中级计量济学作业一上交截止期周

2012年硕士研究生《中级计量经济2012年硕士研究生《中级计量经济学》作业（上交截止日期：12月10/11日周一/二上课前multicollinearit，OLS在存在高度共线性（highmulticollinearity）的情况下，要评价一个或多个偏回归系数（partialregressioncoefficients）的个别显著性是不可能的。specified（inefficient一阶差分（firstdifferenceform）R2与原模型（inlevelform）R2不能够（ineficient2.1’×4450个观测值，4个解释变量，根据如下的Durbin-Watsond检验统计值判断是（a）d=1.05；（b）d=1.40；（c）d=2.50；（d）d=3.(2’×4=8’)Datawerecollectedfromarandomsampleof220homesalesfromacommunityin2003.LetPricedenotethesellingprice(in$1000),BDRdenotethenumberofbedrooms,Bathdenotethenumberofbathrooms,Hsizedenotethesizeofthehouse(insquarefeet),Lsizedenotethelotsize(insquarefeet),Agedenotetheageofthehouse(inyears),andPoordenoteabinaryvariablethatisequalto1iftheconditionofthehouseisreportedas"poor".Anestimatedregressionyields݄ ܿ415ݐSupposethatahomeownerconvertspartofanexistingfamilyroominherhouseintoanewbathroom.Whatistheexpectedincreaseinthevalueofthehouse?Supposethatahomeowneraddsanewbathroomtoherhouse,whichincreasesthesizeofthehouseby100squarefeet.Whatistheexpectedincreaseinthevalueofthehouse?Whatisthelossinvalueifahomeownerletshishouserundownsothatitsconditionbecomes"poor"?ComputetheR2forthe1of4.（2’×8=16’）根据1899-1922年美国制造业部门的年度数据，Dougherty获得如下4.（2’×8=16’）根据1899-1922年美国制造业部门的年度数据，Dougherty获得如下回归结logሺYሻെ◌ൗ2.81െ◌se= R2=F=其中Y实际产出指数K实际资本投入指数，L实际劳动投入指数t时间或趋势。logሺY/Lሻെ◌ൗ se= R2=F=回归(1)中有没有多重共线性？你是如何知道的你如何为回归（1）的函数形式做辩护？（提示：柯布-道格拉斯生产函数解释回归（1）的结果。在此回归中时间趋势变量的作用是估计回归（2）的逻辑在哪里？（Whatisthelogicbehindestimatingregression如果原来的回归（1）有多重共线性，是否已被回归（2）减弱？你是如何知道的值是可比的吗？为什么可以或为什么不可以5.(2’×36有如下两个模ModelA：Yt=β0+β1t+Model Yt=β0+β1t+β2t2+其中Y=labor’sshare，t=时间。根据1949-1964年的年度数据，得到如下结果ModelA：Y୲=0.4529–0.0041(-R2=0.5284d= +0.0005(- R2=0.6629d=其中括号内的数值t比值（tratio（a）ModelA是否存在自相关？Model什么原因引起了自相关如何pureautocorrelationspecificationbias（模型设定偏差2of6.(0.5’×18=9’)请将如下回归结果补充完SourceNumberofobsF(（h）,（i）)Prob>FRoot=====6.(0.5’×18=9’)请将如下回归结果补充完SourceNumberofobsF(（h）,（i）)Prob>FRoot======ModelResidual-------------+-----------------------------TotallbwghtStd.t[95%Conf.||||||||--------7.Dataongasolineconsumptionfortheyears1953to2004aregivenTableF2.2.txt.Note,theconsumptiondataappearastotalexpenditure.Toobtainthepercapitaquantityvariable,divideGASEXPbyGASPtimesPop.TheothervariablesdonotneedComputethemultipleregressionofpercapitaconsumptionofgasolineonpercapitaincome,thepriceofgasoline,alltheotherpricesandatimetrend.Reportallresults.Dothesignsoftheestimatesagreewithyourexpectations?Testthehypothesisthatatleastinregardtodemandforgasoline,consumersdonotdifferentiatebetweenchangesinthepricesofnewandusedcars.Estimatetheownpriceelasticityofdemand,theincomeelasticity,andthecrosspriceelasticitywithrespecttochangesinthepriceofpublictransportation.Dothecomputationsatthe2004pointinthedata.Reestimatetheregressioninlogarithmssothatthecoefficientsaredirectestimatesoftheelasticities.(Donotusethelogofthetimetrend.)Howdoyourestimatescomparewiththeresultsinthepreviousquestion?Whichspecificationdoyouprefer?Computethesimplecorrelationsofthepricevariables.Wouldyouconcludethatmulticollinearityisa“problem”fortheregressioninpart(a)orpart(d)? Noticethatthepriceindexforgasolineisnormalizedto100in2000,whereastheotherpriceindicesareanchoredat1983(roughly).Ifyouweretorenormalizetheindicessothattheywereall100.00in2004,thenhowwouldtheresultsoftheregressioninpart(a)change?Howwouldtheresultsoftheregressioninpart(d)change?3of8.Thepurposeofthisexerciseistohaveyouassesswhetherdisturbancesinanestimatedstatisticalearningsfunctionarehomoskedastic,tocomparetraditionalandrobustestimatesofstandarderrorsofcoefficientswhenheteroskedastictiymaybepresent,andtoexaminethesensitivityofestimatedcoefficientstoalternativestochasticspecificationsinvolvingChooseeitherthe19788.Thepurposeofthisexerciseistohaveyouassesswhetherdisturbancesinanestimatedstatisticalearningsfunctionarehomoskedastic,tocomparetraditionalandrobustestimatesofstandarderrorsofcoefficientswhenheteroskedastictiymaybepresent,andtoexaminethesensitivityofestimatedcoefficientstoalternativestochasticspecificationsinvolvingChooseeitherthe1978orthe1985datasetinCPS78andCPS85,respectively,andusethatdatasetforallportionsofthisexercise.(a)Beginbyestimatingatraditionalstatisticalearningfunction.Morespecifically,employingOLS,estimateparametersintheequationLNWAGEെ◌ൗ Computeboththetraditionalandtheheteroskedasticity-robuststandarderrors.Aretheheteroskedasticity-robuststandarderrorestimatesalwayslargerthantheOLSestimates?Isthiswhatyouexpected?Whyorwhynot?(b)EventhoughOLSestimatedparametersinpart(a)areconsistentifheteroskedasticityispresent,theyarenotefficient.Toobtainefficientestimates,ageneralizedleastsquares(GLS)procedureisrequired.TodoGLS,firstretrievetheresidualsfromtheestimatedequationinpart(a)andsquareeachoftheseresiduals.Mincer(1974),Willis(1986),andothershavearguedthatthevarianceofdisturbancesinastatisticalearningsfunctionmightbepositivelyrelatedtovariablessuchasEDand/orEX.Toexaminethispossibility,useOLSandrunaregressionofthesquaredresidualsfrompart(a)asthedependentvariable,andemployasregressorsaconstant,ED,EX,EXSQ,FE,UNION,NONWH,andHISP.Experimentwithalternativecombinationsoftheseregressors,andthenchooseapreferredresidualregressionequationinwhicheachoftheregressorshasastatisticallysignificantcoefficient.Thenusesquarerootsofthefittedvaluesfromyourpreferredresidualregressiontotransformallyourdata,anddoOLSonthetransformeddata,whichisnumericallyequivalenttodoingGLSontheuntransformeddata.Note1:Youmightrunintoaproblemdoingsuchatransformationifanyofthefittedvaluesfromyourresidualregressionarenonpositive.Checktomakesurethatthisdoesnotoccurwithyourestimatedmodel.CompareyourGLSandOLSestimatedparametersandstandarderrors.Anysurprise?Whyorwhynot?Note2:SomecomputerprogramsallowyoutodoGLSorweightedleastsquareswithoutactuallyrequiringyoutotransformthedata.Ifyousoftwarepermitsthis,simplyuseasaweightinweightleastsquaresthefittedvaluefromyourpreferredresidualregressionequation.(c)Intypicaleconometrictheorytextbooksanumberoftestsarepresentedfortestingthenullhypothesisofhomoskedasticityagainstanalternativehypothesisconsistingofeitheraspecificorsomeunspecifiedformofheteroskedastcity.OneverysimpletestisproposedbyHalbertJ.White(1980);asyouwillnowsee,itisavariantofthesomewhatadhocprocedureusedinpart(b).Asinpart(b),retrievetheresidualsfromthepart(a)regression,andsquarethem.White’sprocedureconsistsofrunninganauxiliaryregressioninwhichthesquaredOLSresidualisthedependentvariableandtheregressorsconsistoftheoriginalsetofregressors,plusthecross-productsandsquaresofalltheregressorsintheoriginalOLS4ofequation.Inourcontextequation.Inourcontextthisimpliesrunningaregressionofthesquaredresidualsonaconstant,ED,EX,EXSQ,FE,UNION,NONWH,HISP,and17cross-productsregrssors,andthetwosquaredterms,ED*EDandEXSQ*EXSQ(notethatsquaresofthedummyvariablessuchasFEareidenticaltoFE,andsotheyarenotincludedasadditionalregressors).Runthisauxiliaryregression,andretrievethemeasurRe2.Whitehasshownthatiftheoriginaldisturbancesarehomokurtic(thatis,iftheexpectedvalueofεସ୧isaconstant),thenundernullhypothesis,N(thesamplesize)timestheR2fromthisauxiliaryregressionisdistributedasymptoticallyasachi-squarerandomvariablewith27degreesoffreedom(thetotalnumberofzeroslopecoefficientsintheauxiliaryregressionunderthenullhypothesis).Computethischi-squaretestforhomoskedasticity,andcompareittothe5%criticalvalue.Areyourresultsconsistentwiththenullhypothesisofhomoskedasticity?Ifnot,maketheadjustmentsandreestimatetheequationinpart(a)byGLSusingaweightedleastsquaresprocedure.Doesadjustingforheteroskedasticityaffecttheparameterestimatessignificantly?Theestimatedstandarderror?Thet-statisticsofsignificance?Isthiswhatyouexpected?9.Firstread“PolicyAnalysisandDifference-in-DifferencesEstimation”andMeyeretal.(1995),andthenusethedatainINJURY.RAWtodofollowingquestions.5of6of77of88ofThiscontentThiscontentdownloadedbytheauthorizeduserfrom192.168.52.70onWed,21Nov201221:12:21PMAllusesubjecttoJSTORTermsandConditionsThiscontentThiscontentdownloadedbytheauthorizeduserfrom192.168.52.70onWed,21Nov201221:12:21PMAllusesubjecttoJSTORTermsandConditionsThiscontentThiscontentdownloadedbytheauthorizeduserfrom192.168.52.70onWed,21Nov201221:12:21PMAllusesubjecttoJSTORTermsandConditionsThiscontentThiscontentdownloadedbytheauthorizeduserfrom192.168.52.70onWed,21Nov201221:12:21PMAllusesubjecttoJSTORTermsandConditionsThiscontentThiscontentdownloadedbytheauthorizeduserfrom192.168.52.70onWed,21Nov201221:12:21PMAllusesubjecttoJSTORTermsandConditionsThiscontentThiscontentdownloadedbytheauthorizeduserfrom192.168.52.70onWed,21Nov201221:12:21PMAllusesubjecttoJSTORTermsandConditionsThiscontentThiscontentdownloadedbytheauthorizeduserfrom192.168.52.70onWed,21Nov201221:12:21PMAllusesubjecttoJSTORTermsandConditionsThiscontentThiscontentdownloadedbytheauthorizeduserfrom192.168.52.70onWed,21Nov201221:12:21PMAllusesubjecttoJSTORTermsandConditionsThiscontentThiscontentdownloadedbytheauthorizeduserfrom192.168.52.70onWed,21Nov201221:12:21PMAllusesubjecttoJSTORTermsandConditionsThiscontentThiscontentdownloadedbytheauthorizeduserfrom192.168.52.70onWed,21Nov201221:12:21PMAllusesubjecttoJSTORTermsandConditionsThiscontentThiscontentdownloadedbytheauthorizeduserfrom192.168.52.70onWed,21Nov201221:12:21PMAllusesubjecttoJSTOR