Boardovernorshe Federalserve SystemInternational Finance iscussion Pap - PDF document

Boardovernorshe Federalserve SystemInternational Finance iscussion Papers Number 1097 A Model of Slow Recoveries from Financial Crises Albert Queralto NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are availableon the Webat www.federalreserve.gov/pubs/ifdp/ This paper can be downloaded without charge from the Social Science Research Network electronic library at www.ssrn.com. AModelofSlowRecoveriesfromFinancialCrisesAlbertQueraltoFederalReserveBoard 2013 Thispaperdocumentshighlypersistenteectsof\fnancialcrisesonoutput,la-borproductivityandemploymentinasampleofemergingeconomies.Toaddressthesefacts,itintroducesaquantitativemacroeconomicmodelthatincludesen-dogenousTFPgrowththrough\frmcreation.Firmcreatorsobtainfundingfroma\fnancialintermediationsectorwhichissubjecttofrictions.Thesefrictionsbecomeespeciallysevereina\fnancialcrisis,increasingthecostofcreditfor\frmcreatorsandtherebyloweringthegrowthrateofaggregateTFP.Asaconsequence,themodelproducesmedium-rundynamicsfollowingcrisesthatareinlinewiththeJELNo.E32,E44,F41,O33Keywords:BusinessCycles,FinancialCrises,TotalFactorProductivity IthankOzgeAkinci,DarioCaldara,DiegoComin,JordiGal,MatteoIacoviello,LeylaKarakas,RobertKollmann,JohnLeahy,VirgiliuMidrigan,VivianYueandseminarparticipantsatvariousvenuesforveryusefulcommentsanddiscussions.IamespeciallyindebtedtoMarkGertlerforhisadviceandguidanceonthisproject.FinancialsupportfromFundacionRafaeldelPinoisgratefullyacknowledged.Theviewsexpressedinthispaperarethoseoftheauthor,andshouldnotbeinterpretedasre\rectingtheviewsoftheBoardofGovernorsoftheFederalReserveSystemorofanyotherpersonassociatedwiththeFederalReserveSystem.DivisionofInternationalFinance,FederalReserveBoard.E-mail:albert.queralto@frb.gov 1IntroductionAstylizedfactofnancialcrises,consistentwiththerecentexperienceintheadvancedeconomies,isthattheiraftermathtendstobecharacterizedbyaslowrecovery.Numerousresearchershavedocumentedhighlypersistentoutputlossesfollowingnancialcrisesusingavarietyofdierentapproaches.1Inthispaper,Irstcomplementtheexistingevidencebydocumentingpersistenteectsofnancialcrisesinasampleofemergingmarketeconomies,usingamethodologysimilartoCerraandSaxena(2008).Ialsodecomposetheeectsonoutputintomove-mentsinlaborproductivityandemployment.Theanalysisrevealsthatlossesinoutput,laborproductivityandemploymentduringthecrisisarenotreversed.Moreover,Indthatasubstantialportionofthemedium-runoutputdeclineisduetoafallinlaborproductivity:ofthe11percentmedium-runoutputloss,laborproductivityaccountsforover6percentofit,withtheremaininglossexplainedbydecreasesinemployment.Themaingoalofthispaperisthentodevelopaquantitativemodeltoaddresstheempiricalresultsontheeectsofnancialcrises.Guidedbytheevidence,Iintroducetwokeymodicationstoarelativelystandardneoclassicaleconomy,thebackboneofmodernquantitativemacroeconomicframeworks.First,Iexplicitlymodeltheprocessofrmcreationasasourceofendogenousmedium-runproductivitygrowth.Second,Iintroducenancialintermediaries(banks,forshort)thatobtainfundsfromsaversandchannelthemtoentrepreneurs,whoaretheagentswiththeabilitytocreatenewrms.Becauseofanagencyproblembetweenbanksandtheircreditors,theremaybefrictionsintheprocessoftransferringfundsfromsaverstoentrepreneurs.Thesefrictionsbecomeespeciallysevereinanancialcrisis.2ThemodelfeaturessustainedTFPgrowththatarisesduetoanendogenouslyex-pandingvarietyofintermediates,asinRomer(1990).Thereisanunboundedmassofentrepreneursinthemodeleconomy,eachwithan\idea"foranewrmorvarietybutlackingthefundstonancethestartupcostsoftheirproject.Toobtainthenecessaryfunds,entrepreneursborrowfrombanks.Onceanentrepreneurpaystheinitialentrycost,hisprojectfollowsasimplelife-cyclepatternwherebyitcaneitherfailorsuccessfullybecomeanewvarietyaccordingtoanexogenouslygivenprobability.Toprovidefundingtoentrepreneurs,banksborrowfrombothdomestichouseholds 1CerraandSaxena(2008)documentlittleevidenceofoutputrecoveryfromnancialcrisesinalargecross-sectionofcountries.SeealsoReinhartandReinhart(2010),ReinhartandRogo(2009)orChapter4inInternationalMonetaryFund(2009)andreferencestherein.2Attheendofsection2,Ipresentsomeevidencesuggestingadeclineinrmcreationduringnancialcrises,byexaminingthebehavioroftimeseriesdataonpatentandtrademarkapplicationsduringthe1997crisisinSouthKorea.2 andinternationalcreditors.Iassumethatbanksareecientatmonitoringentrepreneurialprojects,sothattherelationshipbetweenbanksandentrepreneursisfrictionless:en-trepreneurscanoerthebankperfectlystate-contingentequityinexchangeforfunds.Ontheotherhand,thebankfacesfrictionsintheprocessofobtainingfundsfromcred-itors.AsinGertlerandKaradi(2011)andothers,3Imodelthesefrictionsthroughasimplelimitedenforcementproblem:afterborrowingfunds,thebankcanrenegeonitsdebtanddivertacertainfractionofresourcesforitsownpersonalgain,atwhichpointcreditorscanforceitintobankruptcy.Thelimitedenforcementfrictioneectivelyin-troducesanendogenousconstraintonthebank'slendingthatmaytightenaseconomicconditionsworsen.Animportantdeterminantofthedegreeofnancialconstraintsisthestateofbanks'balancesheets,summarizedbytheirnetworth.Theprimarysourceof uctuationsinbanks'networthisthemovementinthepricesoftheassetsontheirbalancesheets.Theseassetsconsistofclaimsonfullysuccessfulrms(interpretableasmatureoroldrms)aswellasprojectsthathavenotyetsuccessfullyturnedintoanewvariety(interpretableasyoungstartupsorproductsindevelopment).Inthemodel,thepresenceofthelattertypeofassetsintroducesasourceofadversefeedbackbetweenthepriceoftheequityissuedbyentrepreneursandbanks'networth,whichactsasanimportantamplicationmechanism.Inparticular,adeclineinbanknetworthforcesbankstocutbackonprojectfunding.Thislowersthepriceatwhichnewentrepreneurscansellequity,andatthesametimelowersthefranchisevalueofprojectsthathavealreadybeencreatedbuthavenotyetbeensuccessful.4Sincetheassetsideofbanks'balancesheetsincludesthelatter,adeclineintheirpriceleadstofurtherdropsinbanks'networth.Iembedthesetwofeatures,endogenousgrowththroughrmcreationandfrictionalnancialintermediation,intoaconventionalsmallopeneconomymodelthatismodiedtoallowforvariablecapitalutilization,habitformationinconsumptionandaneedforworkingcapitalofintermediategoodsproducers.Thesemodicationsarestandardintheemergingmarketbusinesscyclesliterature.Althoughnotcriticalforobtainingthemainresultsonthepersistenteectsofnancialcrises{whichariseduetothenovelmechanismlinkingrmcreationwithnancialfrictions{thesefeatureshelpenhancethequantitativepropertiesofthemodelatlittlecostofaddedcomplexity.Afterdescribingthemodel,Iturntopresentingaquantitativeanalysisofanancialcrisisexperiment.Theanalysisisdesignedtoexplorethemodel'sabilitytoaccountfor 3SeealsoGertlerandKiyotaki(2010)orGertler,KiyotakiandQueralto(2012).4Sinceprojectsbecomesuccessfulthroughasimpletime-invariantPoissonprocess,atanygivendatethevalueofaunitoftheequityissuedbyanentrantentrepreneurmustequalthefranchisevalueofanentrepreneurthatenteredinthepastbutthathassofarnotbeensuccessful.3 theevidencedescribedinSection2.Thecrisisismodeledasthesimultaneousoccurrenceoftwoexogenousshocks:anincreaseinthecountryinterestrate,torepresentasuddenstopincapitalin ows,andadirectdisruptionofdomesticcapitalmarkets,tocaptureacorrespondinglossofcondenceinthedomesticbankingsector.Themainresultisthatthebaselinemodelissuccessfulatqualitativelyandquantitativelycapturingtheempiricalbehaviorofoutput,laborproductivityandemployment.EndogenousTFPgrowthiscriticalforthemodeltogeneratethehighpersistenceobservedinthedata:itallowsacrisisshocktoinduceaslowdowninthegrowthrateofTFP,leadingtolastingeectsonproductivity,employmentandoutput.Inaddition,Ishowthatnancialfactorsplayacrucialroleingeneratingthispersistence{inthebaselinecalibratedmodel,closetohalfofthemediumrunoutputdeclineisexplainedbythenancialsideofthemodel.Insummary,throughthemechanismsdescribedabovethemodelcancloselyreplicatethemedium-runmovementsinoutput,laborproductivityandemploymentidentiedinthedata.Themodelingapproachinthispapercombineselementsoftheliteratureonendoge-nousgrowththroughanexpandingvarietyofproducts,duetoRomer(1990),withideasfromtheliteratureonnancialfactorsinmacroeconomics,pioneeredbyBernankeandGertler(1989)andKiyotakiandMoore(1997).Amorerecentliteraturehasincor-poratedmechanismsinthespiritofRomer(1990)withinquantitativemacroeconomicframeworks{notablyCominandGertler(2006),whoproposeamodeltostudymedium-termcyclesintheU.S.,5orBilbiie,GhironiandMelitz(2012),whoanalyzeproducerentryoverthebusinesscycle.Likewise,nancialmarketfrictionswererstincorporatedwithinamacroeconomicmodelbyBernanke,GertlerandGilchrist(1999).Thelatestincarnationofthisclassofmodels,whichthispaperfollowsmostclosely,focusesonnancialintermediaries,asinGertlerandKaradi(2011)andothers.Thispaperputstogetherideasfrombothliteraturesbystudyingaquantitativemodelwherenancingfrictionsaectthecreationofnewrms.TheevidenceandthemodelpresentedherearerelatedtoAguiarandGopinath(2007),whoarguethatadistinctivefeatureofemergingmarketbusinesscyclesislargemovementsintrendTFPgrowth,whiledevelopedeconomiesarebettercharacterizedbytransitory uctuationsaroundthetrend.Theevidenceinthispapershowsthatnancialcrisesareanexampleofsuchnonstationarybehavior.Further,themodelinthispaperprovidesafoundationforthetypeofTFPprocessthatAguiarandGopinath(2007)take 5SeealsoComin,GertlerandSantacreu(2009),whoestimateaversionofthemodelinCominandGertler(2006),orComin,Loayza,PashaandServen(2009)whoproposearelatedframeworkfordevelopingcountries.4 asexogenous,andconnectsitexplicitlywithnancialmarketimperfections.Finally,thispaperisalsorelatedtoalargeandgrowingliteraturethatproposesquan-titativemacroeconomicmodelsforemergingmarketeconomies,includingUribeandYue(2006),NeumeyerandPerri(2005)orMendoza(2010).Arelatedbranchofthislitera-turehasproposedquantitativeframeworkstoaccountforaspectsofemergingmarketsnancialcrises,likeGertler,GilchristandNatalucci(2007)orMendozaandYue(2012).Someoftheseframeworks,aswellasseveralothers,6oerexplanationsfortheobserveddeclineinTFPduringnancialcrises,includingdeclinesincapacityutilization,sectoralreallocation,anddisruptionintradeofimportedinputs.WhileIviewthemechanisminthispaperascomplementarytotheirs,thereisakeydierencebasedonmyfocusonaccountingforthemedium-runTFPdeclineanditsroleingeneratingaslowrecovery.Therestofthepaperisorganizedasfollows.InSection2,Ipresenttheevidenceontheeectsofnancialcrises.InSection3Idescribethemodel,andpresentthesimulationresultsinSection4.Section5concludes.2EvidencefromSystemicBankingCrisesInowturntodescribingtheempiricalexercise.Figure1providessomesuggestiveev-idence:itplots(log)output,laborproductivityandemploymentforagroupofAsiancountriesaroundthenancialcrisisof1997.7Therstpanelsuggestsaverypersistentoutputlossfollowingthecrisis:outputdoesnotrecovertothepre-crisistrend(greendashedline),butratherremainspermanentlybelowtrendintheaftermathofthecrisis.Fromthesecondandthirdpanels,thereisaconsiderabledeclineinlaborproductivity,whichisalsoverypersistent,andamoremodestslowdowninemployment.Inparticular,laborproductivityfallsbyabout10percentrelativetothepre-crisistrend,anditneverrebounds.8Toprovidemoreformalevidenceonthebehaviorofoutput,laborproductivityandemploymentfollowingnancialcrises,IemployanapproachsimilartoCerraandSaxena(2008),whoestimateaunivariateautoregressivemodelforoutputgrowth,augmentedto 6Forinstance,GopinathandNeiman(2011),BenjaminandMeza(2009),MezaandQuintin(2007),KehoeandRuhl(2009),PratapandUrrutia(2010)orAoki,BenignoandKiyotaki(2007).7ThecountriesincludedareIndonesia,Malaysia,Phillipines,Korea,ThailandandHongKong,labelled\SEA-6".Areatotalsarecomputedbyaddingconstantdollar,PPP-adjustedGDPforeachofthecountries.Laborproductivityisdenedasoutputperemployedworker.SeeAppendix1fordetailsonthedata.8Thisisrobusttodierentchoicesfortheperiodusedtocomputethepre-crisistrend.Annualizedgrowthoflaborproductivityfortheperiod1980-1996is4.06%,whichisclosetothatfortheentirepre-crisissample(1960-1996),equalto3.69%.Annualproductivitygrowthforthepost-crisisperiodof1998-2007is3.61%,closetothegureforthepre-crisissample.5 includecurrentandlaggedvaluesofdummiesindicatingnancialcrisesandothershocks.Istartbydecomposing(log)outputasthesumofemploymentandlaborproductivity(ni;tandzi;trespectively,inlogs):log(Yi;t)=log(Ni;t)+log(Yi;t Ni;t)ni;t+zi;tIthenestimatethefollowingbivariatemodel:xi;t=xi+Axi;t�1+4Xj=0BjDi;t+"i;t(1)wherexi;t="
ni;t
zi;t#.Thespecicationismotivatedbytheassumptionthatbothhoursandlaborpro-ductivityareintegratedoforderone,sothatrst-dierencingisnecessarytoachievestationarity.9Theregressorsin(1)includeacountryxedeect,onelagoftheendoge-nousvector,andcurrentandlaggedvaluesofadummyvariableDi;tindicatingtheyearinwhichasystemicbankingcrisisstartsincountryi,yeart.Lagselectionproceduresrecommendonelagfortheendogenousvector.Iincludefourlagsforthecrisisindicatorsincecoecientsonlagsabove4areinsignicant,althoughresultsarerobusttotheinclusionofalargernumberoflagsofDi;t.Themodelin(1)isestimatedonasampleof17emergingeconomies.DataforannualrealoutputandemploymentareobtainedfromtheTotalEconomyDatabase.IobtainsystemicbankingcrisisdatesfromLaevenandValencia(2012),anupdatedversionofthedatesinCaprioandKlingebiel(2003),alsousedbyCerraandSaxena(2008)amongmanyothers.10Figure2showstheimpulseresponsesoflaborproductivityandemploymentfromestimatedmodel(1),aswellastheresponseofoutput.11Forthissampleofcountries,theresponseofoutputislargeandhighlypersistent,consistentwiththendingsinCerraandSaxena(2008).Fouryearsafterthecrisis,theoutputlossreachesandremainsat 9ThatassumptionismotivatedbytheoutcomeofstandardaugmentedDickey-Fullertests,whichforvirtuallyallcountriesdonotrejectthenullofaunitrootinthelevelsofouput,employmentandproductivity,butdorejectthesamenullwhenappliedtotherstdierences(atthe1-percentsignicancelevel).10SeeAppendix1fordetailsonthedataandthecompletelistofcrisesdates.11Thelatterisobtainedbyestimatingaunivariatemodelfortherstdierenceoflogoutputanalogousto(1).Thisapproachismoreecientthancomputingoutputasthesumoflaborproductivityandemploymentfrom(1)asitrequiresestimatingasmallernumberofparameters.6 Figure1:Totaloutput,employmentandoutputperemployedworker(logs)forgroupof6SouthEastAsiancountries(Indonesia,Malaysia,Phillipines,Korea,ThailandandHongKong).Pre-crisislineartrend(greendashedline)computedfortheperiod1980-1996.7 1980 1985 1990 1995 2000 2005 2010 14 15 16 Output for SEA-6 (log) 1980 1985 1990 1995 2000 2005 2010 2 2.5 3 Labor Productivity for SEA-6 (log) 1980 1985 1990 1995 2000 2005 2010 11.5 12 12.5 Employment for SEA-6 (log) Figure2:Estimatedimpulseresponsestoabankingcrisis.Thedashedlinesindicate90%con-dencebandscomputedbybootstrapping.Timemeasuredinyears.Allvariablesinlogs.almost12percent.Decomposingoutputintolaborproductivityandemploymentrevealsasubstantialdeclineinproductivity,whichremainsataboutnegative6percentafter4years.Fromthepanelontheright,thedropinemploymentisslightlymoremodestinmagnitude,anditisalsohighlypersistent.TheimpulseresponsesreportedinFigure2constitutethedatamomentsagainstwhichIwillevaluatethemodelpresentedbelow.12Figure3displaystimeseriesonTFPandpatentandtrademarkapplicationsbyresidentsinSouthKorea.Asshowninthetopleftpanel,the1997nancialcrisisinvolved 12TheresultsdocumentedherecontrasttosomeextenttothoseinHoward,MartinandWilson(2011),whondthattherecoveriesfromrecessionsassociatedwithbankingornancialcrisesarenotunusuallyweak.Thediscrepancyispartlybecausetheyfocusongrowthfollowingtherecessiontrough,whiletheanalysisabovestudiestheimpulseresponsetoabankingcrisisshock.BothsetsofndingscanbepartlyreconciledbytheobservationinHoward,MartinandWilson(2011)thatsincebankingandnancialcrisestendtobedeepandlong,andpost-troughgrowthisaboutaverage,theoutputdeclinesintheseepisodesarenotmadeupquickly.8 0 2 4 6 8 10 -0.14 -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 Labor ProductivityYears 0 2 4 6 8 10 -0.14 -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 EmploymentYears 0 2 4 6 8 10 -0.14 -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 OutputYears apersistentslowdowninTFPrelativetotrend.Fromthebottomleftpanel,afteramoderateslowdownpriortothecrisis,in1997TFPplungesbyabout6%relativetotrend.Consistentwiththeevidencejustpresented,thisdeclineisneverrecovered.13TherightpanelshowspatentandtrademarkapplicationsinKorea.Afterrisingforalmosttwodecadespracticallywithoutinterruption,thesevariablesdisplaylargedeclinesduringthecrisisepisode{about25%forpatents,andmorethan35%inthecaseoftrademarks.Thisevidencelendssupporttothemechanismintroducedinthispaper,namelythatanancialcrisissuchastheonesueredbySouthKoreain1997mayleadtoareductioninthepaceatwhichnewrmsarecreated,resultinginahighlypersistenteectofthecrisis.ThemechanismisalsosupportedbyempiricalstudiesontheeectsofnanceonrmcreationinthecaseoftheU.S.14Inturn,thehypothesisthatdicultaccesstoexternalnancehindersinnovationandR&Disbackedbyseveralrm-levelstudies.15Finally,anumberofpapersdocumentsucheectsfordevelopingeconomies.16Tosummarize,theevidencedescribedaboveconrmsthatthelargeandpersistentoutputdeclinesassociatedwithnancialcrisesinemergingcountriesisindeedageneralphenomenonacrossepisodesandcountries.Themagnitudesofthedeclinesinproductiv-ityuncoveredbytheexercisearecomparabletothosefoundbyotherstudiesofemergingmarketcrises.17Further,thesedeclinestendtohaveaverylargepermanentcomponent.InthefollowingsectionsIdescribeandanalyzeaquantitativemodelcapableofgener-atingdropsinTFP,productivityandemploymentofsizeandpersistencecomparabletothoseinthedata.3ModelThecoreframeworkisasmallopeneconomymodelwithendogenousTFPgrowththroughanexpandingvarietyofintermediates,asinRomer(1990)orCominandGertler(2006).Thedierencewithrespecttotheseframeworksisthatthereisanimperfectionin-nancialmarketsthatimpedesthesmooth owofresourcesfromsavers(householdsandinternationalinvestors)tobanks,whonancetheintroductionofnewrms.Iintroduce 13SeeChapter4ofInternationalMonetaryFund(2009)forfurtherevidenceonpersistentdeclinesinTFPfollowingnancialcrises.14KortumandLerner(2000)establishapositiveeectoninnovationoftheavailabilityofventurecapitalfunding,andKerrandNanda(2009)showthatUSnancialreformsenhancedtheprocessofsmallrmentry.15SeeHall(2002)andHallandLerner(2009)forsurveysofworkusingdatafromOECDcountries.16SeeAyyagariet.al.(2007),andparticularlyGorodnichenkoandSchnitzer(2010),forstudiesusingrm-levelsurveydatafromdevelopingeconomies.17ForexampleMezaandQuintin(2005)orKehoeandRuhl(2009).9 Figure3:TFP,PatentsandTrademarks,SouthKorea(inlogs).TrendforTFPcomputedfortheperiod1980-1996.Source:TFPfromCoe,HelpmanandHomaister(2009).PatentandtrademarkapplicationsfromWorldDevelopmentIndicators.threefurthermodicationsthathavebecomecommonintheDSGEliteraturerecently,andthathelpthemodelproduceamorerealisticbehaviorofmacroeconomicaggregatesinresponsetothecrisis:variablecapitalutilization,habitformationinconsumption,andaworkingcapitalrequirementforintermediategoodsproducers.Therearesixtypesofagentsinthemodel:households,entrepreneurs,banks,nalgoodsproducers,intermediategoodsproducersandcapitalproducers.Homogeneousoutputisproducedbynaloutputproducersusinganexpandingvarietyofintermediates.Theentrepreneurialsectorusesfundsborrowedfrombankstonancethecreationofnewrms.Inturn,banksobtainnancingfromdomestichouseholdsandfromforeigncapitalmarkets.Inwhatfollows,Idiscussthebehaviorofeachoftheseagentsinturn,andderivetheaggregaterelationshipsthatcharacterizethedynamicpathoftheeconomy.3.1HouseholdsSupposethereisarepresentativefamilywithaunitmeasureofmembers.Householdsmakedecisionsonconsumption,laborsupply,investmentinphysicalcapitalandsavingthrougharisk-freeinternationalbond.Therearetwotypesofmemberswithineach10 1990 1992 1994 1996 1998 2000 2002 2004 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 TFP, South Korea (log) 1990 1992 1994 1996 1998 2000 2002 2004 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 TFP, South Korea (log, relative to linear trend) 1990 1992 1994 1996 1998 2000 2002 2004 9.5 10 10.5 11 11.5 Patent and Trademark applications by residents, South Korea Patent applications (log) Trademark applications (log) household:workersandbankers,withmeasuresfand(1�f)respectively.Afractionoftheworkersarespecializedor\skilled"workers,andsupplylaborinelasticallytotheentrepreneurialsector.TheirrolewillbeclearasIdiscussentrepreneursbelow.Regularworkerssupplylaborelasticallytointermediatesproducers.Bothtypesoflaborreturnwagestothefamily.Banksuseborrowedfundstomakeloanstoentrepreneurs,andalsotransferanyearningsfromthisactivitybacktothehousehold.Thereisperfectconsumptioninsuranceamongfamilymembers.AsinGertlerandKaradi(2011)andothers,thisformulationisasimplewayofintroducingheterogeneityintermsofborrowersandlenderswhilemaintainingthetractabilityofarepresentativeagentmodel.Thereisrandomturnoverbetweenbankersandworkers:abankerbecomesaworkerwithprobability(1�).Attheendoftheircareers,bankerstransfertheirnetwealthtothefamily.Atthesametime,eachperiodafraction(1�)f 1�fofworkersstartacareerasbankers,exactlyosettingthenumberofbankerswhoexit.Asexplainedbelow,itisassumedthatthefamilytransfersasmallamountofresourcestobankerswhostartoutsotheyareabletostartoperations.Bankexitisintroducedasadevicetoensurethatthenancialimperfectionwillberelevant:otherwisebanksmightreachapointwhereinternalresourcesareenoughtonancealldesiredloanstoentrepreneurs.LettingCtdenoteconsumptionandLthoursofworkinthesectorproducinginter-mediates,ahouseholds'utilityfunctionisu(Ct;Ct�1;Lt)=�Ct�hCt�1��t1 1+L1+t
1��1 1�(2)ThepreferencestructurefollowsUribeandYue(2006),NeumeyerandPerri(2005)andmuchoftheemergingmarketbusinesscycleliterature.Itabstractsfromwealtheectsonlaborsupply,asinGreenwood,HercowitzandHuman(GHH,1988).Thetermmultiplyingthedisutilityofwork,�t,dependsontheaggregatetechnologicallevel,At,asfollows:�t=A t�1� t�1(3)Theterm�t,whichatthelowfrequencygrowsatthesamerateasAt,isintroducedtoensuretheexistenceofabalancedgrowthpathwithstationaryhours.Inthecalibratedversionofthemodel,Iwillset toaverysmallvalue,sothat uctuationsinAthaveanegligibleimpactonthedisutilityoflaborathighandmediumfrequencies.UndertheinterpretationofGHHpreferencesasareducedformforaneconomywithhomeproduction(Benhabib,RogersonandWright(1991)),asmallvalueof canbeviewedascapturingaprocessof\slowdiusion"ofthevarietiesusedinthenalgoodssector11 intothehomeproductionsector.Thehouseholds'decisionproblemistochoosestochasticsequencesforconsumption,laborsupply,purchasesoftheinternationalbondandpurchasesoffollowing-periodphys-icalcapitaltosolvethefollowingproblem:max(Ci;Li;DFi;Ki+1)Et1Xi=0iu(Ct+i;Lt+i)subjecttoCt+PK;tKt+1RktKt+WtLt+1 RtDFt�DFt�1+tAbove,PK;tisthepriceofcapitalandRktisitsrentalrate,WtthewagerateandRtistheinterestrateontheinternationalbond.DFtdenotesthefamily'schoiceofforeigndebtandKt+1isthechoiceforphysicalcapitalholdings.Finally,tdenotesnettransfersfromrmownershippluswagesearnedbyskilledworkers.TheinternationalinterestrateRtdependsonaggregatenetforeignindebtednessBtandonarandomshockrtasfollows:Rt=r+ert+ heBt�B Yt�1i(4)Asisusualinthesmallopeneconomyliterature,thereasonforintroducingade-pendenceofthecostofborrowingonnetforeignindebtednessistoensurestationarydynamics.Ichooseaverysmallvaluefor sothatthisfeaturedoesnotaectthedyamicsofthemodel.Araiseinrt,interpretableasacountryinterestrateshock,isasimplewaytomodelthesuddencapitalout owsthathaveaccompaniedmanyoftheemergingmarketnancialcrisesanalyzedintheprevioussection.Theexpressionformarginalutilityofconsumption,UC;tisthefollowing:UC;t=uC;t� Et(uC;t+1)(5)uC;t=Ct�hCt�1��t1 1+L1+t�(6)Denethehouseholds'stochasticdiscountfactorbetweenperiodstandt+i,t;t+iast;t+iUC;t+i UC;t(7)Thenthehousehold'sdecisiononbondandcapitalholdingsarecharacterizedbytwo12 conventionalEulerequations:1=Et(t;t+1)Rt(8)1=Ett;t+1Rkt+1 PK;t(9)LaborsupplyisgivenbyuC;t�tLt=UC;tWt(10)3.2EntrepreneursIneveryperiodthereisanunboundedmassofprospectiveentrepreneurswiththeabilitytointroducenewvarietiesofintermediates,interpretableas\innovations"ornewtypesofproductsortechnologieswhichmaybeentirelynoveltothesmallopeneconomyorpossiblyadaptationsofvarietiesalreadyinuseinmoreadvancedcountries.18Specically,eachentrepreneurcanuseresourcestocreateanew\potential"rm,whichwillthenbecomeasuccessfulnewvarietywithacertain(exogenous)probabilityeachperiod.Atthesametime,bothsuccessfulandunsuccessfulrmsfacetheriskofanexogenousexitshock.Thisprocessismeanttocaptureinasimplewaythelife-cycledynamicsoftherm.Entrepreneursneedtoobtainfundingfrombankstonanceentry.Heretheideaisthatbanksare\specialists"withskillsinevaluatingandmonitoringentrepreneurs.Contractsbetweenbanksareentrepreneursareassumedtobefrictionless:inexchangeforfunding,eachentrepreneurcanoerthebankasecuritywhichisperfectlycontingentonthesuccessofhisorherproject.Ontheotherhand,asexplainedindetailinthefollowingsection,banksdofacefrictionsinobtainingfunds.Tobemorespecic,eachentrepreneurcanproducenewpotentialrmsbyemployingmaterialsandskilledworkersasinputs,accordingtothefollowingproductionfunction:ZN;t=Nt(AtLS;t)1�(11)Above,Ntistheamountofmaterialsused(inunitsofnaloutput)andLS;tisthenumberofskilledworkershired.Atdenotestheaggregatetechnologicallevelofthe 18Inthelattercase,theassumptionisthatitisstillcostlytointroduceaninnovationthatisalreadyinuseinamoredevelopedeconomy.SeeManseld,SchwartzandWagner(1981)forevidencesuggestingthat\imitation"costscanindeedbesubstantial.13 economy,whichasexplainedbelowisequaltothetotalnumberofrmvarietiesinoperation.AsinRomer(1990),(11)incorporatesanexternalityoftheaggregatelevelofknowledgeontheeciencyofskilledlaborinintroducingnewtypesofrms.Thisassumptioniskeytogenerateendogenousgrowth.Givenconstantreturnstoscaleof(11),theentrepreneurialsectorcanbeformulatedasconsistingofarepresentativeentrepreneurorpotentialentrantwhodecideshowmanynewrmstointroduce,subjecttoproductionfunction(11).Analternative,perhapsmoreplausible,interpretationisthatthereisanunboundedmassofentrepreneurs,eachwithan\idea"foraproject,whichcanbeputintopracticebypayingasunkcostMCtgivenbythemarginalcostassociatedwith(11).DenotingtheskilledlaborwagebyWS;t,theexpressionforthismarginalcostisthefollowing:19MCt=1 WS;t=At 1�1�(12)TheentrepreneurhasnofundstonancethesunkcostMCt.Toobtainfunds,heorsheissuesequitytobanks.LetJtbethepriceofaunitofentrepreneurequity.Therearenocommitmentorenforcementfrictionsbetweenentrepreneursandbanks,sotheentrepreneurcancommittopayallthecontingentproceedsfromtheprojecttotheequityholdingbank.Atthesametime,givenfreeentryofentrepreneurs,thepriceofequityissuedbyentrepreneursmustequalthesunkcostofintroducinganewproject:Jt=MCt(13)Oncetheentrepreneurhaspaidthesunkcost,thedynamicsofthermareasfollows.Armthathasjustenteredisstillnotasuccessfulnewbusiness.Thermbecomessuc-cessfulwithanexogenousprobability.Heretheideaisthatanenteringentrepreneurcannotgrowintoasuccessfulbusinessimmediately,butratherittakestimetoturnhisorherideaintoamarketablenewproduct.Oncetheentrepreneur'sideabecomessuc-cessful,itgeneratesprotstperperiod(determinedbelowwhendiscussingtheproblemofintermediatesproducers).Atthesametime,bothsuccessfulandstill-unsuccessful 19TheexpressionforMCtcanbeobtainedbysolvingthecostminimizationproblemofanen-trepreneuri:minNt(i);LS;t(i)Nt(i)+WS;tLS;t(i)subjecttoNt(i)[AtLS;t(i)]1�1ThemarginalcostMCtisthenequaltothemultiplierassociatedwiththeconstraintoftheproblemabove.14 businessesfacetheriskofreceivinganexogenousexitshock:thecorrespondingsurvivalprobabilitiesaredenotedAandZrespectively.IassumethatA�Z,tocapturethefactthatsmall,youngrmshavehigherexitratesthanrmsthatarelargeandmature.20Finally,asexplainedearlier,thesupplyofskilledlaborisassumedtobeinelasticandxedat LS.Onecanthencombine(12),(13)andtherst-orderconditionforLS;ttoobtainthefollowingrelationbetweenthepriceofentrepreneurequityJtandthenumberofnewentrantsZN;t:Jt=1 1 LS1� ZN;t At1� (14)Equation(14)canbeinterpretedasanaggregatesupplycurveofnewentrantrms,asafunctionofthepriceofaunitofentrepreneurequityJt.3.3BanksBankslendfundsobtainedincapitalmarketstoentrepreneurs.AsinGertlerandKiy-otaki(2011),banksareinterpretedasspecialistswhoassistinchannelingfundsfromsaverstoentrepreneurs.Theypurchasesecuritiesissuedbyentrepreneursthatareper-fectlystate-contingent.Theseclaimsoertopaythefullvalueoftheentrepreneur'sprojectinthecontingencythattheprojectissuccessful.Inaddition,banksengageinmaturitytransformation:theyholdlong-termassets(claimsonentrepreneurialprojects)andfundtheseassetswithshort-termliabilities(beyondtheirownequitycapital).Theagencyfrictioninnancialmarketstakestheformofalimitedenforcementproblembetweenthebankanditscreditors:attheendoftheperiod,afterborrowingfunds,abankcandefaultonhisorherdebtanddivertanexogenousfractiontofresources,withcreditorsonlybeingabletorecovertheremainingpart1�t.Thisimposesalimitonhowmuchdebtthebankisabletotakeonex-ante,aslendersrecognizethatexcessivedebtwillleadtodefault.Iallowthefractiondivertablettobetime-varying.Anincreaseintisinterpretableasareductionintheeciencyofnancialmarkets,aslendersexpecttobeabletorecoverasmalleramountfromdefaultingborrowers.21Giventheseconsiderations,thebank'ssequenceproblemisthefollowing: 20SeeHaltiwanger,JarminandMiranda(2012).21KiyotakiandMoore(2012),DelNegro,Eggertsson,FerreroandKiyotaki(2010)andJermannandQuadrini(2012)useamechanisminthisspirittomotivateadisruptioninnancialmarkets.15 maxfst+i�1;dt+i�1g1i=1"Et1Xi=1i�1(1�)t;t+ifZ[vt+i+(1�)Jt+i]st+i�1�Rt+i�1dt+i�1g#(15)subjecttoJtst+Rt�1dt�1Z[vt+(1�)Jt]st�1+dt(16)Et1Xi=1i�1(1�)t;t+ifZ[vt+i+(1�)Jt+i]st+i�1�Rt+i�1dt+i�1gtJtst(17)Examiningrstthebudgetconstraint,equation(16),thebank'suseoffunds(lefthandside)includesthepurchaseofanamountstofclaimsonentrepreneurs,whichcostsJtst,aswellasdebtrepayments,Rt�1dt�1.Thesourcesoffundsaretherevenuesobtainedfrompreviousloans(thersttermontherighthandside)aswellasnewdebtissued,dt.Projectsnancedthepreviousperiod,st�1,haveasurvivalprobabilityZ.Iftheprojectsurvives,itissuccessfulwithprobability,inwhichcasethebankreceivesitsfullvalue,denotedvt.Iftheprojectisunsuccessfulthisperiod,thengiventhesimplePoissonprocessfortheevolutionofprojectsitisexactlyequivalenttoasecurityissuedbyanewentrantentrepreneur,sothatitsvalueisJt.Asuccessfulprojectgeneratesastreamofprotsft+ig1i=0obtainedfrommanufac-turingandsellingthenewvarietyofintermediate.Therefore,thevalueofasuccessfulprojectisgivenbytheexpecteddiscountedvalueoftheprotstream,accountingforthesurvivalrateAofsuccessfulrms:22vt=Et"1Xi=0iAt;t+it+i#(18)Asindicatedby(15),ifabankaliveattexitsinperiodt+i(whichhappenswithprobabilityi�1(1�))ittheaccumulatedwealthbacktothehousehold.Theresourcesaccumulateduntilperiodt+iaregivenbythetermincurlybracketsin(15).Thebankthusvaluespayosintheperiodandstateatwhichitexitswiththehousehold's 22Heretheunderlyingassumptionisthattheentrepreneur,whensuccessful,sellstheideatoamo-nopolistproducerofintermediates,whothenobtainsthestreamofprotsft+ig1i=0frommanufacturingandsellingthenewvarietyandthereforeiswillingtopayvtfortheproject.16 stochasticdiscountfactor,t;t+i.Equation(17)isthebank'sincentiveconstraint.Attheendofperiodt,afterhavingborrowedincapitalmarkets,thebankmaychoosetodefaultonitscreditorsanddivertfractiontofavailablefunds,whichitthentransfersbacktoitshousehold.Creditorscanthenforcethebankintobankruptcyandrecovertheremainingfraction1�tofresources,butitistoocostlyforthemtorecoverthefractiontoffundsthatthebankdiverted.Accordingly,forcreditorstobewillingtosupplyfundstothebank,equation(17)musthold:thebank'svalueifhehonorsthecontractwithhiscreditorsmustbegreaterthanthevalueofdivertingresourcesintheamounttJtstandbeingshutdown.Tosimplifythebank'sproblem,denersttherateofreturntoonedollarinvestedinentrepreneurialprojects,RZ;t:RZ;tZvt+(1�)Jt Jt�1RZ;tdependsonlyontheaggregatestate,throughpricesvtandJt.Timesoflowrealizationsofthevalueofanewintermediate,vtandofthevalueofentrepreneurequity,Jt,willbetimesoflowreturnsRZ;t.Notingthatbank'sindividualstatevariablesatthebeginningofperiodtarest�1anddt�1,theentrepreneur'sproblemcanbeexpressedrecursivelyasfollows:Vt(st�1;dt�1)=maxst;dt(1�)Et[t;t+1(RZ;t+1Jtst�Rtdt)]+Et[t;t+1Vt+1(st;dt)](19)subjecttoJtst+Rt�1dt�1RZ;tJt�1st�1+dt(20)(1�)Et[t;t+1(RZ;t+1Jtst�Rtdt)]+Et[t;t+1Vt+1(st;dt)]tJtst(21)Above,thetimeindexonthevaluefunctionre ectsaggregateuncertainty.Theproblemcanbesimpliedfurtherbyrealizingthatthekeyindividualstatevariableisthebank'snetworthwt,denedasthedierencebetweenthevalueofassetsanddebt:wtJtst�dt(22)Fromthebudgetconstraint(20)atequality,theevolutionofnetworthis17 wt=(RZ;t�Rt�1)Jt�1st�1+Rt�1wt�1(23)Networthattisgivenbythegrossreturntothebank'sinvestmentsnancedduringt�1,netofrepaymentstocreditors.Equation(23)showsthatnetworthattdependsontheindividualstateatt�1(st�1;wt�1)togetherwiththerealizationoftheaggregatestateatt,throughtherateofreturnRZ;t.Thissuggestsmakingthefollowingguessforthebank'svaluefunction:Vt(st�1;dt�1)= twt(24)Above,theundeterminedcoecient tisconjecturedtodependonlyontheaggregatestate,anddependenceofwton(st�1;dt�1)through(22)and(23)isunderstood.Denealsothefollowingvariables: t+11�+ t+1(25)tEt[t;t+1 t+1(RZ;t+1�Rt)](26)tEt(t;t+1 t+1)Rt(27)Variable t+1isinterpretableastheprospectivevalueofaunitofnetworth,beforethebankndsoutwhetherhewillhavetoexitattheendoftheperiod.Fromequation(26),tisinterpretabletothereturnforthebankofinvestinginexcessofthecostoffunds.Finally,trepresentsthevalueofanextraunitofnetworthtoday.Giventhedenitionsabove,theproblemofthebankreducestothefollowing: twt=maxsttJtst+twt(28)subjecttotJtst+twttJtst(29)Heretre ectsthevaluetothebankoffundinganadditionalproject(increasingst)whileholdingnetworthconstant.Ontheotherhand,tisthevalueofanadditionalunitofnetworth,holdingconstantst.Withfrictionlessnancialmarketsbankswouldbeunconstrained,withtheimplicationthatt=0.Theagencyproblemintroducesafrictionthatmakesbankspotentiallyconstrained,andthatmaythereforeplacelimitsonarbitrage.18 Equation(29)istheincentiveconstraint.Notethataslongast0,itisprotableforthebanktoborrowandfundanadditionalproject.Thus,inthisinstance,andgivenwt�0,theconstraintbinds:Jtst=t t�twt(30)Equation(30)showsthattheamountthebankcanspendonfundingprojects,Jtst,isconstrainedbyhisnetworthwt,throughalimitontheamountthebankisallowedtoborrowincapitalmarkets.23Denethebanksmaximumleverageratiotastt t�t(31)sothatwhenthecreditconstraintbinds,Jtst=twt(32)Thenwithabindingconstraint,solvingtheundeterminedcoecientfrom(28)-(29)wehavethat t=tt+t(33)Thevalueofaunitofnetworthtoday( t)derivesfromitsvalueholdingassetsconstant(t)plusthecapacitythatitgeneratestofundadditionalprojects(t)multipliedbythevaluetothebankofthoseadditionalprojects(t).3.3.1AggregationAggregationaccrossbanksissimplegiventhelinearityof(32).Theaggregateamountofprojectsfunded,St,isconstrainedbyaggregatenetworthofthenancialintermediationsector:JtSt=tWt(34)Atthesametime,aggregatenetworthattisgivenbythesumofnetworthofsurvivingbanks,whichevolvesindividuallyaccordingto(23),andthetransferthat 23Notethatfortheincentiveconstrainttobindwemustalsohavett:otherwise,thevalueofanextraprojectisgreaterthanthegainfromdivertingtheadditionalfunds,sothereisneveranincentivetodefault.Intheequilibriumconstructedbelow,forreasonableparameterizationstheconstraintalwaysbindsalongthebalancedgrowthpath.19 newbornonesobtainfromtheirfamily.ForsimplicityIassumethatthetransferisasmallfractionofthetotalvalueoftheprojectsfundedthepreviousperiod.Accordingly,thelawofmotionofaggregatenetworthisgivenbyWt=[(RZ;t�Rt�1)Jt�1St�1+Rt�1Wt�1]+(1�)Jt�1St�1(35)Notethatthesourceof uctuationsinaggregatenetworthofthenancialintermedia-tionsectoraremovementsinreturnRZ;t,whichasdiscussedearlierarisefrommovementsinthepricesvtandJt.InwhatfollowsIdescribetheevolutionoftheaggregatestockofprojectsfornewvarieties.Atthebeginningofperiodt,atotalnumberofpotentialrmsZtexistintheeconomy.Eachpointin[0;Zt]representsaprojectforadierentintermediate.Thepointsbetween0andAtcorrespondtoalreadysuccessfulnewintermediates,withAtZt.Inperiodt,theentrepreneurialsectorintroducesameasureZN;tofnewpotentialrms.Atthesametime,afraction1�Zofunsuccessfulrmsexiteachperiod.Thus,theaggregatenumberofpotentialrmsZtevolvesasfollows:Zt+1=Z(Zt+ZN;t)(36)InperiodtthepointsbetweenAtandZt+ZN;tcorrespondtoprojects\inprocess",i.e.projectsthattheentrepreneurialsectoriscurrentlyattemptingtoturnintosuccessfulrms.Fractionoftheseprojectswillbecomesuccessfulduringperiodt.Also,onlyfractionAofrmsoperatinginperiodtsurviveintot+1.Therefore,thetotalnumberofvarietiesofintermediates,At,evolvesasfollows:At+1=[Z(Zt+ZN;t)�At]+AAt(37)wheretheterminbracketsisthemeasureofpotentialrmsthathavenotyetbeensuccessful,accountingforthefactthatonlyfractionZofpotentialrmssurviveeachperiod.RecallthatStreferstotheaggregatenumberofprojectsnancedbybanks.Inequilibrium,wemusthaveSt=Z(Zt+ZN;t)�At(38)Thatis,thetotalnumberofprojectsnancedbythenancialintermediationsectormustbeequaltothetotalnumberofprojectsthatentrepreneursarecurrentlyholdingandtryingtodevelop.20 TheseconsiderationsclarifyhownancialfactorsmayaecttheevolutionofTFP.Whennetworthislow,throughequation(34)theaggregatenumberofprojectsthattheintermediationsectorcannance,St,isreduced.Thismakesdemandfornewen-trantsZN;tlower,asequation(38)suggests.Withasmallernumberofproductsbeingattempted,thegrowthrateofTFPwilldecline,asequation(37)indicates.3.3.2TheFrictionlessBenchmarkAsemphasizedearlier,withfrictionlessmarketsthereisperfectarbitrage,sothatexcessreturnstmustbeequaltozero.Itfollowsfrom(25)-(27)and(33)thatEt(t;t+1RZ;t+1)=Et(t;t+1)Rt=1,orJt=Etft;t+1Z[vt+1+(1�)Jt+1]g(39)Thevalueofentrepreneurequity,Jt,isgivenbytheoptionvalueofobtainingasuc-cessfulnewintermediatethefollowingperiod,valuedvt+1{thishappenswithprobability.Withnancialfrictionsandconstrainedbanks,wewillhaveJtEtft;t+1Z[vt+1+(1�)Jt+1]g(40)Thegapbetweentheleftandrighthandsideof(40)widenswheneverbanks'-nancialconstraintsaretighter,whichhappensintimesinwhichthenetworthoftheintermediationsectorislow.Thisimpliesthattherateofnewrmcreationfallsbelowitsfrictionlesslevel.TheimperfectioninnancialmarketsalsoimpliesthatthegrowthrateofTFP,andthereforeofoutput,alongthebalancedgrowthpathisbelowitsvalueinamodelwithoutnancialfrictions.243.4FinalOutputandIntermediatesProducersThenalgoodisproducedinacompetitivesectorwhichaggregatesacontinuumofmeasureAtofintermediates:Yt=ZAt0Yt(s)#�1 #ds# #�1(41)Giventheaggregatorabove,demandforeachintermediatesbythenalgoodsectoris 24SeeLevine(1997,2005)forsurveysofevidencesuggestingthatnancialdevelopmenthasapositiveimpactonlong-runTFPandoutputgrowth.21 Yt(s)=Pt(s) Pt�#Yt(42)wherethepricelevelPtisdenedasPt=ZAt0Pt(s)1�#ds1 1�#(43)Equation(42)givesthedemandfacingeachintermediategoodproducers.Inter-mediatesareproducedusingastandardCobb-Douglastechnologywithcapitalservicesut(s)Kt(s)andlaborLt(s)asinputs:Yt(s)=[ut(s)Kt(s)]Lt(s)1�(44)Intermediategoodsrmsfaceaworkingcapitalrequirementwhichforcesthemtoholdanamountofnon-interest-bearingassetsthatisnosmallerthanamultipleWofthequarterlywagebill:t(s)WWtLt(s)W0wheret(s)denotestheamountofworkingcapitalheldbyrmsinperiodt.AsshowninUribeandYue(2006)andMendozaandYue(2012),thisformulationimpliesthattheeectivecostoflaborbecomesh1+WRt�1 RtiWt,andthereforeanincreaseintheinterestratereducesthedemandoflaborbyintermediatesrms.Theobjectiveofintermediatesproducersistomaximizeprots,includingthevalueoftheremainingpartofcapitaltheyrentfromhouseholds.Firmsfaceareplacementpriceofdepreciatedcapitalequaltounity.25Thus,theirobjectiveistosolvet=maxPt(s);Yt(s);ut(s);Kt(s);Lt(s)Pt(s)Yt(s)+PK;tKt(s)�(ut(s))Kt(s)�1+WRt�1 RtWtLt(s)�RktKt(s)Subjectto(42)and(44).Solvingtherm'sproblemyieldsthefollowingequations:1+WRt�1 RtWt=(1�)Yt Lt(45) 25Asmadeclearbelow,adjustmentcostsareonnetratherthangrossinvestment,sothatreplacingworn-outcapitaldoesnotinvolveadjustmentcosts.Thisformulationmakesthecapitalutilizationdecisionindependentofthepriceofcapital.22 Rkt=Yt Kt+PK;t�(ut)(46)Yt ut=0(ut)Kt(47)Eachintermediatesproducersetsitspricetoaconstantmarkupovermarginalcost{theratioofpricetomarginalcostequals# #�1.Perperiodprotsofintermediatesproducers,t,canthenbeshowntobeequaltot=1 #Yt At(48)Finally,onecancombine(41)withtherst-orderconditionsforintermediatespro-ducersandwithequilibriuminfactormarketstoobtainanexpressionfornaloutput:Yt=A1 #�1t(utKt)L1�t(49)3.5CapitalProducersAttheendofperiodt,capitalproducingrmsrepairdepreciatedcapitalandproducenewcapital.ForsimplicityIassumethatnonancialfrictionsapplytotheproductionandpurchaseofcapitalgoods,inordertofocusontheroleoffrictionsonthecreationofnewrms.However,itwouldbestraightforwardtoextendthemodeltoallowforfrictionsininvestmentofexistingrmsaswell,alongthelinesofGertlerandKaradi(2011)andothers.26AsinandGertleret.al.(2007),repairofoldcapitalisnotsubjecttoadjustmentcosts,buttherearestockadjustmentcostsassociatedwiththeproductionofnewcapital.LetIntbenetinvestment,theamountofinvestmentusedforconstructionofnewcapitalgoods:Int=It�(ut)Kt(50)Toproducenewcapital,capitalproducerscombinenaloutputwithexistingcapitalviatheconstantreturnstoscaletechnology(Int=Kt)Kt,where(
)isincreasingand 26Toelaborateonthis,onecouldfollowGertlerandKaradi(2011)andassumethatrmsneedtoobtainloansfrombankstonancetheirpurchasesofphysicalcapital.Inthisgeneralizedmodel,bankswouldthenmaketwotypesofloans:loanstoexistingrmstoinvest,andloanstoentrepreneurstocreatenewrms.Onecouldpostulatedierentintensitiesofthenancialfrictionforeachtypeofactivity,whichcouldbecapturedbyassumingthatthefractionsdivertablearedierentforeachofthetwotypesofbanks'assets.23 concaveandsatises(In=K)=0and0(In=K)=1,whereIn=Kisthenetinvestmenttocapitalratioalongthebalancedgrowthpath.Theeconomy-widecapitalstockevolvesaccordingto27Kt+1=Kt+Int KtKt(51)AsinGertleret.al.(2007),Iassumethatcapitalproducingrmsmakeproduc-tionplansoneperiodinadvance,withtheobjectiveofcapturingthedelayedresponseofinvestmentobservedinthedata.Accordingly,theoptimalityconditionforcapitalproducersisEt�1(PK;t)=Et�1(0Int Kt�1)(52)3.6MarketClearingTheeconomyusesoutputandinternationalborrowingtonanceconsumption,invest-mentinphysicalcapital,andinvestmentinnewtechnology.Theresultingmarketclearingconditionis1 RtBt�Bt�1+Yt=Ct+It+Nt(53)Btiseconomywideforeignindebtedness,equaltothesumofaggregatefamilyandentrepreneurialdebt(Bt=DFt+Dt).Equation(53)canbederivedbycombiningfamilyandentrepreneurbudgetconstraintswithequilibriumconditions.Thiscompletesthedescriptionofthemodel.4ModelAnalysisThissectionpresentsnumericalresultsfromadynamicsimulationofthemodel,meanttocaptureinaroughwaythetypeofcrisesanalyzedempiricallyinSection2.Thegoalistoillustratehowthenovelmechanismintroducedinthepaper,namelynanciallyconstrainedrmcreation,iscrucialforthemodeltobeabletoproducepersistentdeclinesinoutput,productivityandemploymentthatarequantitativelyclosetothoseidentiedinthedata.28 27Giventheassumptionson(
),toarstordertheevolutionofcapitalalongthebalancedgrowthpathistheusualKt+1=[1�(ut)]Kt+It.28AppendixCcontainssomeadditionalmodelresultsregardingtheeectsofnon-nancialshocks.24 Table1:ParameterValues SymbolValueDescription Conventional0:99Discountfactor1Riskaversion1InverseFrischelasticityh0:25HabitsUribeandYue(2006) 0:01Parameteronlabordisutilityterm0:025Capitaldepreciation1=3Capitalshare00=00:15ElasticityofdepreciationtoutilizationCominet.al.(2009)#2:5DemandelasticityforintermediatesCominandGertler(2006)00(In=K)0:2ElasticityofPktoIn=KGertleret.al.(2007)W0:35Workingcapitalrequirement0:00001ElasticityofinterestratetoforeigndebtB=Y0:2ForeigndebttooutputEntrepreneurs0:125Adoptionprob.2yearssuccesslag{PakesandSchankerman(1984)1�A0:025ExitrateoldBilbiieet.al.(2012)1�Z0:05ExitrateyoungHaltiwangeret.al.(2012)0:125Finaloutputinentrepreneurs'prod.fun.10%ofoutputusedbyentrepreneursalongBGP LS0.033Skilledlaborsupply2%TFPgrowthrate{Young(1995)Banks0:98Survivalrate12yearshorizon0:45Fractiondivertable1%annualspread0:0075Transferrateleverage=44.1ParameterValuesTable1liststhechoiceofparametervalues.Overalltherearetwenty-twoparameters,fourteenofwhichrelatetopreferencesandtechnology.Oftheremainingeight,verelatetotheentrepreneurialsector:thesuccessprobability(),theexitrates(1�A,1�Z),theweightofmaterialsinentrepreneurs'productionfunction()andtheaggregatesupplyofskilledlabor(LS).Theremainingthreeparametersrelatetonancialintermediaries.Theyincludethesurvivalrateofbanks(),thesteadystatedivertablefractionofassets(),andthetransferratetonewbankers().Ichooserelativelyconventionalvaluesforthepreferenceandtechnologyparameters.Thediscountfactorissetat0.99,andriskaversionissetatunity.IsettheinverseFrischelasticityoflaborsupply,,equaltoone.Isetthehabitsparameterhat0.25,similartothevalueestimatedbyUribeandYue(2006).Theparameter governingtheimpactofthetotalnumberofvarietiesAtonthelabordisutilityterm�tissetat0.01,implyingthataggregatetechnologyaectsthedisutilityofworkonlyovertheverylongrun.Turningtotechnologyparameters,Isetthecapitalshareto1=3,andthequarterlydepreciationrateofphysicalcapital,,to2.5%.Capitalutilizationalongthebalancedgrowthpathisnormalizedto1,andtheelasticityofmarginaldepreciationwithrespecttotheutilizationrate(00=0),issetat0.15,asinJaimovichandRebelo(2009)andComin,GertlerandSantacreu(2009).Isettheelasticityofthepriceofcapitalwithrespectto25 theinvestment-capitalratioat0.2,asinGertleret.al.(2007)andBernankeet.al.(1999).Ichoosetheparameterontheintermediategoodsaggregator,#,sothatoutputisproportionaltoTFPalongthebalancedgrowthpath,whichbyexaminingequation(49)amountstoimposing(1�)(#�1)=1.Thisrestrictionmakesprotsperperiod,t,astationaryvariable,andsimpliessomewhatthecharacterizationofthebalancedgrowthpath.Given=1=3,theresultingvalueforthemarkupis#=(#�1)=1:66,closetothevalueof1.6chosenbyCominandGertler(2006).Regardingtheworkingcapitalconstraint,IsetW=0:35,implyingthatrmsneedtopaylessthanamonth'sworthofthewagebillinadvance.29ThedebttoGDPratioalongthebalancedgrowthpathissetat0.2,andtheelasticityoftheinterestratewithrespecttothedebt-outputratioequals0.00001{thelatterensuresthatthedynamicsofthemodelarevirtuallyunaectedbythedebt-elasticinterestrateathighandmediumfrequencies,whilestillmakingtheforeignassetpositionreverttotrendoverthelongrun.Turningtotheparametersrelatingtotheentrepreneurialsector,Isettheprobabilityofsuccessfullyobtaininganewvariety,,to0.125,implyinganaveragesuccesslag(1 )of8quartersor2years.ThisisbasedonevidenceonmeanR&DgestationlagsreportedbyPakesandSchankerman(1984),denedastheaveragetimebetweentheinitialoutlayofresourcesandthebeginningoftheassociatedrevenuestream.Theexitrateformaturerms(1�A)issetto10percentannually,followingBilbiieet.al.(2012),andthecorrespondingnumberforyoungrms(1�Z)issettotwicethatnumber,consistentwiththeevidenceinHaltiwangeret.al.(2012)ofsubstantiallyhigherrmexitbyyoungerrms.Theweightofnaloutputinentrepreneurs'productionfunction,,issetto0.125,implyingthatalongthebalancedgrowthpath10percentofoutputisusedbytheentrepreneurialsector.ThisnumberrepresentsaroughestimateofexpendituresonrmcreationasafractionofGDP.30Finally,theinelasticsupplyofskilledlabor, LS,issettodeliveragrowthrateofTFPalongthebalancedgrowthpathof2percent,similartothenumbersreportedbyYoung(1995).Thechoiceofthenancialsectorparametersismeanttobesuggestive.SimilartoGertlerandKiyotaki(2010),Isettheentrepreneursurvivalrate=0:98,implyinganexpectedhorizonofbankersofabouttwelveyears.Tocalibratethefractionofresources 29Whilehighervaluesofthisparameterarefrequentlyusedintheliterature,MendozaandYue(2012)arguethatitisdesirabletosetthisparameteratarelativelylowvalue,sinceempiricalestimatessuggestthatworkingcapitalisasmallfractionofGDP.Aworkingcapitalrequirementof0.35,togetherwithawagebilloftwothirdsofGDP,impliesaratioofworkingcapitaltoGDPofaround23%.30MacGrattanandPrescott(2010),forexample,estimateinvestmentintechnologycapitalatabout6percentofGNPintheUS.Thisislikelyalowerboundontotalentrycosts,asnotallrmcreationiscapturedbyR&Ddata.26 thatbankerscandivertinsteadystate,,andthetransfertonewbornbankers,,Itargettwofeaturesofthebalancedgrowthpathofthemodeleconomy:abankleverageratio(assetstonetworth)offour,andanexcessreturnE(RZ)�Requaltoonehundredbasispointsannually.Thetargetfortheleverageratiore ectsarelativelyconservativeattempttocaptureanaverageleverageratioofthenancialintermediationsector.Forexample,mosthousingnanceistypicallyintermediatedbynancialinstitutionswithleverageratiosofatleast10onaverageinthecaseofcommercialbanks,andsubstantiallyhigherforinvestmentbanks.31Ontheotherhand,leverageratiosareclearlysmallerinothersectorsoftheeconomy.ThetargetforthespreadalongthebalancedgrowthpathisbasedonevidenceonBBBindustrialcorporatespreadsintheUSandEuropepriortothecrisis.Thesetargetsimplysettingthedivertiblefractionto0.45,andthetransferrateto0.0075.4.2CrisisExperimentInowturntothecrisisexperiment.Theinitiatingdisturbanceisthecombinedimpactoftwoshocks:anincreaseinthecountryinterestrateRt,andanincreaseinthevariablegoverningtheagencyfriction,t.Iconsidera500basispointincreaseintheinterestratethatpersistsasarst-orderautoregressiveprocesswitha0.88coecient.ThesemagnitudesareclosetotheevidenceforthecrisisinSouthKoreain1997,asshownbyGertleret.al.(2007).32Atthesametime,trisesbyftypercent,andtheincreasepersistsasarstorderautoregressiveprocesswithcoecient0.95(thetimepathsforRtandtareshowninFigure5).Theideaistocaptureasituationinwhichnotonlythereisacapitalout ow,ascapturedbyanincreaseinRt,butalsoadisruptionindomesticnancialmarkets,correspondinginthemodeltotheincreaseint.Itisbesttothinkoftheshockasarareevent.Figure4showsthemainresultofthepaper,byplottingadynamicsimulationforthemodeleconomyalongwithitsempiricalcounterpart.Itshowsthebehaviorofout-put,laborproductivityandemploymentfollowingtheshockstoRtandtotheagencyparametert,relativetothebalancedgrowthpathoftheeconomy.Inthebaselinemodel(bluesolidline),thereisalargepermanentcomponenttothedeclineinoutput,whosemagnitudeisclosetothedata.Asanexample,sixyearsaftertheshockoutputisde-pressedbyabout11percentrelativetotheunshockedpathoftheeconomy,verycloseto 31SeeKalemli-Ozcan,SorensenandYesiltas(2012)forcross-countryevidenceonbankleverageratios.32Unanticipatedincreasesincountryinterestrates,re ectingsuddenstopsincapitalin ows,areconsideredanimportantforcebehindrecentnancialcrises,andbehindemergingmarketbusinesscyclesmoregenerally{seeforexampleCalvo(1998),NeumeyerandPerri(2005)orUribeandYue(2006).27 theempiricalvalue.Thisisthecaseeventhoughtheexogenousdrivingforces,Rtandt,havealmostcompletelyreturnedtotheirsteadystatevalues.Asmadeclearinthefollowingsection,behindthisresultisthebehaviorofrmcreationfollowingthecrisis,whichimpliesthatthenancialcrisisshockhasapermanenteectonaggregateTFP.Thisisthemaindrivingforcebehindthebehavioroflaborproductivitydisplayedinthegure.Atthesametime,asshowninthelastpanelofFigure4,thepermanentdeclineinproductivityleadstoadeclineinlabordemandbyproducersofintermediates.Asaresult,employmentalsofallspersistentlyrelativetothebalancedgrowthpathoftheeconomy.Thus,themodelisalsoabletoaccountfortheevidenceprovidedinSection2thatemploymentremainspersistentlydepressedfollowingnancialcrises.Overall,thebottomlinefromFigure4isthatthemechanismsintroducedinthemodelhavepotentialforquantitativelyaccountingforthemedium-runbehaviorofoutput,laborproductivityandemploymentfollowingnancialcrises.33Thenancialintermediationsectorplaysanimportantroleinaccountingforthemodel'sbehavior.Withoutnancialmarketfrictions(greendashedline),theresponsesofallthreevariablesdiersignicantlyfromtheirempiricalcounterparts:forexample,thedeclineinoutputsixyearsaftertheshockhitsisapproximately6percentinthecasewithoutnancialfrictions,comparedtothe11percentinthebaselinecaseandinthedata.Thedierenceisdriventoalargeextentbytheendogenousamplicationimpliedtheinteractionbetweenthenancialintermediationsectorandtheprocessofrmcreation(describedindetailinthefollowingsection).Thiscanbeseenbycomparingthecasewithoutnancialfrictionsandthecasewithnancialfrictionsbutwithouttheshocktot(lightbluedash-dottedline).Theincreaseintthencontributesanextradeclineinallthreevariables{inthecaseofoutputitscontributionisabout2percentagepointsinthemediumrun.Finally,Figure4alsoreportstheresponseinamodelinwhichtheendogenousgrowthchannelisinactive(greydottedline){whatisthenleftisarelativelystandardRBCmodelofasmallopeneconomy,subjectedtoaninterestrateshock.Asmadeclearbythegure,thebehaviorofthemodelinthiscaseisveryfarfromthedata,duetotheabsenceofendogenousmovementsinTFP.Howdoesthemodel'stransmissionmechanismoperate?Figure6documentsthebehaviorofthenancialandentrepreneurialsideofthemodelfollowingthecrisisshock.Thedisturbanceinducesalargedeclineinthevalueofanewvariety,vt,andinthe 33AsFigure4shows,themodelunderstatestheshort-rundeclinesfollowingthecrisis.Thesearelikelyrelatedtophenomenalikenominalpriceorwagerigiditieswhichforsimplicityhavebeenignoredinthemodel,focusinginsteadonthenovelaspectsregardingpersistence.Itwouldbestraightforwardtoextendthemodelalongthesedimensions.28 Figure4:Crisisexperiment:responsesofoutput,laborproductivityandemployment.Timemeasuredinyears.Allvariablesinlogdeviationsfromthebalancedgrowthpath.29 0 2 4 6 8 10 -0.14 -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 OutputYears 0 2 4 6 8 10 -0.14 -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 Labor ProductivityYears 0 2 4 6 8 10 -0.14 -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 EmploymentYears Baseline, R and q Shocks Baseline, R Shock Only No Financial Frictions Exogenous Growth Data Data and 90% Confidence Bands Figure5:ShockpathsforinterestrateR(logdeviation)andfractiondivertable(level)incrisisexperiment.Timemeasuredinyears.30 0 2 4 6 8 10 0 0.02 0.04 0.06 0.08 0.1 R (shock) 0 2 4 6 8 10 0 0.2 0.4 0.6 0.8 1 Fraction divertable, q (level) qt steady state q priceofentrepreneurequity,Jt(toppanels),asthestreamoffutureprotspernewintermediategoodisdiscountedmoreheavily.Thishastheeectofgeneratingalargedropinthenetworthoftheintermediationsector,asequation(35)indicates.Noticethattheinterestrateshockleadsthepriceofentrepreneurequity,Jt,tofallsubstantiallymoreinthebaselinemodelwithfrictions(lightbluedash-dottedline)thaninthemodelwithoutnancialfrictions(greendashed){aboutsixtypercentmoreonimpact.Thisisatthecoreoftheamplicationmechanisminthemodel:asbanks'constraintstighten(asre ectedintheincreaseinthemultiplierontheincentiveconstraint),theyareforcedtocutbackonprojectfundingtoalargerextentthanwhatwouldhappenwithfrictionlessnancialmarkets.Alongtheway,thereisan\adversefeedback"eectbetweenbanknetworthandthevalueofentrepreneurequityJt:astheformerfalls,bank'constraintstighten,forcingadeclineinthecreditavailableforprojectsindevelopment.ThedecreaseindemandfornewprojectsleadstofurtherreductionsinvalueJt,startinganewroundofdeclinesinbanknetworth.Theendresultisalargedeclineintheaggregatenumberofnewprojectsstarted,ZN;t,asmadeclearbythelastpanel.Thetighteningofnancialconstraintsisalsore ectedintheriseinexcessreturnsEt(RZ;t+1)�Rt,whichre ectsthatprotableopportunitiesintheentrepreneurialsectorgounexploitedduetoanintensicationofnancialmarketfrictions.Theriseinthespreadrepresentsawideningofthedeparturefromperfectarbitrage,asexempliedbyequation(40).Itisaccompaniedbyasubstantialreductioninthe owofcredittobanks,asindicatedbytherightpanelinthethirdrow.ThebluesolidlineshowstheeectsoftheRtandtshockscombined.Relativetothecasewiththeinterestrateshockonly,theincreaseintfurtherrestrictsthe owofcredittobanks(rightpanelinthethirdrow),astheyareabletoborrowlessperunitofnetworth.Thisinitiatesanotherroundofcutsinprojectfunding,againampliedbytheadversefeedbackchanneldescribedabove.Thedeclineinthenumberofprojectsfundedbytheentrepreneurialsectordirectlytranslatesintoadeclineintherateofnewlysuccessfulrms.AsshowninFigure7,itfollowsthatthereisasubstantialslowdowninthegrowthrateofTFP,leadingtoapermanentdropinthelevelofthisvariablerelativetothebalancedgrowthpath.Further,themagnitudeofthemedium-rundeclineissubstantiallylargerduetonancialfactors{inthebaselinemodel,thelevelofTFPaftersixyearsfallsmorethan6percentwithbothshocksandalmost5percentwithonlytheinterestrateshock,comparedtoonly3.5percentinthemodelwithoutnancialfrictions.Thus,thenancialfrictionplaysaquantitativelysignicantroleinhelpingthemodelgenerateapersistentdeclineinTFPfollowingacrisis.SuchmovementsinTFPareasalientfeatureofnancial31 Figure6:Crisisexperiment:responsesofgrowthandnancialintermediationvariables.Timemeasuredinyears.Allvariablesinlogdeviationsfromthebalancedgrowthpathexceptnetworth,expressedinleveldeviationasfractionofvalueinthebalancedgrowthpath.32 0 2 4 6 8 10 -0.3 -0.2 -0.1 0 Successful Firm Value, v 0 2 4 6 8 10 -0.6 -0.4 -0.2 0 New Firm Value, J Baseline, R and q Shocks Baseline, R Shock Only No Financial Frictions 0 2 4 6 8 10 -1 -0.5 0 0.5 Aggregate Net Worth, W 0 2 4 6 8 10 -0.05 0 0.05 0.1 0.15 0.2 E(RZ) - R 0 2 4 6 8 10 0 0.1 0.2 0.3 0.4 Multiplier on Incentive Constraint 0 2 4 6 8 10 -0.4 -0.3 -0.2 -0.1 0 Aggregate bank debt, D 0 2 4 6 8 10 -0.25 -0.2 -0.15 -0.1 -0.05 0 Aggregate New Projects, ZN Figure7:Crisisexperiment:responsesofgrowthrateandlevelofTFP.Timemeasuredinyears.Variablesinlogdeviationsfromthebalancedgrowthpath.crises,asillustratedforexampleinthecaseofSouthKoreareviewedearlier,inwhichTFPremainedpersistentlydepressedrelativetotrendbyabout6%.InastandardRBCeconomy,ofcourse,TFPgrowthwouldbeunaectedbythecrisisshock.Finally,Figure8plotstheresponseofasetofstandardmacroeconomicvariables.Overall,themodeldoesarelativelygoodjobofcapturingquantitativelythemacroeco-nomiceectsofthetypicalemergingmarketnancialcrisis.Inparticular,theresponsesofthevariablesdisplayedinFigure8arereasonablyclosetotheevidencefortheKorean1997crisis,asdocumentedforexampleinGertleret.al.(2007).Themechanismsin-troducedinthispapercontributetoexplainingthepersistenceofthedeclineinoutputandothervariablesfollowingtheseepisodes.AnalpointtohighlightfromFigure8isthesubstantialamplicationduetothenancialfrictionofaggregateconsumption,avariablewhichiswellknowntodisplayhighervolatilityrelativetoGDPinemerging33 0 2 4 6 8 10 -5 -4 -3 -2 -1 0x 10-3 Growth Rate of TFP 0 2 4 6 8 10 -0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0 TFP Baseline, R and q Shocks Baseline, R Shock Only No Financial Frictions marketswhencomparedtomoredevelopedeconomies,andalsooftheratioofnetexportstoGDP.5ConclusionThispaperhassoughttoexplainthehighlypersistenteectsofnancialcrises.Ithasarguedthatthephenomenonofslowrecoveriesfromnancialcrisescanbeanaturalconsequenceofanadverseshockinanenvironmentinwhichproductivitygrowthisen-dogenousthroughthecreationofnewrms.Further,ithasshownhowdomesticnancialmarketdisruptionscanworktoamplifythesedeclines.Thankstothesemechanisms,themodeldevelopedhereisabletoquantitativelyreproducethepersistentdeclinesinoutput,laborproductivityandemploymentfollowingnancialcrisesidentiedfromthedata.Theevidencepresentedinthispaperhasbeenbasedontheexperienceofemergingmarketeconomies,ashavebeensomeofthemodelingchoicesmade(forexample,theinterestrateshockusedtomotivateacrisis,orthesmallopeneconomyassumption).Thereasonisthatitisinthesecountrieswheremostnancialcriseshaveoccurredoverthepastdecades.Therecentwaveofnancialcrisesinadvancedeconomies,however,alsoappearstodisplayasubstantialdegreeofpersistence,andmanyhavesuggestedaslowdownintheunderlyingrateofproductivitygrowthasapossibleexplanation.34Withminoradaptation,themechanismsintroducedinthispapercouldbeusedtoaddressthecaseofadvancedeconomiesaswell.Apotentiallyinterestingapplicationoftheframeworkpresentedinthispaperwouldbeanevaluationofthewelfaregainsofgovernmentinterventioninmitigatinganancialcrisis.GertlerandKaradi(2011)andGertler,KiyotakiandQueralto(2012),forexample,analyzedierentgovernmentnancialpoliciesinthecontextoftherecentnancialcrisisintheUS,ndingimportantbenetsofgovernmentintervention.Theendogenouspro-ductivitygrowthmechanismintroducedinthispaperwouldlikelyaectwhatisatstakewhenconsideringinterventionduringanancialmeltdown,andthereforeitcouldhaveasubstantialimpactonthewelfaregainsofgovernmentpoliciesdirectedatamelioratingtheimpactofacrisis. 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AppendixADataDataonrealoutputandemployment(innumberofpersons)areobtainedfromtheTotalEconomyDatabase.35ThedataonemploymentusedisbroadlyconsistentwiththeemploymentdatasetinNeumeyerandPerri(2005)forthesetofcountriesusedinthatanalysis.SystemicbankingcrisisepisodedatesarefromLaevenandValencia(2012).Thelistofcountriesandepisodesusedintheanalysisisthefollowing(episodestart-ingdateinparenthesis):Indonesia(1997),Malaysia(1997),Korea(1997),Thailand(1983,1997),Philippines(1983,1997),Argentina(1980,1989,1995,2001),Brazil(1990,1994),Chile(1976,1981),Colombia(1982,1998),Mexico(1981,1994),Peru(1983),Is-rael(1977),Poland(1990),Turkey(1982,2000),Hungary(1991,2008),CzechRepublic(1996),SlovakRepublic(1998).BCompleteSetofEquilibriumConditionsB.1HouseholdsandFirmsYt=A1 #�1t(utKt)L1�t(B.1)UC;t=uC;t�hEt(uC;t+1)(B.2)uC;t=Ct�hCt�1��t1 1+L1+t�(B.3)uC;t�tLt UC;t=1 1+WRt�1 Rt(1�)Yt Lt(B.4)t;t+1=UC;t+1 UC;t(B.5)1=Et(t;t+1)Rt(B.6)1=Et t;t+1Yt+1 Kt+1+PK;t+1�(ut+1) PK;t!(B.7) 35http://www.conference-board.org/data/economydatabase/40 Et�1(PK;t)=Et�1(0Int Kt�1)(B.8)Int=It�(ut)Kt(B.9)Kt+1=Kt+Int KtKt(B.10)Yt ut=0(ut)Kt(B.11)1 RtBt�Bt�1+Yt=Ct+It+Nt(B.12)Rt=r+ert+ eBt�B Yt�1(B.13)B.2EntrepreneursandFinancialIntermediariest=1 #Yt At(B.14)vt=t+AEt(t;t+1vt+1)(B.15)RZ;t=Zvt+(1�)Jt Jt�1(B.16)Wt=[(RZ;t�Rt�1)Jt�1St�1+Rt�1Wt�1]+(1�)Jt�1St�1(B.17)Jt[Z(Zt+ZN;t)�At]=tWt(B.18) t=1�+(t+tt)(B.19)t=Et[t;t+1 t+1(RZ;t+1�Rt)](B.20)t=Et(t;t+1 t+1)Rt(B.21)t=t �t(B.22)41 At+1=[Z(Zt+ZN;t)�At]+AAt(B.23)Zt+1=Z(Zt+ZN;t)(B.24)Jt=1 1 LS1� ZN;t At1� (B.25)Nt=ZN;tJt(B.26)Inthefrictionlessbenchmark,equations(B.17)-(B.21)becomeirrelevant,andinsteadper-fectarbitrageholds:Jt=Etft;t+1Z[vt+1+(1�)Jt+1]g(B.27)Themodelissolvedbyrstappropriatelydetrendingthevariablesthatexhibitlong-rungrowth,inordertoobtainastationarysystem.Thesteadystateofthatsystemcharacterizesthebalancedgrowthpathoftheeconomy.Dynamicsareobtainedbycom-putingaloglinearapproximationaroundthebalancedgrowthpath.CEectsofNon-nancialShocksHereIanalyzethebehaviorofthemodeleconomyfollowingtwotypesofnon-nancialshocksthathavebeenhighlightedintheliteratureasimportantsourcesofbusinesscycle uctuations:anexogenousTFPshock,andawagemarkupshock.Tointroducetheformer,Imodifytheproductionfunctionofintermediategoodsrmsasfollows:Yt(s)= At[ut(s)Kt(s)]Lt(s)1�(C.1)Above, AtisanexogenousaggregateTFPshock.Tointroducethewagemarkupshock,thelaborsupplyequationismodiedaccordingtothefollowing:Wt=WtuC;t�tLt UC;t(C.2)Wtisamarkupofthewageoverthehousehold'smarginaldisutilityofwork.Severalauthorshavearguedthatcountercyclicalmovementsinthewagemarkupareanimpor-42 tantsourceofbusiness uctuations,36possiblybycapturinginareduced-formwaytheeectsofnominalpriceandwagerigiditiesorlabormarketfrictions.Figures9and10reporttheeectsofa5%declineinexogenousTFPanda5%increaseinthewagemarkup,respectively.BothshockspersistasanAR(1)witha0.95coecient.ThekeypointtonoteisthatbothshocksinduceonlymodestdeclinesintheendogenouscomponentofTFP,andthatthedegreeofamplicationthroughthecreditmarketimperfectionisalsorelativelysmall.Thereasonisthatunlikenancialshocks,thesetwotypesofshocksinducemodestmovementsintheassetpricesvtandJt.Asaconsequence,boththefrictionlesseectonrmcreationissmall(sincethemovementinvtisrelativelysmall)andalsothedegreeofamplicationduetonancialfrictionsissmall,sincetherelativelymodestmovementsinassetpricesleadtoonlymild uctuationsinbanks'networth.Further,inthecaseofwagemarkupshocks,laborproductivitydoesnotdecline{infactitslightlyincreasesinitiallyduetothesharpdropinemployment.Astheguresillustrate,thesetypesofdisturbancesarefollowedbyarecovery,whichisdrivenbytheunwindingoftheshock.Thus,thebottomlinefromFigures9and10isthatthemodelisalsoconsistentwiththeevidencethatespeciallydeepandpersistentoutputlossesareaphenomenonespeciallyassociatedwithrecessionsinvolvingnancialcrises,asReinhartandRogo(2009)andothershavenoted. 36SeeHall(1997),Gal,GertlerandLopez-Salido(2007)andChari,KehoeandMcGrattan(2007).43 Figure9:ResponsestoexogenousTFPshock.Timemeasuredinyears.Allvariablesinlogdeviationsfromthebalancedgrowthpath.44 2 4 6 8 10 -0.06 -0.04 -0.02 0 Exogenous TFP shock 2 4 6 8 10 -1 -0.5 0x 10-3 gA 0 2 4 6 8 10 -0.4 -0.3 -0.2 -0.1 0 Aggregate net worth, W 0 2 4 6 8 10 0 2 4 6 8x 10-3 E(RZ) - R 2 4 6 8 10 -0.04 -0.03 -0.02 -0.01 0 A 2 4 6 8 10 -0.1 -0.05 0 OutputYears 2 4 6 8 10 -0.1 -0.05 0 Labor ProductivityYears 2 4 6 8 10 -0.1 -0.05 0 EmploymentYears Baseline No Financial Frictions Exogenous Growth Figure10:Responsestowagemarkupshock.Timemeasuredinyears.Allvariablesinlogdeviationsfromthebalancedgrowthpath.45 2 4 6 8 10 0 0.02 0.04 0.06 Wage markup shock 2 4 6 8 10 -5 -4 -3 -2 -1 0x 10-4 gA 0 2 4 6 8 10 -0.1 -0.08 -0.06 -0.04 -0.02 Aggregate net worth, W 0 2 4 6 8 10 0 1 2 3x 10-3 E(RZ) - R 2 4 6 8 10 -0.03 -0.02 -0.01 0 A 2 4 6 8 10 -0.06 -0.04 -0.02 0 OutputYears 2 4 6 8 10 -0.06 -0.04 -0.02 0 Labor ProductivityYears 2 4 6 8 10 -0.06 -0.04 -0.02 0 EmploymentYears Baseline No Financial Frictions Exogenous Growth