厦门大学计量经济学II课程试卷

厦门大学《计量经济学II》课程试卷王亚南经济研究院—系2008专业主考教师：BrettGraham试卷类型：（A卷/B卷）UndergraduateEconomicsECONOMETRICSINSTRUCTIONSTOSTUDENTS1Thetimeallowedforthisexaminationpaperis3hours.2Thisexaminationpapercontains32questions.YouareREQUIREDtoanswerALLques-tions.Nomarkswillbedeductedforwronganswers.3ForeachmultiplechoicequestionthereisoneandONLYONEsuitableanswer.4Allnumericalanswersshouldberoundedto3decimalplaces.Iwillaccepteveryanswertowithin0.002ofthecorrectanswer.Allprobabilitiesshouldbeexpressedindecimalform.5Thereare16printedpagesincludingthisinstructionsheetandtwoblankpagesforcalcu-lationsattheendoftheexam.6Thisisaclosed-bookexamination.Youareallowedtobringonehandwritten9cmby9cmpieceofpapertotheexam.Youarealsoallowedtousea�nancialcalculator.7Youarerequiredtoreturnallexaminationmaterialsattheendoftheexamination.8Whererequired,pleaseusethefollowingforstandardnormalcriticalvalues,z0:10=1:28z0:05=1:645z0:025=1:96z0:01=2:33z0:005=2:581.Considerapopulationandarandomsampledrawnfromthatpopulation.Asthenumberofobservationsintherandomsampleincreases,whichofthefollowingstatementsistrue?a.thevarianceofthesamplingdistributionofthesamplemean,andthevarianceofthepopulationdistributiondecrease.b.thevarianceofthesamplingdistributionofthesamplemean,andthevarianceofthepopulationdistributionstaythesame.c.thevarianceofthesamplingdistributionofthesamplemean,andthevarianceofthepopulationdistributionincrease.d.thevarianceofthesamplingdistributionofthesamplemeandecreases,andthevarianceofthepopulationdistributionstaysthesame.e.thevarianceofthesamplingdistributionofthesamplemeanincreases,andthevarianceofthepopulationdistributionstaysthesame.2.Xanduaretworandomvariables.IfXanduareindependent,whichofthefollowingstatementisalwaystrue?a.Var(X+u)=Var(X)+Var(u)b.E(ujX)=E(Xju)c.E(ujX)=0d.E(ujX)=E(X)e.E(X)=E(u)3.Whenweundertakeahypothesistest,withprobability�wemakeaTypeIIerror.Inotherwords,withprobability�a.weacceptthenullwhenthenullistrue.b.wedonotrejectthenullwhenthenullistrue.c.weacceptthenullwhenthenullisfalse.d.wedonotrejectthenullwhenthenullisfalse.e.werejectthenullwhenthenullistrue.4.Youaretoldthecovariancebetweenincomeandyearsofeducationis0.2.Whatisapossiblevalueforthecorrelationbetweenincomeandyearsofeducation?Youshouldassumethatnoneoftheanswerchoiceshavebeenrounded.a.-2b.-0.5c.0d.0.5e.25.Apizzashopisconsideringo�eringcustomersadiscountonanydeliverythattakesmorethan30minutes.Theywillonlybeabletoo�erthediscountiflessthan10%oftheircurrentdeliveriestakemorethan30minutes.Fromarandomsampleof360currentdeliveries,theshop�ndsthat30deliveriestakemorethan30minutes.Whatisthevalueoftheteststatistic?Page26.Supposewewanta95%con�denceintervalforthepopulationmeanofEconometricsmidtermexamscores.Butwedon'twantthelengthofthecon�denceintervaltobelargerthan2(orsaiddi�erently,wedon'twantthewidthofthecon�denceintervaltoexceed1).Weknowthatthepopulationstandarddeviationis5.31.Whatistheminimumsamplesizeweneedtocreatesuchacon�denceinterval?Usethefollowinginformationtoanswerthenext4questions(7-10):TheschoolisconcernedthatWikipediaTMisunreliableforresearchandisconsideringdisallowingitsuseasareferenceinstudents'termpapers.Theyrandomlyselect60articlesfromWikipediaTMand30articlesfromEncyclopediaBrittanicaTM_They�ndthatthereisanaverageof4.3errorsineachWikipediaTMarticle,withastandarddeviationof1.5,andthereisanaverageof3.4errorsineachEncyclopediaBrittanicaTMarticle,withastandarddeviationof1.2.Assumethepopulationvariancesareunknownandunequal.TheschoolwillonlydisallowtheuseofWikipediaTMasareferenceintermpaperswhenthey�ndsu�cientstatisticalevidencetoclaimthatWikipediaTMarticlescontainmoreerrorsthanEncyclopediaBrittanicaTMarticles.7.�1isthepopulationmeanoftheerrorsinWikipediaTM,�2isthepopulationmeanoftheerrorsinEncyclopediaBrittanicaTM,and�Disthepopulationmeanofthedi�erencein�1and�2.Whatareappropriatenullandalternativehypotheses?a.H0:�D=0;H1:�1<�2b.H0:�1=4:3;H1:�2<4:3c.H0:�2=3:4;H1:�1>3:4d.H0:�1��2;H1:�1>�2e.H0:�1��2;H1:�1<�28.Whatisthevalueoftheteststatistic?Page39.Ignoringtheresultofthepreviousquestion,supposetheteststatisticyoucalculatedwas2.467.Atthe1%levelofsigni�cance,whatshouldtheschooldecideandconclude?a.RejectthenullandconcludethattheaveragenumberoferrorsinWikipediaTMarticlesisgreaterthantheaveragenumberoferrorsinEncyclopediaBrittanicaTMarticles.b.RejectthenullandconcludethatthereisnotenoughinformationtoclaimthattheaveragenumberoferrorsinWikipediaTMarticlesisgreaterthantheaveragenumberoferrorsinEncyclopediaBrittanicaTMarticles.c.FailtorejectthenullandconcludethattheaveragenumberoferrorsinWikipediaTMarticlesisgreaterthantheaveragenumberoferrorsinEncyclopediaBrittanicaTMarticles.d.FailtorejectthenullandconcludethatthereisnotenoughinformationtoclaimthattheaveragenumberoferrorsinWikipediaTMarticlesisgreaterthantheaveragenumberoferrorsinEncyclopediaBrittanicaTMarticles.e.Thereisnotenoughinformationprovidedtomakeadecisionorconclusion.10.Whatisthe99%con�denceintervalof�1��2?,Page4Usethefollowinginformationtoanswerthenext4questions(11-14):Supposeyouareconsideringopeningarestaurantatalocationwheretheaveragetra�cvolumeis2,000carsperday.Tohelpyoudecidewhethertoopentherestaurant,youcollectedthedataofrestaurantsales,Y,(measuredinthousandsofdollars)andthetra�cvolume,X,(measuredinhundredsofvehiclesperday)fromarandomsampleof22restaurants.Thenyousetupthelinearregressionmodelas:Yi=�0+�1Xi+ui.YouknowthatPXiYi=17170,PX2i=13055,�X=22:5,�Y=3211.WhichofthefollowingstatementsabouttheleastsquareestimationofyourmodelisNOTtrue?a.Thepoints�X,�Ywillalwayslieontheregressionlineb.Pu^i=0c.E(Y^)=E(Y)d.Thenumberofpointsabovethe�ttedlinearethesameasthosebelowthelinee.TheregressionlineminimizesthesumofthesquaredresidualsP(u2i)12.Estimatethevalueof�1.13.Usingtheanswerfromquestion12,(thatis,roundedto3digits),estimatetheaveragesalesforyourpotentialrestaurantlocation.Page514.Supposeyouchangetheunitofmeasurementfor\Sales"(Y)fromthousandsofdollartodollars,butkeeptheunitofmeasurementfor\Tra�cVolume"(X)unchanged.Whichofthefollowingvariablewillremainunchanged?a.�^0b.�^1c.totalsumofsquares(TSS)d.R2e.explainedsumofsquares(ESS)15.Considerthefollowing�veassumptions.(I)E(uijXi)=0(II)(Xi;Yi);i=1;:::;narei.i.d.(III)XiandYihavenon-zero�nitefourthmoments.(IV)var(uijXi)=�2u.(V)ui�N(0;�2u).Whichoftheaboveassumptionsarenecessaryforderivingthelargesampledistributionof�^1?Recallthat�^1�N(�1;�2�^1)where�2�^1=1nvar[(Xi��X)ui][var(Xi)]2:a.(I),(II)and(III)b.(I),(II)and(IV)c.(I),(III)and(V)d.(II),(III)and(IV)e.(III),(IV)and(V)Page616.Inmultiplelinearregressionwhichofthefollowingisnotarandomvariable?a.�^0b.u^ic.�0d.Yie.Y^i17.Supposewearecreatingamodelforpredictingaperson'sincome.Weidentifythefollowingaspossibleindependentvariables:gender(SEX),age(AGE),yearsofexperience(EXP),andwhetherornotthepersonhasacollegedegree(DEG).Weareconcernedaboutmulti-collinearitybetweentheregressors,sowelookatthefollowingcorrelationmatrixtoseeifthereisaproblem.Whichofthepairsofvariableswouldwebeconcernedaboutregardingmulticollinearity?VariableINCOMESEXAGEEXPDEGINCOME1SEX-0.5321AGE-0.921-0.0341EXP-0.893-0.2560.3411DEG0.245-0.1450.8670.2451a.AGEandDEGb.AGEandEXPc.INCOMEandAGEd.INCOMEandEXPe.SEXandAGEPage718.Considerthefollowingstatementsabouttheerrorsinthelinearregressionmodel.(I)Theerrorsareindependentofoneanother.(II)TheerrorshaveconstantvarianceasafunctionofXi.(III)Theerrorsarehomoskedastic.(IV)Themeanofthedistributionoftheerrorsiszero.(V)Themeanofthedistributionoftheerrorsconditionedontheregressorsiszero.Whichoftheaboveiseitherdirectlyassumedorindirectlyimpliedbythefourassumptionsweuseinthemultiplelinearregressionmodel?a.(I),(II)and(III)b.(I),(II)and(IV)c.(I),(IV)and(V)d.(II),(III)and(IV)e.(III),(IV)and(V)Page819.Considerthefollowingstatements.(I)Theerrorsarenormallydistributed.(II)Theerrorsarehomoskedastic.(III)Theresidualsarenormallydistributed.(IV)Theresidualsarehomoskedastic.Oftheabovestatements,whichareassumptionsneededfortheGauss-MarkovTheorem.a.(II)onlyb.(I)onlyc.(IV)onlyd.(II)and(IV)e.(III),(IV)20.Usingdataonfootballticketsalesinthousandofdollars,SALES,temperatureindegressFahrenheit,DEGandpopulationinthousandsofpeople,POP,youestimatethefollowingregressiondSALES=15:25+10:32DEG+1:03POPWhatistheincreaseinsalesinthousandsofdollarsfromanincreaseinpopulationof1000peopleassumingtemperatureremainsunchanged?Page921.Consideraddinganindependentvariabletoalinearregressionmodel.WhichofthefollowingstatementsisTRUE?a.AdjustedR2neverrises.b.R2alwaysfalls.c.SSRalwaysrises.d.TSSalwaysrisese.TSSalwaysfalls.Usethefollowinginformationtoanswerthenext2questions(22-23):Youwanttoknowhowfastgrassgrows.Yourecordinmillimetershowquicklygrassgrowsperdayasaresultofdi�erentprecipitationlevelsininches.Fromyourobservations,averageprecipitationis0.69inchesandstandarddeviationofprecipitationis0.224inches.Averagegrowthperdayis102millimetersandthestandarddeviationofgrowthis15.1millimeters.Thecorrelationcoe�cientbetweengrassgrowthandprecipitationis0.65.22.Calculatetheslopeofthesampleregressionlineifprecipitationistheindependentvariableandgrassgrowthisthedependentvariable.Hint:Usethecorrelationcoe�cientto�ndthecovariancebetweenprecipitationandgrassgrowth.23.Usingtheroundedanswerfromquestion22calculatetheexpectedamountofgrassgrowthifprecipitationis0.5inches.Page1024.Considertheestimator~Yde�nedinEquation1.~Y=1n�13Y1+53Y2+13Y3+53Y4+:::+13Yn�1+53Yn�:(1)Asanestimatorof�Y,~Ya.isunbiased,consistentandmoree�cientthan�Y.b.isunbiased,consistentandlesse�cientthan�Y.c.isunbiased,notconsistentandmoree�cientthan�Y.d.isbiased,consistentandmoree�cientthan�Y.e.isbiased,notconsistentandlesse�cientthan�Y.Usethefollowinginformationtoanswerthenext4questions(25-28):Thedependentvariable,Y,istestscore.Theindependentvariable,X,isclasssize.Thesamplesize,n,equals1000.Supposeyouhavesetupthefollowinglinearmodelandplantoestimatethemodelwithordinaryleastsquares.Yi=�0+�1Xi+ui;i=1;���;nTheOLSestimatorof�0equals0.8withastandarderrorof0.383,andtheOLSestimatorof�1equals0.4withastandarderrorof0.115.25.Whatisthe95%con�denceintervaloftheslopecoe�cient?26.Supposeyouwanttotestthat\classsize"a�ects\testscores",andyournullhypothesisisH0:�1=0.Whatisthevalueoftheteststatistic?Page1127.Supposethattheteststatisticyougetfromtheprevioustestis2.1.Withinwhatrangedoesthetheassociatedp-valuelie?a.0<p-value<0:01b.0:01<p-value<0:02c.0:02<p-value<0:05d.0:05<p-value<0:1e.0:1<p-value<0:528.Ignorethecon�denceintervalyoucalculatedandsupposethatthe95%con�denceintervaloftheslopecoe�cientis[0:1;0:9],whichofthefollowingstatementsisde�nitelytrue?a.YoucanrejectH0:�0=0vsH1:�06=0ata1%signi�cancelevelorhigher.b.YoucanrejectH0:�0=0vsH1:�06=0ata5%signi�cancelevelorlower.c.YoucanrejectH0:�1=0vsH1:�16=0ata1%signi�cancelevelorhigher.d.YoucanrejectH0:�1=0vsH1:�16=0ata5%signi�cancelevelorlower.e.YoucanrejectH0:�1=0vsH1:�16=0ata5%signi�cancelevelorhigher.29.From100observationsyourunthefollowingtworegressions.Model1:TestScore=644:7+0:671PctEL;R2(restricted)=0:415Model2:TestScore=649:6+0:29STR+3:87Expn�0:656PctEL;R2(unrestricted)=0:437Assumingyouknowthattheerrorsarehomoscedastic,whatisthevalueoftheteststatistictotestH0:�1=�2=0againstH1:atleastone�i6=0inModel2?Page1230.Aneconometricianwanttotestthefollowinghypothesis,H0:�0+2�1=�3vs.H1:�0+2�16=�3;onthefollowinglinearregresisonmodel,Yi=�0+�1X1;i+�2X2;i+�3X3;i+ui:TodososhetransformstheregressionequationtoYi= 1X1;i+�0W2;i+�3W3;i+�2X2;i+ui;sothatshecanperformasimplet-teston 1.Thetwonewvariables,W2;iandW3;iarea.W2;i=2�X1;i2andW3;i=2X3;i+X1;i2b.W2;i=2�X1;i2andW3;i=X3;i�2X1;i2c.W2;i=2+X1;i2andW3;i=X1;i�2X3;i2d.W2;i=X1;i�22andW3;i=X3;i�2X1;i2e.W2;i=X1;i�22andW3;i=X1;i�2X3;i231.Supposethataresearcher,usingdataonclasssize(CS)andaveragetestscoresfrom100third-gradeclasses,estimatestheOLSregression,dTestScore=520:4�5:82CS;R2=0:08;SER=20:Thesampleaverageclasssizeacrossthe100classroomsis21.4.Whatisthesampleaverageofthetestscoresacrossthe100classrooms?Page1332.Supposethataresearcher,usingwagedataon250randomlyselectedmalesand280randomlyselectedfemaleworkers,estimatestheOLSregression,dWage=12:52+2:12�Male;R2=0:06;SER=4:2;whereWageismeasuredin$/hourandMaleisabinaryvariablethatisequalto1ifthepersonisamaleand0ifthepersonisafemale.Anotherresearcherusesthesesamedata,butregressesWageonFemale,avariablethatisequalto1ifthepersonisfemaleand0ifthepersonismale.Whatistheregressionestimatefor�0forthisregression?Page14Page15Page16