联立方程计量经济学模型案例

EquationSstiBation XEquationSstiBation X第六章联立方程计量经济学模型案例1、下面建立一个包含3个方程的中国宏观经济模型，已经判断消费方程式恰好6.1Ct oI6.1Ct oItiYt年份YICG年份YICG19783606137817594691991212807517103163447197940741474200559519922586496361246037681980455115902317644199334501149981568238211981490115812604716199446691192612081066201982548917602868861199558511238772694576891983607620053183888199668330268673215293111984716424693675102019977489428458348551158119858792338645898171998790032954636921125361986101333846517511121999826733070239334126371987117844322596115012000893413250042896139451988147045495763315762001985933746145898152341989164666095852418472001107514423554853516624199018320644491132763表6.1中国宏观经济数据 单位：亿元0It(1)用狭义的工具变量法估计消费方程选取方程中未包含的先决变量 G作为内生解释变量Y的工具变量，过程如下:2cti u1t1Yt U2tCt GtYtSptcificstion加3如缶Equationsp«cificationDtp4nlenlvarit-blaf«llowedLyli工七ofregrtsscriandFDLt*rms?ORuiexplicitaquation1ik@eOle*cdl(-1)Instrumentlist七名Ell(-1Dinclude rtgrsasorstorlintsrsquitionswitJajlkmaEstinatiOILsettingsMethod;TSLS-T^s-StsgeL«»-tSmarts(TSBLS«nd.ARMA) V£皿口工葭B782002取洎熊定取洎结果如下：Depend&ntVariable：C01Method;Two-StageLeastSquaresDate:07/DMBTime20:39Sample(adjusted):19792002Includedobaenrations：24afteradjustmentsInstrumentlist:CGC01(-1)VariableCaefficieniStd.Errort-StatisticProb.C582.27E1192.B6963.0190160.0065Y0.274966O.OZ33DB37493240.DD12001(-1)0.4301240.1702202.5386150.0191R-squarsd0.996744Meandependentvar17685.46AdjustedR-s(iuared0.998624S.D.dependent旧16106.62S.E.afregression5974201SumsquaredrBsid7495127.Durbin-Watsonstat0.6513B9Secord-stageSSR30660161所以，得到结构参数的工具变量法估计量为:0582.2761,710.274856,?20.432124(2)用间接最小二乘法估计消费方程消费方程中包含的内生变量的简化式方程为:Ctio iiCti 12Gt itY20 2iCti 22Gt 2t参数关系体系为:

21 2120 21 2120 0122 010 012用普通最小二乘法估计，结果如下：DependentVariable;C01Method:LeastSquaresDate:07«4/08Time:20:48Sample(adjusted):19792002includedobBsrvationB：24afteradjustmentsVariableCoefTicienitStdErrort-StatisticProb.CC01(-1)G1135.9370.619782123989941口.312口 2,5796700.273112 22683310.7610G1 1E5O3E10D1750,D3390.1136^squared0.993521Meandependent哂n17E85.46AdjustedR-squared0992904SDdependentvar16106.62S.E.ofregression1356820Akaikeinfocrilorion17.38014Sumsquaredresid38660181Schurzcriterion17.62740Loglikelihood-20S.5617Fstatistic1610.049Durbin-Walsonstat06B1227ProbQF'Statistic)0.000000DependentVonable:VMethod:LeastSquaresDate:O7A]J/a8Time-20:49Sample(adjusted):19792DQ2Includedobservations：24afteradjusimenisVariableCoefficientStd,Errort-StatidicProb.C2014.3681036.7351S42992O.OB55CQ120.6927500.6430121061800口.3004G4.51106417S02692.5511010.0185R-squared0992382Weandependent?ar37435.3SAdjustedR-squared0.991656S.D.dependentvar34371.77SEofregression3194.479Akaikein1bcriterion19.09270Sumsquaredresid214E-HJ8Schwarzcriteriori19.23995Loglikelihood山丘】I25/statistic1367765Durbin-Watsonstat0729172Prob(F-statistic)0.000000所以参数估计量为:Z01135.937,?110.619782,?21.239898?20 2014.368,?210.682750,%4.511084所以，得到间接最小二乘估计值为：2c?口0.27485611 12210.432124■10 -1-20582.2758EstmnateIForecast15tatsResids,EstmnateIForecast15tatsResids,1 .一一*JL，— ,20022002?nt2S3S.1G22230.80913.72950ri0294560.0000000.0019120.998088(3)用两阶段最小二乘法估计消费方程第一阶段使用普通最小二乘法估计内生解释变量的简化方程，得到Y?2014.3680.68275cti4.511084Gt用Y的预测值替换消费方程中的Y,直接用OLS估计消费方程，过程如下:^EViews-[^qua-tion:UHiriLEDTorkfile:UHTITLED:rUntitled\]120000100000-B0000-6000040000-2000C-口.*20000-Path二c；\docui»ant£mdia11ings\zhuyixi^tnydocvnantsDE=non*IF二untitlad也可以用工具变量法估计消费方程，过程如下:EquationEsHtiRat:zlon结果如下:neigKtixtgmairix:。neigKtixtgmairix:。agMsection(WhiteCov@rimt (HDependentVariable:001Method:Two-StageLeastSquaresDate:07«4/0eTime:21:03Sample(adjusted):19792002includedoheeivatiuiisr24afteradjustmentsInstrunrtentlist:CYFC01^-1)Vari^t>leCoefficientSid.Errort-Statisti。Prob.502.27611928696 3.019015000650.2743550.073308 3.743c240.0012001(-1)0.4321240.170220 2.5386150.0191ZquarM0.99674Jb/leandependentvar17605.46AdjustedF?-squared0.99时4S.D.dependentvar16106.62S.E.ofregression597.4201Sumsquaredresid7495127Durbin-Watsonst0.651369Second-stageSSR33660161综上所述，可知道，对于恰好识别方程，三种方法得到的结论是一样的。(4)用两阶段最小二乘法估计投资方程，过程同上。(5)投资方程是过度识别的方程，也可以用GMM估计，选择的工具变量为先决变量 C01、GoEquationE2ti&a±ianSp^eifixationOutionsEquatlon.speci£1cationDepeitdentvariatlq£》110时艺dbylisto£OandPDLterm51fORaneiplicitrr±nc^^ae，鱼邕目专口r^gr«ss^rs“rr±nc^^ae，鱼邕目专口r^gr«ss^rs“▼. ”■■L.!H■■L号qiu&OOtaberorBWVariable餐N◎留总厂W*电HACoptions

口*ewhitemrImstrumentlistBuidwidth.ccOl(-1)gBuidwidth.EsAiEsAi哂*settingsMethoA:S削Tl?l*；GflM-(jenerslisedMethodofMomentsirraanz确定 取消估计结果如下:EQuation:UNTITLEDVorkfile:第一痘门匕阮Proc|ObjE-d网闺回旭帕ee闺”[三tm也」以25汨5।ependentVaraljle：Ilethod:GeneralizedMethodofMomentsate:05/04/T]9Time:22Mample(adjusted):19792002icludedlubserotions：24afleradju-strnentsernel：Bartlett(Bandwidth:Fixed(2),Noprewhiteningimultaneousweightingmatrix&coafficientiterationonvergenceachiei^daft削：6weightmatrices,9totalcoefiterations：istrumeritlist:CCO1(-1)GVariableCoefficientSid.ErrorbStatisticProb.C-139.53S815714E5-0.8382720.3840¥0.3323140005292 72.343360.0000R-equared0.996353Maand&pendent-r1431a54AdjusiedR-squared0.99G1S7S.D.dependentvar13464.79S.E.ofregressionS31.4684Sumsquaredresid16209108Durbin-Watsonstat0744K1J-stati&tic0.039126与2SLS结果比较，结构参数估计量变化不大。残差平方和由变为，显著减少。为什么？利用了更多的信息。2.以表6.2所示的中国的实际数据为资料，估计下面的联立模型。Yt 0 1Mt 1ct 2ItU1tMt0 1Y 3Pt u2t表6.2年份货币于准货币M2/亿元国内生产总值GDP/亿元居民消费价格指数P(1978为100居民消费CONS/亿元固定投资I/亿元199015293.418319.5165.29113.24517199119349.921280.4170.810315.95594.5199225402.225863.7181.712459.88080.1199334879.834500.7208.415682.413072.3199446923.546690.7258.620809.817042.1199560750.558510.5302.826944.520019.3199676094.968330.4327.932152.322913.5199790995.374894.2337.134854.624941.11998104498.579003.3334.436921.128406.21999119897.982673.1329.739334.429854.72000134610.389112.533142911.932917.7建立工作文件后，进行如下步骤:建立联立模型，并命名为MY在SYSTEM窗口里面定义联立方程组和使用的工具变量DSystgv;IT lorkfilg=U1TTITLED;;Untitled\[ViewUPr□匚[objEut][Prril:]rianie[Freeze[Mei3P已斌[Estimate|和二匚|.讨日!:与艮/小gdp=c(T^cpp^+^P7^^^7^m2=c(5)+cp)*qdp+c(7)*pinstconsipd 一选择两阶段最小二乘法进行估计得到如下输出结果:

System:MYEsiirri琳innMethod：Two-StageLeastSquaresDate07^05/08Tine:12:38Sample:19902000Includedcbsetvatiions：11TotalSYTiem(b寻Enced)nb日en就ion、22i-oefficientStd.Errort-StatisticProb.-13比E3726.9939-1，四6日56口.□925。1506320.023877-5.2127950.00012063E40Q15396713.403160.00000.G6B3750,1664984.1224240.000943243.344524.6759,5572250.0000293B120O.OS357929804700.0000-51141273563530-14.35126n.noooDeterminarrtresidualcovariance5S4E+1Equation.GDP=C(1^C(2rM2+C(3rCONS+C(4riInstnjrments:COM3IPCObservations;11R'Squared0.399538Meandependentvar54470.32AdjustedR-squared0.999425S.D.dependentvar36264.98S.E.ofregression630.2518Sunnsquaredresid2730522.Durbin-Watsonstat2.261178Equation.M2=C⑸+C⑹*GDP+C(7)*PInstnjnrtents:CONSIPCObservations11R-squared0.993418Meand&pendentvar66245.11AdjustedR-squared0..998023S.D.dependentvar41923.75S.E.o(fregression1864,293Sunnsquaredresid27304720Durbin-Watsonstat1.293522所以得到联立方程计量经济学模型的估计表达式为:Y1306.30.151Mt2.064Ct0.686ItMt43243.342.938丫511.413P3、以Klein（克莱因）联立方程模型为例介绍两阶段最小二乘估计首先建立工作文件，数据如表 7。表6.3Klein联立方程模型数据年份CCPPWPIIKKXXWGGGTTAA192039.812.728.82.7180.144.92.22.43.4-11192141.912.425.5-0.2182.845.62.73.97.7-1019224516.929.31.9182.650.12.93.23.9-9192349.218.434.15.2184.557.22.92.84.7-8192450.619.433.93189.757.13.13.53.8-7192552.620.135.45.1192.7613.23.35.5-6192655.119.637.45.6197.8643.33.37-5

192756.219.837.94.2203.464.43.646.7-4192857.321.139.23207.664.53.74.24.2-3192957.821.741.35.1210.66744.14-219305515.637.91215.761.24.25.27.7-1193150.911.434.5-3.4216.753.44.85.97.50193245.6729-6.2213.344.35.34.98.31193346.511.228.5-5.1207.145.15.63.75.42193448.712.330.6-320249.7646.83193551.31433.2-1.319954.46.14.47.24193657.717.636.82.1197.762.77.42.98.35193758.717.3412199.8656.74.36.76193857.515.338.2-1.9201.860.97.75.37.47193961.61941.61.3199.969.57.86.68.9819406521.1453.3201.275.787.49.69194169.723.553.34.9204.588.48.513.811.610建立Klein联立方程组，模型如下：CC0 1PP 2PP（1） 3（WPWG） （消四程）II 0 1PP 2PP（ 1） 3KK （投加程）WP 0 1XX2XX（ 1） 3AA （私人工资方程）XX CC II GG （均衡需求恒等式）PP XX TT WP （私人利润恒等式）KK KK（1） II （私人存量恒等式）使用的工具变量是：WGGGTTAAPP（-1）KKXX（-1）C过程如下:®EVICTSfileEdit01ject¥ierrFrscckOptionsWindx>wHelj口Ttfrfcf|ViewE^Ell'Rang事1口Ttfrfcf|ViewE^Ell'Rang事1Sample1旦Objtel..LGenerateSeries..EreikLinks..IS画丘丘0SI3叼IsslsIS日日cCC99IIkk吓residttwg螂KXFetohfromDRUpdattseltcledfromDB.StoreselectedtoDE...Copy .FrinASelected选择System,并起名为KleinModel33个方程），不需定义方程（后3个方在窗口空白处输入方程指令，只要求写行为方程（前程），最后一行命令列出的是所用工具变量。□Systft^:KLELNIODELTorktile:CA5ET：:Case7\加网||pr□匚口口bl日三|print|崛me|卜照日旬加日耳鼻T曰虫E罚ma⑹|3pe[J国就5帕日筝也cc=c0)+cQ)*pp+c⑶*pp(-1)十匚(4)*(wp+wg)ii-c(5)+c(6)*pp+c(7rpp(-l：|+c(8)*kkwp=c(9)+c(10)*xx+c(11j「xM*1)+c(12)*a3instwgggtt3app(-1)kkxx(-1)c|对联立方程进行估计：点击 system窗口上的estimate键□Systew;KLELN1ODELWorkfilezCASE?:zCase7\J司Jv«w||PrQc][0bgctl|P2ny^m61FgKlllM^^^^^^^^^^^j|skitsJ|Resids|cc=cf1)+c(2)*pp+c(3)*ppG1)+c(4)*(wp-Hr/g)H-c(5)+c(5)*pp+c(7J*pp(-1j-Fc(8)*kkwp=c[9>c(1口『关瓦十c(11/我1)十c(12)*aainslwgjgttaapp(-1)kkc|选才i2TSLS即两阶段最小二乘估计X]Tstin.akionM*th*dIterationOptionsEstiimationsettingsMethod.OrdinftrjrLe包写tSquares ▼EstiimationsettingsMethod.OrdinftrjrLe包写tSquares ▼OrdinwjrL■电零由Squar*s"idgivlgilLS.(equationweigjits)口吧电1叱电W即室约旦呷_Two-SlaoLaastTwfr-Stij^L号3二t 与Thrs-St*qaL«astSquw”FmII vilM郸iim刖GUM-CrcsESecticn(Whitecov.)01--Timeseries(HACJKernel*,BartleltQuadraticBaridwidtkHNvwnb*ror训£w♦AinilrewsVariable1-敢消确定

敢消得到如下Klein联立方程的估计结果:CoefficientStd.Errort-StatisticPrah.C⑴15564761.467^7911,277250.0000C0□.0173020.1312050.1310720.9956C0)0.21^340.1192221.0137140.07560(4)□,0101930.04473518110G90.0000c⑸2027H218.3832492.4183960J192c⑹0.1502220.19253407802370,4389C(7)0.6159440.1809263.4043980.0013c⑻-0.1577880.040152-3.9297510.D0D3C⑶1.5002971127563611760700.2450C(10)0.438659003960311081650.0000C(11)0.1466740.043164339S0630.0013eg)013039600323BS4.0260010.0002Determinantresidualcomnance0.287714Equation:COC(1)+C0*PP+C(3)*PP(-1)+C(4r(WP-fWG)Instruments:WGGGTTAAPP(-1)KKXX(-1JCObservations:21^squared0.976711Meandsperdentvar53.99624AdjustedR-squared0.972601S.D.dependentvar6.060066S.Eofregression1135659Sumsquaredresid21,92525Dijrbin-Watsorstat1456072Equation:ll=C(5)+C(E)*PP+C(7)*PP(-1)<pfl<l<Instruments:WGGGTTAAPP(-1)KKXX(-1JCObseivations:21^squared□.084884Mearideperdentvar1.266667AdjustedR-squared0.064559S.D.dependentvarm一的g瑞S.E.ofregression1.307149Sumsquaredresid29.046BEDurbin-Watsonst3t2旺6334Equaticn.WP=C®+C(W)*2<X+C(11)*XX(-1)+C02rMInstruments：WGGGTTMPP(-1)KKXX(-1)CObser/ations;21R-squared0.967414Meandependentvar36,36190AdjustedR-squared0.985193S.D.dependentvar5.304401S.E.ofregression0767155Sunsquaredresid10.00496^ijrbin-Watsonstat1.963416上述输出结果与线性单方程分析相同。1.对联立方程组进行预测联立方程的预测是以上述倩计结果为基础进行的。主要分为3步：第1步：建立模型斗，ETievs—[Sys^zcm:ELELHIOftEL Wortfile:CASE7z:CeFlitEAi1Ofcjecl?工色WProC^uickOpli6HSWinlowHelpWew随而曰[ob归d:|[print][hl茵同什ee瑞]〔MetjeTe工t][E5tinnate][5p巳匚][5tatslRe5idi)SysEstDatEstiina.ie...Residual5M0咕Endo^nou.£GrouptSquaresSarMahe瓯册1InclUpdateCoefsfromSys14mTotalsysiemi口即彳ncenjODS?n*anorTS63CoefficientStdErrort-StatisticProbc⑴16.554761.46757911277250.0000CQ)0.017302□1312050.131072□9956cp)02152340.1192221.31371400736出现如下对话框:□■odd:UWTITLEDTarkfilc;C4SE7：:CaseTXMem.||Fr口二||Obi日匚|Prnthjarre|Freeze||5ol-e|Equations||j'sfistiles||~evtEquations:3 BaselineS]KLEINMODEL Eq1.cc,ii.wp=F(33,kk-pp,*vg,wpHxx)第2步：输入定义方程由于在设定联立方程时没有输入定义方程，因此在求解模型时应该加入，否则，模型只识别System中设定的内生变量。加入定义方程的方法如下：输入需要加入的定义方程：YodelSourceEditEntwr电。工moxeIiilss：kjc=cc+li+居工pp=xx-tt-wplri^kk[T)*ii|

这时模型窗口如下:□lodelzUWTITLEDTorkfile：CASE7;：Case7\-LJlgJfeSf「比心［门□匚Robieq[print]Njnie)Fre日回回嗝EqLial:iDrg,[vaHab后已[日Equations:6Baseline■.■■■(■.■■■(Xx=CC-i-ii+ggEq1xx=F(cc,gg,ii)"pp=kx-tt-wp"Eq2叩二F(tt,wp,MX)・kk=kk(-1)十廿”Eq?kk=F(ii,kk)KLEINMODELE咽一GchII,wp=F(aa,kk,pp,wg,wp,kkI第3步：求解模型以随机性、静态预测为例，其他四个模块选择默认状态。□lodelzUNTITLEDTartfilezCiSE7：：Case7\以随机性、静态预测为例