E.O. “Inflation Forecast Targeting: Implementing and Monitoring Inflation Targeting.” EuropeanEconomic Review, June 1997, 41(6), pp. 1111-46.

Svensson, Lars E.O. “Monetary Policy with Judgment: Forecast Targeting.” International Journal of CentralBanking, May 2005, 1(1), pp. 1-54.

Svensson, Lars E.O. and Woodford, Michael. “Implementing Optimal Policy through Inflation-Forecast Targeting,”in B.S. Bernanke and M. Woodford, eds., The Inflation Targeting Debate. Chicago: University of Chicago Press,2005, pp. 19-92.

Taylor, John B. “Discretion versus Policy Rules in Practice.” Carnegie-Rochester Conference Series on PublicPolicy, December 1993, 39(1), pp. 195-214.

Taylor, John B. “Monetary Policy and the State of the Economy.” Testimony before the Committee on FinancialServices, U.S. House of Representatives, February 26, 2008.

van Rixtel, Adrian. “The Exit from Quantitative Easing (QE): The Japanese Experience.” Prepared for theSymposium on Building the Financial System of the 21st Century: An Agenda for Japan and the UnitedStates, Harvard Law School, October 2009.

Woodford, Michael. Interest and Prices: Foundations of a Theory of Monetary Policy. Princeton, NJ: PrincetonUniversity Press, 2003.

Woodford, Michael. “Forecast Targeting as a Monetary Policy Strategy: Policy Rules in Practice.” NBER WorkingPaper 13716, National Bureau of Economic Research, December 2007; http://www.nber.org/papers/w13716.pdf.

Woodford, Michael. “Optimal Monetary Stabilization Policy.” Unpublished manuscript, Columbia University,September 2009.



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