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1、第八章 多元回归分析模型识别和数据问题contentsFunctionalformmisspecificationUsingproxyvariablesMeasurementerrorinvariablesMissingdataandOutlyingobservationsFunctionalfrommisspecificationFunctionalFormWe’veseenthatalinearregressioncanreallyfitnonlinearrelationshipsCanuselogsonRHS,LHSorbothCanusequadraticformsofx’sC
2、anuseinteractionsofx’sHowdoweknowifwe’vegottentherightfunctionalformforourmodel?FunctionalForm(continued)First,useeconomictheorytoguideyouY=AKaLbeuorlnY=lnA+alnK+blnL+uThinkabouttheinterpretationlog(wage)=b0+b1educ+u,orlog(educ)asindependentvariableDoesitmakemoresenseforxtoaffectyinpercentage(us
3、elogs)orabsoluteterms?Doesitmakemoresenseforthederivativeofx1tovarywithx1(quadratic)orwithx2(interactions)ortobefixed?FunctionalForm(continued)Wealreadyknowhowtotestjointexclusionrestrictionstoseeifhigherordertermsorinteractionsbelonginthemodellog(wage)=b0+b1educ+b2exper+b3tenure+ulog(wage)=b0+b
4、1educ+b2exper+b3tenure+b4educ2+b5exper2+b6tenure2+b7educ•tenure+uItcanbetedioustoaddandtestextraterms,plusmayfindasquaretermmatterswhenreallyusinglogswouldbeevenbetterAtestoffunctionalformisRamsey’sregressionspecificationerrortest(RESET)Firstestimatelog(wage)=b0+b1educ+b2exper+b3tenure+uGetfitte
5、dvalueŷ(log(wâge)ofaboveequation)Then,considertheexpandedequationlog(wage)=b0+b1educ+b2exper+b3tenure+d4ŷ2+d5ŷ3+uRESETistheFstatisticfortesingH0:d4=0,d5=0InStata,theRESETtestcommand:ovtestWhetherthemodely=b0+b1x1+…+bkxk+umisspecified?RESETreliesonatricksimilartothespecialformoftheWhitetestInstea
6、dofaddingfunctionsofthex’sdirectly,weaddandtestfunctionsofŷSo,estimatey=b0+b1x1+…+bkxk+d1ŷ2+d1ŷ3+errorandtestH0:d1=0,d2=0usingF~F2,n-k-3orLM~χ22RESETtest,exampleHousingpriceequation(hprice.raw)price=b0+b1lotsize+b2sqrft+b3bdrms+ulog(price)=b0+b1log(lotsize)+b2log(sqrft)+b3bdrms+uRESETtestprocedu
7、reEstimatethemodels:regpriceonlotsize,sqrft,bdrms,andgetfittedvalueofprice,ŷandSSRr=300723.806,n=88R2=0.6724Calculateŷ2,ŷ3,andplugthemtotheoriginalequation,andestimateit.Thatis,regpriceonlotsize,sqrft,bdrms,ŷ2,ŷ3,andSSRur=26
