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1、Chapter1RegressionModels1.1IntroductionRegressionmodelsformthecoreofthedisciplineofeconometrics.Althougheconometriciansroutinelyestimateawidevarietyofstatisticalmodels,usingmanydifferenttypesofdata,thevastmajorityoftheseareeitherregressionmodelsorcloserelatives
2、ofthem.Inthischapter,weintroducetheconceptofaregressionmodel,discussseveralvarietiesofthem,andintroducetheestima-tionmethodthatismostcommonlyusedwithregressionmodels,namely,leastsquares.Thisestimationmethodisderivedbyusingthemethodofmoments,whichisaverygeneral
3、principleofestimationthathasmanyapplicationsineconometrics.Themostelementarytypeofregressionmodelisthesimplelinearregressionmodel,whichcanbeexpressedbythefollowingequation:yt=¯1+¯2Xt+ut:(1:01)Thesubscripttisusedtoindextheobservationsofasample.Thetotalnum-berof
4、observations,alsocalledthesamplesize,willbedenotedbyn.Thus,forasampleofsizen,thesubscripttrunsfrom1ton.Eachobservationcomprisesanobservationonadependentvariable,writtenasytforobserva-tiont,andanobservationonasingleexplanatoryvariable,orindependentvariable,writ
5、tenasXt.Therelation(1.01)linkstheobservationsonthedependentandtheexplana-toryvariablesforeachobservationintermsoftwounknownparameters,¯1and¯2,andanunobservederrorterm,ut.Thus,ofthefivequantitiesthatappearin(1.01),two,ytandXt,areobserved,andthree,¯1,¯2,andut,are
6、not.Threeofthem,yt,Xt,andut,arespecifictoobservationt,whiletheothertwo,theparameters,arecommontoallnobservations.Hereisasimpleexampleofhowaregressionmodellike(1.01)couldariseineconomics.Supposethattheindextisatimeindex,asthenotationsuggests.Eachvalueoftcouldrep
7、resentayear,forinstance.Thenytcouldbehouse-holdconsumptionasmeasuredinyeart,andXtcouldbemeasureddisposableincomeofhouseholdsinthesameyear.Inthatcase,(1.01)wouldrepresentwhatinelementarymacroeconomicsiscalledaconsumptionfunction.Copyright°c1999,RussellDavidsona
8、ndJamesG.MacKinnon34RegressionModelsIfforthemomentweignorethepresenceoftheerrorterms,¯2isthemarginalpropensitytoconsumeoutofdisposableincome,and¯1iswhatissometimescalledautonomousc
