中計(jì)部分課件及作業(yè)答案

(1.(1’×5=經(jīng)驗(yàn)準(zhǔn)則：如果每?jī)蓚€(gè)回歸元的相關(guān)系數(shù)高，比如說(shuō)超 0.8，則多重共線性的3. (2’)（b）和 e(2’×5=????????0.020??0.00026?2age????煙概率要小10.1%。WejustplugthevaluesoftheindependentvariablesintotheOLSregressionke??0.656??0.069log?67.44??0.012log?6,500????0.020?77???0.00026?77???Thus,theestimatedprobabilityofsmokingforthis isclosetozero.(Infact,this notasmoker,sotheequationpredictswellforthisparticularobservation.)(2’×3=Thecoefficientonmaleis87.75,soamanisestimatedtosleepalmostoneandone-halfmoreperweekthanacomparablewoman.Further,

=87.75/34.33≈2.56,whichiscloseto1%criticalvalueagainstatwo-sidedalternative(about2.58).Thus,theevidenceforagenderdifferentialisfairlystrong.Thetstatisticontotwrkis?.163/.018≈?9.06,whichisverystatisticallysignificant.Thecoefficientimpliesthatonemorehourofwork(60minutes)isassociatedwith.163(60)≈9.8minuteslesssleep.ToobtaintheR-squaredfromtherestrictedregression,weneedtoestimatethemodelwithoutageandage2.Whenageandage2arebothinthemodel,agehasnoeffectonlyiftheparametersonbothtermsarezero.(1’×4= 12.Source Numberofobs +Model|Residual+

F( 21) 5 Prob> =.21. =0.9549AdjR-squared=.Total| Root =lny Std. [95%Conf.+lnL lnK - --.lnL_sq|- --.lnK_sq - lnL_K -_cons -13. .gent1=year-.genG1 .reg eGaspPNCPUCPPTPDPNPSSource Numberofobs F( 42)=Model| 9 Prob> =Residual 42 R- = AdjR-squared=Total| Root =G1 Std. [95%Conf.+e| ..|- ---| | -|- --| -| -|.-...|- ---| .._cons - G2.reg eGaspPNCPUCPPTPDPNPSSource Numberofobs F( 42)=Model|5.6708e- 96.3009e- Prob> =Residual|4.9855e- 421.1870e- R- = AdjR-squared=Total|5.7207e- 511.1217e- Root =1.1e-G2 Std. [95%Conf.e|e|2.16e-5.18e-1.11e-3.20e-|-1.11e-3.98e---1.91e--3.06e-|5.77e-1.28e--2.53e-2.65e-|-5.87e-4.87e---1.57e-3.95e-|6.91e-4.84e--2.85e-1.67e-|1.23e-1.19e--2.27e-2.52e-|1.27e-1.26e--1.27e-3.81e-|-2.80e-8.00e---4.42e--1.19e-|7.25e-1.42e-4.39e-1.01e-|1.11e-5.69e--4.32e-2.25e-H?：βPNC??.test(1)PNC-PUC=F( 42) Prob>F OwnpriceelasticityofQ dQp 1e

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dpQ.dQ

QEI??IQ

dIQ

ICrosspriceelasticitywithrespecttochangesinthepriceofpublic

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.reg elnGasplnPNClnPUClnPPTlnPDlnPNlnPSSource Numberofobs F( 42)=Model| 9 Prob> =Residual| 42 R- = AdjR-squared=Total Root =lnG1 Std. [95%Conf.+e -.|- --.|- --- -. |- ---|- ---t2 _cons|- - - -.corrGaspPNCPUCPPTPDPN|+GaspPNCPUCPPTPDPNPSRenormalizationsofpriceInthelinearcase,thecoefficientswouldbedividedbythesamescalefactor,sothatx*bwouldbeunchanged,wherexisavariableandbisthecoefficient.Intheloglinearcase,sincelog(k*x)=log(k)+log(x),therenormalizationwouldsimplyaffecttheconstantterm.Thepricecoefficientswouldbeunchanged.2010中級(jí)計(jì)量經(jīng)濟(jì) 2參考答（1.(3’×3=HoldingprofmargΔ???????0.321Δlog????????0.321?sales??0.321?10%??Forsuchalargepercentageincreaseinsales,thisseemslikeapracticallysmallH0:β1=0versusH1:β1>0,whereβ1isthepopulationslopeonlog(sales).Thetstatisticis0.321/0.216≈1.486.The5%criticalvalueforaone-tailedtest,withdf=32–3=29,isas1.699;sowecannotrejectH0atthe5%level.Butthe10%criticalvalueis1.311;sincethetstatisticisabovethisvalue,werejectH0infavorofH1atthe10%level.Notreally.Itststatisticisonly1.087,whichiswellbeloweventhe10%criticalvalueforaone-tailedtest.2.(3’×4Theturnaroundpointisgiven0.0003??2? sales??sales??Remember,thisissalesinmillionsof

?Probably.Itststatisticisabout–1.89,whichissignificantagainsttheone-sidedalternativeH:β1<0atthe5%level(cv≈–1.70withdf=29).Infact,thep-valueis0aboutBecausesalesgetsdividedby1,000toobtainsalesbil,thecorrespondingcoefficientgetsmultipliedby1,000:(1,000)*(0.00030)=0.30.Thestandarderrorgetsmultipliedby2thesamefactor.Asstatedinthehint,salesbil=sales/1,000,000,andsothecoefficientonthequadraticgetsmultipliedbyonemillion:(1,000,000)*(0. )=0.0070;itsstandarderroralsogetsmultipliedbyonemillion.Nothinghappenstotheintercept2(becauserdintenshasnotbeenrescaled)ortotheR2rdintens=2.613 0.30salesbil–0.0070 2n=32,R=Theequationinpart(c)iseasiertoreadbecauseitcontainsfewerzerostotherightofthedecimal.Ofcoursetheinterpretationofthetwoequationsisidenticaloncethedifferentscalesareaccountedfor.3.Thesecondequationisclearlypreferred,asitsadjustedR-squaredisnotablylargerthanthatintheothertwoequations.Thesecondequationcontainsthesamenumberofestimatedparametersasthefirst,andtheonefewerthanthethird.Thesecondequationisalsoeasiertointerpretthanthethird.4. 9.39＝

?Δy在保持其他條件相同的情況下，當(dāng)人均收入低于1097時(shí)，人均收入增加（Δx/x＝1%），預(yù)期將增加0.0939年（9.39×1%＝0.0939）引入該回歸元的主要目的是為了描述當(dāng)人均收入高于臨界值1097時(shí)，增加人均收入對(duì)于預(yù)期的影響。－3.36表示人均收入大于1097國(guó)家增加收入對(duì)預(yù)期的影響與人均收入小于1097國(guó)家增加收入對(duì)預(yù)期的影響之間的差異是－3.36。但是由于t值為－1.34，在5%水平上不顯著，這種差異在統(tǒng)計(jì)上不顯著。人均收入低于1097國(guó)家的回歸線?人均收入高于1097國(guó)家的回歸線?????.0?9.39lnx???3.36（lnx???也就

?不顯著，所以如果我們定義富裕國(guó)家為人均收入大于1097的國(guó)家，那么富裕國(guó)家和貧窮國(guó)家預(yù)期在統(tǒng)計(jì)上沒(méi)有顯著差異的。5.(3’×2=6.7.(3’×2UnrestrictedModel:Yt=γ1+γ2X2t+γ3X3t+γ4X4t+γ5X5t+γ6X6tRestrictedmodelA:Yt=α1+α2X3t+α3X4t+α4X6t+RestrictedmodelB:Yt=β1+β2X2t+β3X5t+β4X6t+J8.Thereisfunctionalformmisspecificationifβ6≠0orβ7≠0,wheretheseare2populationparameterson

andcomten,respectively.Therefore,wetestthesignificanceofthesevariablesusingtheR-squaredformoftheFF ?0.375??2.97?1??0.375?/?177With2and∞df,the10%criticalvalueis2.30,whilethe5%criticalvalueis3.00.Thus,thep-valueisslightlyabove.05,whichisreasonableevidenceoffunctionalformmisspecification.(Ofcourse,whetherthishasapracticalimpactontheestimatedpartialeffectsforvariouslevelsoftheexplanatoryvariablesisadifferentmatter.)9.(3’×2FortheCEVassumptionstohold,wemustbeabletowritetvhours=tvhours*+e0wherethemeasurementerrorehaszeromeanandisuncorrelatedwithtvhours*and0explanatoryvariableintheequation.(NotethatforOLStoconsistentlyestimateparameterswedonotneedetobeuncorrelatedwith0TheCEVassumptionsareunlikelytoholdinthisexample.ForchildrenwhodonotwatchTVatall,tvhours*=0,anditisverylikelythatreportedTVhoursiszero.Soiftvhours*=0thene=0withhighprobability.Iftvhours*>0,themeasurementerrorcan0bepositiveornegative,but,sincetvhours≥0,emustsatisfye≥?tvhours*.Soe tvhours*arelikelytobecorrelated.Asmentionedinpart(a),becauseitisthedependentvariablethatismeasuredwitherror,whatisimportantisthateisuncorrelatedwiththe0explanatoryvariables.Butthisisunlikelytobethecase,becausetvhours*dependsdirectlyontheexplanatoryvariables.Or,wemightarguedirectlythatmorehighlyeducatedparentstendtounderreporthowmuch evisiontheirchildrenwatch,whichmeanseandtheeducationvariablesarenegativelycorrelated.010.Thesampleselectioninthiscaseisarguablyendogenous.Becauseprospectivestudentsmaylookatcampuscrimeasonefactorindecidingwheretoattendcollege,collegeswithhighcrimerateshaveanincentivenottoreportcrimestatistics.Ifthisisthecase,thenthechanceofappearinginthesampleisnegativelyrelatedtouinthecrimeequation.(Foragivenschoolsize,higherumeansmorecrime,andthereforeasmallerprobabilitythattheschoolreportsitscrimefigures.)11.(3’×3=Ithasbeenfairlywellestablishedthatsocioeconomicstatusaffectsstudentperformance.Theerrortermucontains,amongotherthings,family e,whichhasapositiveeffectonGPAandisalsoverylikelytobecorrelatedwithPCownership.Familieswithhigher escanaffordtobuycomputersfortheirchildren.Therefore,family ecertainlysatisfiesthesecondrequirementforaninstrumentalvariable:itiscorrelatedwiththeendogenousexplanatoryvariable[see(15.5)withx=PCandz=faminc].Butaswesuggestedinpart(a),faminchasapositiveaffectonGPA,sothefirstrequirementforagoodIV,(15.4),failsforfaminc.Ifwehadfamincwewouldincludeitasanexplanatoryvariableintheequation;ifitistheonlyimportantomittedvariablecorrelatedwithPC,wecouldthenestimatetheexpandedequationbyOLS.Thisisanaturalexperimentthataffectswhetherornotsomestudentsowncomputers.Somestudentswhobuycomputerswhengiventhegrantwouldnothavewithoutthegrant.(Studentswhodidnotreceivethegrantsmightstillowncomputers.)Defineadummyvariable,grant,equaltooneifthestudentreceivedagrant,andzerootherwise.Then,ifgrantwasrandomlyassigned,itisuncorrelatedwithu.Inparticular,itisuncorrelatedwithfamily eandothersocioeconomicfactorsinu.Further,grantshouldbecorrelatedwithPC:theprobabilityofowningaPCshouldbesignificantlyhigherforstudentreceivinggrants.Incidentally,iftheuniversitygavegrantpriorityto students,grantwouldbenegativelycorrelatedwithu,andIVwouldbeinconsistent.12(3’×3=LetFLbeabinaryvariableequaltooneifa livesinFlorida,andzerootherwise.Lety90beayeardummyvariablefor1990.Then,fromequation(13.10),wehavethelinearprobabilitymodelarrest=0+0y90+1FL+1y90FL+Theeffectofthelawismeasuredby1,whichisthechangeintheprobabilityofdrunkdrivingarrestduetothenewlawinFlorida.Includingy90allowsforaggregatetrendsindrunkdrivingarreststhatwouldaffectbothstates;includingFLallowsforsystematicdifferencesbetweenFloridaandGeorgiaineitherdrunkdrivingbehaviororlawenforcement.Itcouldbeth