中級計(jì)量濟(jì)學(xué)作業(yè)一上交截止期周

2012年碩士研究生《中級計(jì)量經(jīng)濟(jì)2012年碩士研究生《中級計(jì)量經(jīng)濟(jì)學(xué)》作業(yè)（上交截止日期：12月10/11日周一/二上課前multicollinearit，OLS在存在高度共線性（highmulticollinearity）的情況下，要評價(jià)一個(gè)或多個(gè)偏回歸系數(shù)（partialregressioncoefficients）的個(gè)別顯著性是不可能的。specified（inefficient一階差分（firstdifferenceform）R2與原模型（inlevelform）R2不能夠（ineficient2.1’×4450個(gè)觀測值，4個(gè)解釋變量，根據(jù)如下的Durbin-Watsond檢驗(yàn)統(tǒng)計(jì)值判斷是（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".Anestimatedregressionyields? ?415?Supposethatahomeownerconvertspartofanexistingfamilyroominherhouseintoanewbathroom.Whatistheexpectedincreaseinthevalueofthehouse?Supposethatahomeowneraddsanewbathroomtoherhouse,whichincreasesthesizeofthehouseby100squarefeet.Whatistheexpectedincreaseinthevalueofthehouse?Whatisthelossinvalueifahomeownerletshishouserundownsothatitsconditionbecomes"poor"?ComputetheR2forthe1of4.（2’×8=16’）根據(jù)1899-1922年美國制造業(yè)部門的年度數(shù)據(jù)，Dougherty獲得如下4.（2’×8=16’）根據(jù)1899-1922年美國制造業(yè)部門的年度數(shù)據(jù)，Dougherty獲得如下回歸結(jié)log?Y????2.81??se= R2=F=其中Y實(shí)際產(chǎn)出指數(shù)K實(shí)際資本投入指數(shù)，L實(shí)際勞動(dòng)投入指數(shù)t時(shí)間或趨勢。log?Y/L???? se= R2=F=回歸(1)中有沒有多重共線性？你是如何知道的你如何為回歸（1）的函數(shù)形式做辯護(hù)？（提示：柯布-道格拉斯生產(chǎn)函數(shù)解釋回歸（1）的結(jié)果。在此回歸中時(shí)間趨勢變量的作用是估計(jì)回歸（2）的邏輯在哪里？（Whatisthelogicbehindestimatingregression如果原來的回歸（1）有多重共線性，是否已被回歸（2）減弱？你是如何知道的值是可比的嗎？為什么可以或?yàn)槭裁床豢梢?.(2’×36有如下兩個(gè)模ModelA：Yt=β0+β1t+Model Yt=β0+β1t+β2t2+其中Y=labor’sshare，t=時(shí)間。根據(jù)1949-1964年的年度數(shù)據(jù)，得到如下結(jié)果ModelA：Y?=0.4529–0.0041(-R2=0.5284d= +0.0005(- R2=0.6629d=其中括號內(nèi)的數(shù)值t比值（tratio（a）ModelA是否存在自相關(guān)？Model什么原因引起了自相關(guān)如何pureautocorrelationspecificationbias（模型設(shè)定偏差2of6.(0.5’×18=9’)請將如下回歸結(jié)果補(bǔ)充完SourceNumberofobsF(（h）,（i）)Prob>FRoot=====6.(0.5’×18=9’)請將如下回歸結(jié)果補(bǔ)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,estimateparametersintheequationLNWAGE??? 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,iftheexpectedvalueofε??isaconstant),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