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1、Economics140AIdentificationinSimultaneousEquationModelsSimultaneousEquationModelsOursecondextensionoftheclassicregressionmodel,towhichwedevotetwolectures,istoasystem(ormodel)ofmorethanoneequation.Together,theequationsdescribethesimultaneousevolutionofmultipleendogenousvariablesandareterme
2、dsimultaneousequationmodels.Uptothispoint,wehaveconsideredstructuresinwhichonlyonevariable,thedependentvariable,isendogenous.Weoftenthinkoftheregressorsascausingthemovementsinthedependentvariableinthattheregressorscanbecondi-tioneduponwhenstudyingthedependentvariable.Inmanycasesofinterest
3、toeconomiststheconditionalstructureofasingleequationbreaksdown,astwoormorequantitiesarejointlydetermined.Perhapsthesimplestsuchstructureistoconsiderpriceandquantityforaspeci…cmarket(e.g.VanstennisshoesinSantaBarbara).OnemightthinkofthefollowingstructurePt=0+1Qt+Ut;wherePtisthepriceofapair
4、ofshoesinperiod-tandQtisthequantityofshoessoldinthecorrespondingperiod.Withoutquestion,thepriceofshoesisa¤ectedbythequantityavailable.Surplusinventoriesaresoldatdiscountandgoodsinshortsupplyoftensellatapremium.Yet,unlesstheSantaBarbaramarketformsonlyatinyportionoftotalsupply,thepriceatwhi
5、chtheshoesaresolda¤ectsthequantity.Shoessoldatdiscountre‡ectexcessinventoriesandindicatethatproductionshouldfall,theconverseholdsforshoessoldatapremium.Iftheregressorisalsoafunctionofthedependentvariable,itisclearthattheregressoriscorrelatedwiththeerrorandaclassicassumptionisviolated.Toov
6、ercomethebias(andinconsistency)oftheOLSestimators,onecouldproceedwithIVestimation.Yetnotonlyisanadequateinstrumentrarelyathand,butoftenunderstandingoftheeconomyrequiresthatwemorefullyinvestigatethejointdeterminationoftheendogenousvariables.Todoso,itishelpfultodistinguishbetweenthetheoreti
7、calquantitiesQD,twhichisthequantityofshoesdemandedbyconsumers,andQS,whichisthetquantityofshoessuppliedbyproducers.WethinkofQDasarisingfromademandtfunctionDQt=1+2Pt+U1t;whereweexpect<0.WethinkofQSasarisingfromasupplyfunction2tSQt=1+2Pt+U2t;whereweexpect2>0.Thetwoquan
