The crisis of 1998 and the role of the central bank

2 Economic Perspectives

The crisis of 1998 and the role of the central bank

David A. Marshall

David A. Marshall is a senior economist and economicadvisor at the Federal Reserve Bank of Chicago. Theauthor would like to thank Jim Moser, Eric Swanson,François Velde, and Ruilin Zhou for extensive discussionsand Darrin Halcomb and Genny Pham-Kantor for researchassistance.

Introduction and summary

A key mission of the U.S. Federal Reserve Systemis to safeguard the economy against systemic finan-cial crises. This concern with financial crises stemsfrom a long-held belief that they are associated withdeclines in economic activity. In the U.S., there isclear evidence that financial panics and recessionsare somehow related (Mishkin, 1991). In the case ofthe Great Depression, Bernanke (1983) argues thatthe disruption in financial intermediation transformeda severe downturn into a �protracted depression.�More recently, the Asian financial crisis in 1997 wasfollowed by sharp declines in economic activity.(Indonesia, Korea, Thailand, and Malaysia all expe-rienced two-quarter declines in gross domestic prod-uct [GDP] of over 12 percent.) This historical recordhas led to a pervasive belief that systemic crises inthe financial sector have consequences that are farmore than sectoral. Rather, they appear to affect theentire economy, perhaps through the unique roleplayed by financial intermediation.

The most recent financial crisis in the U.S. oc-curred in late summer and fall of 1998. On August17, the Russian government devalued the rouble, de-faulted on its rouble-denominated debt, and imposeda moratorium on payments to foreign creditors ofRussian financial institutions. Following these actions,asset values fell precipitously in all Group of Seven(G-7) countries, and there is evidence of widespreadwithdrawal of liquidity from financial markets. Par-ticularly dramatic was the near collapse and eleventh-hour recapitalization in late September of Long-TermCapital Management (LTCM), a large hedge fund.

From a U.S. perspective, these events might bedescribed as an �incipient� crisis, because there islittle evidence of damage to western economies. Ar-guably, this is because of the decisive action by theFederal Reserve in cutting the target federal funds

rate in three successive 25 basis-point moves. Thesecond of these moves, on October 15, was particu-larly noteworthy, since it occurred between regularlyscheduled meetings of the Federal Open MarketCommittee (FOMC). Intermeeting rate cuts of thistype are rare; the October 15 action was the first suchaction since April 1994. In the next section, I provideevidence that the end of this incipient crisis coincid-ed almost exactly with the October 15 rate cut. Inparticular, credit spreads abruptly narrowed on Octo-ber 16 (one day after the Federal Reserve move), andstock markets in all G-7 countries started to recover aweek to ten days prior to the October 15 move. (Thatstock markets anticipated the rate cut is no surprise.For at least a week prior to the move the financial pressreported rumors of a possible intermeeting rate cut.)

The way this incipient crisis ended is somewhatpuzzling. The crisis had a clear trigger: the Russiandefault and devaluation in mid-August. Western finan-cial institutions were directly affected by the defaultif they held Russian liabilities. Furthermore, theRussian default may have signaled higher defaultrisk for sovereign debt from other emerging or transi-tion economies. So it is not surprising that uncertaintygrew about institutions� solvency (with attendant in-creases in asset price volatility and credit spreads).What is puzzling is the way the crisis appears to haveabated with the Fed�s second rate cut. Why would theproblems (both direct and informational) associatedwith the Russian default be reduced by a mere 50basis-point cumulative cut in the overnight interest

3Federal Reserve Bank of Chicago

rate? If the crisis was associated with higher defaultrisk of emerging-economy debt, why would the Fed�srate cut have dramatically reduced this default risk?Similarly, if the crisis was associated with an increasedinformational asymmetry among financial institutions,why would the 50 basis-point cut in the federal fundsrate have reduced this asymmetry?

In this article, I argue that the crisis can be char-acterized as an episode of potential coordination fail-ure, triggered by�but ultimately distinct from�theevents in Russia. I propose a simple model of finan-cial crises as coordination failure. The model qualita-tively matches the following features typicallyassociated with financial crises:

1. Abrupt shifts between a state of adequate liquidi-ty provision and a state of aggregate illiquidity(the latter being a case where institutions withliquidity refuse to lend to those needing liquidity);

2. A �flight to quality,� whereby institutions withfunds to invest preferentially choose a low-risk,low-return asset;

3. Fear among lenders that credit quality amongpotential borrowers has deteriorated;

4. Real costs in economic output;

5. Sudden declines in asset values; and

6. A role for the central bank�s open market operationsin containing the crisis.

In particular, the model provides one potentialexplanation for why the Federal Reserve action onOctober 15, 1998, eliminated the danger of a full-blowncrisis. This model contributes to the growing literaturedeveloping formal models of financial crises and finan-cial fragility. Notable examples of these include Changand Velasco (1998), Louganoff and Schreft (1998),DenHaan, Ramey, and Watson (1999), and Chari andKehoe (1998, 2000).

Coordination failure can emerge in any economywhere the profitability of a given agent�s investmentdepends on the decisions of the other agents in theeconomy. In the model of this article, the possibilityof coordination failure arises from the essential func-tion of financial markets: to match potential users ofcapital (borrowers) with potential providers of capital(lenders) in an environment of asymmetric information.Borrowers and lenders match via a search procedure.In this model, multiple equilibria are possible. A high-coordination equilibrium can occur in which alllenders and all borrowers enter the match, maximiz-ing the expected output of the economy. However,there are times when a low-coordination equilibriumis possible in which all good quality (that is, highly

creditworthy) borrowers refrain from entering thematch. Knowing that only poor quality borrowers seekloans, potential lenders refuse to lend. I identify thislow-coordination equilibrium with a financial crisis.

In the model, the low-coordination equilibriumcannot exist if the risk-free real interest rate is suffi-ciently low. This suggests a potential role for the cen-tral bank. If monetary policy can affect real interestrates, the central bank can extinguish the low-coordi-nation equilibrium if it reduces the real interest ratesufficiently via an aggressive monetary expansion.That the Federal Reserve has the power to do so issuggested by the events of 1991�93. As I discuss in alater section, there is evidence that banks cut back onlending activity in the early 1990s. Following a shiftto a more expansionary monetary policy in mid-1991,in which the real federal funds rate fell from 2.5 per-cent to 0.5 percent, lending activity moved back tonormal levels.

Unlike the Federal Reserve action of 1991�93,the monetary expansion in fall 1998 was too small,and the consequent effect on real interest rates toomarginal, to have a substantial direct effect on lenderincentives. Rather, I interpret the intermeeting ratecut of October 15 as a signal that the Federal Reserve�spolicy rule had changed. Before the intermeeting move,market participants were uncertain whether the FederalReserve would compromise its focus on price stability(and the associated tight money policy) even in theface of severe financial market strains. I argue thatthe intermeeting move was interpreted by marketparticipants as signaling a shift to a state-contingentpolicy: focus on price stability unless a financial crisisbecomes imminent; temporarily abandon that focusif the threat of financial crisis becomes severe. In thisarticle, I formally model such a policy, and I showthat, in principle, such a policy can extinguish the low-coordination equilibrium. Furthermore, if this policyis credible, it never has to be implemented: The policyitself removes the possibility of coordination failure.That is, monetary expansion is an �off-equilibriumpath� that enforces the high-coordination equilibrium.

Below, I review the facts of the crisis of fall 1998,highlighting key features that I will seek to replicatein the theoretical model. Then, I describe the basiccoordination failure model. Finally, I show how thecentral bank can avert coordination failure by imple-menting an appropriate and credible state-contingentmonetary policy.

Brief review of the events of fall 1998

Here, I review the crisis and provide evidencefor the following assertions:


1. The crisis was associated with large declines inequity values, increased volatility in financialmarkets, widening credit spreads, and an increaseddemand for U.S. Treasury securities.

2. During the crisis, there was a reduction in availableliquidity, as institutions with loanable funds reducedthe volume of funds available to the market.

3. The crisis rapidly abated following the FederalReserve�s intermeeting cut in the federal fundsrate on October 15, 1998.

Financial markets showed evidence of potentialproblems starting around mid-July 1998. However,the onset of the crisis is usually associated with theRussian devaluation and default in August 1998. Thisdenouement was in large part forced by declininghard currency inflows over the preceding severalmonths as oil prices fell. On August 17, Russia de-faulted on its rouble-denominated public debt. Atthat time, this stock of debt represented $61 billion,17 percent of Russian GDP. At the same time, Russiadeclared a 90-day moratorium on all foreign obliga-tions of Russian financial institutions. Finally, the rou-ble exchange rate zone was substantially widened,amounting to a de facto devaluation of 25 percent.The exchange rate zone was completely abandonedten days later.1 As I discuss below, western financialmarkets reacted negatively to these developments. Inresponse, the FOMC cut the federal funds rate by 25basis points at its next regular meeting on September29. This move by the Federal Reserve did not calmthe financial markets.2 On October 15, in an unusualintermeeting move, the FOMC made an additional25 basis-point rate cut. Observers point to this inter-meeting move as marking the end of the crisis.

The data in figure 1 characterize more fully theimpact of these events on western financial markets.As shown in figure 1, panel A, the U.S. S&P 500 in-dex peaks in mid-July 1998, with a small local peakin mid-August 1998 (vertical dashed line) followingthe Russian default. Thereafter, there is a sharp de-cline in stock values, amounting to more than 18 per-cent over the three months from peak to trough. TheS&P 500 index bottomed out on October 8, one weekbefore the FOMC�s intermeeting rate cut on October15 (vertical solid line). The biggest close-to-closerise of this period was from October 14 to October15. It is no surprise that the market trough occurredone week before the Fed intermeeting action, sincethere was speculation prior to the Fed�s action that anintermeeting rate cut was likely.3 The behavior of thefederal funds futures market supports this interpreta-tion. Through October 7, futures prices implied an

expected federal funds rate through the end of Octoberof 5.22 percent to 5.24 percent, implying little proba-bility of a rate cut. On October 8, this expected federalfunds rate dropped to 5.18 percent, which is consistentwith a 50 percent probability of a quarter-point ratecut around mid-October.4

The behavior of stock indexes for the other sixcountries in the G-7 is roughly comparable to thatof the U.S. indexes. In all cases, the market peaks inmid-July, falls steeply, and starts to turn up about oneweek before the October 15 rate cut. The total marketdeclines over this three-month period were quite pro-nounced, ranging from 18 percent in Japan to over 28percent in Canada, Italy, and France.5

Figure 1, panel B displays the value of the Chi-cago Board Options Exchange (CBOE) volatility in-dex (a measure computed by the CBOE from impliedvolatility on a number of option contracts).6 Thesedata show that uncertainty (and associated risk) infinancial markets rose steeply in mid-August 1998.The date of the first pronounced jump was actuallyAugust 27, when the closing value of this index roseto 39.16 (compared with the previous day�s close of30.66). This date corresponds to the Russian govern-ment�s announcement that it was abandoning its trad-ing band for the rouble. In trading during August 27,the rouble fell 40 percent against the deutschemark.In addition, on that date Deutsche Bank lost its AAArating from Standard and Poor�s when it revealedthat it had unsecured Russian credit risk amountingto almost $750 million. For the next seven weeks thevolatility index stayed at a level that was unprece-dented, except for the period around the 1987 stockmarket crash. The index remained at or near 40 untilOctober 15 (the date of the intermeeting rate cut),7

when it fell to 35.95 (compared with the previousday�s close of 41.31). Within two trading days theindex had fallen to around 30, remaining between20 and 30 through the end of 1999.

Figure 1, panels C, D, and E display three U.S.credit spreads: the interbank spread (three-monthinterbank yield minus three-month T-bill yield), theshort-term credit spread (three-month commercialpaper yield minus three-month T-bill yield), and thelong-term credit spread (ten-year AAA corporate bondyield minus ten-year T-bond yield). These creditspreads confirm the inference from figure 1, panel Bthat there was an abrupt increase in perceived creditrisk from mid-August to mid-October. In particular,they show a pronounced spike starting in late Septem-ber 1998 (around the time of the LTCM rescue) andcontinuing until October 16, one day after the FOMC�sintermeeting rate cut. The peak in the long-term credit


spread during this period is the highest in the 1990s,and the peak in the other two credit spreads is onlyexceeded during this decade by that observed duringthe 1990�91 recession.8

There is evidence that the increase in perceivedcredit risk was associated with a substantial drying-up of liquidity. That is, institutions with loanable

funds became more reluctant to extend unsecuredloans. The Federal Reserve Board of Governors�Senior Loan Officers Survey in September9 revealeda marked increase over the August survey in thenumber of banks tightening loan standards and raisingloan rates. (See figure 2, panels A and B.) A principalreason reported by banks for these actions was �a

FIGURE 1

U.S. financial market indicators, March 1997�June 1999

A. S&P 500 indexindex

B. CBOE volatility indexindex

6/1/97 12/1/97 6/1/98 12/1/98 6/1/99

C. 3-month interbank spreadpercent

D. 3-month default spreadpercent

600

800

1,000

1,200

1,400

0

10

20

30

40

50

0

0.4

0.8

1.2

1.6

0

0.4

0.8

1.2

1.6

0.0

0.5

1.0

1.5

2.0

E. 10-year default spreadpercent

6/1/97 12/1/97 6/1/98 12/1/98 6/1/99

6/1/97 12/1/97 6/1/98 12/1/98 6/1/99 6/1/97 12/1/97 6/1/98 12/1/98 6/1/99

6/1/97 12/1/97 6/1/98 12/1/98 6/1/99

Notes: The vertical dashed lines indicate August 17, 1997, the date of the Russian default. The vertical solidlines indicate October 15, 1997, the date of the Federal Reserve’s intermeeting cut in the federal funds rate.Panels C, D, and E display three U.S. credit spreads: the interbank spread (panel C) is the three-monthinterbank yield minus three-month Treasury bill yield. The three-month default spread (panel D) is the three-month commercial paper yield minus three-month Treasury bill yield. The ten-year default spread is the ten-yearAAA corporate bond yield minus ten-year Treasury bond yield.Sources: Board of Governors of the Federal Reserve System (panels A, C, D, E); Chicago Board OptionsExchange (panel B).


reduced tolerance for risk.� Interestingly, there was asubstantial increase in the number of banks reportingdecreased loan demand. The respondents generallyattributed this reduced demand to reductions in bothmerger and acquisition activity and fixed investment.This suggests that the reduction in loan activity wasdue to both a reduced willingness of lenders to beardefault risk and a reduced interest of borrowers inexpanding economic activity. While reports of tight-ened loan standards continue through the Novembersurvey, the reduction in loan demand appears to havereversed by November.

The Bank for International Settlements (BIS, 1999)surveyed a number of market participants about theevents of fall 1998. The survey results confirm theperception that risk levels were elevated and liquidity

provision diminished in the period from mid-Augustthrough mid-October 1998. They point to an �unprec-edented� widening in bid/ask spreads and even to�one-sided markets,� where sellers of risky securitiescould not find a buyer at any price. On numerousoccasions, market makers in government securitiessimply withdrew from trading and refrained fromposting quotes.10 The BIS interviewees report a flightto the most liquid, �on-the-run� (that is, most recentlyissued) Treasury securities. For example, by earlyOctober, the yield spread between 28-year and 30-year Treasury bonds had widened to 29 basis pointsfrom just 7 basis points in mid-August (although the28-year issues are just as free from default risk as the30-year on-the-run bonds). Salomon Smith Barneyreported that this spread was the widest it had everrecorded.11 Continued ability to trade Treasury secu-rities in any desired quantity was assured only for theon-the-run issues. The flight to quality even devolved,�for a brutal but short-lived period�12 to a flight tocash. A number of participants reported reductions incredit lines to other financial institutions. This drying-up of liquidity exacerbated price volatility and in-creased credit risk associated with institutions thatrelied on market funding. Interestingly, the infusionof funds to LTCM, facilitated by the Federal ReserveBank of New York in late September 1998,13 seemedto exacerbate the liquidity crisis. Participants in theBIS survey interpreted the Federal Reserve�s role asa signal that the Federal Reserve believed that thecrisis was far worse than previously thought. Finally,the BIS interviewees perceived the October 15 ratecut as the turning point of the crisis. In its summaryof interviews with market participants, the BIS states,�The second monetary easing by the Federal Reserve(15 October) signaled the beginning of the abatementof financial strains. At that time, traders clearly under-stood the commitment of the Federal Reserve to fixthe problems.�

To summarize, the period from mid-August tomid-October 1998 was characterized by rapid declinesin stock values, rapid increases in uncertainty, and areluctance of institutions with loanable funds to pro-vide loans. The crisis appears to have abated in U.S.financial markets with the Fed�s intermeeting rate cutof October 15. In particular, the stock market recov-ery, the narrowing of credit spreads in fixed incomemarkets, and the decline in the CBOE volatility indexall commenced around October 15. Other more qualita-tive measures of the crisis, such as the Board of Gover-nor�s Senior Loan Officers Survey, the BIS interviewswith market participants, and reports in the financialpress, are also consistent with this interpretation.

FIGURE 2

Measures of credit market tightness

B. Net percentage of banks increasing spreadsof loan rates over cost of fundspercent

Large/mediumborrowers

Small borrowers

1/97

5/97

8/97

11/97

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5/98

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1/99

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8/99

11/99

Large/mediumborrowers

Small borrowers

-10

0

10

20

30

40

-50

-25

0

25

50

A. Net percentage of banks tighteningstandards for C&I loans

percent

Notes: This figure plots data from the Federal Reserve Board’sSenior Loan Officers Surveys from January 1997 through January2000. Responses to the January, March, August, and Novembersurveys report bank credit policies over the preceding threemonths. The September 1998 survey reports bank credit policiesover the preceding month only.Source: Board of Governors of the Federal Reserve System,Senior Loan Officers Survey.

1/97

5/97

8/97

11/97

1/98

5/98

8/98

9/98

11/98

1/99

5/99

8/99

1/00

11/99

1/00


What generated the crisis?It is perhaps no surprise that the Russian default

and devaluation triggered turmoil in western finan-cial markets. There was a good deal of uncertaintyabout the direct exposure of western financial institu-tions to the Russian default. Furthermore, westerninvestors may have interpreted the Russian default asevidence against the creditworthiness of other emerg-ing economies. Investors were particularly concernedabout Argentina, Brazil, and Mexico, which are farmore important than Russia for U.S. trade.14 (In fact,Brazil devalued its currency in mid-January 1999.)Figure 3, which plots Brady bond yields,15 shows howthe Russian default triggered an increase in perceivedcredit risk for these three Latin American countriesthat eclipsed the increase following the 1997 Asiancrisis. In all three countries, the yields more thandoubled following the Russian default in mid-August1998. (The yield spike for Brazil was particularlypronounced.) However, this explanation for the crisisdoes not fully account for the way it ended. It is hardto imagine that the exposure of western institutions toemerging and transitional economies or the informa-tional asymmetry about these exposures would havebeen reduced by a 50 basis-point reduction in the fed-eral funds rate. Similarly, the creditworthiness ofborrowers in these economies would not have beenaffected substantially by the Federal Reserve�s action.Thus, while the Russian default clearly triggered thefinancial crisis, the crisis appears to have taken on aself-fulfilling aspect over and above the damage attrib-utable to the actions of the Russian government.

Other financial crises have also involved suddenshifts between crisis and non-crisis states without acommensurate change in fundamentals. The Asiancrisis of 1997 provides an example, although in thatcase the sudden shift occurred at the beginning of thecrisis. The Asian crisis was completely unforeseen byfinancial markets. In particular, in none of the Asiancrisis countries do interest rates or forward exchangerates move prior to the speculative attacks leading tothe initial Thai devaluation.16 Furthermore, the Asiancrisis was not triggered by any shock to fundamentalscommensurate with the magnitude of the subsequentdebacle. While there were clear problems with marketfundamentals in these countries (in particular, thepoor state of their banking sectors), these problemswere well known months or even years prior to thecrisis.17 It appears that any theory of systemic financialcrisis must incorporate the possibility of sudden, un-triggered shifts between crisis and non-crisis states.

Modeling financial crisis ascoordination failure18

As described earlier, the financial crisis of fall1998 had a number of characteristics that have beenassociated with crises more generally. There was asudden shift between crisis and non-crisis states with-out a commensurate change in fundamentals. The crisisstate was characterized by a sharp reduction in liquidi-ty provision with a corresponding flight to quality.The crisis was associated with a decline in asset val-ues, as reflected in stock market indexes.19 In addi-tion, the crisis of 1998 shows clear evidence of an

increase in perceived default risk. Final-ly, the end of the 1998 crisis was associ-ated with an unusual action by the centralbank (a change in the target federal fundsrate between regularly scheduled FOMCmeetings).

In this section, I propose a simplemodel of financial crisis that, in principle,can accommodate these patterns. My ap-proach focuses on the possibility of coor-dination failure. In coordination models,an investor benefits if he chooses the samestrategy as other investors. Thus, investorswill tend to �coordinate� on a particularstrategy. A multiplicity of equilibria canemerge, each associated with a differentpattern of coordination. Suboptimal equi-libria are then associated with coordinationfailure: the failure to coordinate on thesocially optimal choices. In a familiarexample, known as external increasing

FIGURE 3

Brady bond yields for Argentina, Brazil, and Mexico(April 1997�January 2000)

0

10

20

30

40percent

Argentina Mexico

Brazil

7/1/97 1/1/98 7/1/98 1/1/99 7/1/99 1/1/00

Note: This figure plots yields from dollar-denominated sovereigndebt (“Brady bonds”) issued by Argentina, Brazil, and Mexico.Source: Bloomberg.


returns to scale, the productivity of a particular firm�scapital investment is high only if there is a high levelof aggregate economic activity. Therefore, a firm mayonly want to choose a high level of investment ifenough other firms also choose a high level of invest-ment (thereby assuring a high level of aggregate activ-ity). If other firms choose low investment, aggregateactivity will be low, and an individual firm�s invest-ment productivity may be too low to justify a high in-vestment level. In this example, there are two equilibria:one where all firms �coordinate� on high investment,the other where all firms have low investment.20

In the model I present here, the possibility of co-ordination failure arises from the essential nature offinancial relationships�the need to match potentialborrowers with potential lenders in an environmentof asymmetric information. In particular, lenders mustsearch for borrowers and vice versa. As the total num-ber of borrowers and lenders rises, this search processbecomes more productive. That is, the rate at whichborrowers and lenders match goes up. In other words,the matching process exhibits a thick markets externali-ty: Everyone benefits as the number of participants inthe market rises.21

This thick markets externality gives rise to thepossibility of a coordination failure equilibrium: Iflenders believe that there are few high-quality bor-rowers searching for loans, and simultaneously thehigh-quality borrowers believe that there are fewlenders willing to extend credit, an equilibrium canemerge where both lenders and borrowers forsakethe loan market in favor of alternative investments.In effect, all parties have �coordinated� on nonpartic-ipation, so the optimal strategy for any individualagent is not to participate.

Basic structure of the modelThe basic model is completely static. There are

two types of risk-neutral agents: borrowers (Nborr

innumber), who are endowed with a project but noliquidity; and lenders (N

lend in number), who are en-

dowed with one unit of liquidity but no project. Aborrower can operate his project in two mutually exclu-sive ways: autarkically, without any liquidity inflowfrom outside; or with investment, which requires bor-rowing one unit of liquidity from a lender. A borrow-er must decide at the beginning of the period whetherto operate the project autarkically or whether to seeka loan. In other words, once the borrower has decidedto seek a loan, the possibility of autarkic productionis precluded.

Borrowers are randomly assigned one of twotypes of projects, bad (assigned with probability pb),and good (assigned with probability (1 � pb)). The

quality of the project is private information to theborrower. Good projects pay Rautarky with certainty ifoperated autarkically; they pay R with certainty ifoperated with investment, provided the borrower hasfound a lender willing to lend. Bad projects pay 0 ifoperated autarkically; if operated with investment,bad projects pay R with probability θ and Rsalvage withprobability (1 � θ), again provided borrower hasfound a lender willing to lend. Informally, a bad bor-rower defaults on his loan with probability (1 � θ);Rsalvage represents the salvage value of the project thatis available to satisfy the lender�s claim. Finally, if aborrower seeks a loan but fails to match with a lender,he receives zero.

An interpretation22 of these two types of borrowersis that bad borrowers are in severe financial distress.If they do not get an immediate liquidity infusion,they will be forced into bankruptcy. Even if they doreceive liquidity, financial distress may impair theirproductivity with probability (1 � θ). In contrast, goodborrowers can stay in operation without liquidity,albeit at a lower output. However, there is an up-frontcost to structuring the project to utilize liquidity. Myassumption that a good borrower who tries to obtaina loan and fails receives zero is equivalent to a speci-fication where the up-front cost equals Rautarky and theoutput with liquidity (before the up front cost is paid)equals R + Rautarky.

Lenders have one unit of liquidity, which theycan use in two mutually exclusive ways. First, theycan invest it at a gross risk-free rate Rf. Second, theycan attempt to find a borrower to whom to lend. If aborrower and a lender match, the loan contract takesthe following exogenous specification:23 If R is pro-duced, the lender receives R

lend (where R

lend is an

exogenous parameter satisfying Rlend

≥ Rsalvage) andthe borrower receives R

borr ≡ R � R

lend; if Rsalvage is pro-

duced, the borrower is in default, so the lender re-ceives the full salvage value Rsalvage and the borrowerreceives nothing. Finally, if a lender does not find aborrower, she simply ends up with her unit of liquidi-ty.24 To summarize, the payoffs are as follows:

1) Payoff to good borrower =

Rborr

if borrower matches with lender

0 if borrower attempts to match withlender and fails

Rautarky if borrower operates project autarkically.

2) Payoff to bad borrower =

Rborr

if borrower matches with lender andproject produces R


0 if borrower attempts to match withlender and fails or if borrower matcheswith lender and project produces Rsalvage

or if borrower operates project autarkically.

3) Payoff to lender =

Rlend

if lender matches with borrower andproject produces R

Rsalvage if lender matches with borrower andproject produces Rsalvage

1 if lender attempts to match with aborrower and fails

Rf if lender uses the risk-free investmentand does not attempt to match with aborrower.

The matching procedureAccording to equations 1, 2, and 3, the expected

payoff to an agent who attempts to match depends onthe probability of consummating the match. Supposethat there are a total of B borrowers seeking loans andL lenders seeking to match with borrowers. I denotethe probability that a given borrower matches with alender by prob

borr (B,L). Similarly, the probability that

a given lender matches with a borrower is denotedprob

lend(B,L). (In equilibrium, the expected number of

matches equals B × probborr

(B,L) = L × problend

(B,L).)If either B or L equals zero, both prob

borr and

problend

= 0. (That is, if there are no borrowers orlenders, there can be no matches.) It is also natural toassume, in the language of Mortensen and Pissarides(1998), that borrowers and lenders are complements.That is, it is easier for a borrower to find a match ifthere are more lenders, and vice versa. (Formally,

0 and 0.borr lendprob prob

L B

∂ ∂> >

∂ ∂) In addition, follow-

ing Mortensen and Pissarides (1998), I assume thatthere is a congestion effect. An increase in the numberof borrowers decreases the probability that a givenborrower will match, and vice versa. (Formally,

0 and 0.borr lendprob prob

B L

∂ ∂< <

∂ ∂)

Finally, I assume that the expected number ofmatches displays increasing returns to scale. This isequivalent to the condition that as the number of bor-rowers and lenders increases equiproportionally, bothprob

lend and prob

borr increase. This is a natural assump-

tion to make for many types of matching problems.Consider the problem of finding a taxi cab in a medi-um-sized city. If there were only one rider lookingfor a cab and one cab looking for a fare (as might bethe case at 2:00 am), the probability of a match would

be very low. If there were 10,000 riders and 10,000cabs, the probability that a given rider would find acab would be much higher. (This intuition is formal-ized in the model developed in appendix A.)25

Increasing returns is implied by a number ofsearch models that have been proposed in the literature.In appendix A, I discuss a number of these and Idevelop one model in detail. Diamond (1982) andothers note that increasing returns in the matchingtechnology can give rise to multiple search equilibria.I exploit this feature below.26

High-coordination and low-coordination equilibriaThe matching technology implies that the deci-

sion of borrowers whether to enter the match affectsthe probability that a given lender will match and,therefore, affects the expected payoff to the lenderfrom entering the match. Similarly, the decisions oflenders affect the expected payoff of the borrower.This implies the possibility of coordination failurebetween borrowers and lenders and, thus, the possibil-ity of multiple equilibria. I define a high-coordinationequilibrium as one in which all lenders enter the matchand all borrowers enter the match. Of course, a lenderwill enter the match if, and only if, her expected pay-off from entering the match equals or exceeds Rf.Using the payoffs given in equation 3, in a conjec-tured high-coordination equilibrium this conditioncan be written as

4) problend

(Nborr

, Nlend

)((pbθ + 1 � pb) Rlend

+

pb(1 � θ)Rsalvage) + (1 � problend

(Nborr

, Nlend

)) ≥ Rf.

Similarly, a good borrower will enter the match,if and only if, his expected payoff from entering thematch equals or exceeds Rautarky. In a conjectured high-coordination equilibrium, this condition is

5) probborr

(Nborr

, Nlend

)Rborr

≥ Rautarky).

Note from equation 2 that the bad borrowers alwaysenter the match, since the payoff from entering thematch dominates the autarkic payoff to the bad borrow-er of zero. Therefore, equations 4 and 5 are sufficientfor the existence of a high-coordination equilibrium.

I define a low-coordination equilibrium as onewhere no lenders enter the match and only bad bor-rowers enter the match. The payoff to lenders in thelow-coordination equilibrium is Rf. The payoff togood borrowers is Rautarky, and the payoff to bad bor-rowers is zero. If there are no lenders in the match,there is clearly no incentive for good borrowers todefect from the equilibrium strategy of autarky (since


probborr

(1,0) = 0). However, there may be an alterna-tive strategy for a lender that could break the low-coordination equilibrium. Let the total number of badborrowers be denoted N

bad. (The expected value of

Nbad

is simply pbNborr

.) If, starting in a low-coordina-tion equilibrium, a lender decides to defect from theequilibrium strategy by entering the match, her prob-ability of matching with a borrower is prob

lend (N

bad, 1)

(since only bad borrowers are in the match in a lowequilibrium). Her expected payoff conditional on asuccessful match is θR

lend + (1 � θ) Rsalvage. Therefore,

a low-coordination equilibrium can only be sustainedif the expected payoff to this alternative strategy isless than the payoff to a lender in the low-coordina-tion equilibrium:

6) problend

(Nbad

, 1)(θRlend

+ (1 � θ)Rsalvage) +

(1 � problend

(Nbad

, 1)) ≤ Rf.

The left-hand sides of equations 4 and 6 give thevalue to a lender of entering the match in the high-coordination and low-coordination equilibria, respec-tively. Similarly, the left-hand side of equation 5 givesthe value to a good borrower of entering the match inthe high-coordination equilibrium. For a particularbase line parameterization,27 figure 4 displays howthese values are affected by changes in the modelparameters. Specifically, the left-hand column ofplots in figure 4 shows how the left-hand sides ofequations 4 (black lines) and 6 (colored lines) changeas a particular model parameter is varied; the right-hand column does the same for the left-hand side ofequation 5 (colored lines). The five parameters thatare varied in figure 4 are: number of lenders, as afraction of total population (first row of plots); Rlend,as a fraction of R (second row); Rsalvage, as a fractionof R (third row); θ (fourth row); and pb (fifth row).

The behavior of these values is intuitive. The val-ue to lenders of entering the match for both equilibriais strictly decreasing in the ratio of lenders to totalpopulation (reflecting the greater competition fromother lenders); the corresponding value to good bor-rowers is strictly increasing in this ratio (reflectingthe higher probability of matching with a lender). Notsurprisingly, increasing R

lend/R, the fraction of output

received by lenders, increases the value of the matchto lenders, but decreases that value to borrowers. Forboth equilibria, the value of the match is increasingfor lenders in Rsalvage and θ (the probability that a badproject produces R). Neither of these parameters affectsthe value of the match for good borrowers. Finally,an increase in pb, the probability of bad projects,reduces the value of the match for lenders in the

high-coordination equilibrium, but increases the valueof the match for lenders in the low-coordination equi-librium. In the high-coordination equilibrium, increas-ing pb simply increases the probability of borrowerdefault. In the low-coordination equilibrium, however,an increase in pb increases the number of borrowersseeking loans. (Recall that only bad borrowers seekloans in the low-coordination equilibrium.) This in-creases the probability of a match for a lender contem-plating deviating from the equilibrium strategy.

Suppose the borrower condition for a high-coor-dination equilibrium (equation 5) holds. That is, sup-pose Rautarky lies below the colored line in any of theplots in the right-hand column of figure 4. Then theexistence of the high- or low-coordination equilibriumdepends on the level of the risk-free rate Rf relative tothe solid and colored lines in the plots in the left-handcolumn. If Rf is above both lines, then neither equi-librium exists for these parameter values. If Rf isbelow the solid line but above the colored line, thenboth low-coordination and high-coordination equilib-ria exist. If Rf is below both the solid line and the col-ored line, then a high-coordination equilibrium existsbut no low-coordination equilibrium exists. Thus, ifequation 5 holds, the high-coordination equilibriumcan be enforced by setting Rf sufficiently low.

Finally, there may also be additional �mixed�equilibria where a fraction of lenders and/or goodborrowers enter the match, while the remaining agentschoose the alternative strategies (investing risk-freefor lenders, operating the project autarkically for theborrowers.) I discuss the conditions for these mixedequilibria in box 1. The possibility of mixed equilib-ria complicates the analysis of this model. For thepurposes of this article, I assume that these mixedequilibria are never observed. For the remainder ofthis section, I focus only on the low- and high-coordi-nation equilibria.

Interpreting the model as a theory offinancial crises

I associate the low-coordination equilibrium inthe model with a financial crisis. This equilibriumcaptures many characteristics associated with financialcrises. In this simple model, asset values and outputcan both be measured by the expected payoff to aborrower�s project; both are clearly lower in the low-coordination equilibrium than in the high-coordinationequilibrium.28 There is a clear flight to quality in thelow-coordination equilibrium, coupled with a drying-upof liquidity: Lenders invest in the risk-free asset in-stead of making loans, so the aggregate quantity ofliquidity provided falls to zero. There is a perceptionof declining credit quality: If we were to ask a lender


FIGURE 4

Effect of changes in model parameters on the value of entering the match

Value to lenders

Value to lenders

Value to lenders

Value to lenders

Value to lenders

Value to good borrowers





number lenders/population number lenders/population

Rlend/total output Rlend/total output

Rsalvage/total output Rsalvage/total output

probability that a bad project is productive probability that a bad project is productive

probability of bad project probability of bad project

0.2 0.4 0.6 0.8 1.001.00

1.05

1.10

1.15

0.2 0.4 0.6 0.8 1.00.00

0.20

0.40

0.60

0.80

0.0 0.2 0.4 0.6 0.8 10.00.50

0.75

1.00

1.25

1.50

0.0 0.2 0.4 0.6 0.8 1.00.00

0.20

0.40

0.60

0.80

0 0.1 0.2 0.3 0.4 0.50.90

1.00

1.10

1.20

0 0.1 0.2 0.3 0.4 0.5-1.00

0.00

1.00

2.00

0 0.2 0.4 0.6 0.80.80

1.00

1.20

1.40

0 0.2 0.4 0.6 0.8-1.00

0.00

1.00

2.00

0.50 0.10 0.15 0.20 0.25 0.301.00

1.05

1.10

1.15

0.05 0.10 0.15 0.20 0.25 0.30-1.00

0.00

1.00

2.00

Notes: For a particular set of baseline parameters, this figure illustrates how the value of entering the match implied by the model changes asfive parameters of the model are varied. The left-hand column of figures plots the value of a lender entering the match in the high-coordinationequilibrium (left-hand side of equation 4, represented by the black lines) and the low-coordination equilibrium (left-hand side of equation 6,represented by the colored lines) changes as the following five parameters change: number of lenders, as fraction of total population (firstsubplot); payoff to the lender Rlend, as a fraction of total output (second subplot); salvage value of a bad borrower’s project Rsalvage, as a fractionof total output (third subplot); probability that a bad project is productive θ, (fourth subplot); and the probability that a given project is bad, pb

(fifth subplot). The right-hand column of figures plots the value of a good borrower entering the match in the high-coordination equilibrium (left-hand side of equation 5), as the same five parameters are varied. The baseline parameters are as follows: Nlend = 20; Nborr = 30; R = 2; Rlend = 1.2(so Rborr = 0.8); Rsalvage = 0.5; pb = 0.2; θ = 0.75. Parameter Nbad is set equal to its expected value of 6. I use the model of problend and probborrdescribed in appendix A, equations 19 and 20, with parameter M = 10.


BOX 1

Mixed equilibria

In a mixed equilibrium, some lenders and/or goodborrowers enter the match, while the remainingagents choose the alternative strategies (investingrisk-free for lenders, operating the project autarki-cally for the borrowers). If there were a continuumof agents, these mixed equilibria would requireagents to be indifferent between entering the matchand using the alternative strategies. If one takes se-riously the constraint that the number of agents ofeach type be an integer, then the conditions for amixed equilibrium must take into account the effecton the matching probabilities were an agent to devi-ate from the equilibrium.

To write down the conditions for a mixed equi-librium, it is convenient to define functions V

lend

and Vborr

that measure the value of entering thematch for lenders and borrowers, respectively. LetB

good denote the number of good borrowers entering

the match, and let L denote the number of lendersentering the match. Recall that all bad borrowersenter the match (since the value of autarky for badborrowers is zero). Therefore, the fraction of bad

borrowers in the match is Nbad

N +Bbad good

, and

(analogously with the left-hand side of equation 4)the value to a lender of entering the match is

( )B1) ,

(1 �(1

)).

lend good lend bad good

goodbadlend

bad good bad good

salvagebadlend bad

bad good

good,

V B L prob (N +B ,L)

BNR

N +B N +B

NR prob (N

N +B

+B L

≡

× +

−+ + −

The value of entering the match for a good borrow-er is given by the analogue to the left-hand side ofequation 5:

B2) Vborr

(Bgood

, L) ≡ probborr

(Nbad

+ Bgood

, L)Rborr

.

If there were a continuum of agents, so the de-fection of a single agent from the equilibrium strat-egy would not affect the matching probabilities,then a mixed equilibrium would be a pair {B

good, L}

satisfying

B3) 0 < Bgood

< Nborr

� Nbad

0 < L < Nlend

for which

B4) Vlend

(Bgood

, L) = Rf

Vborr

(Bgood

, L) = Rautarky.

If (as I assume throughout this article) there arean integer number of agents of each type, then aconjectured defection from the equilibrium strategychanges prob

lend or prob

borr and, therefore, changes

Vlend

or Vborr

. To take this explicitly into consideration,I must modify equation B4. Assume that

B5) Vlend

is decreasing in L.

Since problend

(B,L) is strictly decreasing in L,a sufficient condition for assumption B5 is

B6)

(1 )1.

goodbadlend

bad good bad good

salvagebad

bad good

BNR

N B N B

NR

N B

+

θ + + −θ

+ >+

In other words, the expected payoff to a lender from asuccessful match exceeds the payoff from entering thematch but failing to match. Note that V

borr is decreas-

ing in Bgood

, because probborr

(B,L) is strictly decreas-ing in B. Under assumption B5, a mixed equilibriumis a pair {B

good, L} satisfying equation B3 and

B7) Vlend

(Bgood

, L + 1) ≤ Rf ≤ Vlend

(Bgood

, L)

Vborr

(Bgood

+ 1, L) ≤ Rautarky ≤ Vborr

(Bgood

+ 1,L).

The logic behind equation B7 is straightfor-ward. If the first set of inequalities in equation B7holds, then a lender in the match has no incentive toswitch to the risk-free asset (since the value of be-ing in the match exceeds Rf), and a lender investingrisk-free has no incentive to switch to entering thematch (since, by entering the match, the total num-ber of lenders in the match will equal L + 1, and thevalue to being a lender in the match when the totalnumber of lenders equals L + 1 is dominated by therisk-free rate). A similar logic holds for borrowers ifthe second set of inequalities in equation B7 holds.

why she refrained from making loans, she wouldanswer that the risk of default was too high (sinceall borrowers actually entering the match in the

low-coordination equilibrium are bad borrowers). Thisis the sort of response given by lending institutionsin the BIS interviews and the Board of Governors�


Senior Loan Officers Survey, discussed earlier. It isalso consistent with widening credit spreads. Further-more, there is a reduction in demand for liquidity onthe part of borrowers, a pattern that was also reportedin the September Senior Loan Officers Survey.

This model is also consistent with sudden switchesbetween normal and crisis states without any changein underlying fundamentals (as represented by themodel�s parameters). While I do not model dynamicsexplicitly, a multiple-equilibrium model of this typecan be incorporated into a dynamic model in whichswitches between coordination states are driven sole-ly by changing expectations. If enough lenders in theeconomy become pessimistic about the aggregatenumber of borrowers entering the match (or vice versa),then a low-coordination equilibrium will emerge,validating their pessimism ex post. Thus, all that wouldbe needed to model the abrupt switches between crisisand non-crisis states would be to model switchingbetween optimism and pessimism in the economy.29

Financial crises and the roleof the central bank

Perhaps the most interesting feature of the modelpresented here is that it suggests a role for the centralbank in dealing with financial crises. We can see fromequation 6 that a liquidity crisis (that is, a low-coor-dination equilibrium) is only possible if the real risk-free rate is sufficiently high. If the central bank canaffect the real risk-free rate through open marketoperations, it can extinguish the possibility of a liquid-ity crisis by reducing the risk-free rate until the left-hand side of equation 6 exceeds the right-hand side.Intuitively, if the risk-free rate is so low that a lenderexpects a higher return by seeking to match with aborrower even if all borrowers are believed to be ofbad quality, then the low-coordination equilibriumcannot be sustained.

Example of central bank action:The events of 1991�93

One interpretation of monetary policy in the early1990s is that the Federal Reserve used open marketoperations in the manner suggested in the precedingparagraph. The recovery from the 1990�91 recessionappeared to be impeded by a so-called credit crunch.Responding perhaps to the introduction of risk-basedcapital requirements, banks reduced their volume ofloan provision, investing instead in Treasury securi-ties and other low-risk assets. One can see this processin figure 5, panel A, which displays fixed incomesecurities as a fraction of total banking assets. Notethat fixed income securities as a percentage of totalassets rose from just over 15 percent at the beginning

of 1990 to over 20 percent at the beginning of 1993.While this is far less dramatic than the complete coor-dination failure in the low-coordination equilibrium ofthe model, this process can be interpreted as a slowshift away from full coordination.

In mid-1991, the FOMC started reducing the fed-eral funds rate in an effort to encourage more lending.This policy shift is evident in figure 5, panel B, whichdisplays the real federal funds rate (defined here asthe difference between the nominal federal funds rateand the ex post monthly CPI inflation rate) from 1989through 1997. Note that the real funds rate declinesto an extremely low level (between 0.5 percent and0 percent) between late 1992 and February 1994. Asin the simple model, the effect is to reduce the returnon alternative assets, making even the relatively lowrisk-adjusted return on loans seem reasonably attrac-tive.30 As shown in figure 5, panel A, banks did shift

FIGURE 5

Bank portfolios and monetary policy, 1989�97.

A. Fixed income securities as fractionof total assets, 1989:Q1–97:Q1fraction of assets, quarterly

B. Real federal funds rate, 10/89–3/97

percent

1990 ‘91 ‘92 ‘93 ‘94 ‘95 ‘96

Total fixed debt

>5 year

1–5 year3–12 month<3 month

10/1/90 10/1/92 10/1/94 10/1/96

Notes: Panel A displays fixed income securities as a faction oftotal bank assets. The uppermost black line displays total fixedincome securities. The other lines in the graph disaggregate thesecurities by maturity. Panel B displays the real federal funds rate,computed as the nominal federal funds rate minus the one-monthCPI inflation rate.Sources: Call reports (panel A); author’s calculations, using datafrom the Board of Governors of the Federal Reserve System (panel B).

0.00

0.05

0.10

0.15

0.20

0.25

-2

0

2

4

6


away from non-loan assets to loans following theimplementation of this policy. It is possible that theincreased loan growth was due to some change in theeconomic or regulatory environment other than theextremely low real interest rates. However, these pat-terns in the data are certainly consistent with the intu-ition that lenders are more willing to lend when thereturn to alternative investments is low, and that thecentral bank can influence this alternative return.

Particularly interesting is what happened afterthe FOMC reversed course starting in February 1994and allowed the real interest rate to return to its levelof early 1990. If banks� willingness to lend dependedonly on the return on alternative assets, the bankspresumably would then have cut back on their loanprovision. In fact, figure 5, panel A shows that bankscontinued to increase their lending. This suggests thatthere may have been an element of coordination failurein the credit crunch. Once the economy had securelymoved to a high-coordination state, it could remainthere even after the FOMC raised real interest ratesto a higher level.

Policy alternatives implied by the modelAccording to the model, a central bank can prevent

financial crises by keeping interest rates extremelylow all the time. However, this strategy conflicts withthe central focus of monetary policy: to establish areputation as a force for price stability. Even if the Fedcould act against the possibility of a low-coordinationequilibrium by decisively reducing Treasury yields,such an action would be costly, not only in its directeffect on future inflation, but also in eroding the credi-bility of the Fed�s commitment to containing infla-tionary pressures.

In principle, a central bank could reconcile thesetwo competing imperatives by establishing a crediblestate-dependent policy�enforce a low interest rateonly when there is clear evidence that a financialcrisis is imminent. The advantage of such a policy isthat the low interest rate is rarely implemented, yetthe possibility that it might be implemented movesthe economy to a preferred equilibrium. In fact, whenI incorporate such a state-dependent policy into thesimple model developed earlier, the low interest rateis never implemented. In the language of economictheory, it is an off-equilibrium path that enforces thehigh-coordination equilibrium.

As an example of such a state-dependent policy,consider the aftermath of the October 1987 stockmarket crash. There is considerable anecdotal evi-dence that many banks were reluctant to provide theliquidity needed to settle trades made during the dayof the crash. This withdrawal of liquidity may have

represented a low-coordination equilibrium: If a givenbank is likely to be repaid only if the aggregate pro-vision of liquidity is high, it may be individuallyrational for each bank to withhold liquidity. In response,the Federal Reserve announced a state-contingentpolicy: �The Federal Reserve ... affirmed today itsreadiness to serve as a source of liquidity to supportthe economic and financial system.�31 The operativeword is �readiness.� With the Fed standing ready toensure adequate liquidity in the market, it becamerational for individual banks to provide liquidity totheir clients. In the event, no significant liquiditydisruptions were observed,32 yet the Fed itself didnot actively provide the liquidity�discount windowborrowing by member banks did not increase signifi-cantly, and the increase in non-borrowed reserveswas small.

In September 1998, investors were uncertainwhether a state-dependent policy was in place.33 Onecan interpret the intermeeting rate cut on October 15,1998, as a credible signal that the Fed had shifted to thissort of state-dependent policy. It seems more plausibleto interpret the effect of this rate cut to its role as a sig-nal than to any direct effects. Certainly, the interest ratecuts in fall of 1998 were much smaller than those in1990�91, clearly not sufficient to substantially changeinvestors� incentives directly. There is evidence thatfinancial markets perceived the intermeeting rate cutas signaling a policy change. According to the WallStreet Journal, �the economic indicators that the Fedusually tracks�the unemployment rate, the pace oforders for factory goods and retail sales, among otherthings�don�t explain the Fed�s sudden action, sincemany of those indicators have suggested that theeconomy is relatively healthy. Rather, officials at theFed ... have been focused on unusual signs of stressin the financial markets.�34 In the words of analystsat Morgan Stanley Dean Witter, the Fed�s �unexpectedeasing� signaled a �new aggressiveness.�35 Marketparticipants� perception of a change in Fed emphasisis consistent with the minutes of the FOMC�s delib-erations. In the minutes of the September 29 meeting,36

the financial market turmoil is noted, but it is seenprimarily as one factor among many affecting inflation-ary pressures through aggregate demand. In particular,�The members did not believe that the tightness incredit markets and strong demand for safety and liquidi-ty were likely to lead to a �credit crunch.� ...� A 50basis-point cut is explicitly ruled out because �therisk of rising inflation ... was still present, especiallyin light of the persistence to date of very tight labormarkets and relatively robust economic growth.� Incontrast, the minutes of the FOMC teleconferencepreceding the intermeeting rate cut of October 15 do


not mention inflationary pressures at all. Rather, anadditional rate cut is motivated �to help settle volatilefinancial markets and cushion the effects of morerestrictive financial conditions on the ongoing expan-sion.� Following the October 15 action, members ofthe FOMC describe the move as a (temporary) shift offocus from price stability to financial stability. For ex-ample, the Wall Street Journal cited Federal ReserveBank of St. Louis President William Poole as sayingthat �[the recent market instability] and the circum-stances surrounding it are so unusual in the contextof U.S. history that policy makers must concentrateon dealing with this situation for the time being.�37

According to the same article, Governor Roger Fer-guson �indicated that the Fed would be willing to cutrates aggressively at any hint of a recession.�

In the following section, I incorporate such astate-dependent policy into the simple model out-lined earlier. I argue that such a policy, if credible,may have been sufficient to eliminate the possibilityof coordination failure without requiring the centralbank to actually implement any substantial interestrate reductions. To formalize this idea, I extend themodel so that the central bank acts in real time. I thendemonstrate that the low-coordination equilibrium canbe eliminated if agents believe that the monetary au-thority will act in the future to eliminate coordinationfailure should coordination failure become likely.

Modeling a state-dependent central bank policyTo model a central bank interest rate policy that

actively responds to a developing liquidity crisis, Ineed to modify the simple model to make precise thenotion of �incipient crisis.� I do so in the following(admittedly highly stylized) way. Suppose that thereis a preliminary period before the matching of bor-rowers and lenders. At the beginning of this prelimi-nary period, each lender is assigned at random a moodof pessimism or optimism. A pessimist believes thatthe low-coordination equilibrium will prevail provideda low-coordination equilibrium could exist (that is,provided equation 6 could hold). An optimist believesthat the high-coordination equilibrium will prevail,again provided this equilibrium could exist (that is,equations 4 and 5 could hold). In addition, in the be-ginning of the preliminary period the N

lend lenders are

assigned an index i = 1, ..., Nlend

. They then must declare(irrevocably) in order of their index assignment whetherthey will enter the match or invest in the risk-free tech-nology. After all N

lend lenders have declared, the match

is held, projects are operated, and payoffs are made,as in the simple model.

Let Qi denote the number of lenders who have

declared that they are in the match through the ith

lender, so QNlend

denotes the total number of lenderscommitted to entering the match at the end of thepreliminary period. As I show in proposition 1 below,if Q

Nlend is sufficiently high (that is, if Q

Nlend is greater

than or equal to a particular threshold N*), a low-coordination equilibrium cannot exist. A pessimistwith index i will assume that the low-coordinationequilibrium will prevail unless Q

i�1 (weakly) exceeds

this threshold.Now, I develop this idea more fully. For simplic-

ity, I consider a case where the central bank can chooseone of two interest rates: Rhigh and Rlow, where Rhigh isconsistent with both equilibria. That is, when Rf = Rhigh,equations 4, 5, and 6 all hold. (I discuss conditions onRlow below.) If Rf = Rhigh, the equilibrium that emergesdepends on the beliefs of the lenders about Q

Nlend. In

particular, there exists an N* such that, if it is believedthat Q

Nlend≥ N*, it is optimal for all good borrowers

to enter the match. The smallest such value of N* isgiven by

7) N* = min N s.t. probborr

(Nborr

, N) Rborr

≥ Rautarky.

The existence of N* ≤ Nlend

follows from the as-sumption that a high-coordination equilibrium exists(that is, equation 5 holds.)

To proceed, I must make an additional assump-tion. Let V

lend denote the value to a lender of entering

the match. Vlend

depends on both the total number oflenders in the match and the number of good borrowersin the match. An explicit expression for V

lend is given

in equation B1 in box 1. I assume that

8) Vlend

is strictly decreasing in the total number oflenders in the match.

A sufficient condition for assumption 8 to hold isgiven in equation B6 in box 1.

Proposition 1Suppose equations 4 and 8 hold. If all lenders be-

lieve that QNlend

will be at least as big as N*, then all lendersenter the match, so Q

Nlend= N

lend ≥ N*. This implies, first,

that their beliefs are ratified ex post, and, second, thatthe high-coordination equilibrium prevails. (The proofsof all propositions are in appendix B.)

Proposition 1 tells us that the central bank canensure that the high-coordination equilibrium willprevail if it can ensure that at least N * lenders com-mit to entering the match. As in the previous model,it can do so by setting Rf sufficiently low. To formal-ize this possibility, let us assume that

9) (θRlend

+ (1 � θ) Rsalvage) > 1


and let Rlow satisfy

10) problend

(Nbad

,N*) (θRlend

+ (1 � θ) Rsalvage)

+ (1 � problend

(Nbad

, N*)) ≥ Rlow.

Equation 9 means that the expected payoff to alender conditional on matching with a bad borrowerexceeds the payoff from failing to match. It ensuresthat the left-hand side of equation 10 is increasingin prob

lend.

Proposition 2If the central bank sets Rf = Rlow and equations 9

and 10 hold, the high-coordination equilibrium isenforced.

Proposition 2 tells us that the central bank caneliminate the low-coordination equilibrium by perma-nently setting the risk-free rate sufficiently low (inparticular, low enough so equation 10 holds). In real-ity, however, this low interest rate policy is a verycostly way to deal with the possibility of financialcrisis. As I discussed above, the excessively expan-sionary monetary policy needed to keep interest ratesat Rlow may directly conflict with the central bank�s pri-mary mission of price stability. If so, a better centralbank rule is to set Rf = Rhigh, but commit to switching toRlow if there is evidence of an incipient crisis. Infor-mally, the central bank can measure the tone of themarket by looking at the ratio Q

i/i. This ratio gives

the fraction of the first i lenders who will enter thematch, so this ratio measures the �skittishness� of themarket. If the central bank observes a low value ofQ

i/i (presumably because the random assignment of

the first i indexes fell disproportionately on pessimists),it may be concerned that a financial crisis is brewing.

In the formalism of this model, let �incipientcrisis� be defined as any point i* in the declarationsequence such that

11) Qi* + (N

lend � i*) = N*.

In words, if such an i* is reached, then all of theremaining lenders must declare themselves in thematch to ensure that there are N* lenders seeking tomatch with borrowers. Since the goal of the centralbank is to ensure that at least N* lenders enter thematch, this is the �last chance� for the central bankto do so.

Central bank ruleThe proposed central bank rule is as follows:

■ Set Rf = Rhigh as long as no {i*, Qi*} satisfying

equation 11 is reached.

■ The first time {i*, Qi*} satisfying equation 11 is

reached, set Rf = Rlow from that point on.

Proposition 3If this rule is credible, the only equilibrium is

high-coordination with Qi = i, �i, and Rf = Rhigh.

According to proposition 3, the second branchof the rule is an off-equilibrium path that is neverobserved in equilibrium. Thus, the best of all possibleworlds is obtained: Liquidity crises are ruled outwithout compromising the goal of price stability.Proposition 3 specifies that the rule must be credible.I do not attempt to formalize how �credibility� is tobe established. Authors such as Christiano, Chari, andEichenbaum (1998) and Christiano and Gust (2000)stress the importance of the central bank establishinga credible commitment to price stability if expecta-tions-driven inflationary episodes are to be avoided.Proposition 3 suggests that a credible commitmentto financial stability may serve an analogous role inavoiding financial crises.

DiscussionIs this what happened in October 1998?

One interpretation of the FOMC�s interest ratecut on October 15, 1998, is that it was an intentionalsignal that Federal Reserve had shifted from an un-equivocal focus on price stability to a policy of �pricestability unless there is a pressing need to deter a finan-cial crisis.� In the formalism of the model, the formerpolicy sets Rf = Rhigh always, while the latter policy isgiven by the policy rule described above.

There are clearly other possible explanations forthe ending of the fall 1998 crisis. One such explana-tion is that the reduced interest rates increased thecollateral value of firms� fixed income portfolios,thereby increasing their borrowing capacity. But theeffect of a 50 basis-point interest rate cut on the valueof debt holdings is small, especially for the short-termsecurities generally used as collateral. In any event,the turmoil in fall of 1998 was associated with a �flightto quality,� which raised the value of the Treasury secu-rities that typically collateralize liquidity loans. An-other explanation is that the open market operationsused to implement these interest rate cuts increasedthe total supply of reserves in the system, increasingthe amount of liquidity available to be borrowed.Again, this explanation seems wanting. In contrastto the period from 1991 to 1993, when there was anextended and pronounced increase in the volume ofreserves in circulation, the amount of reserves in fall1998 was relatively unchanged.

Perhaps a more straightforward explanation forthe abrupt reversal of the 1998 crisis is that financial


intermediaries believed that the Federal Reserve hadimplicitly agreed to provide all financial institutionswith a guarantee. In particular, the role of the FederalReserve Bank of New York in the recapitalization ofLTCM may have been interpreted as a commitmentto provide similar services to other intermediarieswith similar problems. I do not believe that the factssupport this explanation. Following the announcementof the LTCM rescue plan, the crisis actually deepened.Measures of credit spreads and market volatility de-teriorated during the two weeks between the LTCMrescue and the Federal Reserve�s intermeeting actionon October 15. Furthermore, market participants re-ported that the Federal Reserve�s role in the rescueserved to exacerbate market fears, not ameliorate them.Thus, the data seem to contradict the hypothesis thatthe LTCM rescue was interpreted as an extension ofthe safety net.

Finally, the October 15 rate cut may have signaleda changed policy stance regarding International Mon-etary Fund (IMF) funding rather than monetary policy.The Russian fiscal crisis virtually assured that a gooddeal of IMF resources would flow to Russia. Withoutan increase in funding levels, the IMF�s resources todeal with other countries� problems (most important-ly, Latin America) would have been substantially re-duced. The increase in Brady bond yields, documentedin figure 3, may have reflected concerns that less IMFfunding would be available to deal with future LatinAmerican problems following the Russian crisis.During 1998 the U.S. Congress was considering anincrease in America�s IMF funding quota. However,there was considerable congressional opposition toincreased funding. Perhaps the October 15 rate cutwas interpreted as a signal that the Federal Reservewould work with greater intensity to secure increasedIMF funding.

This interpretation is certainly possible. Howev-er, it relies on a less direct mechanism than the mon-etary policy interpretation I put forth in this article. Itplaces a good deal of weight on the Federal Reserve�sinfluence with Congress. Furthermore, the FederalReserve was already on record supporting the propos-al to increase IMF funding (see Chairman Greenspan�stestimony to Congress on May 21, 1998), so the Oc-tober 15 rate cut would have represented at best astrengthening of this position, not a reversal of a pre-viously held position. Finally, the data are not entirelyconsistent with this explanation. As shown in figure3, the peak in Latin American Brady bond yields during1998 happened in mid-August (Mexico) or mid-Sep-tember (Brazil and Argentina), not in mid-Octoberwhen the presumed signal occurred.

Costs of a state-contingent policy for financial crisesIn the theoretical model described here, the state-

contingent policy rule is costless to implement, sincethe low interest rate is never actually imposed in equi-librium. Of course, the real world is not so simple. Inreality, there would doubtless be crises that could notbe extinguished by the belief that the central bank�srule specifies a particular off-equilibrium path. As apractical matter, this sort of policy rule would requireaggressive monetary expansion from time to time.Actions of this type have costs. Each time such amonetary expansion is implemented, the central bankcompromises its primary objective of price stability.Any time it injects liquidity into financial markets inan effort to counter potential liquidity it faces the dif-ficult task of negotiating a �soft landing��removingthe liquidity after the crisis has abated without trig-gering a recession. Furthermore, if the state-contingentpolicy rule weakens the commitment to price stability,the resulting instability might even increase the possi-bility of financial crises. Finally, if private marketparticipants believe that the central bank will alwaysact to successfully counter financial turmoil, they mayengage in less vigilant risk management than theywould otherwise. This so-called moral hazard problemmay actually increase the chances of an incipient cri-sis. Policymakers must take all of these issues intoconsideration before adopting a state-contingent ruleas a practical policy doctrine.

Conclusion

In this article, I propose a precise characterizationof financial crisis. I argue that coordination problemsarise generically in financial markets. I associate finan-cial crisis with a condition of coordination failure, inwhich low levels of financial intermediation becomeself-justifying. I also argue that the central bank, throughits ability to affect real interest rates, may be able toextinguish the low-coordination trap. This argumentsupports a role for the central bank in countering sys-temic financial disruptions.

Having said this, there may be circumstances inwhich the central bank�s power to affect real rates isinsufficient to stave off a crisis. In particular, if poten-tial lenders are sufficiently pessimistic about returnsfrom lending, crisis aversion may require a real inter-est rate below that achievable by open market opera-tions. In addition, the use of open market operationsto counter financial crises is not without cost. Openmarket operations can only have a temporary effecton real rates. Prolonged use of this tool to reduce realinterest rates would run directly counter to the centralbank�s primary goal of price stability. In principle,


the central bank is better off establishing a crediblecontingent policy, whereby a liquidity injection is onlymade when there is evidence that a crisis is forth-coming. In the simple model presented here, a crediblepolicy of this type never has to be implemented inequilibrium. In reality, of course, life is not so sim-ple. There would doubtless be cases where the cen-tral bank would have to implement an expansionary

APPENDIX A

Increasing returns to scale in matching

Increasing returns to scale in matching can be de-rived from a number of more primitive search models.For example, Mortensen and Pissarides (1998) de-scribe an environment in which each lender has a listof telephone numbers that includes the numbers ofpotential borrowers, and each borrower has a similarlist that includes the numbers of potential lenders. Ifborrowers and lenders choose numbers at random,the probability of a match displays increasing returns.Kultti (1998) describes a somewhat more elaboratemodel.1 In his approach, lenders are posted at fixedlocations, and borrowers randomly choose a location.If there is a lender at the location and there are noother borrowers, a match is made with certainty. Ifthere is a lender and more than one borrower at thelocation, a borrower is chosen at random to matchwith the lender. Finally, if there is no lender at the lo-cation, no match is made. One can think of these lo-cations as bank branches, where some branches haveexhausted their loan capacity. Kultti (1998) showsthat if the number of locations does not change as thenumber of borrowers and lenders increases, thematching probabilities display increasing returns.2

Now, I consider in greater detail a micro modelof matching, similar to Kultti�s (1998), that impliesincreasing returns. Suppose there are M locations. Tosuccessfully match, a lender and a borrower must goto the same location. They cannot communicate be-fore traveling to a location, so the event of a lenderand a borrower being in the same location is purelyrandom. Ex ante, all locations look the same to bothlenders and borrowers. I assume that lenders and bor-rowers make their location decision at random, inde-pendently of the other lenders and borrowers.Therefore, the probability that a given borrower or agiven lender arrives at any particular location is 1/M.3

An interpretation of this set-up is that the �loca-tions� are banks or other intermediaries. Lenders areagents with excess liquidity. To match with borrowers,the lenders must go through an intermediary. Lenders

choose the intermediary at random. Similarly, borrow-ers visit intermediaries at random to apply for a loan.The loan application process is sufficiently time-inten-sive that a borrower can only apply at one intermediary.

Suppose there are l lenders and b borrowers at agiven location. If l = 0 or b = 0, no matches take placeat that location. If l = b, all the lenders and borrowersat that location match with probability one. If l > b,the b borrowers are allocated randomly among thelenders, so the probability of a given lender obtaininga match is b/l, and all borrowers obtain a match withprobability one. Similarly if b > l, the probability of agiven borrower obtaining a match is l/b, and all lendersobtain a match with probability one. To summarize,

{ , }min ,1 ;b

Prob lender matching b ll

{ , } ,1 .l

Prob borrower matching b l minb

I now compute the unconditional probability thata lender will match. Let B denote the number of bor-rowers seeking loans, and let L denote the number oflenders seeking to match with borrowers. The proba-bility that a given lender will be at a particular loca-tion is 1/M. For n = 0, 1, ..., L, the probability that nlenders will arrive at a particular location is denotedby p

l(n|L), as follows:

! 1 1( ) 1 .

!( )!

n L n

l

Lp n L

n L n M M

− = − −

Similarly, for n = 0, 1, ..., B, the probability that nborrowers will arrive at a particular location isdenoted by p

b(n|B), as follows:

! 1 1( ) 1 .

!( )!

n B n

b

Bp n B

n B n M M

− = − −

monetary policy to counter an incipient crisis. Thus,this article�s policy implications have benefits andcosts that must be carefully weighed by policymakerswhen considering practical policy formulation. None-theless, this article does provide a formal justificationfor the central bank as an essential institution in deal-ing with financial crises.


FIGURE A1

Effect of matching probabilities of increasein numbers of borrowers or lenders

probability of a match



number of borrowers and lenders

number of borrowers

number of lenders

Notes: The top panel gives the probability that a lender orborrower matches as both the number of lenders and thenumber of borrowers increase at the same rate. The middlepanel gives the probability that a borrower matches as thenumber of borrowers increases (holding lenders fixed). Thebottom panel gives the probability that a borrower matches asthe number of lenders increases (holding borrowers fixed).

A. Probability of a match as numberof borrowers and lenders increase

B. Probability that borrower matchesas number of borrowers increases

C. Probability that borrower matchesas number of lenders increases

0 5 10 15 20 25 30 35 40 45 500.0

0.2

0.4

0.6

0.8

0 5 10 15 20 25 30 35 40 45 500.2

0.4

0.6

0.8

1.0

0 5 10 15 20 25 30 35 40 45 500.0

0.5

1.0

To determine probborr

(B,L), the probability that agiven borrower matches, one must sum overall possi-ble values of l and b:

1

0 0

A1) ( )

min ,1 ( 1) ( ).1

borr

L B

b ll b

prob B,L

lp b B p l L

b

−

= =

=

− + ∑∑

In the second summation, I sum only to B�1 becausewe are concerned with the number of other borrow-ers that show up at the same location as the givenborrower. There are only B�1 other borrowers. Theexpression for prob

lend (B, L), the probability that a

given lender matches with a borrower, is analogous:

1

0 0

A2) ( )

min ,1 ( ) ( 1).1

lend

B L

b lb l

prob B,L

bp b B p L

l

−

= =

=

− + ∑∑

The increasing returns property is illustrated inthe first panel of figure A1. As both L and B rise, theprobability of a match (given by equation 19 or 20)increases. As illustrated in the last two panels of fig-ure A1, equation A1 implies that the probability of agiven borrower matching is increasing in the numberof lenders, L, (holding B constant) and decreasing inthe number of borrowers B (holding L constant).Similarly, the probability of a given lender matchingis increasing in B and decreasing in L.

1See also Hall (1999).2More generally, this result holds if the number of locations in-creases at a slower rate than the number of borrowers and lenders.3This explicitly rules out equilibria of the form, �All borrowers andall lenders choose to go to the kth location with probability one.�

APPENDIX B

Proofs of propositions

Proposition 1Let functions V

borr and V

lend be defined as in equations

B1 and B2 of box 1. Probborr

(B, L) is increasing in Land decreasing in B. Therefore, the condition

QNlend

≥ N*

and equation 7 imply that Vborr

(Bgood

, QNlend

) ≥ Rautarky

for all Bgood

≤ Nborr

� Nbad

. This implies that all goodborrowers enter the match. However, if all good bor-rowers enter the match, then equations 4 and 8 implythat the value of entering the match to a lender ex-ceeds Rf, regardless of the decisions of the otherlenders.1 Therefore, all lenders enter the match.This ends the proof.


NOTES

1An account of the events surrounding the Russian default can befound in Perotti (2000).

2Immediately following the announcement of the rate cut, theDow Jones Industrial Average dropped. Press reports indicate thatmany investors expected a bigger rate cut. The U.S. Chamber ofCommerce described the move as �underwhelming in its modesty�(Schlesinger and Wessel, 1998b), and investors in bond futures�were treating a half-point cut by year�s end as a certainty, and ahalf-point cut tomorrow as a reasonable possibility� (Schlesinger,1998). The federal funds futures market supports this assertion.From September 25 through 28, the price of the October federalfunds futures contract implied an expected fed funds rate ofaround 5.16 percent for the month of October (down from 5.5percent before September 29). This implies that investors putsubstantial probability on a cut of 50 basis points or more at theSeptember FOMC meeting.

3�[M]arkets had been rife with rumors about the possibility of anintermeeting move for the past week or so. �� in Greenlaw (1999).

4The fed funds futures market gives a forecast of the 30-day aver-age federal funds rate over the month of October. The funds ratewas already at 5.25 percent. A rate cut in mid-October to 5.00percent would move the 30-day average of October rates to 5.125percent. If investors only assigned a 50 percent probability tosuch a rate cut, the expected average rate would be approximately5.18 percent.

5The magnitudes of the declines were as follows: UK, 23 percent;Germany, 19 percent; Japan, 18 percent; Canada, 28 percent; Italy,32 percent; and France, 29 percent.

6I would like to thank Eileen Smith of the Chicago Board OptionsExchange for providing me with these data.

7The actual peak in the volatility index came on October 8, 1998,the date of the trough in the S&P 500 index.

8The behavior of default spreads for other G-7 countries gives aless clear picture of the start and end of the crisis. For Canada,France, Italy, and the UK, these spreads move roughly in linewith the U.S. data (although the interbank spread for France is

so volatile that it is difficult to identify peaks and troughs withany degree of certainty). The German interbank spread peaks inNovember 1998, several weeks after the peak in U.S. data. Finally,the behavior of default spreads in Japanese data is rather differentfrom the other G-7 countries. In particular, the Japanese interbankspread shows little evidence of a liquidity crisis until a pronouncedspike in mid-November 1998, well after the crisis abated in the U.S.

9The Board of Governors� Senior Loan Officers Survey can befound on the Internet at www.federalreserve.gov/boarddocs/SnLoanSurvey/. The surveys in August and November 1998 fol-lowed the Board�s usual procedure of asking respondents aboutcredit conditions over the preceding three months. Therefore, theNovember survey reflected most of the crisis period. In contrast,the September 1998 survey was a special survey that only askedabout credit conditions over the previous month.

10This characterization of markets during the crisis is confirmedby other sources. For example, Morgan Stanley Dean Witterreported a sharply reduced volume of activity across the corpo-rate borrowing spectrum. (Roach, 1998.) Similarly, a strategist atMerrill Lynch asserted that �there were literally occasions whenyou could not get a bid of any kind for debt that was a reasonablerisk� (The Economist Newspaper Limited, 1998, p. 75).

11See Schlesinger and Wessel (1998a).

12BIS (1999, p. 42).

13The role of the Federal Reserve Bank of New York in the recapi-talization of LTCM was limited to providing meeting facilities forthe involved parties. The Federal Reserve provided no funds inthe LTCM workout.

14According to the U.S. Department of Commerce, Bureau of theCensus (1998), the U.S. exports of goods and services to Argentina,Mexico, and Brazil in 1997 exceeded $93 billion (13.5 percent oftotal U.S. exports), while U.S. imports from these countries totaledalmost $98 billion (11.2 percent of U.S. total). In contrast, U.S.exports to Russia totaled $3.4 billion (0.49 percent of the U.S.total) with imports from Russia totaling $4.3 billion (0.50 percentof the U.S. total).

Proposition 2If Rf = Rlow, equations 9 and 10 together imply

that if Qi�1

< N*, it is optimal for the ith lender to en-ter the match, even if no good borrowers enter thematch. This follows because equation 9 ensures that,for arbitrary N% ,

, ) ( (1 ) )

(1 ( ))

salvagelend bad lend

lend bad

prob (N N R R

prob N ,N

θ + − θ

+ −

%

%

is decreasing in N% . (Recall that ( , )lend badprob N N% isdecreasing in N% : As more lenders compete with agiven lender, the probability that a lender matchesgoes down.) This in turn means that at least N* lend-ers will enter the match, regardless of what any of

the other lenders or good borrowers do, so QNlend

≥ N*.According to proposition 1, this is sufficient for thehigh coordination equilibrium to prevail. This com-pletes the proof.

Proposition 3To prove proposition 3, note that the monetary

policy rule ensures that there will always be at leastN* lenders committing to enter the match. By prop-osition 1, this is sufficient to ensure that the high-coordination equilibrium prevails. This completesthe proof.

1This assertion uses the fact that assumption 8 implies thatVlend (B,L) is decreasing in L. Therefore, if Vlend (Nborr � Nbad, Nlend)≥ R f, then Vlend (Nborr � Nbad, L) ≥ R f, �L ≤ Nlend.


15Brady bonds are U.S. dollar-denominated obligations of variousdeveloping countries, mainly in Latin America.

16For Indonesia and Malaysia, swap yields for maturities up totwo years and forward exchange rates for up to one year closelytrack the spot exchange rates for these currencies. That is, theseforward-looking markets did not anticipate the currency devalua-tions. Data on these particular markets are not available for Koreaand the Philippines, but yields on government bonds (five-yearmaturity for Korea, one-year maturity for the Philippines) displaythe same patterns as the Indonesian and Malaysian swap yields:they did not budge until these countries devalued their currency.The only country where interest rates (as measured by swap yields)and forward exchange rates moved before the devaluation wasThailand. For that country, both rates started to increase six weeksbefore the devaluation of the baht. However, this coincided withthe initial speculative attacks on the baht and the Thai government�sinitial attempts to defend its currency peg. See Halcomb andMarshall (2001).

17See Burnside, Eichenbaum, and Rebelo (1998).

18In developing this model, I benefited from extensive discussionswith François Velde.

19These second and third characteristics were also associated withthe Asian crisis of 1997. The reduction in liquidity provision tookthe form of a reversal of short-term capital flows from westerncountries. Needless to say, stock markets fell precipitously in allfive Asian crisis countries.

20In this example, which is discussed in Cooper and John (1988),there can be more than two equilibria.

21The classic demonstration of how a search model can give riseto a thick markets externality is Diamond (1982).

22I�d like to thank Eric French for suggesting this interpretation.

23It would be preferable to have the contract emerge as the equi-librium outcome of a bargaining game. This approach is not straight-forward to implement. The Nash (1953) axiomatic approach tosolving the two-person bargaining problem does not generalizeto a game with asymmetric information. An alternative would beto specify a noncooperative bargaining game. For example, onecould assume that either the borrower or lender is randomly giventhe right to make a single take-it-or-leave-it offer. (Mortensenand Pissarides, 1998, note that this game under full informationimplies the same solution as a particular version of the Nash bar-gaining problem.) It is beyond the scope of this article to explorethe range of noncooperative game theoretic approaches to thisproblem. As a result, I adopt the simple expedient of an exog-enous contract.

24My assumption that a lender who fails to match gets a zero netreturn captures the idea that there is some opportunity cost tocommitting to provide loans, rather than investing exclusively inthe risk-free investment. However, the analysis would not bechanged substantially if a lender who fails to match received asmall positive return.

25Lagos (2000) develops a model of passenger�cab matching thatimplies constant returns to scale. The difference between thismodel and the model I develop in appendix A is that Lagos (2000)assumes a continuum of passengers and cabs, whereas my modelassumes that both passengers and cabs are discrete and finitein number.

26More recently, DenHaan, Ramey, and Watson (1999) andBurdette, Imai, and Wright (2000) propose search models thatgive rise to nontrivial multiple equilibria even with constantreturns to scale.

27The baseline parameters used in figure 4 are: Nlend = 20; Nborr = 30;R = 2; Rlend = 1.2 (so Rborr = 0.8); Rsalvage = 0.5; pb = 0.2; θ = 0.75.Parameter Nbad is set equal to its expected value of 6. I use themodel of prob

lend and prob

borr described in appendix A, equations

A2 and A1, with parameter M = 10.

28Of course, this static model cannot address the question of whyexisting assets decline in value. If existing productive assets uti-lize a continued flow of credit to maintain high profitability, areluctance of lenders to provide credit would presumably reduceasset values. However, it would require a dynamic extension ofthis model to analyze this effect formally.

29In the literature on financial fragility, this is typically done byassuming an exogenous �sunspot process,� whose realizationdetermines the state of optimism in the economy. (See, for example,Chang and Velasco 1998, Christiano and Harrison 1996, andBurnside, Eichenbaum, and Rebelo 2000.) I do not explicitlyimplement this approach for rendering the model dynamic, butto do so would be straightforward.

30While figure 5, panel B displays the real overnight interest rate,the relevant rate for bank incentives is the expected rate of returnfrom holding longer-term fixed income securities. Forecastingexpected real holding period returns is a process fraught withdifficulty, and I do not attempt to do so here. However, simpleterm structure models (such as the expectations hypothesis) implythat expected real holding period returns move with short-termreal interest rates. Figure 5, panel B suggests that the expectedreturns relevant to bank decisions fell substantially as a result ofthe Federal Reserve�s expansionary policy from 1991 to 1993.

31Quoted in Murray (1987).

32For an account of these events, see the Securities ExchangeCommission report excerpted in Kamphuis et al. (1989).

33For example, the Morgan Stanley Dean Witter Global EconomicForum of September 25, 1998, noted that a large rate cut at theFOMC meeting four days later �� may reflect a potentiallyprofound transformation in the Fed�s basic philosophy.� Theforum argued �� that the biggest risk of all is that the world�spolicymakers may not be up to the task at hand.� Similarly, JacobSchlesinger wrote in the Wall Street Journal of September 28,1998, that �an easing of monetary policy would mark a swift andamazing turnaround in the central bank�s fundamental economicoutlook. For well over a year, the Fed�s greatest concern has beeninflation, not recession.�

34Schlesinger and Wessel (1998a), p. A3.

35Morgan Stanley Dean Witter (1999).

36Minutes of the FOMC can be obtained from the Federal Reservewebsite at www.federalreserve.gov/fomc/minutes/.

37Schlesinger and Ip (1998).


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The crisis of 1998 and the role of the central bank

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