在喧闹的合理预期经济的信息族聚(1)

JournalofFinancialEconomics9(1981)221-235.North-HollandPublishingCompanyINFORMATIONAGGREGATIONINANOISYRATIONALEXPECTATIONSECONOMYChicago,Chicago,IL60637,USAReceivedJuly1980,finalversionreceivedDecember1980Thispaperanalyzesageneralequilibriummodelofacompetitivesecuritymarketinwhtchtraderspossessindependentpiecesofinformationaboutthereturnofariskyasset.Eachtraderconditionshisestimateofthereturnbothonhisownprivatesourceofinformationandprice,whichinequilibriumservesasa‘noisy’aggregatorofthetotalinformationobservedbyalltraders.Aclosed-formcharacterizattonoftherationalexpectationsequilibriumispresented.Acounter-exampletotheexistenceof‘fullyrevealing’equilibriumisdeveloped.1.IntroductionThispaperanalyzesamodelofacompetitivesecuritymarketinwhichthepartialaggregationofdiversesourcesofinformationresultsfromarationalexpectationsequilibrium.Theeconomyanalyzedyieldsaunique,closed-formequilibriuminwhichparticipantsareabletoobtainsupplementaryinformationfrommarketpriceswithoutrenderingtheirowninformationredundant.Theanalysispresentedhereisofinterestforatleasttworeasons.First,itprovidesareasonablecharacterizationoftheeconomicconceptofaninformationallyefficientmarket.Secondly,itintroducesadefinitionofequilibriumwhichrestrictspricestodependontraders’informationonlythroughtheirdemandcorrespondences.Theideathatequilibriumpricesincompetitivesecuritymarketslargelyreflecttheinformationpossessedbyvarioustradersisbothwidelyacceptedandoftenanalyzedbyfinancialeconomists.Empirically,evidencepresentedinFama(1970)andelsewhereshowsthatpredictionsconditionedonmarketpricesarenotdominatedbypredictionsusingmanyothersourcesofinformation.Severaltheoreticalpapershavealsoaddressedthisissue.Lintner(1969)analyzesaneconomyinwhichbeliefsareexogenous.Thisleadstoacharacterizationofequilibriumpricesastheweightedaverageofthesebeliefs[seealsoRubinstein(1975)andVerrecchia(1980)].Green*TheauthorsaregratefultoPhilipDybvig,CurHuberman,JonIngersoll,MichaelJensen,RichardLcftwich,TomTurnbullandthereferee,AlanKraus,forhelpfulcommentsonanearlierdraft.0304405X/81/000&0000/$02.500North-Holland222D.WDiamondandR.E.Verrecchia,Informationaggregationandrationalexpectations(1973),Grossman(1976,1978),Grossman-Stiglitz(1980)andothershaveusedtheconceptofrationalexpectationsequilibrium,whichmakesbeliefsendogenous,tostudytheutilizationofpricesthemsevesassourcesofinformation.Theanalysisoftheinformationcontentofpricesineconomieswithexogenousbeliefs[e.g.,Lintner(1969)]issubjecttotheobjectionthatwhenpricesdocontaininformationthataparticulartraderdoesnotpossessheoughttomakeuseofit;this,however,isnotgenerallyconsistentwithassumingthatbeliefsareexogenous.Grossman(1976,1978)analyzesaneconomyinwhichtradershavediversepiecesofinformationaboutthereturnofriskyassets,andheclaimsthattherationalexpectationsequilibriumpricerevealstoalltradersalloftheinformationofthetraderstakentogether;thatis,itrevealsasufficientstatisticofthatinformation.Amajorimplicationofthisresultisthatwhentraderstakepricesasgiven,theyhavenoeconomicincentivetoacquireinformation.Oneproblemwithfullyrevealingequilibriumisthatitdoesnotexistunderthedefinitionpresentedbelow,whichmaybeamoreplausibledefinitionofequilibriumthanthatofGrossman.Analysesassumingtheexogeneityofpeople’sbeliefsproduceresultswhicharenotconsistentwiththenotionthatexpectationsareformedrationally,andanalysessuggestingthefullrevelationofaggregateinformationproduceresultswhicharetoostrongonempiricalgrounds.Therefore,analternativeistostudymarketsinwhichanequilibriumresultsinsomeaggregationofindividuals’informationwithoutrevealingallofit.Thistypeofpartialaggregationenvironmentimpliesthefollowing.When,inadditiontohisprivatelycollectedinformation,anindividualtraderusesobservableendogenousvariables,suchasprices,aspiecesofinformation,hebenefitsfromtheinformationcollectedbyotherswithoutbelievingthathisownissuperfluous.Thisisconsistentwithaprivateincentivetocollectinformation,andanequilibriumwhereinformationaffectspricethroughsupplyanddemand.Theonlyexistingstudiesofpartiallyrevealingpricesdonotanalyzetheroleofpricesasaggregatorsofinformation.’ThemodelsofGreen(1973)andGrossman-Stiglitz(1980)analyzeeconomieswherethereisonlyasinglepieceofinformationwhichanyonecanobserve,suchasaprivateweatherforecast.Intheiranalysestherearetwofactorswhichmaybeunknowntomarketparticipants,andwhichaffectthedeterminationofprices.Ifasinglepieceofinformation,e.g.,theweatherforecast,istheonlyfactorwhichisunknown,andeachweatherforecastimpliesadifferentequilibriumprice,thenthemarketpricecanfullyrevealthecontentoftheforecast.The‘Aftercompletionofthismanuscript,Itwasbroughttotheauthors’attentionthatHellwig(1980)analyzesasomewhatdifferentmodeloftheaggregationofinfkmation.D.WDiamondandR.E.Verrecchia,Informationaggregationandrationalexpectations223introductionofunobservedvariationofanotherfactor(generallyreferredtoas‘noise’andrepresentedbyaggregatesupply)preventsidentifyingtheaggregatedemandcurvebysimplyobservingtheequilibriumprice.Theresultisanequilibriuminwhichthepricecontainsinformationbutdoesnotful