Financial markets and stochastic growth

InstituteforEmpiricalResearchinEconomicsUniversityofZurichWorkingPaperSeriesISSN1424-0459WorkingPaperNo.66FinancialMarketsandStochasticGrowthLeonardJ.MirmanandKlausReinerSchenk-HoppéNovember2000FinancialMarketsandStochasticGrowthLeonardJ.MirmanDepartmentofEconomicsUniversityofVirginia,U.S.A.KlausReinerSchenk–Hopp´eInstituteforEmpiricalResearchinEconomicsUniversityofZurich,SwitzerlandNovember21,2000AbstractInthispaper,westudytheeffectoffinancialmarketsontheinvest-mentofatwo-goodtwo-countryeconomywithstochasticproductioninadynamicframework.Eachcountryproducesandinvestsonlyonegoodand,therefore,makesdecisionsasacentralplannerinanoptimalgrowthmodel.Tradebetweenconsumersofbothcountries,however,takesplaceoncompetitive(spotorfinancial)markets.Wecomparetheinvestment-consumptiondecisionsofboth‘market’mod-elswiththebenchmark-caseofanintegratedworld-equilibrium.Inthelog-linearcase,wecanuniquelycharacterizethestate-dependentpreferencesofconsumersthatleadtodynamicallyefficientinvestmentdecisions.Weshowthattheinvestmentdecisionsinboth‘market’modelsare,ingeneral,inefficientascomparedwiththeefficient,orintegratedworldeconomy,case.1IntroductionItisawell-knownfactofeconomictheorythatanArrow-Debreuequilib-riumissimplyareinterpretationoftheWalrasianequilibriumconcepttocontingentcommodities,seeArrow[1],Debreu[5],Radner[8].Usingthese1ideasonecanstudytheallocationofriskinageneralequilibriumframe-work.Indeedinthiscontext,completefinancialmarketswithcontingentclaimsleadtoPareto-optimalallocations.Althoughtherehasbeenmuchliteratureontheeffectofvariousmarketstructuresonassetallocationandtheirwelfareeffectsinanuncertainenvironment,thequestionofcapitalac-cumulationinadynamicgeneralequilibriummodelunderuncertaintyhasnotbeenstudied.Forexample,itisnotknownwhethertheexistenceofcompletefinancialmarkets,whichgeneratePareto-optimalallocationsintheArrow-Debreuframework,generateefficientdynamicsolutions.Althoughananalysisofthisquestioninacompetitiveframeworkremainsopenduetothedifficultiesofstudyinginfinitehorizongeneralequilibriummodels,thisisanaturalquestioninthecontextofanoptimalgrowthmodel.Moreover,sinceinthistypeofmodeltheremustbeseveralgoodsinordertotradeandseveralcountrieseachdecidingontheirownamountofinvestment,anaturalsettingforthisquestionisthetypeofmixedeconomy,studiedbyDattaandMirman[4].Indeed,inthepresentpaperwestudytheeffectoffinancialmarketsontheinvestmentoftheeconomywhentherearetwocountries,twogoodsandtwostatesoftheworld.Inthiscontextweshowthattheinvestmentcannot,ingeneral(inparticularwhenthereexiststate-dependentpreferences),beefficient–eveninthefaceofcompletefinancialmarkets.Theuseofamodelwitheachcountryhavingamixedeconomydependsontwothings.Thefirstisthateachcountryproducesandinvests(orequivalentlydecidesonaggregateconsumptionof)theirowngood,i.e.,makesdecisionsasacentralplannerinanoptimalgrowthmodeland,thesecondis,foreachgood(orcountry)thereisarepresentativeagenttradingbothgoodsinaWalrasiancontext.Theseagents,onefromeachcountry,usetheaggregateconsumptionchoicefromthecentralplannerastheinitialendowmentinthetradingenvironment.ThisuseoftheWalrasianparadigmisanaturalsettinginwhichtousetheArrow-Debreucontingentclaimsframework.ThistypeofmixedeconomymodelwasusedbyDattaandMirmantostudyatradeeconomy.Theirmodeliswithoutuncertaintybutcontainspro-ductionexternalities.ItwasshowntherethattheinefficiencyassociatedwithproductionexternalitiesstudiedinFischerandMirman[6]canbemitigatedifitispossibletointernalizetheproductionexternalitiesbytrade,throughthepreferencesoftherepresentativeagents.Inourmodelinefficienciesarealsogeneratedbuttheseareduetotheuncertainty,nottoproductionex-ternalities,andtheassumptionthattastesarestate-dependent.Methodsof2FischerandMirman[6]areusedtostudytheseproblemsandareusedinthispaperaswell.Inthispaper,asinDattaandMirman[4],weconsidertherelationshipbetweenaintegratedworldeconomy–inwhichthereisonecentralplanner–andtheallocationsgeneratedbyvariousassumptionsonthetypeofmar-kets.Inthecaseofthesedifferentmarkettypes,eachcountrymusthaveacentralplannertodecideonitsownaggregateconsumptionsandthusadifferentialgameisentailed.Thisisthedynamicinvestmentgamebetweenthetwocentralplanners.Indeedwestudytwocasesofmarkets.Thefirstiscompletefinancialmarketsinwhichriskisallocatedefficiently.Thesecondcaseiswhenthereareonlyspotmarkets–sothatingeneralriskisnotal-locatedefficiently.Inbothcases,wefindanindirectutilityfunctionwhichtheplannersusetodeterminetheoptimalaggregateconsumptionfortherepresentativeagentintheircountry.Thisoptimalaggregateconsumptionisusedinturnbytherepresentativeagentasinitialendowmentsintradingwiththerepresentativeagentoftheothercountry.Eachcountry’srepresen-tativeagenttakesthepriceasgiveninthetradingprocess.However,thecentralplannerofeachcountrydoesnottakethepriceasgiven.Werestricttheanalysistoalog-lineareconomysothatthereisa(com-putable)solutiontothedifferentiablegamebetweenthetwocentralplanners.WeshowthatinthecaseofonlyspotmarketsallocationsareonlyPareto-optimalforparticularspecificationsoftheparameterswhileinthecompletefinancialmarketcaseallallocationsderivedf