A Theory of Rollover Risk, Sudden Stops, and Foreign Reserves

BoardofGovernorsoftheFederalReserveSystem InternationalFinanceDiscussionPapers Number1073 February2013 A Theory of Rollover Risk, Sudden Stops, and Foreign Reserves SewonHurandIlleninO.Kondo NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Networkelectroniclibraryatwww.ssrn.com.

A Theory of Rollover Risk, Sudden Stops, and Foreign Reserves Sewon Hur Illenin O. Kondo University of Pittsburgh Federal Reserve Board February 15, 2013 Abstract Emergingeconomies,unlikeadvancedeconomies,haveaccumulatedlarge foreign reserve holdings. We argue that this policy is an optimal response to an increase in foreign debt rollover risk. In our model, reserves play a key roleinreducingdebtrollovercrises(“suddenstops”),akintotheroleofbank reserves in preventing bank runs. We find that a small, unexpected, and permanent increase in rollover risk accounts for the outburst of sudden stops in the late 1990s, the subsequent increase in foreign reserves holdings, and the salient resilience of emerging economies to sudden stops ever since. Finally, weshowthatapolicyofpoolingreservescansubstantiallyreducethereserves neededbyemergingeconomies. Keywords: rolloverrisk,reserves,suddenstops JELclassification: F42,F34,H63 Hur: sewonhur@pitt.edu|Kondo: kondo@illenin.com. WethankCristinaArellano,AndrewAtkeson,V.V.Chari,Daniele Coen-Pirani,BoraDurdu,TimKehoe,EnriqueMendoza,FabrizioPerri,MarlaRipoll,andJohnRogersformanyvaluable comments. WehavealsobenefitedfromcommentsbyseminarparticipantsattheUniversityofMinnesota, Washington UniversityinSt. Louis,theSocietyforEconomicDynamics2011meetings,theCantabriaNobelCampus2012meetings, theUniversityofPittsburgh,theFederalReserveBoard,theMidwestMacroeconomics2012FallMeetings,andtheFederal ReserveBankofMinneapolis. Thedatausedinthispaperareavailableonline. Firstdraft: September2010. Theviewsin thispaperaresolelytheresponsibilityoftheauthorsandshouldnotbeinterpretedasreflectingtheviewsoftheBoardof GovernorsoftheFederalReserveSystemorofanyotherpersonassociatedwiththeFederalReserveSystem.Allerrorsand shortcomingsareoursalone.

1 Introduction Sincetheturnofthecentury,emergingeconomieshaveaccumulatedmassiveamounts ofinternationalreserves. AccordingtoBernanke (2005),thishasbeenthemostimportant channel through which the global “savings glut” widened the U.S. current account deficit. For instance, in 2007, the foreign reserve holdings of China (1.5 trillion US dollars) alone represented approximately 65 percent of the (negative) netforeignassetpositionoftheUnitedStates. Whilemassivefromanabsoluteperspective,China’sreservesasapercentageofGDP,whichaveraged33percentfrom 2002-2007, are comparable to that of other emerging economies such as Korea (25 percent),Malaysia(47percent),andRussia(23percent). This raises the question of why emerging economies have accumulated such largeamountsofreserves. Onestrandoftheliteraturefocusesonreservesasaform ofprecautionarysavingsineconomieswherecrisesoccurexogenously(Alfaroand Kanczuk 2009; Bianchi et al. 2012; Caballero and Panageas 2007; Jeanne and Ranciere 2011). These theories imply that reserves should be higher when crises are more frequent. However, Gourinchas and Obstfeld (2012) find that reserves are negatively associated with crises in the data. Another strand of the literature considers the role of a country’s net foreign asset (NFA) position in preventing crises, without explicitly modeling reserves (Durdu et al. 2009; Mendoza 2010). In contrast, we document that a country’s NFA is not significantly associated with crisesinthedata. In this paper, we develop a theory in which reserves endogenously prevent crises. In particular, we focus on sudden stops (unusually large reversals of externalcapitalinflows)becausetheyareacommonsymptomoffinancialcrisessuch as currency crises, banking crises, and default crises in emerging economies.1 In thistheory,suddenstopsoccurwhenforeignlenderschoosenottorolloveracoun- 1While acknowledging other potential motives for holding reserves such as foreign exchange management(seeforexampleDooleyetal. 2004),wefocusontheroleofreservesasabuffer(and preventive measure) against sudden stops. This is consistent with the view of policymakers. For example, Ben Bernanke stated that “foreign reserves have been used as a buffer against potential capitaloutflows”(Bernanke 2005)andarecentIMFsurveyofreservemanagersfoundthatbuilding a“bufferforliquidityneeds”wastheforemostreasonforbuildingreserves(InternationalMonetary Fund 2011). 2

try’s external liabilities. We consider the problem of a small open economy that borrows short-term from foreign lenders to finance long-term investments. This maturity mismatch gives rise to rollover risk: in the interim, a random fraction of creditors can choose to roll over while the other creditors cannot.2 Rollover risk in thisenvironmentisendogenousbecausetheactualamountofdebtthatisrolledover is determined by the optimal debt arrangement. Faced with stochastic interim liquidityneeds,thegovernmentmaypaywiththereservesithadsetasideorliquidate its investment. For small enough liquidity shocks, interim payments are optimally paidwithreservesandnosuddenstopoccurs. Forsufficientlylargeshocks,thegovernment cannot finance its debt obligations without liquidation. Sufficiently large shocks therefore result in a sudden stop as all lenders refuse to roll over. Reserves inturnreducetheprobabilityofsuddenstopsandincreasewithrolloverrisk. This paper makes empirical, theoretical, and quantitative contributions. First, using the panel discrete-choice approach of Gourinchas and Obstfeld (2012), we show that reserves are negatively associated with sudden stops in addition to default crises, banking crises, and currency crises. In contrast, we document that a country’snetdebtisnotassociatedwithmostcrisesinemergingeconomies. These results suggest that reserves should be modeled explicitly to understand financial crises. Second, we develop a tractable model in which reserves endogenously reduce the probability of a sudden stop. Using closed form solutions, we show that both the optimal reserves-to-debt ratio and the induced probability of sudden stop increaseastherolloverriskrises. Themodelisthencalibratedfortwoquantitativeapplications. First,asmallbut unanticipated, and permanent increase in rollover risk can account for the shortlived outburst of sudden stops in the late 1990s, and the large accumulation of foreignreservessincethen. Amodelinwhichreservesdonotaffecttheprobability of a sudden stop cannot jointly match these facts. Second, mutual insurance across emerging economies could reduce the amount of reserves needed by as much as two-thirds: poolingorswappingreserveslowersrolloverriskacrosstheboard. This paper builds on a large body of literature on reserves, sudden stops, and 2ArellanoandRamanarayanan (2012)andBroneretal. (2007)exploremodelsofdebtmaturity andwhyemergingeconomiesissueshort-termdebt. 3

debt crises. In particular, it relates to other papers on reserves (Aizenman and Lee 2007;Calvoetal. 2012;FrenkelandJovanovic 1981;Heller 1966;Obstfeldetal. 2010),andonsuddenstops(Calvoetal. 2004;Kehoeetal. 2012;Mendoza 2010 ). Ourworkdepartsfromtheliteraturebyexplicitlymodelingtherolloverdecision offoreignlenders,therebycruciallyendogenizingtheprobabilityofasuddenstop. The endogenous relationship between reserves, rollover risk, and sudden stops is precisely what allows our model to generate an outburst of sudden stops with a smallbutunexpectedincreaseinrolloverrisk. Our paper is also related to the literature on coordination problems and selffulfilling crises (Cole and Kehoe 2000; Chang and Velasco 2001). In contrast, this paper focuses on debt rollover crises that arise from an optimal arrangement between a borrower and its lenders. Morris and Shin (2006) and Kim (2008) alternatively use the global games framework of Morris and Shin (1998) to study optimal external bailout and optimal reserves. In these coordination games, information dispersion across creditors and aggregate risk interact to induce rollover risk. This paper generates rollover risk from heterogeneous liquidity shocks and canquantitativelyaccountforboththelargebuildupinreservesandtheoutburstof suddenstopsinthedata. This paper is structured as follows. Section 2 empirically analyzes foreign reserves and sudden stops in emerging economies from 1990 to 2007. In section 3, wepresentamodelofrolloverrisk,suddenstops,andreserves,andcharacterizeoptimalreservesandendogenoussuddenstopprobabilities. In section4,wecalibrate a multi-country dynamic extension of the model applied to emerging economies. Section5concludes. 2 Reserves and Sudden Stops in Emerging Economies Inthissection,wedocumentasetofstylizedfactsregardingforeignreserves,externaldebtliabilities,andsuddenstopsin23emergingeconomiesduring1990-2007.3 3The dataset stops in 2007 because the external debt liabilities series constructed by Lane and Milesi-Ferretti (2007)stopsin2007. Otherdataontheseemergingeconomiesafter2007indicates thatsuddenstopswerestillrareandreservesremainedhighcomparedtothelate1990s. Thedataset 4

We use the International Financial Statistics (IFS) dataset in conjunction with the updatedandextendedversionofthedatasetconstructedbyLaneandMilesi-Ferretti (2007). The list of emerging economies used in this paper includes Argentina, Brazil, Chile, China, Colombia, the Czech Republic, Egypt, Hungary, India, Indonesia, Malaysia, Mexico, Morocco, Pakistan, Peru, Philippines, Poland, Romania, Russia, South Africa, South Korea, Thailand, and Turkey. This list includes countries appearinginmostclassificationsofemergingcountries. 2.1 Sudden Stops in Emerging Economies Following Calvo et al. (2004), we define a sudden stop episode as a spell with exceptionallylargecurrentaccountreversalsandarecession. Wefind13suddenstop experiences during 1990-2007 across the 23 emerging economies with an outburst of10suddenstopsbetween1997and2001.4 To highlight the outburst of sudden stops after the mid-1990s, we divide this time frame into three periods as shown in Figure 1: 1990-1996 is a period of low-frequency sudden stops (with 3 occurrences), 1997-2001 is a period of highfrequency sudden stops (with 10 occurrences), and 2002-2007 is a period of lowfrequencysuddenstops(withnooccurrence). 2.2 Foreign Reserves In the IFS dataset, foreign reserves are defined as all official public sector foreign assets, except gold, that are readily available to and controlled by the monetary authorities. Wehighlighttwonotablefactsregardingforeignreservesholdings. startsafter1990becauseofdataavailability,especiallyforcurrentaccountdata.Moreover,financial liberalizationinemergingeconomieswaslargelystillongoinginthelate1980s,asdocumentedby Bueraetal. (2011). 4Our sudden stop episodes are: Turkey (1994), Argentina, Mexico (1995), Thailand (1997), CzechRepublic,Indonesia,Philippines,SouthKorea(1998),Chile,Peru,Russia(1999),Argentina, Turkey (2001). Durdu et al. (2009) report other episodes: Malaysia (1997), Brazil, Colombia, Pakistan (1999). In any case, there was an outburst in sudden stops between 1997 and 2001. Our methodologyforconstructingsuddenstopepisodesisexplainedinthedataappendix. 5

Figure1: SuddenStopsinEmergingEconomies 10 3 0 sedosipe pots neddus fo rebmun 01 8 6 4 2 0 Sudden Stops in Emerging Economies 1990−1996 1997−2001 2002−2007 The first fact is that foreign reserves in emerging economies, both as a percent ofGDPandandasapercentofexternaldebtliabilities,aresignificantlyhigherthan those in advanced economies5. The second fact is that these ratios have increased in emerging economies while they have decreased in advanced economies. These factsaresummarizedinFigures2and3. Figure2: ForeignReserves(percentofGDP) 20 17 15 10 7 5 3 2 0 PDG fo tnecrep Foreign Reserves over GDP 1990−19962002−2007 1990−19962002−2007 emerging economies advanced economies Note:Thevalueforeachperiodandeachblocisthemedianacrosseconomiesoftheperiod-averageforeacheconomy. It is worth noting that this phenomenon of increasing reserves is not limited to 5Advanced economies here include the major reserve currencies: France, Germany, U.K., and U.S. 6

just a few countries. In fact, foreign reserves are increasing in almost all emerging economies with Chile being the only case in which reserves are decreasing in both measures. ThisrobustobservationisshowninTableA.1(seeappendix)ofaverage foreignreservesbycountryandperiod. Figure3: ForeignReserves(percentofExternalDebtLiabilities) 41 40 30 20 17 10 4 1 0 tbed lanretxe fo tnecrep Foreign Reserves over External Debt Liabilities 1990−19962002−2007 1990−19962002−2007 emerging economies advanced economies Note:Thevalueforeachperiodandeachblocisthemedianacrosseconomiesoftheperiod-averageforeacheconomy. 2.3 Reserves and Sudden Stop Probabilities Following Gourinchas and Obstfeld (2012), we use a panel discrete-choice model to document the effect of foreign reserves on sudden stops. They documented that foreign reserves are associated with reduced banking crisis, currency crisis, or sovereign default. We further document that higher foreign reserves are also associatedwithreducedsuddenstoplikelihood. Incontrast,netforeignassetsarenot typicallyassociatedwithareducedprobabilityofacrisis. Weuseapanellogitmodelwithcountryfixedeffects: Pr (cid:0) Si =1|x (cid:1) = exp(α i +βx i ) k i 1+exp(α +βx) i i where Si denotes whether country i is in a sudden stop episode in the next k years k 7

and x are foreign reserves and net foreign assets in country i during a year that is i not0to3yearsafterasuddenstopepisode(thatis,“tranquil”timesusingtheterminology of Gourinchas and Obstfeld (2012)). The sample is restricted to “tranquil” timestoavoidpost-crisisbias. The results of the panel logit estimation are reported in Table 1. Foreign reserves are significantly associated with a reduced probability of sudden stops. For instance, an increase of one standard deviation in the ratio of foreign reserves to external debt liabilities (around 20 percent) is associated with a fall of 7 percent in the probability of a sudden stop over the next two years. The results in Table 1 thereforeextendthefindingsinGourinchasandObstfeld (2012)ontheimportance of foreign reserves. Table 1 also shows that, unlike foreign reserves, net foreign assets are not commonly associated with crises.6 These findings therefore suggest that foreign reserves should be explicitly modeled to understand financial crises in emerging economies. We develop a theory of rollover risk, sudden stops, and foreignreservesinthenextsection. 3 Model 3.1 Environment We consider a small open economy model with three stages: s=0 (initial), 1 (interim), 2 (final). There is a unit measure of risk neutral foreign lenders who can lendtothedomesticcountry.7 Thedomesticcountryhasarepresentativeagentwho has linear preferences u(C)=C over final stage consumptionC. The government chooses allocations and debt arrangements to maximize the expected utility of the domestic agent. An overview of the sequence of actions taken by the government andthelendersispresentedinFigure4. 6Weobtainsimilarresultswhenweseparatelyestimatethemodelforeachvariable.Thefindings are also similar using alternative measures of reserves such as the reserves-to-GDP ratio used by GourinchasandObstfeld (2012). Wepreferreservesasafractionofexternaldebtliabilitiessinceit isameasureconsistentwithourtheory. 7Weassumethattheforeigners’capitalendowmentisfiniteandlargeenough. 8

Table1: PanelLogitEstimationacrossEmergingEconomies 1-2years 1-3years S.D. δp ∂p δp ∂p ∂x ∂x PanelA:SuddenStops Reserves 20.16 -7.13*** -0.52*** -10.43*** -0.68*** overExternalDebt (1.45) (0.14) (2.28) (0.19) NetForeignAssets 10.07 -3.86* 0.46 -8.33** -1.00*** overGDP (2.30) (0.32) (2.87) (0.42) Probabilityinpercent(p) 11.76 20.37 PanelB:DefaultCrises Reserves 21.58 -8.08*** -0.71*** -12.41*** -1.11*** overExternalDebt (2.15) (0.21) (3.10) (0.29) NetForeignAssets 7.79 -3.95* 0.63 -6.16** -0.98* overGDP (2.34) (0.47) (2.88) (0.56) Probabilityinpercent(p) 10.11 15.01 PanelC:BankingCrises Reserves 27.98 -3.92 -0.42** -7.12** -0.69*** overExternalDebt (2.47) (0.17) (3.00) (0.18) NetForeignAssets 7.42 -0.89 -0.14 -1.64 0.25 overGDP (0.95) (0.16) (1.45) (0.24) Probabilityinpercent(p) 4.12 7.67 PanelD:CurrencyCrises Reserves 24.54 -2.00 -0.36* -4.52* -0.70** overExternalDebt (1.65) (0.21) (2.49) (0.25) NetForeignAssets 8.60 -0.43 0.04 1.95 0.19 overGDP (0.94) (0.09) (2.10) (0.18) Probabilityinpercent(p) 2.02 4.62 Note: *,**,and***denotesignificanceatthe10,5,and1percentlevel. ∂p/∂xisthemarginaleffectinpercentageat “tranquil”samplemean. s.d.(x)istheunconditionalstandarddeviationofxover“tranquil”times. Robuststandarderrors inparenthesesarecomputedusingthedelta-method. Theestimationsampleisanunbalancedpanelthatspans20emerging countriesbetween1990and2007.Currency,banking,anddefaultcrisesdatesfollowGourinchasandObstfeld (2012). 9

Figure4: Timeline Govt. pays Govt. sets Govt. repays Govt. offers the debt called reserves and the rolled over debt contract with reserves investments debt or liquidation Liquidity Final Domestic shocks output consumption realized occurs 0 1 2 Each lender Each lender chooses to lend chooses to roll over or not or not The domestic country has access to two technologies à la Diamond and Dybvig (1983). The first technology transforms the investment K made in the initial stage into AK units in the final stage if production is uninterrupted. However, if productionisinterruptedintheinterimthroughtheliquidationofL∈[0,K]unitsof investment,thetechnologyyieldsλLintheinterimandA(K−L)inthefinalstage. Weassumethatliquidationiscostly, λ <1. (1) Further,weimposethatthereisnopartialinterimliquidation, L∈{0,K}. (2) Thisassumptionoffullliquidationismadeforanalyticaltractabilityandisrelaxed inthenextsection. Thesecondtechnologystoresresources(reserves)acrossstages withoutdepreciation. Thesetechnologiesaresummarizedbythefollowingtable: 10

Technologies s=0 s=1 s=2 Productionandliquidation −K λL A(K−L) investment liquidation finaloutput Reserves −R R 1 1 initialreserves −R R 2 2 interimreserves Intheinitialstage,thedomesticgovernmentborrowsDfromforeignlendersto financeitsinitialstageinvestments, R +K ≤D. (3) 1 In the interim, a random fraction ϕ of the foreign lenders receive liquidity shocks denoted by ϕi = 1, meaning that they must call the loan and be repaid back. The remaining fraction (1−ϕ) of lenders with ϕi =0 can call or roll over their loans. Therandomaggregateliquidityshockϕ ∈[0,1]hasacumulativedistributionfunction that follows the bounded Pareto distribution given by F (ϕ)=1−(1−ϕ)1/σ σ withσ >0. We denote ψi = 0 if lender i rolls over the loan and ψi = 1 otherwise. The ´ fraction of lenders calling the loan is: ψ ≡ ψ(cid:96)d(cid:96). We assume that individual lenders cannot coordinate on rollover decisions. We call it a sudden stop when all lenders refuse to roll over in the interim (ψ =1). However, all lenders may panic andrefuse to rolloverregardless ofthestateof theeconomy. Inthispaper,we rule out these self-fulfilling “panic” runs, and instead focus on “rational” sudden stops thatoccuraspartoftheoptimalcontractdependingonthestateoftheeconomy.8 We allow the debt repayment of the debt D to be contingent on whether or not the economy is facing a sudden stop. During normal times, foreign lenders receive 8This is in contrast to Diamond and Dybvig (1983) who focus on the limits to optimal risksharingamongcreditorsthatarisefromself-fulfilling“panic”runs. Moregenerally,onecanallow forboth“panic”crisesand“rational”suddenstopstooccurusingasunspotvariable. Ourrestriction iswithoutlossofgeneralityifcrisispayoffforthegovernmentiszeroasisthecaseinthissection. 11

P = D if they call the loan in the interim, and P = (1+r )D in the final stage 1 2 N if they roll over the loan.9 During a sudden stop, however, all the lenders call the debt and receive P =(1+r )D in the interim. The debt repayment schedule can 1 S besummarizedas: InterimpaymentP FinalpaymentP 1 2 Normaltimes(ψ <1) D (1+r )D N Suddenstop(ψ =1) (1+r )D 0 S Because the interest rate can be different when the economy is in sudden stop, the government can choose to partially default during sudden stop episodes by setting r <r . However, there is a limit to the haircut the lenders can suffer because S N theycancollectivelybargainandextractafractionθ oftheinterimresourcesavailable(R +λK).10 Theconstraintarisingfromthiscollectivebargainingoutcomeis 1 givenby: (1+r )D≥min{(1+r )D,θ(R +λK)} (4) S N 1 Inthissection,weimposeθ =1. Thisassumptionisrelaxedinthenextsection. 3.2 Feasible Debt Contracts We now define the feasibility constraints that the debt contract offered by the government must satisfy in this environment. First, we define a debt contract as a list of: • four scalars: {R , K, r , r } representing the initial reserves, the invested 1 N S capital,thenormalinterestrate,andthesuddenstopinterestrate,and • four state-contingent functions: (cid:8) C(ϕ), R (ϕ), L(ϕ), ψi(cid:0) ϕ,ϕi(cid:1)(cid:9) , which 2 denote the final consumption, the interim reserves, the interim liquidation, andtheindividualrolloverpolicies,respectively. 9Theassumptionthatlendersreceivezeronetreturnondebtcalledintheinterimisnotessential. 10Thesovereigndebtliterature(seeYue 2010)documentstheuseofcollectiveactionduringdebt renegotiation. 12

Resource feasibility A debt contract is resource feasible if it satisfies equations (2)and(3)aswellasthefollowingconstraints: R (ϕ)+ψ(ϕ)P (ψ(ϕ)) ≤ R +λL(ϕ) ∀ϕ (5) 2 1 1 C(ϕ)+(1−ψ(ϕ))P (ψ(ϕ)) ≤ R (ϕ)+A(K−L(ϕ)) ∀ϕ (6) 2 2 0 ≤ R , R (ϕ), C(ϕ) ∀ϕ. (7) 1 2 Equation (5) requires that interim debt payments and interim reserves cannot exceedinitialreservesandinterimliquidation,whileequation(6)requiresthatfinal debtpaymentsandconsumptioncannotexceedinterimreservesandfinaloutput. Interimindividualrationality Adebtcontractisinterimindividuallyrationalif, foreachaggregateliquidityshockϕ andindividualliquidityshockϕi, V (cid:0) ψi|ϕ,ϕi(cid:1) ≥V (cid:0) 1−ψ i|ϕ,ϕ i(cid:1) (8)    P 1 (ψ(ϕ)) ifψi =1 where V (cid:0) ψi|ϕ,ϕi(cid:1) = 1 ·P (ψ(ϕ)) ifψi =0.  ϕi=0 2 This condition requires that the rollover policy yields a payoff at least as high as that from deviating. The lender payoff is given by P (ψ(ϕ)) when calling, and 1 P (ψ(ϕ))whenrollingover,ifthelenderdidnotreceivealiquidityshock. 2 Ex ante participation constraint A debt contract satisfies the ex ante participation constraint if ex ante the debt contract is as profitable as investing at the world interestrater : W E (cid:2) V (cid:0) ψ i|ϕ,ϕ i(cid:1)(cid:3) ≥ (1+r )D. (9) W Expostrenegotiationproofness Finally,adebtcontractisexpostrenegotiationproof ifitsatisfiesequation(4). Thisconditionlimitsthehaircutsufferedbylenders inasuddenstop. 13

3.3 Optimal Debt Contract Anoptimaldebtcontract isatuple, B∗ = (cid:8) R∗,K∗,r∗,r∗,C∗(ϕ),R∗(ϕ),L∗(ϕ),ψ i∗(cid:0) ϕ,ϕ i(cid:1)(cid:9) , 1 N S 2 which maximizes the expected utility of the domestic agent subject to resource feasibility,interimindividualrationality,theexanteparticipationconstraint,andex postrenegotiation-proofness. Inotherwords,thegovernmentsolves: max E [C(ϕ)] B ϕ subjectto (2)−(9). 3.4 Characterization Wenowcharacterizethesolutiontotheoptimaldebtcontractproblem. Proposition1. OptimalDebtContract AnoptimaldebtcontractB∗ satisfies: (i)Interimpaymentsarepaidexclusivelywithreservesuntiltheyaredepleted:  R∗(ϕ)>0 ⇐⇒ ϕ ∈[0,ϕ∗) ∃ ϕ∗ ∈[0,1]s.t. 2 R R L∗(ϕ)=0 ⇐⇒ ϕ ∈[0,ϕ∗) R R∗ (cid:20) A−1 (cid:18) σ (cid:19)(cid:21)σ Furthermore,theoptimalreservesratiois: ϕ∗ = 1 =1− . R D A−λ σ+1 (ii)Forsufficientlylargeaggregateshocks,alllenderscalltheirloans:  ψ(ϕ)=ϕ ∀ϕ ∈[0,ϕ ) S ∃ ϕ∗ ∈[0,1]s.t. S ψ(ϕ)=1 ∀ϕ ∈[ϕ ,1] S Furthermore,suddenstopsoccurwheneverreservesaredepleted: ϕ∗ =ϕ∗. S R Proof: Seeappendix. 14

Proposition 1(i) and 1(ii) establish that there are cutoff rules for reserves, liquidation, and sudden stops. In Proposition 1(i), ϕ∗ is the liquidity shock at which R reservesaredepletedandthegovernmentmustliquidatetheinvestedcapitaltomeet the promised payments. Because λ <1, the government uses existing reserves to meet payments before eventually liquidating the invested capital. Proposition 1(i) alsoestablishesthattheoptimalreserves-to-liabilitiesratioisϕ∗. R In Proposition 1(ii), ϕ∗ is the liquidity shock above which all lenders exit. We S identify this debt rollover crisis as a sudden stop. The sudden stop cutoff ϕ∗ is S equaltotheoptimalreserves-to-debtratioϕ∗becauseweassumedthereisnopartial R liquidation. Asuddenstopthereforeoccursassoonasthenormalinterimpayments cannot be met using reserves. We later relax the full liquidation assumption. With partialliquidation,thesuddenstopcutoffandthereservescutoffnolongercoincide. The following corollary establishes the endogenous relation between the optimal reserves and the probability of sudden stops. In this environment, reserves are settobalancethesuddenstoprisksincurredwhenreservesarenothighenoughand thecostofholdingidlereserves. Corollary1. EndogenousSuddenStopProbability TheoptimalcontractB∗ inducesapositiveprobabilityPr(ψ =1)>0thatasudden stopoccurs. Furthermore,Pr(ψ =1)=1−F (ϕ∗). σ R Proof: ThisfollowsimmediatelyfromProposition1. 3.5 Comparative Statics In this subsection, we discuss how reserves and sudden stop probabilities are affectedbychangesintheunderlyingliquidityrisk,thatis: changesinσ. Proposition2. Reserves,SuddenStopProbability,andDebtRolloverRisk (i)Theoptimalreservesratioisincreasingintheaggregateliquidityrisk. Thatis: ∂ϕ∗ R >0 ∂σ 15

(ii) The sudden stop probability is also increasing in the aggregate liquidity risk. Thatis: ∂Pr(ψ(ϕ)=1|σ) >0 ∂σ Proof: Seeappendix. Proposition 2 establishes that both the optimal reserves and the implied sudden stopprobabilityareincreasingintheliquidityrisk. Alargerliquidityriskσ induces larger interim shocks and prompts the domestic government to invest in additional reserves. However, the increase in reserves does not completely offset the higher probability of larger shocks, thus leading to an increase in the debt rollover risk. Basedonthisproposition,wesimplyrefertotheaggregateliquidityriskparameter σ as“rolloverrisk”throughoutthepaper. Figure5: SuddenStopandDebtRolloverRisk c.d.f. F L 1 F H Pr1|,* L R L Pr1| ,* H R L Pr1|,*  L R H  0 *  *  1 R L R H A central question that we address using Proposition 2 is: what happens during an unexpected increase in rollover risk, say in the wake of globalization? Figure 16

5 shows how an unexpected increase in σ from σ to σ >σ leads to a increase L H L in sudden stop probability as represented by the dashed vertical line. Obviously, the government does not hold enough reserves, given the unexpected increase in rollover risk. We later show quantitatively that a small, but unanticipated increase inrolloverriskleadstoashort-livedoutburstofsuddenstopsandadramaticrisein reservesasseeninthedata. 3.6 Self-Insurance versus Mutual Insurance In the self-insurance setup above, a government faces aggregate uncertainty stemming from its debt rollover risk. An individual government may over-accumulate reservescomparedtoaworldinwhichgovernmentscanpoolreservesandmutually insure against their idiosyncratic rollover risk. We now characterize the extent of reservesover-accumulation. Forsimplicity,considertheproblemofaplannerwhocanswapresourcesacross a continuum of countries facing i.i.d. idiosyncratic liquidity shocks ϕj with c.d.f. F . By the law of large numbers, the total measure of lenders who must call the σ debt is E[ϕ] = σ/(σ+1). In that sense, there is no aggregate uncertainty across countriesastheyinsureeachother.11 In fact, the planner could set reserves to E[ϕ] and thereby prevent any sudden stopfromoccurringinanycountry. Thispolicyisindeedoptimalwhentheliquidity riskissufficientlylow. Proposition3. Self-InsuranceversusMutualInsurance Consider a continuum of countries subject to i.i.d. liquidity shocks. Each country individuallyover-accumulatesreservescomparedtothemutualinsuranceoutcome ϕC. Thatis: R ϕ ∗ >E[ϕ]≥ϕ C ∀σ ∈(0,1) R R Moreover,ifσ ≤(1−λ)/A,thenϕC =E[ϕ]. R 11Clearly, totheextentthatliquidityshocksarecorrelatedacrosscountries, thei.i.d. caseoverstates the gains from mutual insurance. Akinci (2012) finds that global factors account for 20 percentofmovementsinaggregateactivityinemergingeconomies. 17

Proof: Seeappendix. Proposition 3 establishes that countries hold more reserves than needed if they could mutually insure against idiosyncratic liquidity shocks. The mutual insurance problemhassimilaritieswiththeliquidityprovisionproblemstudiedbyHolmström and Tirole (1998). Under mutual insurance, economies that face large liquidity shocks in the interim can access the reserves of economies with small liquidity needs, thereby reducing the overall debt rollover risk and the reserves required to manage it. In the next section, we quantify the over-accumulation of reserves after calibratingtheliquidityriskfacedbyemergingeconomies. 4 A Multi-Country Dynamic Application The previous section highlighted the relationship between rollover risk, sudden stops,andreserves. Inthissection,weextendthismodelalongtwodimensions. First, the model is extended to an infinite horizon environment in which each period t contains the three stages, s = 0,1,2, of the basic model. At the end of each period t, the government chooses how much reserves to transfer to the next period. Second, the model is extended to a multi-country environment in which agentslearnabouttheunderlyingrolloverrisk,σ ,usinginformationonthesudden t stopoccurrenceseachperiod. 4.1 Environment WeconsiderN identicalsmalleconomiesindexedby j=1,...,N. Timeisinfinite, discrete,andindexedbyt =0,1,...,∞. Eachcountryispopulatedbyaninfinitelylived representative agent and a welfare-maximizing government. The agents in (cid:104) (cid:105) country j order consumption sequences according to E ∑ ∞ βtC j where β is 0 t=0 t the discount factor. There is a continuum of infinitely lived risk-neutral foreign lendersindexedbyi∈[0,1]. Anoverviewofthetimelineofthisextendedmodelis showedinFigure6. Each time periodt is divided into three stages, s=0,1,2, and encapsulates the threestagesofthepreviousmodel: 18

Figure6: ExtendedTimeline Govt. sets Govt. pays Govt. repays reserves and the debt called rolled over debt, investments using with reserves saves reserves,and loan and savings or liquidation household consumes Liquidity Final shocks output t t1 realized occurs s0 s1 s2 update beliefs belief  t  and t1 using saved Each lender chooses sudden stops reserves to roll over or not across the world (sudden stop if no rollover) • s=0istheinitialcontractingstage, • s=1istheinterimstagewhenliquidityshocksoccurandrolloversdecided, • s=2isthefinalproductionandconsumptionstage. j Theaggregateinterimliquidityshockincountry jattimet isdenotedbyϕ ∈[0,1]. t j Asinthebasicmodel,thismeansthatafractionϕ ofcountry j’screditorsmustcall t thedebtintheinterimwhiletheotherscanrolloverorcallthedebt. Theaggregate (cid:110) (cid:111)∞ j shocks ϕ : j=1...N are independent and identically distributed across t t=0 countriesandtime,withcumulativedistributionfunctionF (ϕ)=1−(1−ϕ)1/σt. σt Weassumeσ ∈{σ ,σ }withσ <σ . t L H L H Thisrolloverriskparameterσ isunobservedandunknowntotheagents. Howt ever,allagentsshareacommonbeliefρ attimet: t ρ ≡Pr(σ =σ ) t t L At the end of each period t, agents observe the sudden stop occurrences in the N countries. Using these sudden stop occurrences and the endogenous sudden stop probabilities, agents update their beliefs according to Bayes’ rule as detailed in section4.3. 19

Withineachperiodt,thetechnologiesavailableatastagesareidenticaltothose intheprevioussection.12 Inaddition,attheendofeachperiod,thegovernmentcan j j saveR reservesforthenextperiodusingtheremainingreservesR : 0,t+1 2,t (cid:104) (cid:105) j j R ∈ 0, R . 0,t+1 2,t Wenowallowforpartialliquidationintheinterim: (cid:104) (cid:105) j j L ∈ 0, K . t t Thisimpliesthatsuddenstopsmaynotoccurassoonasreservesaredepleted. 4.2 Optimal Recursive Debt Contracts Werepresentthegovernment’sinfinitehorizonproblemasarecursivedynamicprogramming problem. The problem has one endogenous state, the level of incoming j saved reserves, R , and one exogenous state, the common belief, ρ . The state of 0,t t (cid:16) (cid:17) j economy j attimet isthengivenby(R ;ρ)= R ;ρ . 0 0,t t The optimal recursive debt contract, B∗(R ;ρ), is a set of policy functions 0 for initial reserves: R (R ;ρ), invested capital: K(R ;ρ), normal interest rates: 1 0 0 r (R ;ρ), sudden stop interest rates: r (R ;ρ), sudden stop cutoffs: ϕ (R ;ρ), N 0 S 0 S 0 consumption: C(R ,ϕ;ρ),interimreserves: R (R ,ϕ;ρ),liquidation: L(R ,ϕ;ρ), 0 2 0 0 saved reserves: R(cid:48) (R ,ϕ;ρ), and rollover policies: ψi(cid:0) R ,ϕ,ϕi;ρ (cid:1) which satisfy 0 0 0 thefunctionalequation: W(R ;ρ)= max E (cid:2) u(C(ϕ))+βW (cid:0) R(cid:48);ρ (cid:1)(cid:3) 0 ϕ|ρ 0 B∈Γ(R ) 0 As in the previous section a debt contract is feasible, that is, B ∈ Γ(R ), if it 0 satisfies resource feasibility, interim individual rationality, the ex ante participation constraint, and ex post renegotiation proofness. Resource feasibility is modified to allow for saved reserves and partial liquidation. The initial (s = 0) resource 12The superscript j and the subscript t are therefore added to the variables from the previous model to denote the country and the period. We keep the subscripts indicating the stage s when necessary. 20

constraint,whichincorporatesincomingreservessaved(R ),isnow: 0 R +K ≤D+R . (10) 1 0 The final (s=2) resource constraint, modified to allow for inter-temporal reserves (cid:48) savings(R (ϕ)),isnow: 0 C(ϕ)+(1−ψ(ϕ))P (ψ(ϕ))≤R (ϕ)−R(cid:48) (ϕ)+A(K−L(ϕ)). (11) 2 2 0 Also,savedreservesandliquidationmustsatisfy R(cid:48) (ϕ) ∈ [0, R (ϕ)] ∀ϕ (12) 0 2 L(ϕ) ∈ [0, K] ∀ϕ (13) 4.3 Bayesian Learning The common belief ρ ≡ Pr(σ =σ ) is dynamically updated using the sudden t t L stop occurrences and sudden stop probabilities in the N countries.13 Let us denote N j χ ∈{0,1} as the vector of sudden stops where χ =1 denotes that country j ext t periencedasuddenstopinperiodt. Foreachcountry j,giventheincomingreserves (cid:16) (cid:17) j j j R , the probability of a sudden stop Pr χ |R ;ρ is endogenously determined 0,t t 0,t t bytheoptimalpolicyfortheprevailingbeliefρ . t Bayes’Ruleimpliesthat: ρ Pr(χ |σ ) t t L ρ = t+1 ρ Pr(χ |σ )+(1−ρ )Pr(χ |σ ) t t L t t H (cid:110) (cid:111) 13Alternatively, agents can update their priors using the realized liquidity shocks, ϕ j . t j=1,..,N Thisspecificationyieldssimilarresultswiththeonlynoticeabledifferencebeingthatthespeedof learning is faster, and therefore slightly fewer sudden stops in the interim. However, there is still anoutburstofsuddenstopsduringthetransition. Wefinditmoreappealingtohavecountrieslearn usingsuddenstopoccurrencesaroundtheworldinstead. 21

withthejointendogenoussuddenstopprobabilitiesPr(χ |σ )givenby: t t N (cid:16) (cid:17) Pr(χ |σ ) ≡ ∏Pr χ j |R j ;ρ =1 t L t 0,t t j=1 and N (cid:16) (cid:17) Pr(χ |σ ) ≡ ∏Pr χ j |R j ;ρ =0 t H t 0,t t j=1 (cid:16) (cid:17) (cid:16) (cid:16) (cid:17)(cid:17) j j j wherePr χ =1|R ;ρ =1 =1−F ϕ R ;ρ =1 t 0,t t σL S 0,t t (cid:16) (cid:17) (cid:16) (cid:16) (cid:17)(cid:17) j j j andPr χ =1|R ;ρ =0 =1−F ϕ R ;ρ =0 . t 0,t t σH S 0,t t 4.4 Quantitative Analysis Inthissection,weusethecalibratedmodeltoestablishhowasmallbutunexpected increaseindebtrolloverriskcanexplainthesharpincreaseinreservesandthetemporary outburst in sudden stops documented in section 2. Based on our theory, an unexpected increase in the rollover risk will temporarily cause an underinvestment in reserve holdings which increases the probability of sudden stops. Governments and investors, seeing the rise in sudden stops, rationally update their common belief about the prevailing debt rollover risk. Once agents have fully learned the new regime,reservesremainsteadilyhigherandsuddenstopssubside. Calibration A period in the model is assumed to be a quarter. We choose N = 23 as we have 23 emerging economies in our dataset. We assume the aggregate liquidityshockdistributions(F ,F )belongtotheclassofParetodistributionson σL σH [0,1]: F (ϕ)≡1−(1−ϕ)1/σ. An increase in σ shifts the cumulative distribution σ function F to the right as illustrated in Figure 5. An increase from σ to σ σ L H thereforerepresentsanincreaseintheunderlyingdebtrolloverrisk. The discount factor β is set to match average interest rates of two percent in emerging economies over 1990-2007 and the world interest rate r is set to match W a risk-free rate of one percent. The bargaining parameter θ is set to match the average haircut of 19.4 percent in sovereign defaults from 1990 to 2007 using the data from Benjamin and Wright (2009). The debt rollover risk parameter σ and L 22

Table2: Calibrationvalues Name Symbol Value Target Discountfactor β 0.98 averageinterestrates(emerging) Worldinterestrate r 0.01 risk-freerate W Lowrolloverrisk σ 0.061 averagereserves-to-debt,1990-1996 L Highrolloverrisk σ 0.172 averagereserves-to-debt,2002-2007 H Divestmentparameter λ 0.75 seediscussion Productivity A 1.2 - Bargainingparameter θ 0.965 averagehaircutonsovereigndebt Numberofeconomies N 23 emergingcountriesinsample σ are set to match median reserves-to-debt ratios in the emerging economies for H the periods of 1990-1996 and 2002-2007 respectively. We set the liquidation cost 1−λ to be 25 percent, which is conservative relative to the range of estimates and values used in the literature.14 The long-term technology productivity A is set to 1.2.15 TheparametersaresummarizedinTable2. Seethecomputationappendixin section6.2fordetailsonthecomputationandcalibrationstrategy. Quantitative Results We assume that after 1996, there was an unexpected increase from a σ -regime to a σ -regime. This is motivated by the idea that global- L H ization and widespread financial liberalization led to an unprecedented increase in capitalmobilityanddebtrolloverrisk. TheNexanteidenticaleconomiesexperiencedifferentaggregateliquidityshock (cid:110) (cid:111) j paths ϕ . As a result, their reserves holdings and sudden stops paths also t j,t evolvedifferently. TheresultsshownaretheaverageacrossalargenumberofsimulatedpathsfortheseN countries. Table3summarizesourkeyresults. Thecalibrationrevealsthatthedebtrollover risk σ increased from 0.061 to 0.172. This is a small increase in the sense that the 14Forexample,estimatesforliquidationcostsinclude30.5percent(James 2012)and49.9percent (BrownandEpstein 1992)inbankfailures,and37percent(AldersonandBetker 1996)inChapter 7liquidations,whileEnnisandKeister 2003useliquidationcostsof60percentand70percentin theiranalysis. Wealsorunsensitivityanalysiswithdifferentvaluesofλ,andfindlittlevariationin themainresults. SeeTableA.2intheappendixfordetails. 15Theresultsholdaslongastheproductivityissufficientlyhigh. 23

Table3: SummaryofResults 1990-1996 1997-2001 2002-2007 Data Reserves-to-ExternalDebtLiabilities 0.17 0.28 0.41 SuddenStops 2 10 0 Model Reserves-toExternalDebtLiabilities 0.17 0.33 0.41 SuddenStops 0.40 7.28 1.10 RolloverRisk(σ) 0.061 0.172 0.172 SuddenStopProbabilities(percent) 0.06 1.58 0.19 impliedsuddenstopprobabilitiesonlyrisefrom0.06percentto0.19percent,comparedtoa1.58percentprobabilityduringthetransition. Despitethissmallincrease indebtrolloverrisk,thereisanoutburstofsuddenstopswiththemodeacrosssimulations reaching 7 before subsiding (see Figure 7). In the meantime, the optimal reserves-to-debtratiosclimbedfrom17percentto41percent. Thetemporarysurge in sudden stops is consistent with our discussion of Proposition 2 in the simple model (see Figure 5): as governments learn the higher rollover risk, they choose to hold a higher level of reserves, thus returning sudden stop probabilities to lower levels. The calibration establishes quantitatively how a small increase in rollover risk can explain the surge we observed in the data. As can be seen in Figure 8, our model can jointly generate the temporary outburst of sudden stops in the transition (1997-2001)alongwiththepermanentriseinreserveseversince. InternationalMutualInsuranceandReserves Proposition3showedthatcountries over-accumulate reserves compared to an allocation with mutual insurance with other countries. We now use the calibrated parameters to quantify the magnitudeoftheover-accumulationofreservesduetoself-insurance. GiventhecalibratedparametervaluesandusingProposition3,theinternational planner facing no aggregate uncertainty will optimally set reserves to the mean liquidity shock because σ < (1−λ)/A. Therefore, in the higher rollover risk H (σ ) regime, the international planner optimally sets the reserves-to-debt ratio at: H 24

Figure7: HistogramofSuddenStopsFrequenciesbyEra 1990−1996 1 0.5 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 1997−2001 1 0.5 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 2002−2007 1 0.5 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Number of Sudden Stops Figure8: Results-ReservesandSuddenStops 0.5 0.4 0.3 0.2 0.1 1990199119921993199419951996199719981999200020012002200320042005200620072008 oitaR tbeD−ot−sevreseR Reserve Allocation and Sudden Stops 2 1.5 1 0.5 0 1990199119921993199419951996199719981999200020012002200320042005200620072008 time (quarters) spotS nedduS 25

σ /(1+σ )=14.68percent. Thisamountstonearlyone-thirdsofthelevelof41 H H percentinreserves-to-debtthatemergingeconomiesheldfrom2002to2007.16 This result clearly underscores the importance of mutual insurance or internationalcoordinationacrossgovernmentsfacinguninsurableidiosyncraticdebtrollover risk. Infact,duringtherecentglobalfinancialcrisis,reservesswapagreementssuch as the ASEAN+3 Chiang Mai Initiative were expanded. The U.S. and Japan also extendedswaplinestoemergingeconomiessuchasKorea. The IMF could in principle assume the role of an international planner for rollover risk insurance. However, many economists and policymakers argue (see Ito (2012)) that emerging economies still bear the scar and the stigma from the inadequate liquidity assistance provided by the IMF during the crises of the late 1990s. Reserves in the Euro Area Periphery Economies Interestingly, before 1999, the Euro Area Periphery economies (Greece, Ireland, Italy, Portugal, Spain) held the same levels of reserves as the 23 emerging economies we consider. However, upon joining the Euro Area, these economies slashed their reserves holdings, as illustratedinFigure9.17 The common currency certainly explains part of the reduction in foreign reserves. However, to the extent that these economies still faced debt rollover risk, they may have under-invested in reserves. For instance, they may have mistakenly believed that they no longer faced rollover risk as they joined the Euro. Alternatively, the Periphery economies ex ante may have counted on a mutual insurance policyagainstliquidityneedswhichshoweditslimitsduringtheEurocrisis. In the meantime, self-insurance through reserves helped emerging economies weather the global financial crisis as noted by Dominguez et al. (2012) as well as Gourinchas and Obstfeld (2012). This is also consistent with our findings on the preventiveroleofreserves. 16Technically,aplannerwithadiscretenumberofcountriesstillfacesaggregateuncertainty. The caseofacontinuumofcountriesismoretractableandcorrespondstoanupperboundontheoveraccumulationofreserves. 17ReservesrelativetoGDPshowexactlythesamepattern. 26

Figure9: ForeignReservesintheEuroAreaPeriphery 41 40 30 22 20 17 10 4 1 2 0 tbed lanretxe fo tnecrep Foreign Reserves over External Debt Liabilities 1990−199 2 6 002−2007 1990−199 2 6 002−2007 1990−199 2 6 002−2007 emerging economies advanced economies euro area periphery Note:Thevalueforeachperiodandeachblocisthemedianacrosseconomiesoftheperiod-averageforeacheconomy. 5 Conclusion In this paper, we developed a theory of rollover risk, sudden stops, and reserves that can jointly account for the dynamics of foreign reserves and sudden stops in emergingeconomies. In our theory, governments choose reserves to prevent “patient” foreign creditorsfromrefusingtorollovertheirclaimsandinducingasuddenstop. Wecalibrate a dynamic multi-country extension of the model with Bayesian learning to emerging economies. A small, unexpected, but permanent change in rollover risk leads to the surge in sudden stops in the late 1990s, the subsequent rise in reserves, and thesalientfallinsuddenstopseversince. Wealsofindthatapolicyofinternational mutualinsurancecansubstantiallyreducethereservesheldbyemergingeconomies. Several caveats are in order. Our model ignores the decision to issue reserve assets. In particular, U.S. Treasuries, the most popular reserve asset, are being increasingly held by foreign officials as they accumulate reserves (see Figure 10). Can the U.S. sustainably issue large amounts of reserve assets? Moreover, our 27

model does not consider the maturity composition of a country’s debt. We leave theseinterestingconsiderationsforfutureresearch. Figure10: ForeignHoldingsofU.S.Treasuries 40 30 20 10 0 seirusaerT SU fo tnecrep Foreign Holdings of Outstanding US Treasuries Foreign official EMEs only Foreign private 2000 2002 2004 2006 2008 2010 2012 28

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6 Appendix 6.1 Tables TableA.1: ForeignReserves (percentofGDP) (percentofExternal DebtLiabilities) 1990-1996 2002-2007 1990-1996 2002-2007 Argentina 4.9 13.5 14.3 21.4 Brazil 4.9 8.6 19.5 35.3 Chile 20.4 16.5 50.9 39.0 China 8.4 33.2 54.3 271.4 Colombia 9.9 10.8 35.6 35.1 CzechRepublic 17.4 25.3 57.2 77.5 Egypt 20.9 19.8 35.2 65.5 Hungary 15.5 16.6 26.6 26.2 India 3.5 18.4 11.8 101.0 Indonesia 6.5 12.4 11.7 25.2 Korea 5.4 24.6 28.0 97.4 Malaysia 28.5 47.1 77.0 125.6 Mexico 4.6 8.2 12.2 40.9 Morocco 10.4 28.6 15.9 99.1 Pakistan 1.8 10.4 4.3 28.2 Peru 11.2 18.4 16.7 49.1 Philippines 8.0 17.3 13.3 28.4 Poland 6.9 14.2 15.9 35.8 Romania 4.2 18.5 22.7 53.9 Russia 3.0 23.2 7.3 68.5 SouthAfrica 1.0 7.1 4.7 34.9 Thailand 19.3 30.6 41.8 112.1 Turkey 3.9 10.9 13.0 25.5 33

TableA.2: SensitivityAnalysis 1990-1996 1997-2001 2002-2007 λ =0.7 Reserves-toExternalDebtLiabilities 0.17 0.32 0.41 SuddenStops 0.40 7.56 1.22 RolloverRisk(σ) 0.058 0.161 0.161 SuddenStopProbabilities(percent) 0.06 1.64 0.21 λ =0.8 Reserves-toExternalDebtLiabilities 0.17 0.33 0.41 SuddenStops 0.26 7.60 1.69 RolloverRisk(σ) 0.061 0.198 0.198 SuddenStopProbabilities(percent) 0.04 1.65 0.19 6.2 Computational Appendix The computation strategy involves solving for policy functions and simulating the induced equilibrium paths with Bayesian learning. The government problem has two state variables: (i) the incoming reserves, R , and (ii) the belief, ρ. The policy 0 functions are : (i) the initial reserves, R , (ii) the sudden stop policy, ϕ ,18 (iii) the 1 S liquidation policy, L(ϕ), and (iv) the saved reserves, R(cid:48)(ϕ), where ϕ is the interim 0 aggregateliquidityshock. Thesepolicyfunctionsaresolvedbyvaluefunctioniteration. Wediscretizethestatespaceanddecisionvariablesbychoosingafinitegrid, anduseinterpolationmethods. Algorithmforsolvingequilibriumandcalibration 1. Guessavectorofparameters{σ ,σ ,θ} L H 18Forcomputationalconvenience,weimposethatthecutoffrulesuchthatsuddenstopsoccurif and only if ϕ ≥ϕ (R ;ρ). While this condition was an equilibrium result in the basic model, we S 0 cannotanalyticallyprovethecutoffruleintheextendedmodel. Thecutoffrulesignificantlylowers thecomputationalburden. Wefindthatthisrestrictionisnotbindinginoursimulations. 34

2. For each belief on the belief grid, using value function iteration, solve for valuefunctionsandpolicyfunctions. (cid:110) (cid:111) j 3. Set initial reserves for N countries R =0, and initial belief ρ = 0,0 0 j=1,..,N 0.97 4. Fort =1,...,T,  σ ift <T L 1 (a) Setσ = t σ ift ≥T H 1 (cid:110) (cid:111) j (b) Drawaggregateliquidityshocks ϕ fromF t σt j=1,..,N (cid:110) (cid:111) j (c) Using distribution of incoming reserves, R , policy func- 0,t j=1,..,N (cid:16) (cid:17) (cid:16) (cid:17) (cid:16) (cid:17) j j j j tions,R R ;ρ ,ϕ R ;ρ ,L R ,ϕ ;ρ , 1 0,t t−1 S 0,t t−1 0,t t t−1 (cid:16) (cid:17) (cid:110) (cid:111) R(cid:48) R j ,ϕ j ;ρ , and shock realizations, ϕ j , compute dis- 0 0,t t t−1 t j=1,..,N (cid:110) (cid:111) j tributionofsavedreserves, R 0,t+1 j=1,..,N (d) using sudden stop probabilities and realizations, compute posterior as detailedinsection4.3 5. Repeat step 4 M times, compute averages over M simulations. When computingaverages,excludet =1,..,5. 6. Repeat steps 1-5 until the difference between model moments and correspondingdatatargetsarelessthanaspecifiedthreshold. 6.3 Proofs PROOFOFPROPOSITION1: Weproceedineightsteps. Step1: Interestratessatisfy r∗ <0<r∗ (14) S N 35

1+r∗ ≥1followsfromequation(8). Equation(3)andλ <1implythatR +λK< N 1 D. Sinceθ =1,equation(4)implies1+r∗ =(R +λK)/D. Hencer∗ <r∗. S 1 S N Step2: Ifψ∗(ϕ)=1,then L∗(ϕ) = K∗ (15) R∗(ϕ) = 0 (16) 2 C∗(ϕ) = 0 (17) By definition, if ψ∗(ϕ) = 1, then P∗(ϕ) = (cid:0) 1+r∗(cid:1) D. From step 1, we have 1 S thatr∗ =(R +λK)/D. Equations(5)and(7)implyequations(15)and(16). Then S 1 equation(17)followsfromequations(6)and(7). Step3: Ifψ∗(ϕ)=ϕ,then L∗(ϕ) = 0 (18) R∗(ϕ) = R∗−ϕD (19) 2 1 C∗(ϕ) = AK∗+R∗(ϕ)−(1−ϕ)(1+r∗)D (20) 2 N Bydefinition,ifψ∗(ϕ)=ϕ,thenP∗(ϕ)=DandP∗(ϕ)=(1+r∗)D. Suppose 1 2 N for contradiction that L∗(ϕ)=K. Then equation (5) implies R∗(ϕ)=R∗+λK∗− 2 1 ϕD. Thenwehavethat C∗(ϕ) = R∗+λK∗−ϕD−(1−ϕ)(1+r∗)D 1 N ≤ R∗+λK∗−D 1 < 0 wherethefirstequalitycomesfromequation(6),thesecondinequalitycomesfrom 36

1+r∗ ≥1, and the third inequality comes from (3) and λ <1. This violates equa- N tion(7). Henceequation (18)holds. Then equation(19)follows fromequation (5), andequation(20)followsfrom(6). Step4: If ψ∗(ϕ )=ϕ <ϕ =ψ∗(ϕ ),then 1 1 2 2 R∗(ϕ ) > R∗(ϕ ) (21) 2 1 2 2 C∗(ϕ ) < C∗(ϕ ) (22) 1 2 Equation(19)impliesthatR∗(ϕ )=R∗−ϕ D>R∗−ϕ D=R∗(ϕ ). Similarly, 2 1 1 1 1 2 2 2 step3impliesthat C∗(ϕ ) = AK∗+R∗−ϕ D−(1−ϕ )(1+r∗)D 1 1 1 1 N < AK∗+R∗−ϕ D−(1−ϕ )(1+r∗)D 1 2 2 N = C∗(ϕ ). 2 Step5: Suddenstoppolicysatisfies  ψ∗(ϕ)=ϕ ∀ϕ ∈[0,ϕ ) ∃ϕ ∗ ∈[0,1]s.t. S S ψ∗(ϕ)=1 ∀ϕ ∈[ϕ ,1] S First, note that ψ∗(ϕ)∈{ϕ,1}, which follows from symmetry. Then, suppose, withoutlossofgenerality,thattheoptimaldebtcontractB∗ hasϕ∗ <ϕ∗ <ϕ∗ such 1 2 3 that  ϕ ∀ϕ ∈[0,ϕ )  1   ψ ∗(ϕ)= 1 ∀ϕ ∈[ϕ ,ϕ ) 1 2    ϕ ∀ϕ ∈[ϕ ,ϕ ) 2 3 Then consider an alternative debt contract Bˆ that is identical to B∗ except that ψˆ(ϕ) = ϕ ∀ϕ ∈ [ϕ −ε,ϕ ) for some ε > 0. From equations (7) and (22), we 2 2 know that C∗(ϕ ) >C∗(0) ≥ 0. By continuity, Cˆ(ϕ) > 0 ∀ϕ ∈ [ϕ −ε,ϕ ] for ε 2 2 2 37

small enough. In contrast, from step 2, C∗(ϕ) = 0 ∀ϕ ∈ [ϕ −ε,ϕ ]. Similarly, 2 2 fromequations(7)and(21),weknowthatR∗(ϕ )>R∗(ϕ −ε)≥0. Bycontinuity, 2 2 2 3 Rˆ (ϕ)>0∀ϕ ∈[ϕ −ε,ϕ ] for ε small enough. It remains to show that equation 2 2 2 (9) holds. This is obvious since P∗(ϕ) = (cid:0) 1+r∗(cid:1) D < 1 = Pˆ (ϕ) < (1+r∗)D = 1 S 1 N Pˆ (ϕ) ∀ϕ ∈ [ϕ −ε,ϕ ]. Hence Bˆ is feasible, yet has strictly higher consumption 2 2 2 thanB∗,whichisacontradiction. Step6: ReservesandLiquidationpoliciessatisfy  R∗(ϕ)>0 ⇐⇒ ϕ ∈[0,ϕ ) ∃ϕ∗ ∈[0,1]s.t. 2 R R L∗(ϕ)=0 ⇐⇒ ϕ ∈[0,ϕ ) R Fromstep5,weknowthat  ψ∗(ϕ)=ϕ ∀ϕ ∈[0,ϕ ) ∃ϕ ∗ ∈[0,1]s.t. S S ψ∗(ϕ)=1 ∀ϕ ∈[ϕ ,1] S Let ϕ∗ = ϕ∗. Then the result follows from steps 2 and 3. It also follows that R S ϕ∗ =R∗/D. R 1 Step7: TheOptimalReserves-to-Debtratiosatisfies (cid:20) A−1 (cid:18) σ (cid:19)(cid:21)σ ϕ∗ =1− R A−λ σ+1 The cutoff conditions imply that the state-contingent policy and payment functionscanbewrittenas: 38

 0 ifϕ <ϕ∗ L∗(ϕ) = R K∗ otherwise  R∗−ϕD ifϕ <ϕ∗ R∗(ϕ) = 1 R 2 0 otherwise  0 ifϕ <ϕ∗ andϕ =0 ψ∗(ϕ,ϕ) = R i i i 1 otherwise  D ifϕ <ϕ∗ P∗(ϕ) = R 1 R∗+λK∗ otherwise 1  (1+r∗)D ifϕ <ϕ∗ P∗(ϕ) = N R 2 0 otherwise Theparticipationconstraint,holdingwithequality,canbewrittenas(1+r )= ´ W G(ϕ∗)+(1+r∗)(F(ϕ∗)−G(ϕ∗))+(1−F(ϕ∗)) (cid:0) 1+r∗(cid:1) whereG(x)= x ϕdF(ϕ). R N R R R S 0 Substituting the resource constraints and the condition ϕ =R /D, the optimal R 1 debtcontractproblemcanbewrittenas: ´ (cid:20) (cid:21) G(ϕ )+(1−F(ϕ ))(λ+(1−λ)ϕ )−(1+r ) max D ϕR A(1−ϕ )+ϕ −ϕ+(1−ϕ) R R R W dF(ϕ) ϕR 0 R R F(ϕ )−G(ϕ ) R R Thefirstorderconditionisgivenby: A−1 (1−ϕ∗) f(ϕ∗)+1−F(ϕ∗)= R R R A−λ UsingtheboundedParetodistribution,weget: (cid:20) A−1 (cid:18) σ (cid:19)(cid:21)σ ϕ∗ =1− R A−λ σ+1 Step8: Toverifytheequilibrium,itsufficestoshowthat C∗(ϕ)≥0∀ϕ ∈[0,ϕ ∗). R SinceC∗(ϕ)isstrictlyincreasinginϕ,itsufficestoshowC∗(0)≥0. 39

G(ϕ∗)+(1−F(ϕ∗))(λ+(1−λ)ϕ∗)−(1+r ) C∗(0) = (A(1−ϕ∗)+ϕ∗)D+ R R R W D R R F(ϕ∗)−G(ϕ∗) R R (1−λ)(1−ϕ∗)(1−F(ϕ∗))+r = (A−1)(1−ϕ∗)D− R R W D R F(ϕ∗)−G(ϕ∗) R R = (A−1)(1−ϕ∗)D−(σ+1) (1−λ)(1−ϕ R ∗)(1−ϕ R ∗)σ 1 +r W D R 1−(1−ϕ R ∗)σ 1+1 (cid:18) A−1 (cid:18) σ (cid:19)(cid:19)σ+1 (cid:20) A−1 (cid:18) σ (cid:19)(cid:21)σ (1−λ) A−λ σ+1 +r W = (A−1) D−(σ+1) D A−λ σ+1 (cid:18) A−1 (cid:18) σ (cid:19)(cid:19)σ+1 1− A−λ σ+1 Notethat  (cid:18) A−1 (cid:18) σ (cid:19)(cid:19)σ+1   (cid:20) A−1 (cid:18) σ (cid:19)(cid:21)σ (1−λ) A−λ σ+1 +r W lim (A−1) −(σ+1) =+∞ A→∞   A−λ σ+1 (cid:18) A−1 (cid:18) σ (cid:19)(cid:19)σ+1   1− A−λ σ+1 Hence∃A∗(λ,σ,r )suchthat∀A≥A∗,C∗(0)≥0. W PROOFOFPROPOSITION2: (i)FromProposition1,weknowthat (cid:20) A−1 (cid:18) σ (cid:19)(cid:21)σ ϕ∗ =1− . R A−λ σ+1 Then, ∂ϕ∗ R > 0 ∂σ ⇔ (cid:26) (cid:20) A−1 (cid:18) σ (cid:19)(cid:21) 1 (cid:27)(cid:20) A−1 (cid:18) σ (cid:19)(cid:21)σ − log + > 0 A−λ σ+1 σ+1 A−λ σ+1 ⇔ (cid:20) (cid:18) (cid:19)(cid:21) A−1 σ 1 log + < 0 A−λ σ+1 σ+1 Sinceλ <1<A,itsufficestoshow (cid:18) (cid:19) σ 1 h(σ)≡log + ≤0 σ+1 σ+1 40

,whichistruesinceh(σ)isincreasinginσ, lim h(σ)=0+,and lim h(σ)=−∞, σ→+∞ σ→0+ whichimpliesthath(σ)<0forallσ >0. (ii)FromCorollary1,weknowthat Pr(ψ =1)=1−F(ϕ∗) R Substitutingforϕ∗,weget R (cid:18) (cid:19) A−1 σ Pr(ψ =1)= A−λ σ+1 Theresultisobvious. PROOFOFPROPOSITION3: Reserves Shortfall Before writing the planner’s problem, it is useful to derive how many countries have to suffer a crisis for a given level of reserves shortfall. Suppose all countriescoordinate to setϕC =(ϕ¯ −ε)reserves aside andinvest K¯ + R εD19. Theinterimshortfallis: εD. Somecountrieswillhaveto(fully)liquidatetopay1+r (ε)=ϕ¯+λK¯/D−(1−λ)ε S sincetheirnormalinterimpaymentscannotbemet. Letusdenote(cid:96)(ε),themeasure ofcountriesthatfaceacrisis. Wehave: 1−(cid:96)(ε)=F (ϕ(ε)) σ (cid:98) where: ˆ ϕ(cid:98) (ε) ϕ¯ −ε = ϕdF (ϕ)=G (ϕ(ε)) ⇔ ϕ(ε)=G−1(ϕ¯ −ε) σ σ (cid:98) (cid:98) σ 0 So: (cid:96)(ε)=1−F (cid:2) G−1(ϕ¯ −ε) (cid:3) σ σ 19ϕ¯D+K¯ =D 41

Thereservesdecisionε determinestheprobability(cid:96)(ε)thatacountryisinasudden stop. The shortfall limits the interim insurance since the interim debt repayment of somecountries,theoneswiththelargestshocks,cannotbemet. Weknow: • (cid:96)(0)=0and(cid:96)(ϕ¯)=1 • (cid:96)(ε)isstrictlyincreasinginε • G σ (ϕ)= σ σ +1 (cid:104) 1− (cid:0) 1− σ 1ϕ (cid:1) (1−ϕ)σ 1 (cid:105) ⇒ (cid:96)(ε)= (cid:2) 1−G− σ 1(ϕ¯ −ε) (cid:3) σ 1 Wenowwritetheplanner’sproblemaschoiceofreservesshortfall. Planner’s Problem Noting that the interim decision has been solved above, the planner’sproblemis: max C ε subjectto (ϕ¯−ε)D+(K¯+εD)−D ≤ 0 (23) (cid:34)ˆ (cid:35) ϕ(cid:98)(ε) C+ (1−ϕ)dF (ϕ) (1+r )D−A(1−(cid:96)(ε))(K¯+εD) ≤ 0 (24) σ N 0 ˆ ϕ(cid:98)(ε) (cid:96)(ε)(1+r (ε))+ [ϕ+(1−ϕ)(1+r )]dF (ϕ)−(1+r ) ≥ 0 (25) S N σ W 0 (1+r (ε))−[(ϕ¯−ε)D+λ(K¯+εD)] ≥ 0 (26) S C, ε ≥ 0 (27) Equations (23) - (27) represent initial resource constraint, final resource constraint, participation constraint, renegotiation proofness, and non-negativity constraint, which are analogous to equations (3), (6), (9), (4) , and (7), respectively. Thissimplifiesto: max C ε subjectto 42

C+[1−(cid:96)(ε)−(ϕ¯ −ε)](1+r )D−A(1−(cid:96)(ε))(K¯ +εD) ≤ 0(28) N ˆ ϕ(cid:98) (ε) (cid:96)(ε)(1+r (ε))+ [ϕ+(1−ϕ)(1+r )]dF (ϕ)−(1+r ) ≤ 0(29) S N σ W 0 (1+r (ε))−[(ϕ¯ −ε)D+λ(K¯ +εD)] ≥ 0(30) S C, ε ≥ 0(31) Equation(29)canbewrittenas20: (cid:96)(ε)(1+r (ε))+(ϕ¯ −ε)+(1+r )[1−(cid:96)(ε)−(ϕ¯ −ε)] = (1+r ) (32) S N W Substituting(32)into(28)yields: C+((1+r )−(ϕ¯ −ε)−(cid:96)(ε)(1+r (ε)))D−A(1−(cid:96)(ε))(K¯ +εD)≤0 W S Theplanner’sproblemcanthenbewrittenas: (cid:18) K¯ (cid:19) max A(1−(cid:96)(ε)) +ε −((1+r )−(ϕ¯ −ε)−(cid:96)(ε)(1+r (ε))) ε W S D ⇔ K¯ K¯ max −(cid:96)(ε)A +A(1−(cid:96)(ε))ε−ε+(cid:96)(ε)(1+r (ε))+A +ϕ¯ −(1+r ) ε S W D D ⇔ K¯ (cid:20) K¯ (cid:21) max −(cid:96)(ε)A +A(1−(cid:96)(ε))ε−ε+(cid:96)(ε) ϕ¯ +λ −(1−λ)ε ε D D 20This is assuming the shortfall is not too high. Otherwise, the consumption would be negative duetothehighinterestimpliedbythehighreservesshortfall. 43

Thisisnotalinearprobleminε since(cid:96)(ε)isnotlinear. However,weknowthat: (cid:96)(ε) = 1−F (cid:2) G−1(ϕ¯ −ε) (cid:3) σ σ ⇓ (cid:32) (cid:33) (cid:96) (cid:48) (ε) = −F (cid:48) (cid:2) G−1(ϕ¯ −ε) (cid:3) × 1 ×(−1) σ σ G(cid:48) (cid:2) G−1(ϕ¯ −ε) (cid:3) σ σ F (cid:48) (cid:2) G−1(ϕ¯ −ε) (cid:3) σ σ = G(cid:48) (cid:2) G−1(ϕ¯ −ε) (cid:3) σ σ f (cid:2) G−1(ϕ¯ −ε) (cid:3) σ (cid:48) (cid:48) = asF = f andG (ϕ)=ϕf (ϕ) (cid:2) G−1(ϕ¯ −ε) (cid:3) f (cid:2) G−1(ϕ¯ −ε) (cid:3) σ σ 1 = G−1(ϕ¯ −ε) σ 1 = ϕ(ε) (cid:98) TheF.O.C.w.r.t. ε gives: K¯ (cid:20) K¯ (cid:21) (cid:48) (cid:48) (cid:48) −(cid:96) (ε)A −(cid:96) (ε)Aε+A(1−(cid:96)(ε))−1+(cid:96) (ε) ϕ¯ +λ −(1−λ)ε −(1−λ)(cid:96)(ε)≥0 D D withequalityifε >0. Rearrangingyields: (cid:18) K¯ (cid:19) (cid:48) (cid:48) −(cid:96) (ε)A +ε +A(1−(cid:96)(ε))−(1−λ)(cid:96)(ε)+(cid:96) (ε)(1+r (ε))−1 ≥0 S D ⇔ (cid:20) (cid:18) K¯ (cid:19) (cid:21) (cid:48) (A−1)−(A+1−λ)(cid:96)(ε)−(cid:96) (ε) A +ε −(1+r (ε)) ≥0 S D ⇔ (cid:18) K¯ (cid:19) (cid:18) K¯ (cid:19) A +ε − ϕ¯ +λ −(1−λ)ε D D (A+1−λ)F (ϕ(ε))− −(2−λ) ≥0 σ (cid:98) ϕ(ε) (cid:98) ⇔ A(1−ϕ¯ +ε)−(ϕ¯ +λ −λϕ¯ −(1−λ)ε) (A+1−λ)F (ϕ(ε))− −(2−λ) ≥0 σ (cid:98) ϕ(ε) (cid:98) ⇔ (A−λ)−(A+1−λ)(ϕ¯ −ε) (A+1−λ)F (ϕ(ε))− −(2−λ) ≥0 σ (cid:98) ϕ(ε) (cid:98) 44

Atε =0,theL.H.S.oftheF.O.C.is: (A+1−λ)−[(A−λ)−(A+1−λ)(ϕ¯)]−(2−λ) =(A+1−λ)ϕ¯ −(1−λ) 1−λ >0 iffσ > A Therefore, ϕC =ϕ¯ if and only if σ ≤(1−λ)/A. Otherwise, ϕC <ϕ¯. Obviously, R R inanycase: ϕC ≤ϕ¯. R Finally,giventhatϕ∗ =1−[(A−1)/(A−λ)σ/(σ+1)]σ andϕ¯ = σ : R σ+1 1 (cid:18) A−1 (cid:19)σ(cid:18) σ (cid:19)σ ϕ ∗ >ϕ¯ ⇔ > R σ+1 A−λ 1+σ Sinceλ <1<A,itissufficienttoshowthat: (cid:18) (cid:19)σ 1 σ > σ+1 1+σ Thisisalwaystrueforσ ∈(0,1). 45