計量經(jīng)濟分析（第六版）答案 Answers5

DepartmentofEconomicsNYUfSTERNDepartmentofEconomicsNEWYORKUNIVERSITYLEONARDN.STERNSCHOOLOFBUSINESSECONOMETRICSIFall2007-Tuesday,Thursday,l：00-2：20ProfessorWilliamGreeneOffice:KMC7-78ProfessorWilliamGreeneOffice:KMC7-78OfficeHours:OpenURLforcoursewebpage:Homepage:/^wgreeneEmail:wgreene@/^wgreene/Econometrics/Econometrics.htmAssignment5HypothesisTestsandPredictionThefollowingexercisesusethegasolinedatawhichwehaveusedatvariouspointsbefore.Allvariablesinallregressionsdiscussedbelowareassumedtobelogarithms.Assuch,intheresultstofollow,allestimatedcoefficientsareestimatesofelasticities.Inthefollowing,g=log(1QOQOO^GasQ/Pop\Ps=log(GasP),y=\og(PCIncome),etc.Thecorrelationofgandpsispositive.Intheregressionofgonaconstantterm,pgandy,theslopeonpgisnegative.Obtaintheempiricalvaluesofthesetwocoefficients,thenreconcilethenumericalresults(i.e.,explainhowthisresultarises).+ +1Ordinaryleastsquaresregression1IModelwasestimatedDec09,2005at03:33:16PM |ILHS=GMean =3.309784 |1Standarddeviation=.2384918 |IWTS=noneNumberofobservs. =52 |IModelsizeParameters =3 |1Degreesoffreedom=49 |1ResidualsSumofsquares =.1768978 |1Standarderrorofe=.6008459E-01|1FitR-squared =.9390175 |1AdjustedR-squared=.9365284 |1ModeltestF[2, 49](prob)=377.25(.0000)|IDiagnosticLoglikelihood =73.98430 |1Restricted(b=0) =1.257919 |1Chi-sq[ 2](prob)=145.45(.0000)|IInfocriter?LogAmemiyaPrd.Crt.=-5.567914 |1AkaikeInfo.Criter.=-5.568042 |IAutocorrelDurbin-WatsonStat. =.0875278 |1+ Rho=cor[e,e(-1)] =.9562361 | +TOC\o"1-5"\h\z+ + + + + + +IVariable | Coefficient | StandardError |t-ratio |P[|T|>t] I Meanof X|+ + + + + + +ConstantPGY-5.42315723-.17124062.96864830.58200599.03788798.07376161-9.318-4.52013.132.0000.0000.00003.729302969.67487347Thisisanapplicationofthe“l(fā)eftoutvariable“result.ThepartialcorrelationbetweenlogGandlogPGisnegativewhenlogYisincludedintheequation.Consideranonlinearregressionmodeloftheformg=Pi+P2Pg+P3y+^y2+￡?Uselinearleastsquarestoestimatethecoefficientsofthemodel.ThemarginaleffectofyonE[g\pgfy]isdE[g\pgfy]/dy=p3+2p4y,whichdependsony.Formaconfidenceintervalforthismarginaleffectatincome二PCIncome二$27,208(log=10.2113,the2004value).[Note,theestimateisoftheform卬也+w2b4wherew\=land卬2=log(40).]Youwillneedtoestimatethevarianceofthisstatisticusingyourregressionresults.(IfyouareusingLIMDEP,include;PRINTVCinyourregressioncommandtodisplaythematrixyouneed.YoucanaccessthismatrixfromtheprojectwindowintheMatriceslist-itisVARB.Ifyouareusingsomeotherprogram,usewhatevercommandyouneedtodisplaythecovariancematrixforyourregressioncoefficientestimates.)OrdinaryleastsquaresregressionModelwasestimatedDec09,2005at03:34:01PM |LHS=GMean=3.309784 |Standarddeviation—.2384918 |WTS=noneNumberofobservs.=52 |ModelsizeParameters=4 |Degreesoffreedom=48 |ResidualsSumofsquares—.4212751E-01|Standarderrorofe=.2962527E-01|FitR-squared=.9854773 |AdjustedR-squared—.9845696 |ModeltestF[ 3, 48](prob)=1085.72(.0000)|DiagnosticLoglikelihood=111.2909 |Restricted(b=0)=1.257919 |Chi-sq[ 3](prob)—220.07(.0000)|Infocriter.LogAmemiyaPrd.Crt.=-6.964147 |AkaikeInfo.Criter.=-6.964452 |AutocorrelDurbin-WatsonStat.=.2957574 |Rho=cor[e,e(-1)]—.8521213 |+ ++ + + + + + +IVariable | Coefficient | StandardError |t-ratio |P[|T|>t] | Meanof X|+ + + + + + +Constant-51.77453633.75147646-13.801.0000PG-.12775157.01900782-6.721.00003.72930296Y10.6526137.7823269213.617.00009.67487347Y2-.50683621.04090090-12.392.000093.7224759Cov.Mat.has4rowsand4columns.123411| 14.07358-.00822-2.93352.152992| -.00822.00036.00210-.0001431 -2.93352.00210.61204-.031964I .15299-.00014-.03196.00167Matrix-->calc;y2004=10.2113$->calc;me=b(3)+2*b(4)*y2004$->calc;twoY=2*y2004$->matr;gme=[0,0,1,twoy]$->matr;vme=gme*varb*gme1$->calc;list;sdme=sqr(vme);lower=me-l.96*sdme;upper=me+l.96*sdme$SDME=?64957406920785750D-01LOWER=?17438393601108600D+00UPPER= .42901697114056610D+00

UseanFtesttotestthehypothesisthatthethreemacroeconomicpriceindexes,PN,PD,PS(remembertotakelogs)donothaveasignificantinfluenceong.->crea;lpd=log(pd);lpn=log(pn);lps=log(ps)$-->regr;lhs=g;rhs=onezpg,y$+ +OrdinaryleastsquaresregressionModelwasestimatedDec09,2005at03:40:10PMLHS=GMean=3.309784Standarddeviation—.2384918WTS=noneNumberofobservs.=52ModelsizeParameters=3Degreesoffreedom=49ResidualsSumofsquares=.1768978Standarderrorofe=.6008459E-01FitR-squared=.9390175AdjustedR-squared=.9365284ModeltestF[ 2f 49](prob)—377.25(.0000)TOC\o"1-5"\h\z+ + + + + + +IVariable | Coefficient | StandardError |t-ratio |P[|T|>t] | Meanof X|+ + + + + + +Constant -5.42315723 .58200599 -9.318 .0000PG -.17124062 .03788798 -4.520 .0000 3.72930296Y .96864830 .07376161 13.132 .0000 9.67487347-->calc;ss0=sumsqdev$-->regr;lhs=g;rhs=one,pgzy,Ipn,Ipd,lps$+ +OrdinaryleastsquaresregressionModelwasestimatedDec09,2005at03:40:10PMLHS=GMean=3.309784Standarddeviation—.2384918WTS=noneNumberofobservs.=52ModelsizeParameters=6Degreesoffreedom=46ResidualsSumofsquares—.6931595E-01Standarderrorofe=.3881840E-01FitR-squared=.9761045AdjustedR-squared—.9735072ModeltestF[5, 46](prob)=375.81(.0000)+ +TOC\o"1-5"\h\z+ + + + + + +IVariable | Coefficient | StandardError |t-ratio |P[|T|>t] | Meanof X|+ + + + + + +Constant-11.5868243.86301823Constant-11.5868243.86301823-13.426.0000PG-.00010939.06072810-.002.9986Y1.66842867.0964487017.299.0000LPN-.14775813.25408578-.582.5637LPD.38989123.102788463.793.0004LPS-.54403942.14749686-3.688.0006-->calc;ssl=sumsqdev$-->calc;list;f=((ss0-ssl)/2)/(ssl/(n-6))$F = .35697146682999960D+023.729302969.674873474.236890804.239066034.17535768ThisFvalueisstatisticallysignificantatanylevel.Thenullhypothesiswouldberejected.UseanFtesttotestthehypothesisthatthecoefficientonthelogofthepriceofgasolinechangedin1974whileallothercoefficientsinthemodelwereunchanged.Retainthethreemacroeconomicpriceindicesinyourequation.

-->calc;ssl=sumsqdev$-->calc;list;f=((ss0-ssl)/2)/(ssl/(n-6))$F = .35697146682999960D+02-->crea;post73=(year>1973);pgpost=pg*post73$IStandardError|t-ratio|P[|T|>t]IMeanofX|——>regr;lhs=g;rhs=onezpg,yzlpnzlpdzlpszpgpost$IStandardError|t-ratio|P[|T|>t]IMeanofX|Ordinaryleastsquaresregression |ModelwasestimatedDec09,2005at03:44:41PM |LHS=GMean=3.309784 |Standarddeviation—.2384918 |WTS=noneNumberofobservs.=52 |ModelsizeParameters=7 |Degreesoffreedom=45 |ResidualsSumofsquares—.6492501E-01|Standarderrorofe=.3798392E-01|FitR-squared=.9776182 |AdjustedR-squared—.9746340 |ModeltestF[ 6, 45](prob)=327.59(.0000)|DiagnosticLoglikelihood=100.0451 |Restricted(b=0)=1.257919 |Chi-sq[ 6](prob)=197.57(.0000)|Infocriter.LogAmemiyaPrd.Crt.=-6.414891 |AkaikeInfo.Criter.=-6.416535 |AutocorrelDurbin-WatsonStat.—.4675473 |Rho=cor[eze(-1)]=.7662264 |++++——4-Constant-10.44207171.06944563-9.764.0000PG-.01819773.06032044-.302.76433.72930296Y1.60143627.1018889915.717.00009.67487347LPN-.46157859.30687690-1.504.13954.23689080LPD.33622707.105177733.197.00254.23906603LPS-.28821546.20575297-1.401.16814.17535768PGPOST.02365052.013556941.745.08792.52846745IVariable|Coefficient++++-->calc;ss2=sumsqdev;list;fpost=((ssl-ss2)/I)/(ss2/(n-7))$FPOST= .30433917587987170D+01TheFisnotsignificant-thePvalueis.0879.NotethatFisthesquareofthetstatisticintheregressionresults.Continuingpartd,testthehypothesisthattheentiremodelshiftedin1974,i.e.,thatentirelydifferentregressionmodelsappliedbefore1974andfrom1974onward.UseaChowtest.-->Sample;1-52$-->regr;lhs=g;rhs=one,pg,y,Ipn,Ipd,lps$OrdinaryleastsquaresregressionModelwasestimatedDec09,2005at03:49:35PM |LHS=GMean=3.309784 |Standarddeviation=.2384918 |WTS=noneNumberofobservs.=52 |ModelsizeParameters=6 |Degreesoffreedom=46 |ResidualsSumofsquares=.6931595E-01|Standarderrorofe=.3881840E-01|FitR-squared—.9761045 |AdjustedR-squared=.9735072 |ModeltestF[5, 46](prob)=375.81(.0000)|DiagnosticLoglikelihood=98.34362 |Restricted(b=0)=1.257919 |Chi-sq[ 5](prob)=194.17(.0000)|Infocriter.LogAmemiyaPrd.Crt.=-6.388522 |AkaikeInfo.Criter.—-6.389555 |

TOC\o"1-5"\h\zIAutocorrelDurbin-WatsonStat.= .4511786 |I Rho=cor[e,e(-1)]=.7744107 |+ 4-+ + + + + + +IVariable | Coefficient| StandardError|t-ratio |P[|T|>t]| MeanofX|+ + + + + + +ConstantPGYLPNLPDConstantPGYLPNLPDLPS-11.5868243-.000109391.66842867-.14775813.38989123-.54403942863018230607281009644870254085781027884614749686-13.426-.00217.299-.5823.793-3.688.0000.9986 3.72930296.0000 9.67487347.5637 4.23689080.0004 4.23906603.0006 4.17535768->Calc;ss_all=sumsqdev$-->Reje;post73=0$-->regr;lhs=g;rhs=one,pg,y,Ipn,Ipd,lps$+ +IOrdinaryleastsquaresregression |IModelwasestimatedDec09,2005at03:49:36PM |->Calc;ss_all=sumsqdev$-->Reje;post73=0$-->regr;lhs=g;rhs=one,pg,y,Ipn,Ipd,lps$+ +IOrdinaryleastsquaresregression |IModelwasestimatedDec09,2005at03:49:36PM |I LHS=G Mean = 3.469481 |I Standarddeviation = .7095988E-01 |I WTS=none Numberofobservs. = 31 |I Model size Parameters = 6 |I Degreesof freedom = 25 |I Residuals Sumofsquares = .5248486E-02 |I Standarderrorofe = .1448929E-01 |I Fit R-squared = .9652554 |I AdjustedR-squared = .9583065 |IModeltestF[5, 25](prob)=138.91(.0000)|I Diagnostic Loglikelihood = 90.61185 |I Restricted(b=0) = 38.53601 |I Chi-sq[5] (prob)=104.15(.0000)|Infocriter.LogAmemiyaPrd.Crt.= -8.291761AkaikeInfo.Criter.=-8.296706IAutocorrelDurbin-WatsonStat.= .9925038 |I Rho=cor[eze(-1)] = .5037481 |+ +Constant-3.680227741.28954452-2.854.0086PG-.16037492.03091908-5.187.00004.24130024Y.75407900.133205885.661.00009.92138226LPN.40440099.199409772.028.05334.70939062LPD.01238540.06367906.194.84744.61615756LPS-.33722011.15797771-2.135.04284.78397912+ + + + + + +IVariable | Coefficient | StandardError |t-ratio |P[|T|>t] | Meanof X|+ + + + + + +-->Calc;ss_pre=sumsqdev$-->Include;new;post73=1$-->regr;lhs=g;rhs=one,pg,y,Ipn,lpdzlps$OrdinaryleastsquaresregressionModelwasestimatedDec09,2005at03:49:36PMLHS=GMean—3.469481Standarddeviation=.7095988E-01WTS=noneNumberofobservs.=31ModelsizeParameters=6Degreesoffreedom=25ResidualsSumofsquares=.5248486E-02Standarderrorofe=.1448929E-01FitR-squared=.9652554AdjustedR-squared=.9583065ModeltestF[5, 25](prob)=138.91(.0000)DiagnosticLoglikelihood—90.61185Restricted(b=0)—38.53601Chi-sq[ 5](prob)=104.15(.0000)Infocriter.LogAmemiyaPrd.Crt.—-8.291761AkaikeInfo.Criter.=-8.296706AutocorrelDurbin-WatsonStat.=.9925038+ ++ + + + + + 4-IVariable| Coefficient | StandardError |t-ratio |P[|T|>t] I Meanof X|+ + + + + + +Constant-3.680227741.28954452-2.854.0086PG-.16037492.03091908-5.187.00004.24130024Y.75407900.133205885.661.00009.92138226LPN.40440099.199409772.028.05334.70939062LPD.01238540.06367906.194.84744.61615756LPS-.33722011.15797771-2.135.04284.78397912Rho=cor[ezRho=cor[eze(-1)].5037481->Calc;ss_post=sumsqdev$-->Calc;list;F=((ss_all-(ss_pre+ss_post))/6)/((ss_pre+ss_post)/(n-12))$F- = .17744175824374870D+02TheFstatisticisquitelarge.Thehypothesisthattheparametersareunchangedshouldberejected.2.Usingthemodelfrompart1,reestimatetheregressionmodelusingthe1953-2003data(leavingout2004).Then,useyourestimatedmodeltopredictthe2004valueofGasQ(notlog100000*logGasQ/Pop).Howwelldidyoudo?Explainallyourcalculations,andshowthecomputationsindetail.-->