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1、c04-SelectedTopicsPage127Thursday,October26,20062:02PMCHAPTER4SelectedTopicsinRegressionAnalysisnthepreviouschapterweprovidedthebasicsofregressionanalysis—Itheoryandestimation.Therearenumerousspecializedtopicswithintheareaofregressionanalysis.Whilewecannotcoverallofthespecial-izedtopicsinthisbo
2、ok,inthischapterwecoverthefollowing:usingcat-egoricalanddummyvariablesinregressionmodels,constrainedleastsquares,andestimationusingthemethodofmomentsanditsgeneraliza-tion.InChapter12,wediscussrobustestimationofregressions.CATEGORICALANDDUMMYVARIABLESINREGRESSIONMODELSCategoricalvariablesarevari
3、ablesthatrepresentgroupmembership.Forexample,givenasetofbonds,theratingisacategoricalvariablethatindicatestowhatcategory—AA,BB,andsoon—eachbondbelongs.Acategoricalvariabledoesnothaveanumericalvalueoranumericalinterpretationinitself.Thusthefactthatabondisincate-goryAAorBBdoesnot,initself,measure
4、anyquantitativecharacteris-ticofthebond;thoughquantitativeattributessuchasabond’syieldspreadcanbeassociatedwitheachcategory.Makingaregressiononcategoricalvariablesdoesnotmakesenseperse.Forexample,itdoesnotmakesensetomultiplyacoefficienttimesAAortimesBB.However,inanumberofcasesthestandardtoolsofr
5、egressionanalysiscanbeappliedtocategoricalvariablesafterappropriatetransformations.Let’sfirstdiscussthecasewhencategori-127c04-SelectedTopicsPage128Thursday,October26,20062:02PM128FINANCIALECONOMETRICScalvariablesareindependentvariablesandthenproceedtodiscussmodelswherecategoricalvariablesaredep
6、endentvariables.IndependentCategoricalVariablesCategoricalinputvariablesareusedtoclusterinputdataintodifferentgroups.1Thatis,supposewearegivenasetofinput-outputdataandapartitionofthedatasetinanumberofsubsetsAisothateachdatapointbelongstooneandonlyoneset.TheAirepresentacategoricalinputvariable.I
7、nfinancialeconometricscategoriesmightrepresent,forexample,differentmarketregimes,economicstates,ratings,countries,industries,orsectors.Wecannot,perse,mixquantitativeinputvariablesandcategoricalvariables.Forexample,wecannotsumyields
