CrisesandG rowth: A R e-evaluation¤

R omainR anciere

N Y U andCER A S

A aronTornell

U CL A andN BER

FrankW estermann

U niversityofM unichandCESifo

This Version: O ctober2003

FirstD raft: M ay2002

JEL Classi…cationN o.F34, F36, F43, O 41Keywords: boom-bustcycles, volatility, lendingbooms, currencymismatch,

bailouts, creditmarketimperfections.

A bstract

W e address thequestion ofwhethergrowth and welfare can be higherin crisis

proneeconomies. First, we showthatthere is arobustempiricallinkbetweenper-

capitaG D P growthandnegativeskewnessofcreditgrowthacrosscountrieswithactive

…nancialmarkets. T hatis, countriesthathaveexperiencedoccasionalcriseshavegrown¤W ethankJessB enhabib, SudiptoBhattacharya, P ierreO livierG ourinchas, T horvaldurG ylfason, Jürgen

von H agen, L utz H endricks, FabrizioPerri, Joris P inkse, FranckPortier, D ebraj R ay, H ans-W ernerSinn,

Carolyn Sissoko, JeanT irole, JaumeVenturaandseminarparticipants atBonn, H arvard, M unich, N Y U ,

Toulouse, andtheBancaD ’Italia/CEPR ConferenceonM oneyBankingandFinanceforhelpfulcomments.

0

on averagefasterthan countries with smooth creditconditions. W ethen presenta

two-sectorendogenousgrowthmodelinwhich…nancialcrises canoccur, andanalyze

therelationship between…nancialfragilityandgrowth. T heunderlyingcreditmarket

imperfections generateborrowingconstraints, bottlenecks andlowgrowth. W eshow

thatundercertainconditionsendogenousrealexchangerateriskarisesand…rms…nd

itoptimaltotakeoncreditriskintheformofcurrencymismatch. A longsucharisky

pathaveragegrowthishigher, butself-ful…llingcrisesoccuroccasionally. Furthermore,

weestablish conditions underwhichtheadoptionofcreditrisk iswelfareimproving

andbringstheallocationnearertotheParetooptimallevel. T hedesignofthemodelis

motivatedbyseveralfeaturesofrecentcrises: creditriskintheformofforeigncurrency

denominateddebt;costlycrises thatgenerate…resales andwidespreadbankruptcies;

andasymmetricsectorialresponses, wherethenontradablessectorfallsmorethanthe

tradablessectorinthewakeofcrises.

1

1 Introduction

O verthelasttwodecadesmostofthefastestgrowingcountriesofthedevelopingworldhave

experiencedlendingboomsand…nancialcrises. Countries inwhichcreditgrowthhasbeen

smooth have, bycontrast, exhibitedthe lowestgrowth rates. Itwouldthus appearthat

factorsthatcontributeto…nancialfragilityhavealsobeenasourceofgrowth, evenifthey

haveledtooccasionalcrises.

T helinkbetween …nancialfragilityandlongrungrowth is associatedwithtwoviews

of…nancialliberalization. Inoneview, …nancialliberalizationinducesexcessiverisk-taking,

increasesmacroeconomicvolatilityandleadstomorefrequentcrises. Inanotherview, lib-

eralizationstrengthens…nancialdevelopmentandcontributestohigherlong-rungrowth.

Inthispaperwebringthesetwoviewstogether. First, wedocumentarobustempirical

linkbetweenhighergrowthandapropensityforcrisis. Second, wepresentamodelthat

establishes alinkbetweencrisesmodels andgrowthmodels, andshowthatthetwoviews

ofliberalizationarecomplementary. W eanalyzetherelationshipbetween…nancialfragility

and growth in an economywherecreditmarketimperfections implythatahigh growth

pathrequires creditriskandthepossibilityofcrisis. Furthermore, wecarryoutawelfare

analysisandestablishconditionsunderwhichthewelfarecostsofcrisesareoutweighedby

thebene…tsofhighergrowth.

Thepaperis intwoparts. T he…rstpartis empiricalandthesecond is amodel. T he

empiricalsection establishes thelinkbetweenhigherG D P growthandnegative skewness

increditgrowthacrosscountrieswithactive…nancialmarkets. T his …ndingindicatesthat

countries with stable creditmarketconditions haveon averagegrown more slowly than

countriesthathaveexperiencedoccasionalcrises, andhaveacreditgrowthratedistribution

withalonglefttail.1 B utthisdoes notimplythat…nancialcrisesaregoodforgrowth. It

suggests thatundertakingcreditriskhas ledtohighergrowth, butas aside-e¤ect, ithas

alsoledtooccasionalcrises.

Inourempiricalanalysis, we…ndthatthelinkbetweenbumpiness andgrowth is not

evidentacrosscountrieswithahighdegreeofcontractenforceability(H ECs), butonlyacross1 N egativeskewness indicates thatgoodresults areclusteredclosertothemean thanbadresults. In

otherwords, creditcontractionsaremoreabruptandrarethancreditexpansions.

2

thosewithmoderatecontractenforceability(M ECs). Infact, overthepasttwodecadesmost

H ECshaveexperiencedskewnessofcreditgrowththatisnearzero.

T hailandandIndiaarecontrastingexamplesofasteepbutcrisispronegrowthpathand

aslowbutsafegrowthpath. T hailandhasexperiencedlendingboomsandcrises, whileIndia

haspursuedasafegrowthpathforcredit(seeFigure1). G D P percapitagrewbyonly9 9 %

between19 80 and2001 inIndia, whereasThailand’sG D P percapitagrewby148% , despite

havingexperiencedamajorcrisis.2

T heliteraturehasshownthateconomicgrowthisnegativelycorrelatedwiththevariance

ofseveralmacroaggregates. T hese…ndingsdonotcon‡ictwithourresults: varianceisjust

notagoodinstrumentwithwhichtocapturetheunevenprogressassociatedwith…nancial

fragility. Forinstance, acountrywhichexperienceshighfrequencyshockswillexhibitahigh

variance in creditgrowth even though itexperiences neitherthebooms northebusts of

countriesthatare…nanciallyfragile.

T hesecondpartofthepaperpresentsamodelthatlinks…nancialfragilityandlong-run

growth, andderivesthewelfareimplicationsofsuchalink. T hemodelisdesignedtoaccount

alsoforprominentfeaturesofrecentcrisisepisodesinM ECs. N otonlyarecrisesmarkedby

dramaticrealdepreciations, …resalesandwidespreadbankruptcies, buttheyarecharacterized

byasharp sectorialasymmetry: outputdropsfarmoreinthenontradables(N ) sectorthan

in thetradables (T ) sector. Closelyrelated tothis asymmetricsectorialresponse is the

denominationofN -sectordebtinforeigncurrency. Inthemodelthiscurrencymismatchis

thesourceof…nancialfragility.

Toexplainthelinkbetweenbumpinessandgrowthandatthesametimeaccountforthe

sectorialasymmetricresponsetocrises, weconsideratwo-sectorendogenousgrowthmodel

withtwocreditmarketimperfections. First, therearecontractenforceabilityproblemsthat

generatedomestic…nancingconstraints. T heseconstraints a¤ectprimarily N -…rms, as T -

…rmshaveaccesstoworldcapitalmarkets. Second, therearebailoutguaranteesthatinsure

lendersonlyagainstsystemiccrises.3

T here is an equilibrium where crises neveroccur. A longthis safe path the N -sector2T hisfactismoreremarkablegiventhatin19 80 India’s G D P wasonlyaboutone…fthofT hailand’s.3W emodelthesetwoimperfections as in Schneiderand Tornell(2003). T heirempiricalrelevance in

M ECs isanalyzedinTornellandW estermann(2003) .

3

exhibits lowgrowthbecauseits investmentis constrainedbyits cash ‡ow. SinceN -goods

serveasintermediateinputsforbothsectors, theN -sectorconstrainsthelong-rungrowthof

theT -sectorandthatofG D P : thereisabottleneck.

H owever, undersomecircumstancesthereisalsoariskyequilibriuminwhichendogenous

realexchangerateriskarisesand…rms…nditoptimaltotakeoncreditriskintheform of

currencymismatch. T hisriskybehavioreases borrowingconstraints, increases investment,

alleviates thebottleneckandallowsbothsectorstogrowfaster. H owever, italsogenerates

…nancialfragility, asashiftinexpectationscancauseasharprealdepreciationandlandthe

economyinacrisis.

Crisesarecostly. R ealdepreciationleadsto…resalesandbankrupts N -sector…rmswith

foreigncurrencydebtontheirbooks. Furthermore, theresultantcollapseincash‡owde-

pressesnewcreditandinvestment, hamperinggrowth. W easkthequestion: doesthecredit

riskthatleadsto…nancialfragilityincreaselongrunG D P growthbycompensatingforthe

e¤ectsofcontractenforceabilityproblems?O ur…rsttheoreticalresultisthata…nancially

fragileeconomywill, onaverage, growfasterthanasafeeconomyeven ifcrisis costs are

large, providedthatcontractenforceabilityproblems aresevere, butnottoosevere. T his

resultfollows, inpart, from thefactthatcrisesmustberareevents inorderforcreditrisk

tobepro…tableforindividualborrowers. Sincecrisesmustberareevents inorderforthem

tooccurinequilibriumandduringacrisiscreditfallsabruptlybutrecuperatesgradually, in

themodelnegativeskewnessofcreditgrowthisassociatedwithhigherlong-rungrowth.

H avingamicrofoundedmodelallows us toexaminetherelationship between …nancial

fragility, productione¢ciencyandsocialwelfare. Becausebothsectorscompeteeveryperiod

fortheavailablesupplyofN -goods, whencontractenforceabilityproblemsareverysevere,

theN -sectorattainslowleverageandcommandsonlyasmallshareofN -inputs. T hisresults

in a socially ine¢cientlowgrowth path: a centralplannerwould increase the N -sector

investmentsharetoattaintheParetooptimalallocation.

Clearly, the…rstbestcanbeattainedinadecentralizedeconomybyreducingtheagency

problems thatgeneratethe…nancingconstraints. H owever, ifsuch areform is notfeasi-

ble, creditriskmaybeasecondbestinstrumenttoincreasesocialwelfaredespite…nancial

fragility. O ursecondtheoreticalresultisthatwhencontractenforceabilityproblemsarese-

4

vere, butnottoosevere, andcrisiscostsarenottoolarge, creditriskincreasessocialwelfare

andbringstheallocationnearertotheParetooptimallevel.

T heexistenceoftheriskyequilibrium depends on systemicbailoutguarantees. Since

theseguaranteesarefundedbydomestictaxationthequestionarisesastowhethersucha

policycanbeimplemented. W eshowthatifN -inputsareintensivelyusedinT -production,

theT -sectorwill…nd itpro…tabletofundthe…scalcostoftheguarantees. T hefunding

oftheguaranteesactuallye¤ectsaredistribution from thenon-constrainedT -sectortothe

constrained N -sector. T his redistribution is tothemutualbene…tofbothsectors because

T -productionenjoys cheaperandmoreabundantN -inputs, and its growthrate increases:

thebottleneck iseased. T hus, eventhosewhobearthecostsofcrisesmaybewillingtopay

theirprice.

W ewishtomakeafewcommentsonhowourmodelrelatestotheliterature.4 First, the

creditcycles inthispaperaredi¤erentfrom Schumpeteriancycles inwhichtheadoptionof

newtechnologiesplaysakeyrole. R atherourcyclesresembleJuglarcreditcycles. Second,

althoughourmodelcontainssomeelementsofthirdgenerationcrisismodels, itisprimarily

atwo-sectorlong-rungrowthmodelwherecrisescanoccur. T hisallowsforexplicitwelfare

analysis.

Finally, ourempirical…ndingthatbumpiness is associatedwithhigherlong-rungrowth

o¤ersanexplanationforthepositivelinkbetween…nancialliberalizationandgrowthfound

bysomeresearchers, andthepositiveimpactof…nancialliberalizationonthefrequencyof

crises …ndbyothers. O urmodelcanhelp explainwhy, byallowingagentstotakeonmore

creditriskandeasingborrowingconstraints, …nancialliberalizationmayleadtobothhigher

growthandagreaterincidenceofcrises.

Section2 containsourempirical…ndings. Section3presentsthemodel. Section4derives

thelimitdistributions ofoutputandcreditgrowth, and links themodeltoourempirical

…ndings. Section5 analyzes productione¢ciencyandwelfare. Section6relatesourpaper

totheliterature. Section 7 concludes.4SeeSection6foradetailedreviewoftheliterature.

5

2 B umpinessandG rowth: TheEmpiricalL ink

H ere, weinvestigatewhethercountrieswithriskycreditpathsthathaveexperienced…nancial

crises havegrownfaster, onaverage, thanothercountries. W ewillmeasuretheincidence

of…nancialcrises withthenegative skewness ofrealcreditgrowth.5 A longaboom-bust

episodethereishighcreditgrowthduringthelendingboom, asharpandabruptdownward

jumpduringthecrisis, andslowcreditgrowthduringthecreditcrunchthatdevelopsinthe

wakeofthecrisis. Sincecreditdoesnotexperiencesharpjumpsduringtheboomandcrises

happenonlyoccasionally, thedistributionofcreditgrowthratesischaracterizedbynegative

outliers.6 T herefore, countries thatexperience aboom-bustepisode exhibitanegatively

skeweddistributionofcreditgrowth. Forthisreasonwewillrefertonegativeskewnessas

bumpiness.7

B oom-bustepisodesareassociatednotonlywithnegativeskewness, butalsowithhigh

varianceofcreditgrowth –thetypicalmeasureofvolatility in the literature. W e choose

nottousethevariancetoidentifyriskycreditpathsthatleadtoinfrequentcrisesbecause

highvariancemayalsore‡ecthighfrequencyshocks, whichmightbeexogenous ormight

beself-in‡ictedby, forinstance, badeconomicpolicy. Sincehighfrequencyshocksaremore

abundantin the sampleweconsiderthan therarecrises thatpunctuate lendingbooms,

varianceisnotagoodmeansofdistinguishingriskyfrom safepaths.

Inprinciple, wecouldalsoidentifycountries thathavefollowedriskypaths bylooking5Skewness isameasureofasymmetryofthedistributionoftheseriesarounditsmeanandiscomputed

asS = 1n

X n

i=1(yi¡y)3

b¾ ;where¹y isthemeanand ¾ isthestandarddeviation. T heskewnessofasymmetric

distribution, suchas thenormaldistribution, is zero. Positiveskewnessmeans thatthedistributionhas a

longrighttailandnegativeskewness impliesthatthedistributionhasalonglefttail.6D uringalendingboom therearepositivegrowthrates thatareabovenormal. H owever, theyarenot

positiveoutliersbecausethelendingboomtakesplaceforseveralyears. O nlyapositiveone-periodjump in

creditwouldcreateapositiveoutlieringrowthrates. Forinstance, T hailandexperiencedalendingboom

foralmostallofthesampleperiodandmostofthedistribtuioniscenteredaroundaveryhighmean.7 Crises arerareevents and inashortsampleperiodnotallriskylendingboomsneedtoend inabust

(seeG ourinchaset. al(2001)andTornellandW estermann(2002)). Countriesthatexperienceriskylending

booms withouthavingacrisis donotexhibitanegatively skeweddistribution ofcreditgrowth. N otice,

however, thatduringoursampleperiod (19 80-19 9 9 ) mostcountries thathavefollowedriskycreditpaths

haveexperiencedatleastonemajorcrisis.

6

Figure1: Safevs. R iskyG rowthPaths

Credit: GDP per capita:

0.8

1.2

1.6

2.0

2.4

2.8

3.2

80 82 84 86 88 90 92 94 96 98 00 02

India Thailand

0.8

1.2

1.6

2.0

2.4

2.8

80 82 84 86 88 90 92 94 96 98 00 02

India Thailand

Note: The values for 1980 are normalized to one.

attheskewness ofG D P growth. Inpractice, however, thismaybeunreliablebecausethe

tradablessectoristypicallynotnegativelya¤ectedduringcrises. Sincethissectorhasaccess

toworldcapitalmarkets, tradables productiondoes notdeclineas muchas nontradables

productionduringcrises andoftengoes up (duetotherealdepreciation in theexchange

rate). A saresult, thedeclineinG D P ismuchmilderthanthedeclineincredit.8

T hekerneldistributionsofcreditgrowthratesforIndiaandThailandaregiveninFigure

2.9 India, thesafecountry, hasalowmeanandisquitetightlydistributedaroundthemean

–withskewnessclosetozero. M eanwhile, T hailand, theriskycountry, hasaveryasymmetric8Furthermore, ourmodelindicatesthatskewnessofG D P isnotasgoodatestofariskypathasskewness

ofcreditgrowth. B ecausetheT -sectorhasaccesstointernationalcapitalmarketsandbene…tsfromthereal

depreciation, themodelpredictsthatacrisiswilla¤ectG D P muchlessthanita¤ectsthebank-dependent

N -sectorandcreditgrowth.9 T hesimplestnonparametricdensityestimateofadistributionofaseriesisthehistogram. T hehistogram,

however, is sensitivetothechoiceoforiginandisnotcontinuous. W ethereforechoosethemoreillustrative

kerneldensityestimator, whichsmoothesthebumps inthehistogram (seeSilverman19 86). Smoothingis

donebyputtinglessweightonobservations thatarefurtherfrom thepointbeingevaluated. T heKernel

functionbyEpanechnikovisgivenby: 34(1 ¡(¢ B )

2)I(j¢ B j·1 );where¢ B isthegrowthrateofrealcredit

andIistheindicatorfunctionthattakesthevalueofoneifj¢ B j·1 andzerootherwise. T hebandwidth,

h, controls forthesmoothness oftheofthedensityestimate. T helargerish, thesmoothertheestimate.

Forcomparability, wechoosethesamehforbothgraphs.

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distributionandischaracterizedbyamuchlargernegativeskewness.

Figure2: D istributionsandKernelD ensitiesofR ealCreditG rowth

0

1

2

3

4

5

6

7

8

-.3 -.2 -.1 .0 .1 .2 .3

India

Kernel Density (Epanechnikov, h = 0.1000)

0

1

2

3

4

5

-.2 -.1 .0 .1 .2 .3

Thailand

Kernel Density (Epanechnikov, h = 0.1000)

India Thailand Mean 0.021 0.109 Std. Dev. 0.014 0.125 Skewness -0.370 -1.108

Toestablishthatthepositiverelationship betweenG D P growthandnegativeskewness

ofrealcreditgrowthisnotspeci…ctoIndiaandThailand, weusecross-countryregressions.

B ecauseourmodelindicates thatcountrieswithextremecontractenforceabilityproblems

willnotbeabletogeneratecreditrisk, werestrictourdatatothosecountrieswithfunctioning

…nancialmarkets. O urcriterionforinclusioninthesetisthatacountryhaveastockmarket

turnover-to-G D P ratioofatleast1% in19 9 8.10 T his setcontains66countries, 52 ofwhich

havedataavailableduringthe19 80sand19 9 0s.11

Toassessthelinkbetweenbumpinessandgrowthweaddthethreemomentsofrealcredit

growthtoastandardgrowthregression:

¢ yit= ¸yi0 + °0X it+ ¯ 1¹ ¢ B ;it+ ¯ 2 ¾ ¢ B ;it+ ¯3S¢ B ;it+ "it; (1)

where¢ yitistheaveragegrowthrateofper-capitaG D P ;yi0 istheinitiallevelofpercapita

G D P;¹ ¢ B ;it; ¾¢ B ;itandS¢ B ;itarethemean, standarddeviationandskewness ofthereal10W ehavechosen19 9 8 becauseitistheyearwithmaximumdataavailability.11Inordertocomputethehighermoments, weconsideronlyseriesforwhichwehaveatleasttenyearsof

data. O ursourceofdatais W orldD evelopmentIndicators(W D I) oftheW orldBank.

8

creditgrowth rate, respectively. X it is avectorofcontrolvariables thatincludes initial

human capital, averagepopulation growth rate, and life expectancy. W edonotinclude

investmentin(1)asweexpectthethreemomentsofcreditgrowth, ourvariablesofinterest,

toa¤ectG D P growththroughhigherinvestment.12

W eestimatetheregressioninthreedi¤erentways. First, weestimateastandardcross-

sectionregressionbyO L S. Inthis case19 80 is theinitialyearandthemomentsofcredit

growtharecomputedovertheentiresampleperiod19 80-19 9 9 . Second, weestimateapanel

regressionusingtwonon-overlappingwindows: 19 80-19 89 and 19 9 0-19 9 9 . Inthis casewe

usetwosets ofcreditgrowthmoments, oneforeachwindow. L astly, weuseoverlapping

averages. W econstruct10-yearaverages startingwiththeperiod19 80-19 89 androllingit

forwardtotheperiod 19 9 0-19 9 9 , foreachcountryandeachvariable. T hus, eachcountry

hasup to10 datapoints inthetimeseriesdimension.13 W eestimatethepanelregressions

usinggeneralizedleastsquares. W edealwiththeresultingautocorrelationintheresiduals

byadjustingthestandarderrorsaccordingtoN eweyandW est(19 8 7 ).14

Table 1 reports the estimation results forthe three regressions. W e …nd that, after

controllingforthestandardvariables, themeangrowthrateofcredithas apositivee¤ect

on long-run G D P growth. This has alreadybeen established in theliterature. W hatwe

establishisthebumpinessofcreditthataccompanieshighgrowthacrossthesetofcountries

withfunctioning…nancialmarkets. T he…rstthreecolumnsshowthatnegativeskewness–a

bumpiergrowthpath– isonaverageassociatedwithhigherG D P growth. Theseestimates

aresigni…cantatthe5% levelinthepanelregressionsandthe10% levelinthecross-section.

T hemodelshowsthatthelinkbetweengrowthandbumpinessexistsonlyacrosseconomies

withsigni…cantcontractenforceabilityproblems(thatarenottooextreme). Intheabsence

ofsuchproblems, theborrowingconstraintsthatdriveourresultsdonotariseinequilibrium.

Tocapturethisdistinction, wedivideoursampleintocountrieswitheitherhighormiddle

enforceabilityofcontracts (H ECs and M ECs). W eclassifyas H ECs theG 7 countries and12T heselection ofcontrolvariables follows theselection in theprevious studies mostcloselyrelatedto

ours: B ekaert, et.al. (2001), andL evineandR enelt(19 9 1).13B ekaertet.al. (2001) alsoconsideroverlappingaverages. T heylookatshorteraverages, butthis isnot

feasibleinourcase, asthehighermomentsofcreditgrowthcannotbecomputedinameaningfulway.14O urpanelisunbalancedbecausenotallseriesareavailableforallcountriesandforallperiods.

9

thosewithaKraayandKaufman’sruleoflawindexofnolessthan1:4 . T hisclassi…cation

generates35 M ECsand17 H ECs.15

T hefourthcolumninTable1 reportstheestimationresultsforaregressionequationthat

addsto(1) thefollowingthreeterms: ¯ 4 ¤h ec¤¹¢ B ;it+ ¯5¤h ec¤¾¢ B ;it+ ¯6¤h ec¤S¢ B ;it;whereh ecisadummyvariablethatequalsoneforH ECsandzerootherwise.16 T hiscolumn

showsthatacross M ECsthereisastronglinkbetweenbumpinessandgrowth. Incontrast,

this linkis notevidentacross H ECs. T hepointestimateofthebumpiness coe¢cientfor

M ECs is ¯3 = 0:2 5, anditis signi…cantatthe5% level. M eanwhile, thatforH ECs isonly

¯3 + ¯6 = 0:18, and W aldtests revealthatalthoughthemeanandthevarianceofcredit

growthhaveasigni…cante¤ectonG D P growth(atthe5% level), skewnessdoesnot. Infact,

H ECshaveexperiencednearzeroskewness increditgrowthduringthelasttwodecades.

Tointerprettheestimateof0.265 forbumpiness, considerIndia, withnearzeroskewness,

andThailandwithskewnessofminustwo. A pointestimateof0.265 impliesthatanincrease

inthebumpiness indexoftwo(from 0 to-2), increases theaveragelongrun G D P growth

rateby0.53% peryear. Isthisestimateeconomicallymeaningful?Toaddressthisquestion

notethataftercontrollingforthestandardvariables Thailandgrows about2% moreper

yearthanIndia. T hus, aboutaquarterofthisgrowthdi¤erentialcanbeattributedtocredit

risktaking, asmeasuredbytheskewnessofcreditgrowth.

N ext, considerthevarianceofcreditgrowth. Consistentwiththeliterature, thevariance

enters with anegative sign and itis signi…cantatthe 5% levelin allregressions.17 W e

can interpretthenegativecoe¢cientonvarianceas capturingthee¤ectof‘badvolatility’

generatedby, forinstance, procyclical…scalpolicy. M eanwhile, thepositivecoe¢cienton15T heH ECs are: A ustralia, A ustria, Canada, D enmark, Finland, France, G ermany, Italy, Japan, L ux-

embourg, N etherlands, N ewZ ealand, N orway, Sweden, Switzerland, U K, and U nited States. T he M ECs

are: A rgentina, B angladesh, B elgium, B razil, Chile, China, Colombia, Ecuador, Egypt, G reece, H ongKong,

H ungary, India, Indonesia, Ireland, Israel, Jordan, Korea, M alaysia, M exico, M orocco, Pakistan, Peru, Philip-

pines, Poland, Portugal, SouthA frica, Spain, Sri L anka, T hailand, Tunisia, Turkey, U ruguay, Venezuelaand

Z imbabwe.16T hee¤ectsofthemomentsofcreditgrowthonG D P growtharecapturedby( 1 ; 2; 3)in M ECs, and

by ( 1 + ¯4; 2 + ¯5; 3 + ¯6)inH ECs.17 R ameyandR amey(19 9 5), andFatasandM ihov(2002) …ndthat…scalpolicyinducedvolatilityisbad

foreconomicgrowth.

10

Table1: B umpinessandG rowth Dependent variable: Real per capita GDP growth

(1)

(2)

(3)

(4)

Cross section Panel (non-overlapping)

Panel (overlapping)

HEC vs. MEC (overlapping)

Initial per capita GDP -0.914** -1.165** -1.269** -1.061** (0.320) (0.242) (0.060) (0.068) Secondary schooling -0.002 0.009 0.005 0.006 (0.014) (0.014) (0.003) (0.004) Population growth -0.010** -0.009** -0.010** -0.009** (0.002) (0.002) (0.001) (0.001) Life expectancy 0.072** 0.165** 0.166** 0.169** (0.015) (0.029) (0.016) (0.016) Credit_mean 0.091* 0.151** 0.154** 0.184** (0.048) (0.034) (0.011) (0.014) Credit_Variance -0.044** -0.036** -0.030** -0.041** (0.017) (0.017) (0.004) (0.006) -(Credit_Skewness) 0.211* 0.302** 0.265** 0. 250** (0.119) (0.148) (0.040) (0.093) Credit_mean*HEC -0.142** (0.023) Credit_Variance*HEC -0.009 (0.009) -(Credit_Skewness)*HEC -0.072 (0.113) # of observations 51 84 424 424

Note: The table shows the results of the regression.:

ititBitBitB S ???????? ??????? ??? Xyy ,3,2,1itinii,it ,where ?yit is the average growth rate of per-

capita GDP; inii,y is the initial level of per-capita GDP; and itB ,?? , itB,?? and itBS ,? are the mean, standard

deviation and skewness of the real credit growth rate, respectively. itX is a vector of control variables that includes initial human capital, the average population growth rate, and life expectancy. Column (1) shows the results for a standard cross section regression, estimated by OLS for the sample period 1980 to 1999. Column (2) shows the results for a non-overlapping panel regression with two periods, one from 1980-1989 and one from 1990 to 1999. Column (3) reports the results from an overlapping panel regression. For each country and each variable, we construct 10-year averages starting with the period 1980-1989 and rolling it forward to the period 1990-1999. Column (4) separates the sample in HEC and MEC countries. The panel regression is estimated using a GLS estimator. Heteroscedasticity consistent standard errors are computed using the Newey and West procedure and are reported in parentheses; * indicates significance at the 10 percent level and ** indicates significance at the 5 percent level.

Wald Tests H0: Sum of HEC and MEC coefficient=0

F-statistic (p-value) Credit-mean 5.029 0.025 Credit-variance 4.430 0.038 Credit skewness 0.005 0.942

11

bumpiness captures the‘goodvolatility’associatedwiththetypeofrisktakingthateases

…nancialconstraints andincreases investment.18 N oticethatacountrywithhighvariance

neednothavenegativeskewness.

Figure3 shows graphicallythelinkbetween G D P growthand themoments ofcredit

growthacross M ECs. Itis evidentthathigherlongrun G D P growth is associatedwith

(a) ahighermeangrowthrate incredit, (b) lowervarianceand(c) negativeskewness. In

otherwords, high G D P growthrates areassociatedwithariskyandbumpycreditpath.

Considerspeci…cexamples: Chile, T hailand andKorea, exhibitnegatively skewedcredit

growthandhighG D P growth. Incontrast, countriesthatdonotexhibitnegativeskewness,

like Pakistan, Bangladeshand M oroccohavelowgrowth. Chinaand Irelandarenotable

outliers: theyhaveexperiencedveryhigh G D P growth inthelasttwentyyears, buthave

notexperiencedacrisis.

In sum, our…ndings showthatM ECs thatfollowedariskycreditpath andhaveex-

periencedboom-bustepisodes haveonaveragegrownfasterthan M ECswithstablecredit

conditions. T heseresultsdonotimplythatcrisesaregoodforgrowth. Theysaythatunder-

takingcreditriskhasledtohighergrowth, butasaside-e¤ect, ithasalsoledtooccasional

crises.

3 M odel

W econsideranin…nitehorizonendogenousgrowthmodelofatwo-sectorsmallopeneconomy

withcreditmarketimperfections. T herearetwogoods: atradable(T ) good, which is a

consumptiongood, andanontradable(N )good, whichisusedasaninputintheproduction

ofboth goods. W ewilldenotetherelativepriceofN -goods (i.e., the inverseofthereal

exchangerate) bypt= pNt=pTt:T heonlysourceofuncertaintyisendogenousrealexchange

raterisk: inequilibrium pt+ 1 mayequalpt+ 1 withprobabilityut+ 1 orpt+ 1 withprobability

1¡ut+ 1:T heprobabilityut+ 1 mayequaleither1 oru;andthis isknownatt:

T herearecompetitiveriskneutralinternationalinvestorswhosecostoffundsequalsthe

world interestrate r:T hese investors lend any amountas longas they arepromised an18 T hisviewisconsistentwiththe…ndingsofImbs (2002).

12

Figure3: M omentsofCreditandG D P G rowth

a) Growth and Mean

GRC

SOU

SPA

PER

ARG

PHL

BRA

MEX

ECU

PRTCOL

JOR

BGD

TUR EGY

PAK

TUN

URU

CHL

IND

ZWE

IDN

MYSIRL

POL

VENMOR

HUN

KOR

THAISR

CHN

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

-0.1 -0.05 0 0.05 0.1 0.15 0.2

Credit growth, mean

GDP growth, mean

b) Growth and Variance

GRC

SOU

SPA

PER

ARGPHL

BRA

MEX

ECU

PRT

COL

JOR

BGD

TUREGY

PAK

TUN

URU

CHL

IND

ZWE

IDN

MYSIRL

POL

VEN

MOR

BEL

HUN

KOR

T H AISR

CHN

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

-0.1 0 0.1 0.2 0.3 0.4 0.5

Credit growth, variance

GDP growth, mean

c) Growth and Skewness

GRC

SOU

SPA

PER

ARGPHL

BRA

MEX

ECU

PRT

COL

JOR

BGD

TUREGY

PAK

TUN

URU

CHL

IND

ZWE

IDN

MYSIRL

POL

VENMOR

HUN

KOR

THA ISR

CHN

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

Credit growth, skewness

GDP growth, mean

Note: The graphs plot the moments of real credit growth from 1988-1999 against the residuals of a growth regression that controls for initial per capita GDP and population growth. 13

expected payo¤ of1 + r. T heyalsoissuedefault-freebonds: an N -bond andaT -bond.

T he T -bondpays 1 + r nextperiod, whilethe N -bondpays (1 + rnt)pt+ 1. T heexistence

ofriskneutraldeep-pocketinvestors impliesthatuncoveredinterestparitywillholdinany

equilibrium

(1 + rnt)pet+ 1 = 1 + r; where pet+ 1 := ut+ 1pt+ 1 + (1¡ut+ 1)pt+ 1 (2)

T here is acontinuum, ofmeasureone, ofcompetitive …rms thatproducethe T -good

usinganontradable input(d t) andanon-reproduciblefactor(lTt). T herepresentativeT -

…rm maximizes pro…ts takingasgiventhepriceofN -goods (pt) andthepriceofthenon-

reproduciblefactor(vTt) :

maxfd t+ j;lTt+ jg1j= 0

£yt+ j¡pt+ jd t+ j¡vTt+ jl

Tt+ j

¤; yt+ j= at+ jd ®t+ j(l

Tt+ j)

1¡® ; ® 2 (0 ;1) (3)

T here is acontinuum, ofmeasureone, ofconsumers. T herepresentativeconsumeris

in…nitelylived, consumesonlyT -goods, andisendowedwithoneunitofthenon-reproducible

factor, whichhesuppliesinelastically(lTt = 1):Furthermore, hecanbuyandsellanyamount

ofthetwodefault-freebondsdescribedabove. Sincecapitalmarketsarecomplete, hesolves

thefollowingproblem

maxfct+ jg1j= 0

EtP 1

j= 0 ±jU(ct+ j); st. Et

P 1j= 0 ±

j[ct+ j¡vTt+ j+ Tt+ j]·0 ; ± :=1

1 + r(4)

whereTtisthetaxthatwill…nancethebailouts.

T hereisacontinuum, ofmeasureone, of…rmsthatproduceN -goodsusingentrepreneurial

labor(lt);andcapital(kt). CapitalconsistsofN -goods investedduringthepreviousperiod

(It¡1);whichfullydepreciatesafteroneperiod. T heproductionfunctionis

qt= £ tk¯tl1¡¯t ; £ t= :µkt

1¡¯; kt= It¡1; ¯ 2 (0 ;1) (5)

T hetechnologicalparameter£ tembodiesanexternale¤ect, wherektistheaverageN -sector

capital, thateach…rmtakesasgiven.

T heinvestablefundsofan N -…rm consistofitscash‡owwtplusthedebtitissues. In

ordertocapturethedebtdenominationdecisionweassumethatthe…rm canissueT -debt

(bt) andN -debt(bnt) thatpromisetorepaynextperiodLt+ 1 = (1 + ½t+ 1)btand pt+ 1Lnt+ 1 =

14

pt+ 1(1+ ½nt+ 1)bnt;respectively. Fundscanbeusedtobuydefault-freebonds(st;snt)orN -goods

(ptIt) inordertoproduceN -goods inthefollowingperiod. Sincebtandbnt aremeasuredin

T -goods, thetimetbudgetconstraintandtimet+ 1 pro…tsare, respectively

ptIt+ st+ snt = wt+ bt+ bnt (6)

¼(pt+ 1) = pt+ 1qt+ 1 + (1 + r)st+ pt+ 1(1 + rnt)snt¡vt+ 1lt+ 1¡Lt+ 1¡pt+ 1Ln

t+ 1 (7 )

Firms are run byoverlappinggenerations ofentrepreneurs wholive fortwoperiods and

consumeonlytradablesinthesecondperiodoftheirlife.A tthebeginningoftimetayoung

entrepreneursupplies inelasticallyoneunitoflabor(lt= 1) andreceivesawagevt:A tthe

endoftimetshetakes controlofthe…rm andmakes investmentand…nancingdecisions.

T hecash‡owofthe…rmequalstheentrepreneur’swage: wt= vt.

N -sector…nancingis subjecttotwocreditmarketimperfections: contractenforceability

problems andsystemicbailoutguarantees thatcoverlenders againstsystemiccrises. T he

formerwillgiverisetoborrowingconstraintsinequilibrium, whilethelatterwillinduce…rms

toundertakeinsolvencyriskthroughcurrencymismatch. W emodeltheseimperfectionsusing

thecreditmarketgameofSchneiderandTornell(2003), henceforthST .

ContractEnforceabilityProblems. Entrepreneurscannotcommittorepaydebt: ifattimet

theentrepreneurincursanon-pecuniarycosth [wt+ bt+ bnt]; thenatt+ 1 shewillbeable

todivertallthereturnsprovidedthe…rm is solvent.

SystemicBailoutG uarantees. T hereisabailoutagencythatpayslenderstheoutstanding

debtsofalldefaulting…rms ifmorethan50% of…rmsbecomeinsolvent(i.e., ¼(pt¡1) < 0 ):

T heguaranteeappliestobothN - andT -debt. T hebailoutagencyrecuperatesashare¹ of

theinsolvent…rms’revenues. T heremainderis …nancedbylump-sumtaxesonconsumers.

T hegoalofeveryentrepreneuristomaximizenextperiod’sexpectedpro…tsnetofdiver-

sioncosts. Sinceguaranteesaresystemic, thedecisionsofentrepreneursareinterdependent.

T herefore, theirdecisionswillbedeterminedinthefollowingcreditmarketgameconsidered

byST . D uringeachperiodt, takingprices as given, everyyoungentrepreneurproposes a

planPt = (It;st;snt;bt;bnt;½t;½nt) thatsatis…es budgetconstraint(6). L enders thendecide

whethertofund these plans. Finally, funded youngentrepreneurs make investmentand

diversiondecisions.

15

Payo¤s aredeterminedatt+ 1:Consider…rstplans thatdonotleadtodiversion. If

the…rm is solvent(¼(pt+ 1)¸ 0 ); theoldentrepreneurpays vt+ 1 totheyoungentrepreneur

and Lt+ 1 + pt+ 1Lnt+ 1 tolenders. Shethenconsumes thepro…tcet+ 1 = ¼(pt+ 1):Incontrast,

ifthe…rm is insolvent(¼(pt+ 1) < 0 ); youngentrepreneursreceive¹w pt+ 1qt+ 1 (¹ w < 1¡¯),

lendersreceivethebailoutifanyisgranted, andoldentrepreneursgetnothing. Ifadiversion

schemeis inplaceandthe…rm is solvent, theoldentrepreneurgets ¯pt+ 1qt+ 1 andnothing

otherwise;youngentrepreneursget[1¡¯]pt+ 1qt+ 1 andlendersreceivethebailoutifanyis

granted. T heproblemofayoungentrepreneuristhentochooseaninvestmentplanPtand

diversionstrategy´ttosolve:

maxPt; t

Et(»t+ 1fpt+ 1qt+ 1 + (1 + r)st+ pt+ 1(1 + rn)snt¡vt+ 1lt+ 1

¡[1¡´t][Lt+ 1 + pt+ 1Lnt+ 1]¡h ´t[wt+ bt+ bnt]g) s.t. (6),

where ´t = 1 iftheentrepreneurhas setup adiversion scheme, and zerootherwise;and

»t+ 1 = 1 if¼(pt+ 1)¸ 0 , andzerootherwise. T hefollowingde…nition integrates thecredit

marketgamewiththerestoftheeconomy.

D e…nition. A symmetricequilibrium isacollectionofstochasticprocesses

fIt;st;snt;bt;bnt;½t;½nt;d t;ct;yt;qt;ut;pt;wt;vt;vTtg suchthat, (i) givencurrentpricesand

thedistributionoffuturepricestheplan (It;st;snt;bt;bnt;½t;½nt) isdeterminedinasymmetric

subgame perfectequilibrium ofthe creditmarketgame, d tmaximizes T -…rms pro…ts and

ctmaximizes consumers expectedutility;(ii) factormarkets clear;and(iii) themarketfor

non-tradablesclears: d t+ It= qt.

Toclosethemodelweassumethatdate zeroyoungentrepreneurs areendowedwith

w 0 = (1¡¯)poqo units ofT -goods, whileoldentrepreneurs areendowedwith qo units of

N -goodsandhavenodebtinthebooks. Finally, weimposetheconditionthatguarantees

aredomestically…nancedthroughtaxation:

EtP 1

j= 0 ±j[1¡»t+ j][Lt+ j+ pt+ jLn

t+ j¡¹pt+ jqt+ j¡Tt+ j]= 0 ; ¹ 2 [0 ;¯]: (8)

3.1 D iscussionoftheSetup

Toinvestigatehowtheforces thatgeneratehighergrowthalsogenerate…nancialfragility

weconsiderasetupwithnoexogenousshocks. Inequilibriumfragilitywillarisefromaself-

16

reinforcingmechanism: N -…rms…nditpro…tabletoissueT -debtinthepresenceofsystemic

guaranteesandsu¢cientrealexchangeratevariability. T hisvariability, inturn, mayarise

becausethereis enoughT -debtissuedbyN -…rms. Clearly, thereareotherself-reinforcing

mechanismsthatgenerateendogenous…nancialfragility. T heconcretemechanismwemodel

here, however, capturessomefeaturesofrecentboom-bustepisodes.

In oursetup therearecompletemarkets. Sinceduringeach periodtherealexchange

ratecantakeonlytwovalues, themenuofsecurities allowsconsumers and…rmstohedge

allrisk.19 T hiswillallowustomakethepointthatgrowthandwelfaregainsarisefromthe

undertakingofcreditrisk, notfromconsumptionsmoothing.

T he assumption thatN -goods are used as inputs is key. T he use ofN -inputs in N -

productionisnecessaryfortheexistenceofendogenousrealexchangeratevariability. O th-

erwise, self-fullingcrisescouldnotoccur. T heuseofN -inputsinT -productiontogetherwith

externale¤ects inN -productionimplythattheN -sectoristhesourceofendogenousgrowth

in theeconomy. T his, inturn, underlies theresultthattheundertakingofcreditriskby

increasingN -productionmayincreasesocialwelfare, andthattheT -sectormayderiveanet

bene…tfrom …nancingthe…scalcostsoftheguarantees. Incontrast, theassumptionsthat

N -goodsarenotconsumedandT -goodsarenotintermediateinputsareconvenientbutnot

essential.20

Tocapturethedynamicandthestatice¤ectsofcriseswehaveallowedfortwotypesof

crisis costs: …nancialdistress ((1¡¯)=¹w ) andbankruptcycosts ( =¹). A lltheequilibria

wecharacterizeexistforany¹ w 2 (0 ;1¡¯)and¹ 2 [0 ;¯]:Financingopportunities areasymmetricacross sectors becauseonly N -sectorcreditis

a¤ectedbycontractenforceabilityproblems. T hisassumptioncaptures thefactthatmost

ofthe…rmsinM ECsthatcanaccess international…nancialmarketsareintheT -sector. In

contrast, mostN -sector…rmsaredependentondomesticbankcredit.21

T heagencyproblemandthetwo-periodlivedentrepreneurset-up istakenfromST .T he19 Inparticular, N -debtisaperfecthedgeforN -sector…rms.20IfN -goodswereconsumed, therewouldadeeperfallinthedemandofN -goodswhen N -…rms become

insolvent, accentuatingtheself-ful…llingdepreciationthatgeneratescrisis.21T his is inpartbecauseT -…rmscaneitherpledgeexportreceivablesascollateral, orcangetguarantees

fromcloselylinked…rms. TornellandW estermann(2003)documentsectorialasymmetriesaswellassystemic

guarantees inM ECs.

17

advantageofthis set-up is thatonecananalyze…nancialdecisionsperiod-by-period. T his

willallowustoexplicitlycharacterizethestochasticprocessesofpricesandinvestmentand

derivethelimitdistributionofgrowthrates.

Finally, theassumptionthatbailoutguaranteesaresystemicisessential. Ifinstead, guar-

anteeswereunconditionalandabailoutweregrantedwheneverasingleborrowerdefaulted,

thentheguarantees wouldneutralizethecontractenforceabilityproblems andborrowing

constraintswouldnotariseinequilibrium.

3.2 SymmetricEquilibria(SE)

W econstructSEintwosteps. First, wetakeprices(pt)andthelikelihoodofcrisis(1¡ut+ 1)asgiven, andderivetheequilibrium atapointintime. W ethenendogeneizeptandut+ 1.

Inordertosimplifynotationwewillsetat= 1 in(3).

T herepresentativeT -…rmmaximizespro…ts, takinggoodsandfactorpricesasgiven. It

thus sets ptd t = ®ytand vTtlTt = (1¡®)yt:Sinceconsumers supply inelasticallyoneunit

ofthenon-reproduciblefactor, equilibrium T -output, consumer’s incomeandtheT -sector

demandforN -goodsare, respectively:

yt= d ®t; vTt = [1¡® ]yt; d (pt) =·®pt

¸ 11¡®

(9 )

Sincetheconsumerhasaccess tocompletecapitalmarkets andhis subjectivediscount

rateequalstheriskfreerate, ineachperiodheconsumesaconstantfractionofhisexpected

discountedincome:

ct= [1¡±]Et

³P 1j= 0 ±

j[(1¡®)yt+ j¡Tt+ j]´

(10)

InanySEtherepresentativeN -…rm’s capital(kt) is equaltoaggregateaveragecapital

(¹kt):T hus, (5) impliesthatN -outputequals: qt+ 1 = µkt+ 1 = µIt:N -sectorinvestment(It) is

determinedbytheequilibriaofthecreditmarketgame, whicharecharacterizedinST and

summarizedinthenextproposition.

18

Proposition3.1 (SymmetricCreditM arketEquilibria(CM E)) Thereisinvestment

intheproductionofN -goods ifandonlyif

R et+ 1 := ¯µ

·ut+ 1

¹pt+ 1pt

+ [1¡ut+ 1]pt+ 1

pt

¸¸1±>

hut+ 1

(11)

Suppose(11) holds. Then,

i Therealways exists a‘safe’CM E inwhichinsolvencyriskis hedged(bt= 0 ):Creditand

investmentare: bnt = [m s¡1]wtandIt= m swtpt;withm s = 1

1¡h ±:

ii Ifin additionut+ 1 = u< 1 and¯µp

t+ 1pt

< hu, therealsoexists a ‘risky’CM E inwhich

currencymismatchis optimal(bnt = 0 ):Creditandinvestmentare: bt = [m r ¡1]wt

and It= m r wtpt;withm r = 1

1¡u¡1h ±:

G iventhatallotherentrepreneurschoosethesafeplan (i), anentrepreneurknowsthat

nobailoutwillbegrantednextperiod. Sincelenders mustbreak-even, theentrepreneur

mustinternalizeallbankruptcycosts. T hus, shewillnotsetadiversion schemeandwill

hedgeinsolvencyriskbydenominatingalldebtinN -goods. Sincethe…rmwillnevergobust

andlendersmustbreakeven, theinterestratethattheentrepreneurhas too¤ersatis…es

[1 + ½nt]Et(pt+ 1) = 1 + r:Since(11) holds, investmentyields areturnwhichishigherthan

theopportunitycostofcapital.22 T hus, theentrepreneurwillborrowuptoanamountthat

makes thecreditconstraintbinding: (1 + r)bnt · h(wt+ bnt):Substitutingthis borrowing

constraintinthebudgetconstraintptIt= wt+ bntgeneratestheinvestmentequation. N otice

thatanecessaryconditionforborrowingconstraintstoariseis h < 1 + r:Ifh ; theindexof

contractenforceability, weregreaterthanthecostofcapital, itwouldalwaysbecheaperto

repaydebtratherthantodivert.

G iventhatallotherentrepreneurschoosetheriskyplan(ii), ayoungentrepreneurexpects

abailoutinthelowstate, butnotinthehighstate. T hepropositionshowsthat, inspiteof

theguarantees, diversionschemesarenotoptimal. T hus, borrowingconstraintsbind. W ill

theentrepreneurchooseT -debtorN -debt? Sheknowsthatallother…rmswillgobustin

thebadstate(i.e., ¼(pt+ 1) < 0 )providedthereis insolvencyrisk– i.e.,

¯µpt+ 1pt

< hu. H owever,

22T hemarginalreturntoinvestmentis E t(pt+ 1)£t k¯¡1t l1 ¡t ¡(±pt)¡1 = E t(pt+ 1)µ¯¡(±pt)¡1 :T his is

becauseinanSE£t=µ¹k1 ¡t ;¹kt=ktandlt=1 :

19

sincetherearesystemicguarantees, lenderswillgetrepaidinfull. T hus, theinterestrateon

T -debtthatallowslenderstobreak-evensatis…es 1 + ½t= 1 + r:Itfollowsthatthebene…ts

ofariskyplanderivefrom thefactthatchoosingT -debtoverN -debtreduces thecostof

capitalfrom 1+ r to[1+ r]u. L owerexpecteddebtrepaymentseasetheborrowingconstraint

aslenderswilllenduptoanamountthatequatesu[1 + r]bttoh [wt+ bt]:T hus, investmentis

higherrelativetoaplan…nancedwithN -debt. T hedownsideofariskyplanisthatitentails

aprobability1¡uofinsolvency. W illthetwobene…tsofissuingT -debt–moreandcheaper

funding– belargeenoughtocompensateforthecostofbankruptcy in thebad state? If

thereissu¢cientrealexchangeratevariabilityanduisnottoolow, expectedpro…tsunder

ariskyplanexceedthoseunderasafeplan: u¼ r(pt+ 1) > u¼ s(pt+ 1)+ (1¡u)¼s(pt+ 1):

Tosumup, Proposition3.1 makesthreekeypoints. First, bindingborrowingconstraints

ariseinequilibriumandinvestmentisconstrainedbycash‡ow, providedtheproductionof

N -goods is apositive N P V undertaking: R et+ 1 ¸ 1 + r. Second, agents optimallychoose

T -denominateddebtifthereissu¢cientrealexchangeratevariabilitysothat…rmsgobust

inthelowpricestate: ¼(pt+ 1) < 0 . T hird, suchariskycurrencymismatcheasesborrowing

constraintsandallows…rmstoinvestmorethanunderperfecthedging: m r > m s:

3.2.1 EquilibriumD ynamics

Inthissubsectionweendogeneizepricesanddeterminetheconditionsunderwhichthereisa

self-validatingprocessfpt; ¹pt+ 1; pt+ 1;ut+ 1g1t= 0 thatsatis…esthereturnconditionsspeci…edin

Proposition3.1. W estartbycharacterizingthetransitionequations. Ifa…rm issolvent, the

youngentrepreneur’swageequalsthemarginalproductofherlabor, whileunderinsolvency

shejustobtainsashare¹w ofrevenues. T hus, inanySEtheyoungentrepreneur’scash‡ow

is

wt=

8<:[1¡¯]ptqt¹w ptqt

if¼(pt)¸0if¼(pt) < 0 ;

¹ w 2 (0 ;1¡¯) (12)

Suppose foramomentthat(11) holds, sothatitis optimalto investallfunds in the

productionofN -goods: ptIt= m twt:Itthenfollowsfrom (12) thatN -sectorinvestmentis

It= Átqt; Át=

8<:[1¡¯]m t

¹w m t

if¼(pt)¸0if¼(pt) < 0 ;

m t2fm s;m rg (13)

20

Since in an SE qt = µIt¡1; itfollows from (9 ), (13) and themarketclearingcondition

(d t+ It= qt) thatequilibrium N -output, pricesandT -outputevolveaccordingto

qt = µÁt¡1qt¡1 (14)

pt = ® [qt(1¡Át)]®¡1 (15)

yt = [qt(1¡Át)]® =

1¡Át®

ptqt (16)

Clearly, forpricestobepositiveitisnecessarythattheshareofN -outputpurchasedbythe

N -sectorÁtis lessthanone:

h < ut+ 1¯±¡1 (17 )

Equations (13)-(16) form anSEprovidedtheimpliedreturnsvalidatetheagents’expecta-

tions (speci…edinProposition3.1). T henexttwopropositionscharacterizetwosuchSE: a

safeoneinwhichcrisesneveroccur, andariskyonewhereall…rmsbecomeinsolventinthe

lowpricestateandaresolventinthehighpricestate.

Proposition3.2 (SafeSymmetricEquilibria(SSE)) ThereexistsanSSE ifandonly

ifthedegreeofcontractenforceability h is lowenoughandN -sectorproductivityµ is large

enough. InanSSEthereisnocurrencymismatch(bt= 0 )andcrisesneveroccur(ut+ 1 = 1):

Thus, theN -sectorinvestmentshareis Ás = 1¡¯1¡h ±.

T his propositionstatesthatanSSE exists providedenforceabilityproblemsaresevere,

sothatthereareborrowingconstraintsandÁt< 1;andproductivityishighenough, sothat

thereturnoninvestmentisattractiveenough.

InanSSEallentrepreneurs selectthesafeplanofProposition3.1 duringeveryperiod.

T his implies thatthereis nocurrencymismatch intheaggregate, andself-ful…llingcrises

arenotpossible(ut+ 1 = 1). T herefore, theproductionofN -goodshasapositivenetpresent

value(i.e., (11) holds) ifandonlyif¯µpt+ 1pt

= ¯µ®(Ás)®¡1 ¸±¡1:T his condition, aswellas

(17 ), holdprovidedh is lowenoughandµ ishighenough.

N ext, wecharacterizeR iskySymmetricEquilibria(R SE). W ehaveseenthatentrepre-

neurswilltakeonT -debtonlyifthereisenoughanticipatedrealexchangeratevariabilityto

generatehighreturns inthegoodstateandacriticalmassofinsolvencies inthebadstate.

W enowreversethequestionandaskinsteadwhenariskydebtstructureimplies enough

21

realexchangeratevariability. T hatis: (i)willthelowpricebelowenoughsothattherewill

bewidespreadinsolvencies (¼(pt+ 1) < 0 )?(ii)willtherebeasu¢cientlyhighreturninthe

goodstatetoensurethattheex-anteexpectedreturnishighenough(R et+ 1 ¸1 + r)?

Thefollowingpropositionprovidesanswerstothesequestions, anditestablishesthatthe

self-reinforcingmechanismwedescribedaboveisatwork. O ntheonehand, expectedreal

exchangeratevariabilitymakesitoptimalforentrepreneurstodenominatedebtinT -goods

andruntheriskofgoingbust. O ntheotherhand, theresultingcurrencymismatchatthe

aggregatelevelmakestherealexchangeratevariable, validatingagents’expectations.

Proposition3.3(R iskySymmetricEquilibrium (R SE)) ThereexistsanR SE ifand

onlyifthe probabilityofcrisis (1¡u) is smallenough, N -sectorproductivity (µ) is large

enough, andthedegreeofcontractenforceability(h) is low, butnottoolow.

1. InanyR SEmultiplecrisescanoccurduringwhichallN -sector…rmsdefaultandthere

isasharprealdepreciation. H owever, twocrisescannotoccurinconsecutiveperiods.

2. In theR SEwherethere is areversionbacktoariskypathintheperiodimmediately

afterthecrisis, all…rmschooseriskyplans inno-crisistimesandsafeplans incrisis

times. Theprobabilityofacrisis andtheN -sector’s investmentsharesatisfy:

1¡ut+ 1 =

8<:1¡u ift6= ¿i0 ift= ¿i

Át=

8<:

Ál := 1¡¯1¡h ±u¡1 ift6= ¿i

Ác:= ¹w1¡h ± ift= ¿i

(18)

where¿idenotesacrisis time.

A keypropertyoftheR SE characterizedinProposition3.3 is thatacrisis stateis not

anabsorbingstate: acrisis canoccureveryotherperiod independentlyofthenumberof

previouscrises. Sinceweareinterestedinlongrungrowth, itisessentialthattheeconomy

followsariskypathforalongtime. T hisentailshavingmultiplecrises.

Toseethe intuitionconsideratypicalperiodtand supposethatallinheriteddebtis

denominatedinT -goodsandagentsexpectabailoutatt+ 1 incaseamajorityof…rmsgoes

bust. Sincethedebtburdenis independentofpricestherearetwomarketclearingpricesas

inFigure4. Inthe‘solvent’equilibrium (pointA inFigure4), thepriceishighenoughto

22

Figure4: N onTradables M arketEquilibrium

PR

ICE

Q U A N T I T Y

A

B

lt

tD

t ppq

?? ?

?????

?????

?

11)(

11

ct

tD

ppq

?? ?

?????

?????

?

11)(

11

11)( ??? tttSt qpq ? ?

(N-Firms are Solvent)

(N-Firms are Bankrupt)

tp

tp

23

allowtheN -sectortobuyalargeshareofN -output. Incontrast, inthe‘crisis’equilibrium

ofpointB , thepriceissolowthatN -…rmsgobust: ¯ptqt< Lt:23

T hekeytohavingmultipleequilibriais thatpartoftheN -sector’sdemandcomesfrom

the N -sectoritself. T hus, ifthepricefellbelowacuto¤ leveland N -…rmswentbust, the

investmentshareoftheN -sectorwouldfall(from Ál toÁc):T his, inturn, wouldreducethe

demandforN -goods, validatingthefallintheprices. N oticethattheupperboundonh and

thelowerboundon µ ensurethatwhencrises arerareevents, borrowingconstraints arise

andinvestmentispro…table(i.e., (11)holds). M eanwhile, thelowerboundonh ensuresthat

…rmswithT -debtgobustinthebadstate, andthatthefallincash‡owistranslatedinto

alargefallincreditandN -investment. T hisvalidatesthefallinprices.

Twopointsareworthemphasizing. First, Proposition3.3holdsforany¹w 2 (0 ;1¡¯)

and¹ 2 [0 ;¯]:T hatis, crisiscostsarenotnecessarytotriggeracrisis. A shiftinexpectations

issu¢cient: acrisiscanoccurwheneverentrepreneursexpectthatotherswillnotundertake

creditrisk, sothatthereis areversion tothesafeCM E characterized in Proposition3.1.

Second, twocrisescannotoccurconsecutively. Sinceinvestmentinthecrisisperiodfalls, the

supplyofN -goodsduringthepost-crisisperiodwillalsofall. T hiswilldrivepost-crisisprices

up, preventingtheoccurrenceofinsolvencies evenifalldebtwereT -debt. T hatis, during

thepost-crisisperiodadrop inpriceslargeenoughtogenerateinsolvencies is impossible.

4 G rowthandSkewness

H erewewilllinkPropositions 3.2 and3.3 toourempirical…ndings bycharacterizingthe

growthrates ofG D P andcreditalongriskyandsafeSE. Since N -goods are intermediate

inputs, whileT -goodsare…nalconsumptiongoods, grossdomesticproductequalsthevalue

ofN -sectorinvestmentplus T -output: gd pt= ptIt+ yt:Itthenfollowsfrom (13)-(16) that,

inanySE, G D P isgivenby

gd pt= ptÁtqt+ yt= q®tZ (Át) = ytZ (Át)[1¡Át]

; Z (Át) =1¡(1¡®)Át[1¡Át]1¡®

(19 )

A swecansee, thekeydeterminantoftheevolutionofG D P istheshareofN -outputinvested

bytheN -sector: Át. T hisshareisdeterminedbythecash‡owofyoungentrepreneursandby23Foradiscussionoftheroleofmultipleequilibriainexplaining…nancialcrisesseeColeandKehoe(2000).

24

thecredittheycanobtain. ItfollowsfromProposition3.1 thatinanSEthecreditextended

totheN -sector, expressedintermsofN -goods, isgivenby

B t=

8<:[Át¡(1¡¯)]qt[Át¡¹ w ]qt

if¼(pt)¸0if¼(pt) < 0

(20)

4.1 G rowthinaSafeEconomy

InanSSEtheinvestmentshareÁtisconstantandequaltoÁs. T hus, (19 ) impliesthatG D P

andT -outputgrowatthesamerate.

1 + °s :=gd ptgd pt¡1

=ytyt¡1

=¡µ 1¡¯1¡h ±

¢®= (µÁs)® (21)

A bsentexogenoustechnologicalprogress intheT -sector, theendogenousgrowthoftheN -

sectoristheforcedrivinggrowthinbothsectors. A stheN -sectorexpands, N -goodsbecome

moreabundantandcheaperallowingtheT -sectortoexpandproduction. T hisexpansionis

possibleifandonlyifN -sectorproductivity (µ) andtheN -investmentshare(Ás) arehigh

enough, sothatcreditandN -outputcangrowovertime: BtB t¡1

= qtqt¡1

= µÁs > 1. N oticethat

foranypositivegrowthrateofN -output, °s increaseswiththeintensityoftheN -inputin

theproductionofT -goods(® ).

T hemechanism bywhichhighergrowth in the N -sectorinduces highergrowth in the

T -sectoristhedeclineintherelativepriceofN -goodsthattakesplaceinagrowingeconomypt+ 1pt= [µÁs]®¡1:IfthereweretechnologicalprogressintheT -sector, therewouldbeaBalassa-

Samuelsone¤ectandtherealexchangeratewouldappreciateovertime.24

4.2 G rowthinaR iskyEconomy

Proposition3.3showsthatanyR SEiscomposedofasuccessionofluckypathspunctuated

bycrisisepisodes. IntheR SEcharacterizedby(3.3)theeconomyisonaluckypathattime

tiftherehasnotbeenacrisiseitheratt¡1 oratt. Sincealongaluckypaththeinvestment

shareequals Ál, (19 ) impliesthatthecommongrowthrateofG D P andT -outputis

1 + °l :=gd ptgd pt¡1

=ytyt¡1

=µµ

1¡¯1¡h ±u¡1

¶®

=¡µÁl

¢® (22)

24SupposethetechnologicalparameterintheT -productionfunctiongrowsovertime at+ 1at =(1 + g). T hen

pricedynamicsaregivenby pt+ 1pt

=(1 + g)[µÁs]®¡1 :

25

A comparisonof(21)and(22)revealsthataslongasacrisisdoesnotoccur, growthinarisky

economy is higherthan inasafeeconomy. A longtheluckypaththeN -sectorundertakes

insolvencyriskbyissuingT -debt. Sincetherearesystemicguarantees, …nancingcosts fall

and borrowingconstraints arerelaxed, relativetoasafeeconomy. T his increases the N -

sector’s investmentshare(Ál > Ás):Sincetherearesectoriallinkages(® > 0 ); this increase

intheN -sector’s investmentsharebene…tsboththeT - andtheN -sectorsandfostersfaster

G D P growth.

H owever, inariskyeconomyaself-ful…llingcrisiscanoccurwithprobability1¡u;and

duringacrisisepisodegrowthislowerthanalongasafepath. W ehaveseenthatanycrisis

episodeconsistsofatleasttwoperiods: inthe…rstperiodthe…nancialpositionoftheN -

sectoris severelyweakenedandtheinvestmentsharefalls from Ál toÁc< Ás;then inthe

secondperiod itjumps backtoÁl:Sincethesetransitions occurwithcertainty, themean

crisisgrowthrateisgivenby

1 + °cr =µ¡

µÁl¢® Z (Ác)

Z (Ál)

¶1=2

| {z }

µ(µÁc)®

Z (Ál)Z (Ác)

¶1=2

| {z }=

³µ(ÁlÁc)

12

®

crisisperiod post-crisisperiod

(23)

T hesecondequalityin(23) showsthattheaverageloss inG D P growthstemsonlyfromthe

fallintheN -sector’saverageinvestmentshare: (ÁlÁc)12 :T hisreductioncomesaboutthrough

twochannels: …nancialdistress(indexedby ¹w1¡¯ )andareductioninrisktakingandleverage

(indexedby 1¡h ±1¡h ±u¡1). N oticethatvariationsinG D P growthgeneratedbyrealexchangerate

changesat¿ and¿ + 1 cancelout. W ewillcomebacktothisbelow.

A crisis has long-rune¤ects because N -investmentis thesourceofendogenousgrowth,

andsothelevelofG D P fallspermanently. T hisraisestwoquestions: ismeanlong-runG D P

growthinariskyeconomygreaterthaninasafeone?D oesanincreaseinrisktaking(i.e.,

an increase in theprobabilityofcrisis) in arisky economy increasemean long-run G D P

growth?Theanswerstothesequestionsarenotstraightforwardbecauseanincreaseinthe

probabilityofcrisis (1¡u) hasopposinge¤ectsonlong-rungrowth. O netheonehand, a

greater1¡uincreasesinvestmentandgrowthalongtheluckypathbyincreasingthesubsidy

implicitintheguaranteeandallowing…rms tobemoreleveraged. O n theotherhand, a

greater1¡umakescrisesmorefrequent. T herefore, togiveapreciseanswertothequestions

26

wehaveraised, wecomputethelimitdistributionofG D P’sgrowthrate.

Figure5 exhibitsonerealizationofthepathsofG D P, credit, T - andN -outputassociated

withasetofparameters satisfyingtheconditions inPropositions 3.2 and3.3. T his …gure

makes clearthatgreaterlongrungrowthcomes atthecostof(rare) crises. N oticethat

sinceN -goodsareusedasinputsinbothsectors, higherN -sectorinvestmentleadstoalower

initiallevelofT -ouputinariskyeconomy(yl0 =£q0 (1¡Ál)

¤®< [q0 (1¡Ás)]® = ys0 ):O ver

time, however, T -outputalongtheriskypathwillovertakethatinasafepath.

G rowthL imitD istribution. InanyR SEtwocrisescannotoccurinconsecutiveperiods.

H ere, wewillderivethelimitdistributionofG D P’scompoundedgrowthrate(log(gd pt)¡log(gd pt¡1)) alongtheR SE characterized in Proposition3.3. Inthis R SE …rmsundertake

creditrisktheperiodafterthecrisis. Itfollows from (18), (22) and(23) thatthegrowth

processfollowsathree-stateM arkovchaincharacterizedby

¡ =

0BBB@

log¡(µÁl)®

¢

log³(µÁl)® Z (Á

c)Z (Ál)

´

log³(µÁc)® Z (Ál)

Z (Ác)

´

1CCCA ; T =

0BB@

u 1¡u 0

0 0 1

u 1¡u 0

1CCA (24)

T he three elements of¡ are the growth rates in the lucky, crisis and post-crisis states,

respectively. T heelementTijofthetransitionmatrixisthetransitionprobabilityfromstatei

tostatej:Sincethetransitionmatrixisirreducible, thegrowthprocessconvergestoaunique

limitdistributionoverthethreestates thatsolves T0¦ = ¦ :T hus, ¦ =¡ u2¡u;

1¡u2¡u;

1¡u2¡u

¢0;wheretheelementsof¦ arethesharesoftimethataneconomyspendsineachstateoverthe

long-run. ItthenfollowsthatthemeanlongrunG D P growthrateisE(1+ °r) = exp(¦ 0¡):25

T hatis,

E(1 + °r) = (1 + °l)!(1 + °cr)1¡! = µ®(Ál)®!(ÁlÁc)®1¡!2 ; where ! =

u2 ¡u

(25)

A comparisonoflongrunG D P growthratesin(21) and(25) revealsthetrade-o¤sinvolved

infollowingsafeandriskygrowthpaths, andallowsus todeterminetheconditions under

whichcreditriskisgrowthenhancing.25E (1 + ° r)isthegeometricmeanof1 + ° l;1 + ° lcand 1 + ° cl:

27

Figure5: R iskyvsSafeEconomy

0 20 40 60 800

1

2

3

4

5

6a:GDP

time

log(

gdp)

0 20 40 60 80-2

0

2

4

6

8

10

12

14b:credit to the N-sector

time

log(

B)

0 20 40 60 800

2

4

6

8

10

12

14c:N-production

log(

q)

time

0 20 40 60 80-1

0

1

2

3

4

5

6d:T-production

time

log(

y)

Risky EconomySafe Economy

(in N-tems)

(in N-tems)

%51%702.0176.035.065.1: ???????? ulhparameters d???

28

Proposition4.1 (L ong-runG D P G rowth) If…nancialdistressduringcrises isnottoo

severe(ld ´1¡ ¹w1¡¯ < ld ), thereexistsanh¤< u ±¡1, suchthatmeanlong-runG D P growth

isgreaterinariskythaninasafeequilibrium ifandonlyifthedegreecontractenforceability

satis…es h > h¤:

h¤=1¡(1¡ld )1¡u

u¡1¡(1¡ld )1¡u1± ld = 1¡

³1¡¯1¡¯u

´ 11¡u: (26)

Ifld ¸ld ; then h¤¸u ±¡1 andanR SEdoesnotexist.

R ewritingh > h¤as (1¡u)[log(1¡¯)¡log(¹w )]< log(Ál)¡log(Ás)makesclearwhat

arethecosts andbene…ts associatedwith ariskypath. A riskyeconomyoutperforms a

safeoneifthebene…tsofhigherinvestmentinno-crisis times (Ál > Ás) compensateforthe

shortfallincash‡owandinvestmentincrisistimes(¹ w < 1¡¯)weightedbythefrequency

ofcrisis (1¡u):

N oticethatanincreaseindistresscostscanbecompensatedbyanincreaseinthedegree

ofcontractenforceability. T helatterincreases leverageandampli…es thebene…ts ofrisk-

taking(@Ál=@h > @Ás=@h). H owever, as h is boundedabovetoensuretheexistenceofan

R SE(Ál < 1 , h < u ±¡1), anincreaseincontractenforceabilitycancompensateforlarge

butnotarbitrarilylargedistresscosts (i.e., ¹w ! 0 ).26

Figure6illustratesthelimitdistributionofG D P growthratesbyplottingdi¤erentG D P

pathscorrespondingtodi¤erentrealizationsofthesunspotprocess. M ostoftheriskypaths

outperformthesafepath, exceptforafewunluckyriskypaths. Ifweincreasedthenumber

ofpaths, thecrosssectiondistributionwouldconvergetothelimitdistribution.

Figure 7 exhibits thetwoe¤ects ofan increase in theprobabilityofcrisis (1¡u):A

reductioninuincreasestheinvestmentmultiplierm r atapointintime, butitalsoincreases

thefrequencyofcrises. T he…gureshowsthatforhighuthe…rste¤ectdominatesandthe

long-runmeangrowthrateofG D P goesup. Importantly, ucannotbereducedinde…nitely.

A fteracertainpointanR SEceasestoexist.26H owlargecan“nottoolarge” be?

1 ¡¯ =0 :2 1 ¡¯ =0 :4

u 0 :85 0 :99

ld 95:4% 98%

u 0 :85 0 :99

ld 74:2% 77:4%

29

Figure6: L imitD istributionofG D P

0 10 20 30 40 50 60 70 800

1

2

3

4

5

6

time

log(

GD

P)

GDP risky path with 3 crisesGDP risky path with 5 crisesGDP risky path with 9 crisesGDP safe path

NB: with 1-u=5%, the mean number of crises is 3.8

%51%702.0176.035.065.1: ???????? ulhparameters d???

30

Figure7 : G D P G rowthandCreditR isk

0 10 20 30 40 50 60 70 800

1

2

3

4

5

6

7

time

log(

GD

P)

1-u=8%; mean number of crises=5.91-u=5.4%: mean number of crises=4.51-u=2.3%: mean number of crises=2.09 Safe Economy

%702.0176.035.065.1: ?????? dlhparameters ???

31

Figure8: G D P G rowthandFinancialD istressCosts (ld = 1¡ ¹w1¡¯ )

%512.0176.035.065.1: ??????? uhparameters ???

0 10 20 30 40 50 60 70 800

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

time

log(

GD

P)

ld=40%

ld=70%

ld=90%

Finally, Figure 8 shows riskygrowthpaths associatedwith di¤erentdegrees ofcrisis’

…nancialdistress. A swecansee, evenif9 0% ofN -sectorcash‡owislostduringacrisis, a

riskyeconomycanoutperformasafeeconomyoverthelongrun.

A Crisis Episode. A lthough themain objectiveofthemodelis toaddress long-run

issues, itis reassuringthatitcanaccountforkeystylizedfactsofrecent…nancialcrises in

M ECs. Inparticular, therealdepreciationthatcoincideswithasharpfallincreditgrowth,

aswellastheasymmetricsectorialresponseofN - andT -sectors.

Ifaself-ful…llingcrisisoccursatsomedate, say¿;thereisa…resale: thereisasteepreal

32

exchangeratedepreciation, andsincethereiscurrencymismatch, allN -…rmsdefault. A sa

result, theinvestmentsharefallsfrom ÁltoÁc:27 T hepriceofN -goodsmustfalltoallowthe

T -sectortoabsorbagreatershareofN -output, whichispredeterminedby¿¡1 investment.

A t¿ + 1; N -outputcontractsduetothefallininvestmentatthetimeofthecrisis. H owever,

entrepreneursadoptriskyplansagain, sotheinvestmentshareincreasesfrom Ás backtoÁl:

T hus, thereisarealappreciation. A t¿ + 2 ; theeconomyisbackonaluckypath, butthe

levelofcash‡owandN -outputarebelowtheirpre-crisistrend.

A lthough G D P ‡uctuations re‡ectchanges intherealexchangerate, T -outputandN -

investment, and thesevariables move in di¤erentdirections, G D P growth duringacrisis

episodeissolelydeterminedbythemeaninvestmentshare[ÁlÁc]12 (by(23)). Tounderstand

whythisissonotethatG D P growthhastwocomponents: (i)realexchangerate‡uctuations

(capturedby Z (Át)Z (Át¡1)

)and(ii)output‡uctuations(capturedby(µÁt)®).28 Inthecrisisperiod,

G D P growthfallsbelowtrendbecausethereisarealexchangeratedepreciation(Z (Ál)

Z (Ác) < 1):

Inthepostcrisis period, therearetwoe¤ects: (i) since investmentcontractedduringthe

previousperiod, N -outputfallsbelowtrendanddepressesgrowth;but(ii)thereisarebound

oftherealexchangerateastheinvestmentsharejumpsfrom itscrisislevel³Z (Ác)Z (Ál)

> 1´:A s

wecansee, variationsinG D P growthgeneratedbyrealexchangeratechangesat¿ and¿ + 1

cancelout. T hus, theaveragelossinG D P growthstemsonlyfromthefallintheN -sector’s

averageinvestmentshare.27 T hisisbecauseyoungentrepreneursincomeisonly¹wp¿q¿ insteadof[1¡¯]p¿q¿;andat¿ entrepreneurs

canonlychoosesafeplans inwhichthereisnocurrencymismatch(byProposition3.3).28 To interpret(23) note thatvariations in the investmentshare Át have lagged and contemporaneous

e¤ects on G D P. T helagged e¤ectcomes aboutbecauseachange in Át a¤ects nextperiod’s G D P via its

e¤ecton N -output: qt+ 1 = µIt= µÁtqt:U sing(19 ) andyt=([1 ¡Át]qt)® , thecontemporeneous e¤ectcan

bedecomposedas:@gdpt@Át

=¡ ®yt1 ¡Á t

+ ptqt+ qtÁt@pt@Át

= qtÁt@pt@Át

T he…rsttwotermscapturevariations inT -outputandN -investment, whilethethirdre‡ectsrealexchange

rate‡uctuations. M arketclearingintheN –goodsmarket–i.e., (1 ¡Át)ptqt=®yt– impliesthattheinduced

changes in N -sectorinvestmentand T -outputcancelout. T herefore, thecontemporeneous changes inthe

investmentsharea¤ectG D P contemporaneouslyonlythrough its e¤ectontherealexchangerate. Since

GDP t = Z (Át)q®t , wecanexpress qtÁt@pt@Át

as q®t @Z t@Át

. T hus, wecan interpret Z (Át)Z (Át¡1)

as thee¤ectofreal

exchangerate‡uctuationsonG D P.

33

Insum, acrisishastwodistincte¤ects: sectorialredistributionanddeadweightlosses. A t

thetimeofthecrisistheT -sectorbene…tsfromthe…nancialcollapseoftheN -sectorbecause

itcanbuyN -outputat…resalepricesandexpandproduction. T hisleadstoasharp fallin

theN -to-T outputratiointhewakeofcrisis. T hedeadweightlossesderivefromthe…nancial

distress andthebankruptcycosts impliedbycrises. T heformerleads toacontraction in

N -investmentandthushasalong-rune¤ectonoutput. Incontrast, bankruptcycostshave

onlyastatic…scalimpact.

4.3 CreditG rowth

H ere, wederivetestableimplicationsregardingthelinkbetweenbumpinessandgrowth. W e

startbyshowingthattheskewness ofcreditgrowth is agoodindicatoroftheriskiness of

aneconomy’screditpath. W ethencombinethisresultwithProposition4.1 tointerpretour

empiricalresults.

Itfollowsfrom(20)thatinanR SEthelimitdistributionofthecompoundedgrowthrate

ofcreditischaracterizedby

³ =

0BB@

³l = log(µÁl)

³c= log(µÁlu¹w1¡¯

1¡h ±u¡11¡h ± )

³p = log(µÁl1u)

1CCA ; ¦ =

0BB@

u2¡u1¡u2¡u1¡u2¡u

1CCA (27 )

A sbefore, theelementsof¦ arethesharesoftimethattheeconomyspends ineachstate.

Itfollowsthat

Proposition4.2 (Skewness) Thelimitdistributionofcreditgrowthinariskysymmetric

equilibrium exhibitsnegativeskewness

E(³¡³)3

¾3=

£d 2 (2 (1¡!)¡1)¡3

¤[1¡!]!d¾3D3 < 0 ;

where d = (³l¡³c)¡(³p¡³l)³p¡³c < 1; D := ³p¡³c

2 > 0 and! = u2¡u:

In an R SE N -…rms face endogenous borrowingconstraints, and so N -sectorcreditis

constrainedbycash‡ow. Sincealongtheluckypath–inwhichnocrises occur– cash‡ow

accumulates gradually, creditcan growonlygradually. In contrast, when acrisis erupts

34

Figure9 : KernelD istributionofCreditG rowth

0

1

2

3

-0.4 -0.2 0.0 0.2 0.4

Epanechnikov, h = 0.2

0

1

2

3

4

-0.4 -0.2 0.0 0.2 0.4

Epanechnikov, h = 0.2

Safe Economy Risky Economy

therearewidespreadbankruptciesandcash‡owcollapses. T hus, creditgrowthfallssharply

(³c< ³l). Inthewakeofcrisiscreditgrowthreboundsbeforereturningtoitslevelinnormal

times(³p > ³c).

O ntheonehand, as longas crises arerareevents, thecreditgrowthrates duringthe

post-crisisperiodandtheluckypathareveryclose(³p¡³l) = log(u¡1). O ntheotherhand,

thefallincash-‡ow(1¡¯¹w) andintheinvestmentmultiplier(m r

m s) thatoccurduringacrisis

generateasharpfallincredit:

³l¡³c= log(1¡¯¹ w

)+ log(m r

m s)+ log(1u) > ³p ¡³c> 0 (29 )

T hepointmadeby Proposition 4.2 is thatsincefalls andrebounds occurwiththesame

frequency, (29 ) translates intoanegativelyskewedcreditgrowthratedistribution. T hatis,

inalongenoughsample, thedistributionof³ ischaracterizedbynegativeoutliers.

Figure9 exhibits thekerneldistributionofcreditgrowthforsafeandriskyeconomies

forthesamesetofparametervalues as inFigure5. A swecansee, thereis aremarkable

similaritybetweenthesedistributionsandthoseofIndiaandThailandinFigure2.

35

4.3.1 From M odeltoD ata

T hedegreeofcontractenforceabilityh iskeyinourmodel. R ecallfromPropositions3.1 and

3.2 thatborrowingconstraintsariseinequilibrium onlyifcontractenforceabilityproblems

aresevere: h < ¹h = u ±¡1:Inborrowingconstrainedeconomies, creditriskcanariseonly

ifh > h (Proposition 3.3). Furthermore, creditrisk increases average long-run growth

only ifh > h¤ (Proposition4.1). T hus, creditriskmaybegrowth-enhancingonly inthe

setofcountrieswherecontractenforceabilityproblemsaresevere, butnottoosevere: h 2(maxfh ;h¤g;¹h):W ithinthissetofeconomies, anegativelyskewedcreditgrowthdistribution

identi…esthosethathavefollowedariskycreditpath(byProposition4.2).

N oticethatifenforceabilityproblemswereeithernotsevereortoosevere, therewould

benoendogenous forcetomakegrowthrates negativelyskewedtobeginwith. T hus, the

linkbetweennegativeskewness andgrowthwouldnotexist. T his argumentunderlies our

sampleselectionruleintheempiricalsection.

In otherwords, ifcreditrisk is introduced intoan economywith severe, butnottoo

severe, creditmarketimperfectionsandalendingboom issetinmotion, thenaverageG D P

growthmayincrease. H owever, higheraveragegrowthcomesatthecostofnegativeskewness

becausetheboom willbepunctuatedbyrarebusts. Ifthiswerenotthecase–i.e., busts

eitherneveroccurredortheywereveryfrequent– thentheboomwouldnotstartinthe…rst

place. W hethergrowth is greaterinariskyeconomydepends onthemagnitudeofcrisis

costs. T his isanempiricalquestionthattheregressions inSection2 address.

Inourmodel, growthratesexhibitmorevarianceintheriskyeconomythaninthesafe

one. Empirically, however, thevarianceisnotagoodinstrumentforidentifyingeconomies

thathavefollowedgrowth-enhancingriskycreditpathsthatleadtoinfrequentcrises. T hisis

becausehighervarianceofcreditandoutputgrowthmayalsore‡ecthighfrequencyshocks,

whichmaybeexogenousormaybeself-in‡ictedby, forinstance, badeconomicpolicy. In

oursetup, greatermeanG D P growthisnotassociatedwithhighervarianceofcreditgrowth

generatedbyhighfrequencyshocks.

In sum, inordertouncoverthelinkbetweenbumpiness andgrowth, itis essentialto

distinguish infrequentbustsfrom highfrequencyshocks. Bothleadtohighervariance, but

onlytheformerleadstonegativeskewness. T hisiswhytheempiricalpartofthepaperuses

36

theskewnessofcreditgrowthandnotthevariance, asameasureofbumpiness.

5 ProductionE¢ciencyandW elfare

W ehaveconsideredanendogenousgrowthmodelwherethe…nanciallyconstrainedN -sector

is theengineofgrowth because itproduces the intermediate inputused throughoutthe

economy. T hus, theshareofN -outputinvestedintheN -sector, Át; is thekeydeterminant

ofeconomicgrowth. W hen Át is toosmallT -outputishigh intheshort-run, butlong-run

growthisslow. Incontrast, whenÁtistoohigh, thereisine¢cientaccumulationofN -goods.

Inthissectionweaskthreequestions. First, whatistheParetooptimalN -investmentshare

sequencefÁtg?Second, canthisParetooptimalinvestmentsequencebereplicatedinasafe

equilibrium? Ifnot, canex-antesocialwelfarebehigherinariskyeconomywhereagents

undertakecreditriskandcrisescanoccur?Third, is suchawelfareimprovingreallocation

implementable?Inparticular, willconsumersbewillingtofootthebillto…nancethebailout

guaranteesassociatedwithariskyeconomy?

5.1 ParetoO ptimality

Inourset-up, N -goodsareintermediateinputs, whileT -goodsare…nalconsumptiongoods.

Considerthen acentralplannerwhomaximizes socialwelfareby investingthesupplyof

N -goods intheT -sector([1¡Át]qt:= d t) andtheN -sector(Átqt); aswellas byassigning

sequencesofT -goodstoconsumersandentrepreneursfortheirconsumption:

maxfct;cet;Átg1t= 0

P 1t= 0 ±

t[[1¡º]u(ct)+ ºcet]; s.t.P 1

t= 0 ±t[ct+ cet¡yt]·0

yt= [1¡Át]®q®t; qt+ 1 = µÁtqt(30)

Clearly, Paretooptimalityimpliese¢cientaccumulationofN -inputs: becauseoptimalcon-

sumptionisafunctionofthepresentvalueofincome, theplannershouldchoosetheinvest-

mentsequencefÁtg tomaximizethepresentvalueofT -production:P 1

t= 0 ±tyt. W eshowin

theA ppendixthattheParetooptimalN -investmentshareisconstantandequalto

Á po = (µ®±)11¡® ; if ® < log(±¡1)=log(µ) (31)

37

T heParetooptimalshareequalizesthediscountrate±¡1 totheintertemporalrateoftransfor-

mation. A marginalincreaseintheN -sectorinvestmentshare(@Á)reducestoday’sT -output

by® [(1¡Á)qt]®¡1 @Á;butincreasestomorrow’s N -outputbyµ@Á andtomorrow’sT -output

by® [(1¡Á)µÁqt]®¡1 µ@Á:T hus, atanoptimum µ®Á®¡1 = ±¡1:

CanadecentralizedeconomyreplicatetheParetooptimalallocation? T heoptimalN -

investmentshareis determinedbyinvestmentopportunities: µ®±:Incontrast, inadecen-

tralizedsafeeconomythe N -investmentshare(Ás = 1¡¯1¡h ±) is determinedbythedegreeof

contractenforceability(h) andbytheN -sector’scash‡ow(1¡¯):T herefore, ifeitherh or

1¡¯ arelow, theN -sectorinvestmentsharewillbelowerthantheParetooptimalshare:

Ás < Á po:T hatis, whentheN -sectorisseverelycreditconstrained, lowN -sectorinvestment

willkeeptheeconomybelowproductione¢ciency. Forfuturereferencewesummarizewith

thefollowingProposition.

Proposition5.1 (B ottleneck) N -sectorinvestmentinasafeeconomyisbelowthePareto

optimallevel(i.e., there is a‘bottleneck’) ifthere is lowcontractenforceability: h < (1¡(1¡¯)µ (µ±)¡

11¡® )±¡1:

W henthereis abottleneck, theshareofN -inputs allocatedtoT -productionshouldbe

reducedandthatallocatedtoN -productionshouldbeincreased. T hisreallocationreduces

theinitiallevelofT -output, butincreaseitsgrowthrateandthepresentvalueofcumulative

T -production. Cantheadoptionofcreditriskinducethisreallocationandbringtheeconomy

nearertotheParetooptimum? Is thereasense inwhich socialwelfare increases? R ecall

thatalongaluckypathofanR SEtheinvestmentshareisgreaterthantheshareinasafe

economy. H owever, creditriskthroughcurrencymismatchmakestheeconomyvulnerableto

crises, whichentaildeadweightlosses fortheeconomy. Inthenextsubsection, weconsider

thee¤ectsofcrisesandaskwhetherex-antewelfareinariskyeconomyisgreaterthanina

safeeconomy.

5.2 SocialW elfare

Inourmodeleconomyconsumershaveaccesstocomplete…nancialmarketsandtheirdiscount

rateequalstherisklessinterestrate, sotheirconsumptionisconstantovertime. Furthermore,

38

N -sectorentrepreneurs arerisk-neutral. T hus, wecanmeasureex-antesocialwelfarewith

theexpecteddiscountedsumofconsumersandentrepreneurs’consumption:

W = E0¡P 1

t= 0 ±t(ct+ cet)

¢= E0

¡P 1t= 0 ±

t[(1¡®)yt+ ¼t¡Tt]¢

(32)

Toderivethesecondequationin(32)noticethatinequilibriumconsumers’incomeis[1¡®]yt,entrepreneurs’incomeis equaltotheirpro…ts ¼t; andthe…scalcostofbailouts is …nanced

withlump-sumtaxes. A tanyt¸1 pro…tsequaloldentrepreneursshareinrevenuesminus

debtrepayments: ¼t= ¯ ptqt¡Lt= ®1¡Ás¯yt¡ ®

1¡ÁshuÁ

syt¡1:M eanwhile, sinceatt= 0 there

isnodebtburden, ¼ 0 = ®1¡Ás¯y0:

Inasafeeconomy…rms arealways solventandcrises neveroccur. T hus, thereareno

bailoutsandnotaxes. Itthenfollowsfrom (32) thatsocialwelfareequalsthepresentvalue

ofT -output

W s =P 1

t= 0 ±tyst=

11¡±(µÁs)®

yso =(1¡Ás)®

1¡±(µÁs)®q®o if±(µÁs)® < 1 (33)

Considerariskyeconomy. A longtheluckypath, theinvestmentshareisgreaterthanin

asafeeconomy. T hus, ifthereisabottleneckandcrisesarerareevents, thepresentvalue

ofT -outputalongtheluckypath is greaterthan inasafepath. H owever, alongalucky

pathacrisis canoccurwithprobability1¡u:T hequestionthenarisesastowhetheritis

worthwhiletoincurthecrisiscosts inordertoattainhigherT -outputgrowth.

A crisisinvolvesthreecosts. First, thereisa…scalcost. L endersreceiveabailoutpayment

equaltothedebtrepaymenttheywerepromised: L¿ = u¡1h Álp¿¡1q¿¡1:Sincethebailout

agencyrecuperatesonlyashare¹ ·¯ of…rmsrevenues p¿q¿;whiletherestisdissipatedin

bankruptcyprocedures, the…scalcostofacrisis isT(¿) = L¿ ¡¹p¿q¿:Second, investment

falls: inacrisis theinvestmentshareis Ác= ¹w1¡h ± insteadofÁs inasafeeconomy. D uring

crisisborrowingconstraintsaretighterthaninasafeeconomybecauseanN -…rm’snetworthis ¹ w p¿q¿ insteadof[1¡¯]p¿q¿ andrisktakingis curtailed: onlysafeplans are…nanced.

Finally, sinceduringacrisisallN -…rmsgobust, oldentrepreneurs’pro…tsarezero.

T hedeadweightloss ofacrisis fortheeconomyas awhole is lowerthan the sum of

thesethreecosts. D uringacrisisthereisasharpredistribution fromtheN - totheT -sector

generatedbyasevererealdepreciation(a…resale). T hus, someofthecosts incurredinthe

N -sectorshowupasgreaterT -outputandconsumers’income. W eshowintheA ppendixthat

39

afternettingoutthecosts andredistributions, acrisis involves twodeadweightlosses: (i)

therevenuesdissipatedinbankruptcyprocedures: [¯ ¡¹]p¿q¿;and(ii) thefallinN -sector

investmentduetoits weakened …nancialposition: [(1¡¯)¡¹w ]p¿q¿:U singthemarket

clearingcondition ®yt= [1¡Át]ptqt;wehavethatthesum ofthesetwodeadweightlosses

equals ®1¡Ác[1¡¹ ¡¹w ]y¿ intermsofT -goods. T hus, inanR SEsocialwelfareisgivenby

W r = E0

1X

t= 0

±tktyt; kt=

8<:

kc:= 1¡® [1¡¹¡¹w ]1¡Ác ift= ¿i

1 otherwise,(34)

where¿iisacrisistime. Inordertocomputethisexpectationweneedtocalculatethelimit

distributionofktyt:W edothis intheA ppendixandshowthatex-antewelfareinarisky

economyis

W r =1 + ±(1¡u)

hµÁl1¡Á

c

1¡Áli®kc

1¡£µÁl

¤®±u¡

£µ2 ÁlÁc

¤®±2 (1¡u)

[(1¡Ál)q0 ]® (35)

B ycomparing(33)and(35)wecandeterminetheconditionsunderwhichex-antewelfareis

greaterinariskyeconomy. T henextPropositionprovides asu¢cientconditionforcredit

risktobewelfareimproving.

Proposition5.2 (SocialW elfare) Ifcrises arerareevents andthecostsofcrises ( =¹;

(1¡¯)=¹w ) aresmall, then ex-antesocialwelfare in ariskyeconomyis greaterthan ina

safeeconomyifandonlyifthereisabottleneck(Ás < Á po).

Ifcrisesentailsmallbankruptcycosts(¹ ! ¯)andmild…nancialdistress(¹ w ! 1¡¯);

theonly…rstordere¤ectofacrisis istoreducetransitorilytheN -sector’s investmentshare

from Ál towhatitwould havebeen in asafeeconomy(Ás):T hus, in this limitcasethe

investmentshareintheriskyeconomywouldneverbelowerthaninthesafeone. H ence, if

thereisa‘bottleneck’(Ás < Á po) andcrisesarerareevents, thegreateraverageinvestment

sharewillincreasethepresentvalueofT -outputandhencewelfare.

Smallcrisiscostsaresu¢cient, butnotnecessary, fortheresultstatedinProposition5.2.

W elfareinariskyeconomycanbegreaterthaninasafeoneevenifcrisis costs arelarge.

Figure10 shows thewelfaredi¤erentialbetween safeandriskyeconomies (W r ¡W s) for

di¤erentbankruptcycosts(lb = 1¡¹¯ )and…nancialdistresscosts(ld = 1¡ ¹w

1¡¯ ). A swecan

see, thewelfaregainscanbepositiveevenif100% ofrevenuesaredissipatedinbankruptcy

40

Figure10: SocialW elfareandCrisisCosts

50 55 60 65 70 75 80 85 90 95 100-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

lc (%)

Wel

fare

Ris

ky E

cono

my

-Wel

fare

Saf

e E

cono

my

lb = 50%

lb = 100%

Financial Distress Costs (%)

lb = Bankruptcy Costs (%)

%512.0176.035.065.1: ??????? uhparameters ???

41

procedures(¹ ! 0 ):T herecanalsobepositivewelfaregainsforsevere…nancialdistresscosts

(ld = 80 % ). H owever, theyarenegativewhenld ! 10 0 % :T hereasonforthisasymmetryis

thatbankruptcycostsareastaticloss, while…nancialdistresscostshavedynamice¤ects. In

ourendogenousgrowthset-up, thereductioninN -sectorinvestmentshiftsthegrowthpaths

ofbothsectorsdownwards. Suchanunrecoverablelongtermlossreducesthediscountedsum

ofT -productionoverthewholepost-crisis period.29 B ycontrast, welfaregains arealmost

insensitivetobankruptcycosts.

T hewelfaregainassociatedwithundertakingcreditriskis increasingintheprobability

ofcrisis (1¡u):T his does notmeanthatthis probabilitycanbearbitrarilylarge. A swe

havediscussedearlier, anR SEexistsonlyifcrisesarerareevents. Inpanel(a)ofFigure11,

weshowhowW r¡W s variesoverarangeofcrisisprobabilitiesbetween0 and8% . Except

whenthe…nancialdistresscostofcrises isveryhigh, theriskyeconomydominatesthesafe

economy. Thisdi¤erenceisampli…edbyalimitedincreaseincreditrisk. Incontrast, ifcrisis

costsareverylarge, W r¡W s < 0 andanyincreaseinriskreducesW r further. Finally, panel

(b)ofFigure11 showsthatthesocialwelfaregainsareincreasingintheintensityofN -inputs

in T -production (®). A greater® strengthens thesectoriallinkageandthus increases the

welfarebene…tsofrelaxingtheborrowingconstraintintheN -sector.

5.3 Implementability

Proposition5.2 has establishedthatsocialwelfarecanbegreaterinariskyeconomyeven

ifbailoutcosts arefundeddomesticallyvialump-sum taxes. Systemicbailoutguarantees

arenecessarytoinduceagents toundertakeinsolvencyrisk(throughcurrencymismatch).

W ehaveseenthatsuchariskystrategyeasesborrowingconstraintsandleadstoagreater

meangrowthofN -outputevenalongapathwherecrisesdooccur. A saresult, T -production

willenjoycheaperandmoreabundantN -inputs, anditsgrowthratewillalsoincrease. T his

bene…tsconsumersbecausetheyreceiveashare1¡® ofT -outputasincome.

B ut, is abailoutschemeimplementable?W illconsumersbewillingtofootthebill?In

particular, willconsumersatdatezerobewillingtopurchaseaninsurancethatpromisesto29 A secondorderwelfarecostofcrises isthevariabilityinthelevelofinvestment(shiftfrom ÁltoÁcand

back). R ecallthattheParetooptimalinvestmentshareisconstant.

42

Figure11: SocialW elfareG ainsandCreditR isk

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08-2

-1

0

1

2

3

4

5

6

probability of crisis

Wel

fare

Ris

ky E

cono

my

-Wel

fare

Saf

e E

cono

my

a. For different levels of Financial Distress Costs

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.080

2

4

6

8

10

12

14

16

18b: for different intensit ies of Non-Tradables Input in Tradable Production

probabil i ty of crisis

Wel

fare

Ris

ky E

cono

my

- Wel

fare

Saf

e E

cono

my

%40?dl

%70?dl

%90?dl

%100?dl

5.0??

35.0??

2.0??

%702.0176.035.065.1: ?????? blhparameters ???

%702.0176.065.1: ?????? bd llhparameters ??

43

coveranyfuturebankruptcycostsassociatedwiththeguarantees?Sincetherepresentative

consumerhas access tocompletecapitalmarkets, hecanperfectlysmooththecostofthe

guarantees. H is lifetimebudgetconstraintis: E0P 1

t= 0 ±t[ct¡(1¡®)yt+ Tt]·0 ;whereTt

isthetaxthatwill…nancethebailouts. Sincetheconsumer’sshareinT -outputis1¡® ;his

ex-antewelfareinasafeandariskyeconomyare, respectively:

C s = [1¡® ]W s; C r = E0X 1

t= 0±t(yt[1¡®]¡Tt) (36)

Theconsumerwillbewillingto…nancethebailoutifandonlyifC s > C r :

1 + ±(1¡u)hµÁl1¡Á

c

1¡Áli®K T

c

1¡u£µÁl

¤®±¡[1¡u]

£µ2 ÁlÁc

¤®±2[(1¡Ál)q0 ]® >

[(1¡Ás)q0 ]®

1¡± (µÁs)®; (37 )

whereK Tc isde…nedin(53) intheA ppendix. T hefundingoftheguaranteesbyconsumers

operatesaredistribution from thenon-constrainedT -sectortotheconstrainedN -sector. If

(37 ) holds, sucharedistribution is tothemutualbene…tofboth sectors. Itis aPareto-

improvingpolicy. Figure12 exhibits theconsumer’s netwelfaregainwhenhe…nances all

thebailoutcostsfor1¡® = 0:35% :BycomparingFigures11 and12 wecanseethatwhen

socialwelfaregainsarepresent, consumerswelfaregainsarealsopresent, butinasmaller

proportion.

6 R elatedL iterature.

O urempirical…ndingsarerelatedtotheliteraturethatlinks…nancialliberalizationto…nan-

cialdeepeningandgrowth. Inparticular, Beckaertet.al. (2001)…ndthatcountriesthathave

liberalizedtheirstockmarketsgrowfasterthanothercountries. ChariandH enry(2002)…nd

similarevidenceatthe…rmlevel. L evine(2001) showsthat…nancialopeningfostersgrowth

byincreasingstockmarketliquidityandthee¢ciencyofthebankingsystem. Kaminskyand

Schmukler(2002) showthatthelong-rungainsassociatedwithbetterfunctioning…nancial

marketsmaycomeatthecostofexcessivevolatilityintheshortrun. T heseresults stress

thepositivee¤ectof…nancialliberalizationon…nancialdeepeningandtheresultingincrease

inlongrungrowth. Theydonotimplyhoweverthat…nancialopennessisgrowth-enhancing

44

Figure12: ConsumersW elfareG ainsnetofBailoutCosts

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

probability of crisis

Con

sum

ers

Wel

fare

Ris

ky-B

ailo

ut C

osts

-Con

sum

er W

elfa

re S

afe

for different levels of Financial Distress Costs

%702.0176.035.065.1: ?????? blhparameters ???

%40?dl

%70?dl

%90?dl

%100?dl

acrossallsetsofcountries. Inparticular, theydonotcontradictthe…ndingssuchasR odrik

(19 9 8) thatopennessdoesnotperseaccelerategrowth.30

O ur…ndingthatnegative skewness ofcreditgrowth correlates positivelywithgrowth

is linkedwith Imbs (2002) …ndingthataggregatevolatility is badgrowth, while sectorial

volatilityisgoodforgrowth. Inoursetup sectorialvolatilityarisesbecausethecreditcon-

strainedsectorundertakescreditriskasameanstoincreaseinvestment. L evineandR enelt

(19 9 1) andR ameyandR amey(19 9 5) …ndthatthevarianceofsomemacroeconomicaggre-

gates isnegativelyassociatedtogrowth. This is notinconsistentwithour…ndings, asthe

varianceofcreditgrowthalsoentersourregressionswithanegativesign.

Inusingskewnesstoproxyfortheoccurrenceofoccasionalcrisesourpaperislinkedto30SeePrasad, et. al. (2003) foranempiricalsynthesisofthelinkbetween…nancialopenessandgrowth.

45

papersinFinancethatusetheskewnessofreturnstoidentifybusts(e.g. Veldkamp(2000)).

Intheneoclassicalgrowthliterature…nancialopenness increasesgrowthandwelfareby

allowingfasteraccumulationofcapitalandconsumptionsmoothing(Barro, et. al. (19 9 5)).

G ourinchas andJeanne(2003) showthatthewelfarebene…ts associatedwiththis mecha-

nism arenegligibleincomparisontotheincreaseindomesticproductivity. O bstfeld(19 9 4)

demonstratesthatdomesticproductivitygainsoccurwheninternationalrisk-sharingallows

ashiftfromsafetoriskyprojects. Inourframeworkthegainsalsostemfromanincreasein

productione¢ciencynotfrominternationalrisksharing. T hegainsareobtainedbyreducing

thecontractenforceabilityproblem nottheincompletemarkets problem: welfaregains are

obtainedbylettingentrepreneurstakeonmorerisk, notbyhavingconsumersfacelessrisk.

InT irole(2000b)foreigndebtdenominationalsoresultsinsocialwelfaregains, butthrough

adisciplinee¤ectongovernmentpolicy.

Inourmodelthecycleequilibrium (“theriskyeconomy”) outperforms thepuretrend

equilibrium (“thesafeeconomy”) intermsofmeangrowthandwelfare. A similarresultis

found in M atsuyama(19 9 9 ) wheretheeconomyevolves along“Solowtype” pathsofhigh

investmentand“R omertype” pathsofhighinnovation;inJovanovic(2003)wherecyclesare

generatedbytheriskyadoptionofnewtechnology;andinFrancoisandEllis (2003)where

endogenousclusteringininnovationandimplementationgeneratesgrowth-enhancingcycles.

T hecreditcyclesinthispaperaredi¤erentfromSchumpeter’s(19 34)cyclesinwhichthe

adoptionofnewtechnologiesplaysakeyrole. O urcyclesaremoresimilartoJuglar’scredit

cycles. Juglar(1862, 1863) characterizedasymmetriccreditcyclesalongwiththeperiodic

occurrenceofcrises inFrance, England, andU nitedStatesover17 9 4-1859 as adistinctive

featureoffastdevelopingeconomies.31

Inemphasizingthat…nancialdevelopmentleadsbothtohigherlongrungrowthandto

moreshorttermvulnerabilityto…nancialcrisesthispaperisrelatedtoL oayzaandR anciere

(2001)andG aytanandRanciere(2002). Inaddressingthee¤ectsof…nancialliberalizationin

thepresenceofasymmetric…nancingopportunities, thispaperrelatestoR ajanandZ ingales

(19 9 8). T heyshowthat…nancialdevelopmentfavors thesectors thataremoredependent31“T heregulardevelopmentofwealthdoes notoccurwithoutpainandresistance. In crises everything

stops forawhilebutitis onlyatemporaryhalt, preludetothemostbeautifuldestinies.” Juglar(1863),

page13(ourtranslation).

46

onexternal…nance.

Instudyingtheroleofagencyproblems inemergingmarkets this paperconnectswith

B ernanke, et.al. (2000), M ckinnon and P ill(19 9 8), T irole (2002a), and third generation

crisesmodels likeSchneiderandTornell(2003) andthereferencestherein. O urmodeldif-

fersfrom theSchneiderandTornell(ST ) modelinthatweconsidertheinteractionoftwo

productivesectors(N andT ), wecharacterizethelong-rungrowthpathofaneconomythat

canexperienceseveralcrises, andwemakeanexplicitwelfareanalysis. Instead, ST concen-

trateonhowtheinteractionofcontractenforceabilityproblemssystemicbailoutguarantees

generate…nancialfragilityandaboom-bustepisode. InST therearenoproductivelinkages

as T -outputis exogenous, thereis nolinkbetweenskewness andgrowthbecauseonlyone

crisisoccursinequilibriumandthereisnowelfareanalysis.

T hegrowthenhancinge¤ectofreal-exchangeraterisk-takingbytheconstrainedsector

shares somesimilarities withtheroleofbubbles in therecentliterature. Ventura(2002)

showsthatstochasticbubblesonuselessassetscanboostgrowthbyshiftingresourcesfrom

ine¢cienttoe¢cientinvestors, while introducing…nancialfragility. O llivier(2000) …nds

thatbubblesonrealassetscanfostergrowthbyencouraginginvestmentintheR &D sector,

andthuscanbeseenasasubsidytoresearch. A speculativeelementisalsopresentinour

framework. H owever, inoursetuptherearenobubbles. O urriskyequilibriaaresustainable

overthe in…nitehorizon. O urresults dependon the presenceofbottlenecks and donot

exploitanyform ofdynamicine¢ciency. Finally, themechanismwepresentisreminiscent

oftheliteratureonriskasafactorofproductionasSinn(19 86)andKonrad(19 9 2).

7 Conclusions

W ehaveshownthatthereisastrongempiricallinkbetweengrowthandnegativeskewness

ofcreditgrowthacrosscountrieswithsigni…cantcontractenforceabilityproblems(M ECs).

T hatis, M ECs thathaveexperiencedboomsandbustshavegrownonaveragefasterthan

countrieswithsmoothcreditconditions.

W ehaveshowntheoreticallythatinaneconomywithseverecreditmarketimperfections,

theadoptionofcreditriskisameanstoovercometheobstaclestogrowthbyeasing…nancing

47

constraints. H owever, asasidee¤ect…nancialfragilityarisesandthuscrisesoccurfromtime

totime. Inotherwords, thetrade-o¤ is notfragilityversus nofragility. T hetrade-o¤ is:

fragilityandgrowthversusnofragilityandnogrowth.

W ehaveestablishedconditionsunderwhichthewelfarecostsofcrisesareoutweighedby

thebene…tsofhighergrowth. Furthermore, wehaveestablishedconditionsunderwhichthe

unconstrainedtradablessectorwill…nditpro…tabletofundthesystematicbailoutguarantees

thatsupporttheriskycreditpathalongwhichtheconstrainednontradables sectorgrows

faster. U nderthisschemethetradablessectorcanalsogrowfasterbecauseitfaceslesssevere

bottlenecks(i.e., moreabundantnontradables inputs).

O urresults shouldprovideacautionwhen interpretingthee¤ects of…nancialliberal-

ization. From the…ndingthatliberalizationhas leadtomorebumpiness, oneshouldnot

concludethatliberalization perse is bad eitherforgrowthorforwelfare. Furthermore,

policies intendedtoeliminaterisktakingandfragilitymighthavetheunintendede¤ectof

blockingtheforcesthatgenerate…nancialdeepeningandgrowth.

Finally, onepointofclari…cation is in order. O ne should di¤erentiatetheonsetofa

crisis, thetippingpoint, from afull-blowncrisis. Typically, inthewakeofatippingpoint

authoritiestrytodelaytheinevitableandavoidthenecessaryrealdepreciation– aswasthe

caseinbothM exico19 9 4andA rgentina2001. T heresultantfull-blowncrisis endsupbeing

muchmoreseverethanwhatis necessary. W ewouldliketoemphasizethattheresultsof

thispaperdonotjustifythistypeofbettingforresurrection.

A ppendixA . ProofsandD erivations

ProofofProposition3.2. InanSSE, duringeveryperiod, allentrepreneurschoosethe

safeplan characterized in Proposition 3.1. Each entrepreneurwill…nd itoptimaltodo

soprovided amajorityofentrepreneurs chooses a safe plan and themarginalreturn to

investmentin theproduction ofN -goods is nolowerthan 1 + r : R et+ 1 :=

¯µpet+ 1pt

¸ ±¡1:

Since in an SSE crises neveroccur, prices aredeterministic: ut+ 1 = 1 and pet+ 1 = pt+ 1:

U sing(14) and(15) itfollows thatR et+ 1 = ¯µ®(Ás)®¡1:T hus, an SSE exists ifandonlyif

¯µ®(Ás)®¡1 > ±¡1 and(17 ) holds. T hesetwoconditionsareequivalentto

h < ¹h = ¯±¡1; µ > µ = [±¯(Ás)®¡1]¡1=® (38)

48

ProofofProposition3.3. T heproofis intwoparts. InpartA weconsiderthecasein

whichtwocrises donotoccurinconsecutiveperiods. T hen, in partB weshowthattwo

crisescannotoccurinconsecutiveperiods.

PartA . ConsideranR SEinwhichallentrepreneurschoosetheriskyplancharacterizedin

Proposition3.1 duringeveryperiod, exceptwhenacrisiserupts, inwhichcasetheychoose

safeplans. In ano-crisis period, given thatallotherentrepreneurs choosearisky plan,

anentrepreneurwill…nd itoptimaltodosoifandonlyifR et+ 1 := u µ ¹pt+ 1pt

¸ 1 + r, and

¼(pt+ 1) < 0 . TodeterminewhethertheseconditionsholdnotethatinanR SEtheinvestment

shareÁt+ 1 equals Ál ifN -…rmsaresolvent, whileÁt+ 1 = Áciftheyareinsolvent. R eplacing

theseexpressionsintheequationsforcash‡ow(12), N -output(14)andprices(15), itfollows

that

R et+ 1 ¸ 1

± , uR (u)+ [1¡u]R (u)¸ 1±; R (u) := ¯µ®

·1Ál

1¡®(39 )

¼(pt+ 1) < 0 , R (u) < h

u; R (u) := ¯µ®·1Ál

1¡® ·1¡Ál

1¡Ác1¡®

(40)

Toderive(40)wehaveused¼(pt+ 1) = ¯p

t+ 1qt+ 1¡Lt+ 1 = ¯® [1¡Ác]®¡1[µÁcqt]® ¡u¡1h ® [1¡

Ál]®¡1q®t:Considernextacrisisperiod. G iventhatallotherentrepreneurschooseasafeplan,

anentrepreneurwill…nditoptimaltodosoifandonlyifR et+ 1 := ¯µpet+ 1=pt¸±¡1:Sincein

thepost-crisisperiodtherecanbenocrisis, itfollowsfromtheproofofProposition3.2 that

thisconditionis equivalentto¯µ®(Ás)®¡1 ¸±¡1:Clearly, this conditionis impliedby(39 ).

Itfollows thatthereexists anR SEwheretwocrises donooccurinconsecutiveperiods if

andonlyif(39 ) and(40) holdandparameterssatisfy(17 ), whichisgivenby

h ± < u (41)

“O nlyif.” W eprovethatanR SEexistsonlyifu> u; µ > µ;andh < h < h inthreesteps.

Step 1. Foranyµ 2<+ andanyh 2<+ thereexistsnoR SE ifu! 0:Toprovethis, let

u! 0:Sinceµ is boundedand 1¡¯ < Ál < 1; itfollowsthatlimu! 0 +

uR (u) = 0:T herefore,

(39 )-(41) implythatwhenu! 0 anR SE exists ifandonlyif hu < ¯

± and 1± < R (u) < h

u;

whichisacontradiction.

49

Step2. Foranyu2 (0 ;1)andforanyµ 2<+ thereexistsnoR SEifh > h orh < h ;where

h =¯u±, h =

1±

õ1¡Ác

1¡Ál

¶1¡®+

µ1u¡1

¶! ¡1; 0 < h < h (42)

N oticethath < h isequivalentto(41), andthat(39 )and(40)holdifandonlyif±¡1µu+ (1¡u)

h1¡Ál1¡Ác

i1

R (u) < hu

h1¡Ál1¡Ác

i®¡1;whichholdsonlyifh > h .

Step3. Foranyu2 (0 ;1)andforanyh 2<+ thereexistsnoR SEifµ < µ;where

µ =

Ãhu

£Ál¤1¡®

·1¡Ác

1¡Ál1¡®

! 1=®

(43)

N oticethatuR (u)+ (1¡u)R (u) isdecreasinginh andanR SEexistonlyifh > h . T hus, a

necessaryconditionforanR SEtoexistisuR (u)+ (1¡u)R (u)¦h= h > ±¡1;whichisequiva-

lentto(43).

“If.” ToestablishtheexistenceofanR SEweshowthatwhenu! 1 parameterrestrictions

(39 ), (40)and(41)aremutuallyconsistentif(µ;h)2S= f(µ;h )2 R 2+ jµ > µ; h 0< h < h 00g;withh ·h 0< h 00·h:W edothisintwosteps. First, weallowforanupperboundµ < µd (h):

T hen, wereplaceµ < µd (h) bytighterboundson h:

Step 1. W eshowthatforany± 2 (0 ;1); ® 2 (0 ;1); and¹w 2 (0 ;1¡¯) anR SE exists if

(µ;h)2S0= f(µ;h )2 R 2+ jh < h < h ; µn(h ) < µ < µd (h)g:L etu= 1, forany± 2 (0 ;1)and® 2 (0 ;1), (41) holds i¤ h < h = ¯±¡1 and(39 ) holds i¤ µ¸µd (h) = [±¯(Ás)®¡1]¡1=® . N ext,

ifu= 1, (40) becomesh1¡Ás1¡Ác

i1¡®< h (Á

s)1¡®

¯µ® :T his conditionholdsforany¹ w 2 (0 ;1¡¯);

h < ¹h andµ > µn(h) i¤

µ < µd (h) =

÷1¡Ác

1¡Ás1Ás

1¡® h¯

! 1=®

and h > h =1±

·1¡Ás

1¡Ác1¡®

(44)

N otice that h > h is necessary forµn(h) < µd (h) and that h is unique. Furthermore,

µn(h) < µd (h ) , h ¡ 1±

h1¡Ás1¡Ác

i1¡®> 0 . T his expression is strictly increasing in h ; itis

satis…edifh ! h andviolatedifh = 0 . T hisensuresexistenceandunicityofalowerbound

h:

Step2. W eshowthatthesetsS0andSareequivalent. Considerthefollowingthreeproperties

ofµn(h) andµd (h) over(h ;h);whichareillustratedinthe…gurebelow: (i) µn(h) < µd (h);

50

(ii) µn(h) and µd (h) arecontinuous andstrictlyincreasingin h;and(iii) µn(h) = µd (h) =

µ; limh¡> h

µn(h) = 1 and limh¡> h

µd (h ) = ( ±¡1)1=®:Itfollowsthatforany(µ;h)2S0; µ > µ and

h 2 (h 0;h 00); where h 0 = µ¡1n (µ) and h 00 = min(µ¡1n (µ);h) where µ¡1() denotes the inverse

function. Sinceh ·h 0< h 00·h ;wehavethat(µ;h) 2S0) (µ;h)2S:Similarly, forany

(µ;h)2S; h < h < h andµn(h) < µ < µd (µ):T herefore, (µ;h)2S) (µ;h)2S0:

h

h

)(hn?

h

)(hd?

RSE

?

)(' ?h )(" ?h p

PartB . W eprovebycontradiction thattwocrises cannotoccurin consecutiveperiods.

Supposethatifacrisisoccursat¿; …rmschooseriskyplansat¿:W ewillshowthatitisnot

possible, underanycircumstances, for…rmstobecomeinsolventinthelowpricestateat¿+ 1

(i.e., ¼(p¿+ 1) < 0 ):Itsu¢cestoconsiderthecaseinwhich…rmsundertakesafeplansat¿+ 1;

as p¿+ 1

isthelowestinthiscase. A longthispaththeN -investmentshareequals Á¿ = ~Ác:=

¹w m r andÁ¿+ 1 = Ác:= ¹w m s. T hus, ¼(p¿+ 1) = ¯® [1¡Ác]®¡1[µ~Ácq¿]® ¡u¡1h ® [1¡Ác]®¡1q®¿ ;

and

~¼(p¿+ 1) < 0 , ¯µ®

"1¡~Ác

1¡Ác1~Ác

# 1¡®<hu

(45)

N oticethattheL H S of(39 ) is strictlylowerthantheL H S of(45) because: (i) ¹w < 1¡¯;

so 1¡~Ác~Ác > 1¡Ác

Ác ;and(ii)Ál > Ác:H owever, theR H S of(39 ) isstrictlyhigherthantheR H S of

(45) becauseu> h± isnecessaryforanR SEtoexist. T his isacontradiction.¤ProofofProposition4.1. W ederive…rstthelimitdistributionofthegrowthrateprocess

¢ log(gd pt) := log(gd pt)¡log(gd pt¡1):SinceinanR SEcrisescannotoccurintwoconsecutive

periods, ¢ log(gd pt)followsathree-stateM arkovchaincharacterizedbythefollowinggrowth

51

vectorandtransitionmatrix

¡ =

0BB@

log(¡µÁl

¢®)

log(¡µÁl

¢® Z (Ác)Z (Ál))

log((µÁc)® Z (Ál)Z (Ác))

1CCA T =

0BB@

u 1¡u 0

0 0 1

u 1¡u 0

1CCA

Sincethetransitionmatrix is irreducible, thegrowthprocess converges toauniquelimit

distribution overthe three states thatsolves T0¦ = ¦ :T hus, ¦ 0 =¡ u2¡u;

1¡u2¡u;

1¡u2¡u

¢and

the geometricmeanlongrunG D P growthrate–equation(25) inthetext– isE(1 + °r) =

exp(¦ 0¡):Itthenfollowsfrom (21) and(25) that

°r > °s ,µ

¹ w1¡¯

¶1¡u>1¡h ±u¡1

1¡h ±, h > ¹h 0:=

1±

1¡³

¹w1¡¯

1¡u

1u¡

³¹w1¡¯

1¡u

N otice thatan R SE exists only ifh < ¹h = u =±:T hus, ¹h 0 < ¹h ifand only if ¹w1¡¯ >

³1¡¯1¡¯u

´ 11¡u:¤

ProofofProposition4.2. Itfollowsfrom limitdistribution(27 ) thatthemean, variance

andskewnessofthegrowthrateofcreditare

³ ´ E(³) = [!³n + 1¡!2 (³c+ ³p)]µÁ

l; ! =u

2 ¡u¾ 2 ´ E(³¡³)2 = [!(³n ¡³)2 + 1¡!

2 [(³p ¡³)2 + (³c¡³)2 ]

sk ´ E(³¡³)3

¾3= [!(³n ¡³)3+ 1¡!

2 [(³p ¡³)3+ (³c¡³)3]]1¾3

L etl = ³n ¡³c+ ³p2 ; L = ³p¡³c

2 ; d := lL ; sothat³n ¡³ = 1¡!

2 l; ³ ¡³c= L + !l; and

³p ¡³ = L¡!l:T hen,

³ = L + !l

¾ 2 L 2 = ! [(1¡!)d ]2 + 1¡!2

¡[1¡!d ]2 + [1 + !d ]2

¢= (1¡!)[1 + !d 2 [(1¡!)2 + !]

sk¾3L3 = ! [(1¡!)d ]3+ 1¡!2

¡[1¡!d ]3¡[1 + !d ]3

¢= d (1¡!)!

£d 2 (2 (1¡!)¡1)¡3

¤

N otethat³c< ³n < ³p ) jd j< 1. Since 2 (1¡!)¡1 < 1 forallu2 (0 ;1); itfollowsthat(1¡!)! [d 2 (2 (1¡!)¡1)¡3]< 0 . T herefore, sk< 0 , d > 0 , ³n ¡³c> ³p ¡³n:T hus,

sk< 0 ifandonlyif³n ¡³c> ³p ¡³n :

³n ¡³c> ³p ¡³n , log(u¹w1¡¯

1¡h ±u¡1

1¡h ±) < ¡log(u), S(u) =

¹w1¡¯

u2 ¡h ±u1¡h ±

¡1 < 0

52

G iventheparameterrestriction¹w < 1¡¯ andthenecessaryconditionforexistenceofan

R SEu> h±; itfollowsthatS00(u) > 0 ; S(1) < 0 andS(0 ) < 0 . T herefore, S(u) < 0 forany

u2 [0 ;1]:¤

D erivationof(30). A nysolutiontotheParetoproblem is characterizedbytheoptimal

accumulationofN -goodsthatmaximizesthediscountedsumofT -production

maxfd tg2C1

1X

t= 0

±td ®t; st kt+ 1 =

8<:

µkt¡d t ift¸1q0 ¡d 0 ift= 0

; d t¸0 ; qo given

TheH amiltonianassociatedwiththisproblem isH t= ±t[d t]® + ¸t[µkt¡d t]:Since® 2 (0 ;1),thenecessaryandsu¢cientconditionsforanoptimumare

0 = H d = ±t® [d t]®¡1¡¸t; ¸t¡1 = H k = µ¸t; limt!1

¸tkt= 0 (46)

Thus, theEulerequationis

d t+ 1 = [±µ]1

1¡® d t= µÁ d t; Á := [±µ®]11¡® t 1 (47 )

Togetaclosedform solutionford twereplace(47 ) intheaccumulationequation:

kt= µt¡1k1¡d 0X t¡2

s= 0µt¡s¡2 [±µ]

s+ 11¡® = µt¡1

"k1¡d 0 Á

1¡Át¡1

1¡Á

#= µt¡1

"k1¡

d 1µ1¡Á

t¡1

1¡Á

#

(48)

R eplacing(47 ) and(48) inthetransversalityconditionweget

0 = limt! 1

±t® [d t]®¡1kt= limt! 1

±t®h[±µ]

t1¡® d 0

i®¡1"µt¡1k1¡d 0 Á

1¡Át¡1

1¡Á

#

=® d ®¡10

µ

·k1¡d 0 Á

11¡Á

¸i¤ Á < 1

Sincek1 = q0 ¡d 0 ; the bracketed term equals zero ifand only if d 0 = [1 ¡ Á]q0 . T he

accumulationequationthenimpliesthattheuniqueoptimalsolutionis d t= [1¡Á]qt:¤D erivationof(34). Tosimplifynotationweassumetemporarilythatthereis onlyone

crisis(attime¿):Itfollowsthatpro…tsandthebailoutcostare:

¼t= ®1¡Ál¯yt¡

®Ál

1¡Álhuyt¡1; t6= f0 ;¿;¿ + 1g

¼ 0 = ®1¡Ál¯y0 ; ¼ ¿ = 0 ; ¼¿+ 1 = ®

1¡Ál¯y¿+ 1¡®Ác1¡Áchy¿

(49 )

53

T(¿) = L¿¡1¡¹p¿q¿ =®

1¡ÁlhuÁly¿¡1¡¹p¿q¿ =

®1¡Ál

huÁly¿¡1¡¹

®1¡Ác

y¿ (50)

R eplacingtheseexpressionsinwelfarefunction(32)andusingthemarketclearingcondition

ptqt[1¡Át]= ®yt, weget

W (¿) = (1¡®)yo +®¯yo1¡Ál +

¿¡1Pt= 1

±t·[(1¡®)yt+ ®¯yt

1¡Ál¡®Ályt¡11¡Ál

hu

¸+ ±¿

·(1¡® )y¿ + ¹®y¿

1¡Ác¡®Ály¿¡11¡Ál

hu

¸

+ ±¿+ 1·(1¡® )y¿+ 1 + ®

1¡Ál¯y¿+ 1¡® h Ác

1¡Ácy¿

¸+

1Pt= ¿+ 2

±t·(1¡® )yt+

®¯1¡Ál

yt¡®Ál

1¡Álhuyt¡1

=Pt6= ¿

±t·(1¡®)yt+

®1¡Ál

¯yt¡®

1¡Ál±huÁlyt

¸+ ±¿

·(1¡®)y¿ + ¹

®1¡Ác

y¿ ¡® Ác

1¡Ác±hy¿

¸

=Pt6= ¿

±tyt+ Kcy¿; Kc:= 1¡® + ¹®

1¡Ác¡ ®1¡Ác

±h Ác= 1¡® [1¡(¹ + ¹w )]1¡Ác

N oticethatKccanbesimpli…edasfollows

Kc= ® +®

1¡Ác(¹¡(1¡¹w )+ (1¡¹w )¡±h Ác) = ® +

®1¡Ác

((1¡¹w )¡±h Ác)¡® [1¡(¹ + ¹w )]

1¡Ác

N oticethat 11¡Ác((1¡¹w )¡±h Ác) = (1¡¹w )(1¡h ±)¡h ±¹w

1¡h ±¡¹w = 1¡h ±¡¹w1¡h ±¡¹w = 1:T hus, Kc= 1¡

® [1¡(¹+ ¹w )]1¡Ác . T heexpressionforexpectedwelfarein (34) followsbyallowingmultiplecrises

totakeplace.

D erivationof(35). ConsiderT -outputnetofbankruptcycosts: ~yt= Ktyt;whereKt is

de…nedin(34). N oticethatW r = E0

1X

t= 0

±tKtyt= E0

1X

t= 0

±teyt;and ~yteyt¡1

followsathree-state

M arkovchainde…nedby:

eT =

0BB@

u 1¡u 0

0 0 1

u 1¡u 0

1CCA ; eG =

0BB@

g1g2g3

1CCA =

0BBB@

(µÁl)®hµÁl1¡Á

c

1¡Áli®Kch

µÁc1¡Ál

1¡Áci®

1Kc

1CCCA (51)

ToderiveW r inclosedformconsiderthefollowingrecursion

V (ey0 ;g0 ) = E0X 1

t= 0±teyt= ey0 + ±E0 V (ey1;g1)

V (eyt;gt) = yt+ ¯EtV (eyt+ 1;gt+ 1) (52)

Suppose thatthefunction V is linear: V (eyt;gt) = eytw (gt); with w (gt) an undetermined

coe¢cient. Substitutingthisguessinto(52), wegetw (gt) = 1 + ±Etgt+ 1w (gt+ 1):Combining

54

thisconditionwith(51), itfollowsthatw (gt+ 1) satis…es0BB@

w 1w 2w3

1CCA =

0BB@

1

1

1

1CCA + ±

0BB@

u 1¡u 0

0 0 1

u 1¡u 0

1CCA

0BB@

g1w 1g2 w 2g3w3

1CCA )

w 1 = 1+ (1¡u)±g21¡(1¡u)±2 g2 g3¡u±g1

w 2 = 1+ ±g3¡u±g11¡(1¡u)±2 g2 g3¡u±g1

w3 = 1+ (1¡u)±g21¡(1¡u)±2 g2 g3¡u±g1

T his solutionexistsandisuniqueprovidedg1±u+ g2 g3±2 (1¡u) < 1:Equation(35) follows

bynotingthatattime0 theeconomyisintheluckystate: V (y0 ;g0 ) = w 1yl0 ;andbymaking

thesubstitutiong2 g3 =¡µÁl

¢®(µÁc)®:

ProofofProposition5.2. T hewelfareofariskyandasafeeconomyaregivenby(33)

and(34), respectively. Clearly, ifu= 1, bothareequal. SinceW s does notdependonu;

wewillprovethepropositionbyshowingthatwhencrisescostsaresmall(i.e., ¹ ! ¯ and

¹w ! 1¡¯; sothatkc! 1) thederivativeW ru := @W r=@uju= 1 is negativeifandonlyif

Ás < Á po:L etusdenote:

L = 1¡£µÁl

¤® ±u¡£µ2 ÁlÁs

¤® ±2 (1¡u); T =µ1 + ±(1¡u)

·µÁl

1¡Ás

1¡Ál®¶(1¡Ál)®

T hederivativesofL andT evaluatedatu= 1 are:

Lu = ¡±(µÁ)® ¡®Á0±(µÁ)®¡1 + [µÁ]2 ® ±2

Tu = ¡®Á0[(1¡Á)]®¡1¡± [µÁ]® (1¡Á)® = (1¡Á)®¡1(¡®Á0¡± [µÁ]® (1¡Á));

whereÁ = Ás andÁ0= @Ál=@uju= 1:SinceW r(u) = T=L; itfollowsthat

T 2W ru

q®0= (D¡1)(1¡Á)®¡1(®Á0+ D(1¡Á))+ (1¡Á)®(D + ® Á0

DÁ¡D 2 )

T 2 W ru

(1¡Á)®¡1q®0= (D¡1)(®Á0+ D(1¡Á))+ (1¡Á)D(1 + ®Á0

Á ¡D) = ® Á0(DÁ ¡1) = ®Á0(±(µ)®Á®¡1¡1)

where D = ±(µÁ)® : Since Á < 1 and Á0 < 0 ; we have thatW ru < 0 ifand only if

±(µ)®(Ás)®¡1 > 1:R ecallfrom (31) thattheParetooptimalshareis Ápo = (µ®±)1

1¡® :H ence,

wecanrewritethisconditionasW ru< 0 ifandonlyifÁs < (±µ®)

11¡® = Á po:Sincethesystem

iscontinuousinu; ¹ and¹w ;theresultinthePropositionfollows.¤

D erivationof(37 ). Suppose foramomentthatthere is only onecrisis (at¿):T hen

consumerswelfareis

C (¿) = (1¡® )yo +X

t6= ¿±t(1¡®)yt+ ±¿ [(1¡®)y¿¡T(¿)]

55

U singT(¿) = ®1¡Á

huÁ

ly¿¡1¡¹ ®1¡Ácy¿ andy¿ = (µÁl)®

h1¡Ác1¡Ál

i®yt¡1; itfollowsthat

(1¡®)y¿ ¡T(¿) = y¿

0@1¡® ¡ ®

1¡Ác

24 huµ®

"1¡Ác1Ál¡1

# 1¡®¡¹

351A (53)

= (1¡®)y¿

Ã1¡ ®

(1¡Ác)(1¡®)

"h

uµ®

·1¡Ác1Ál¡1

1¡®¡¹

# !´(1¡®)y¿K T

c

Ifweallowmultiplecrisestooccur, consumer’swelfareis

C r = (1¡®)E0

1X

t= 0

±tKtyt; Kt=

8<:

1 ift6= ¿iK T

c ift= ¿i

Followingthesamestepsas inthederivationof(35)weget(37 ).

B . M odelSimulationsT hebehaviorofthemodeleconomy is determinedbyeightparameters: u;r;® ;µ;h ;¯ ,

¹w and¹. W ewillsettheprobabilityofcrisis 1¡u, theworldinterestrater andtheshare

ofN -inputs inT -production® equaltosomeempiricalestimates. T hen, giventhevaluesof

u; r and® ;wedeterminethefeasiblesetforthedegreeofcontractenforceabilityh andthe

indexoftotalfactorproductivityintheN -sectorµ suchthatbothanR SEandanSSEexist.

T hevaluesof¯ , ¹w and¹ areirrelevantfortheexistenceofequilibria.

Inapanelof39 M ECs studiedinTornellandW estermann(2002), theprobabilityofa

crisis inagivenperiodrangesfrom 5% to9 % . T heinterestrater, is settotheaverageU S

interestratefrom19 80:1 to19 9 9 :4, whichequals 0:075. A surveyofM exicanmanufacturing

…rms suggests aconservativevalue for® equalto35% . W e then choose ¯; µ and h so

that: (i) both an R SE and an SSE existfortherangeu2 [0:91;1], and (ii) weobtain

plausiblevalues forthegrowthrates alongasafeeconomyandalongaluckypath. Inthe

baselinecase: h = 0:76; µ = 1:65; ¯ = 0:8 andu= 0:95:T heseparameters implyasafe

G D P growth rateof(1 + °s) = (1¡¯)® µ1¡h ± = 3:8% andalucky G D P growth rateof

(1 + °l) = (1¡¯)®¡

µ1¡h ±u¡1

¢® = 8:7% :Bycomparison, theaveragegrowthrateofIndiaover

theperiodis5:14 % andthatofT hailandis 8:14 % .

W echoosethe…nancialdistresscostsofcrisesld = 1¡ ¹w1¡¯ sothatthecumulativedecrease

ofG D P duringacrisis episodeis 13% , which is themeanvalueinthesampleconsidered

byTornellandW estermann(2002). Inthemodel, thecumulativedecreaseinG D P growth

56

duringacrisis episodeis (1 + °cr)2 =h¹w1¡¯

i®(µ2 ÁlÁs)®:U singthebaselinecase h = 0:76;

µ = 1:65; and ® = 0:35wegetthat(1 + °cr)2 = (1¡0:13) ifh¹w1¡¯

i= 0:4 5:T hus, weset

conservativelyld = 0:7. Inthebaselinecase, thelevelofbankruptcycosts isfree.

Finally, inorderforthewelfaremeasurestobebounded, theexpecteddiscountedsumof

tradableproductionhastobe…nite. Inthesafeeconomythisrequires ±(µÁs)® < 1:Inthe

riskyeconomy:£µÁl

¤® ±u+£µ2 ÁlÁc

¤® ±2 (1¡u) < 1:T hesetwoconditions imposeanupper

boundon®:32 Inparticular, theyholdif® < 0:6:Summingup:

Parameters baselinecase rangeofvariation

N -sectorproductivity µ = 1:6

Enforceabilityofcontracts h = 0:76 [0:6;0:8]

IntensityofN -inputs inT -production ® = 0:35 [0:2 ;0:6]

Cash‡ow/sales inN -sector 1¡¯ = 2 0 %

Financialdistresscosts ld = 70 % [30 % ;9 9 % ]

B ankruptcycosts lb = 10 0 % [30 % ;10 0 % ]

Probabilityofcrisis 1¡u= 0:0 5 [0 ;0:9]

D iscountfactor ± = 0:9 2 5

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