聯(lián)立方程計量經(jīng)濟學模型案例

1、.word格式,第六章聯(lián)立方程計量經(jīng)濟學模型案例1、下面建立一個包含3個方程的中國宏觀經(jīng)濟模型，已經(jīng)判斷消費方程式恰好識別的，投資方程是過度識別的。對模型進行估計。樣本觀測值見表6.1Ct =入二 iYt ,二 2孰Ut，I t = £ * BlYt * U2tYt=It +Ct +Gt表6.1中國宏觀經(jīng)濟數(shù)據(jù)單位：億元年份YICG年份YICG19783606137817594691991212807517103163447197940741474200559519922586496361246037681980455115902317644199334501149981568238

2、211981490115812604716199446691192612081066201982548917602868861199558511238772694576891983607620053183888199668330268673215293111984716424693675102019977489428458348551158119858792338645898171998790032954636921125361986101333846517511121999826733070239334126371987117844322596115012000893413250042896

3、139451988147045495763315762001985933746145898152341989164666095852418472001107514423554853516624199018320644491132763(1 )用狹義的工具變量法估計消費方程選取方程中未包含的先決變量G作為內(nèi)生解釋變量 Y的工具變量，過程如下：結果如下：Dependent Variable: C01Method: Two*Stage Least SquaresDate: 07/D4/08 Time: 20Sample (adjusted): 1979 2002Included observatio

4、ns: 24 after adjustmentsInstrument list: C GVariableCoefficientStd. Errort-StatisticProb.C5822761192.869B30190150.0065Y0,2748560.07330S37493240 001281(-1)0.4321240.1702202.5336150.0191R-squaned0.998744Mean dependent var1769546Adjusted R-squared0.998624S.D. dependent var16106.62S.E of regression597 4

5、201Sum squared resiid7495127.Durbin-Wartson stat0.851389Second-stage SSR38660181所以，得到結構參數(shù)的工具變量法估計量為20=582.2761, 2=0.274856, % =0.432124(2)用間接最小二乘法估計消費方程消費方程中包含的內(nèi)生變量的簡化式方程為Ct =二10Y =二20二 11Cj 二 12Gt":二 21ct,二 22 Gt參數(shù)關系體系為用普通最小二乘法估計，結果如下：Dependent Variable: C01Method: Least SquaresDate: 07AJ4ZJ8

6、Time: 20:48Sample (adjusted): 1979 2002Included observations: 24 after adjustmentsVariable Coefficient Sid Error i-Statistic ProbC1135.937440 34202.5796700.01758(-1)0.61197820.2731122.2693310.0339G1.23989807510611.6608610.1136R-squared0.993521Mean dependent var17685 46Adjusted F?-squared0.992904S.D.

7、 dependent var16106.62S E. of regression1356 820Akaike info crrterion17.3S014Sum squared resid38660101Schwarz criterion17.52740Log likelihood-205.5617F-statistic1610049Durbin-Watson stat0.661227Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate 口7也Ml日 Time: 20:49Sample (adjusted

8、): 1979 2002Included observations: 24 alter adjustmentsVariableCoefficientStd. Error t-St8ti9ticProb.C2014.3681036.7351 9429920.0655C01(1)0 6827500 6430121.0610000.3004G4.5110841.7682892.5511010.0186R-squared0 992382Mean dependent var37485.38Adjusted R-squared0.991696S.D. dependentvar34971.77S E. of

9、 regression3194.479Akaike info cniterion19 09270Sum squared resid2.UE+OBSchwarz criterion19.23996Log likelihood-226.1125F，statistic1367.765Durbin-Watson stat0.729172P ro b(F-statistic)0.000000所以參數(shù)估計量為病0 =1135.937,% =0.619782,闕2 =1.239898%0 =2014.368, 221 = 0.682750, ?22 = 4.511084所以，得到間接最小二乘估計值為=0.2

10、74856?2:?2 =?1- ？1?0 = 582.2758(3)用兩階段最小二乘法估計消費方程第一階段使用普通最小二乘法估計內(nèi)生解釋變量的簡化方程，得到Y? =2014.368 0.6827 4.511084Gt用Y的預測值替換消費方程中的Y,直接用OLS估計消費方程，過程如下：Equation: TJWTITLED Torkf lie: UKTITLED: sUntitled, v"jpif ¥*|PrQc|.Objet: |印叫|W嘩晌日電e 同門日匕任口再陽1回 R坐i由150000100000-SOOOQ-6000040000200000-：0000-29B8.

11、162 2280.309 1372950 O02S456OOOOOOO 0.001912 0.996038iir30 022002200224or3 ntYFFith = c：JocumorLt£ uid s«ttingszhuyiximy documenteDB = non府WF 二 皿titled也可以用工具變量法估計消費方程，過程如下：Equation EstisationSpicifi cati t>n 口似jgS |Equation specificatioiiBep«ikdent variablt followed Ly list of regr

12、essors 皿d PDL ter曲5,OR 皿 explicit equation liGeuDl c:產(chǎn) ul D.Instruxnent list c yf cOl (T)eluderegres Ears tor Linear equticns wi tn JUiMA確定取消 -結果如下：Dependent Variable: C01Method: Two-Stage Least SquaresDate: O7yD438 Time; 21 03Sample (adjusted): 1979 2002Included observations: 24 after adjustmentsIn

13、strument list: C YF C01(-1)VariableCoefficientStd. ErrorProbC502.2761192.86963.0190150.0065Y0.274356 0733083.7493240.00120.43212400.0191R-s(uared0.998744Mean dependent var17685.46Adjusted R-squared0.998624S.D dependent var16106,62S E. of regression597.4201Sum squared resid7495127.Durbin

14、-Watson stat0.851389Second-stage SSR38660181綜上所述，可知道，對于恰好識別方程，三種方法得到的結論是一樣的(4)用兩階段最小二乘法估計投資方程，過程同上。(5)投資方程是過度識別的方程 ，也可以用 GMM 估計，選擇的工具變量為先決變量C01、 Go估計結果如下Equation: UNTITLEDforkf ilez 第一題二二 Dirt.I1 H I Xiiwproi: | Object (Print (Name Freeze | E&tim就e幟e與也.ependent Variable. Ilethod: Generalized Met

15、hod of Mamentsate: 05/OW9 Time: 22:14ample (adjusted): 1979 2002icludedl observations: 24 after adjustmentsernel： Bartlett, Bandwidth: Fixed (2), No prewhiteningimultaneous weighting matrix & coefficient iterationonvergence achieved after: B weight matrices, 9 total ccef iterations istirument li

16、st: C C01(-1) GVariableCoefficientStd Errort-StatislicProb.C-139.6888157.1465-0.8882720 3840Y0 3828140 00529272.3433B0.0000R-squared0.996353Mean dependent var14318.54Adjusted R-equared0 996187S D dependentvar1346479S.E. of regression831.4584Sum squared resid15209106Durbin-Watson stat0.744531J-statis

17、tic0.039126與2SLS結果比較，結構參數(shù)估計量變化不大 。殘差平方和由81641777變?yōu)?5209108 ,顯著減少。為什么？利用了更多的信息。2.以表6.2所示的中國的實際數(shù)據(jù)為資料，估計下面的聯(lián)立模型。Y = -0 - -M t ,Ct , 2It UnMt 二01Y3Ptu2t表6.2年份貨幣于準貨幣M2/億元國內(nèi)生產(chǎn)總值GDP/億元居民消費價格指數(shù) P(1978 為 100居民消費CONS/億元固定投資I/億元199015293.418319.5165.29113.24517199119349.921280.4170.810315.95594.5199225402.2258

18、63.7181.712459.88080.1199334879.834500.7208.415682.413072.3199446923.546690.7258.620809.817042.1199560750.558510.5302.826944.520019.3199676094.968330.4327.932152.322913.5199790995.374894.2337.134854.624941.11998104498.579003.3334.436921.128406.21999119897.982673.1329.739334.429854.72000134610.389112

19、.533142911.932917.7建立工作文件后，進行如下步驟：RaSa面 DIS IS 00sUpdate from UE.Store to DBCopy Object.H迫e.DeleteFrteie OutputPrintVi«w Options199519961997199S19992000302.6000327.9000337 1000334.4000329.7000331.0000forkfiler UHTTTLED; ;Untitled 口叵|Freeze DeFaultv scrt Trariwpcisc歸業(yè)+戶歸mpl+卜叵CONS 15682.4020609.

20、0026944 5032152.3034654.6036921.1039334 4042911.9013072.3017042.1020019.3022913.6024941.1026406.2029854.7032917.70®EViewsFile Edi t ObjectVi ew Fracck Ogti ans Window Helplew Object.Fetch from DB.un建立聯(lián)立模型，并命名為MY在SYSTEM窗口里面定義聯(lián)立方程組和使用的工具變量 Systew： BYTorkfile: UKTITLED：:Untitled 口 口I卜| 'ErgETE

21、,tE%l:innal：E(5pe；匚 SLatsR.&sids gdp=c(1)+c(2)*m2+c(3)*cons+c(4)*i m2=c(5)+c (6)*gdp +c(7)+p inst 8ns i 口 c選擇兩階段最小二乘法進行估計專業(yè).專注.word格式,口 Systo:tnmiLED：Free甸雨rgeTEXtjEsHnnatenngdjj= HgC2rm2 +cG)*GQn8+c(4)*iSyste* Estimationtj- xlr .nJ .I. 11. SJ UNO©也好O c c c c c c c*1306.303726.99991.7968560

22、.0925-0 1505320 0288775.2127950 00012 0636400.15396713,403160 00000.6063750.16649B4.1224240.000943243.344624.6759 5572250 000D2930120009857929B04780 0000*511,412735,63538-14.361260.0000Determinant residual covariance 5.84E+11R-squred0.999598Mean dependent var54470,82Adjusted R-squared0.999425S.D, de

23、pendent var26284.98S.E of regression630.2518Sum squared resid2780522Durbin-Watson stat2.281178Equation: GDP=C(1)+C(2)*M2+C(3rCONS4-C(4)*1Instruments: CONS I P CObservations: 11得到如下輸出結果：卜的同詞 Objatt Printlhiana jSystem: MYEstimation Method: Two-Stage Least SquaresDate: 07AJ5/08 Time: 12:3BSample: 1990

24、 2000Included obseivations: 11Total system (balanced) observations 22Coefficient Std Error t-Statistic ProbsquaredAdjusted R-squared S.E. of regression Durbin-Watson statEquation: M2-C(5)+C(BfGDP+C(7)*P Instruments: CONS I P CObservations: 11二I 三 .一. U'：J . Jr，. . 三二三 I 0.998023 S O, dependent v

25、ar41923,751864.293 Sum squared resid278047201 298522.word格式,所以得到聯(lián)立方程計量經(jīng)濟學模型的估計表達式為：Y =-1306.3 -0.151Mt 2.064Ct 0.6861tMt =43243.34 2.938丫 -511.413PJ3、以Klein （克萊因）聯(lián)立方程模型為例介紹兩階段最小二乘估計 首先建立工作文件，數(shù)據(jù)如表7。表6.3 Klein聯(lián)立方程模型數(shù)據(jù)年份CCPPWPIIKKXXWGGGTTAA192039.812.728.82.7180.144.92.22.43.4-11192141.912.425.5-0.2182

26、.845.62.73.97.7-1019224516.929.31.9182.650.12.93.23.9-9192349.218.434.15.2184.557.22.92.84.7-8192450.619.433.93189.757.13.13.53.8-7192552.620.135.45.1192.7613.23.35.5-6192655.119.637.45.6197.8643.33.37-5192756.219.837.94.2203.464.43.646.7-4192857.321.139.23207.664.53.74.24.2-3192957.821.741.35.1210.

27、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.

28、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聯(lián)立方程組，模型如下：CC =% +%PP +o(2PP(1)+o(3(WP+WG)(消費方程)（投資方程）（私人工資方程）（均衡需求恒等式）（私人利潤恒等式）（私人存量恒等式）II = '0'1PP -2PP(-1)-3kkWP = 0 1XX2XX(-1) 3AAXX =CC II

29、ggPP = XX -TT -WPKK =KK(-1) II使用的工具變量是 ：WG GG TT AA PP(-1) KK XX(-1) C過程如下：©EVieTSFile£ditQbject YieK £r oc Quids QrH。工N«w Objtct.genejirate Series.Breik Linkq一 Pts Window Help ¥orkfi2casei. rf 1) . EEJ(View | Proc 出±i5torelDeletejSi7|5amplBRange: 1Sample: 1Fateh from D

30、B,Display Filter *Update sel«ctd from DE.St or* selactad to DE, 一Copy selected.0aa c cc gg ii kk PP resid碗e selected. . nDelate selectedPrint Selectedttw息 wp XX選擇System ,并起名為KleinModel在窗口空白處輸入方程指令，只要求寫行為方程（前3個方程），不需定義方程（后3個 方程），最后一行命令列出的是所用工具變量專業(yè).專注Q Syst e»: KLEIVIODELlorkfile: CASE7:Case

31、7Mew|Pr(x|ob匣H 回毗)|帕臉|卜通日司 |MetgETexl:(Siniate|r|El:at5Resjd5, cc=c(1)+c(2)*pp+c3)*pp(*1)+c(4)*(wp+wg)i i=c +c (6)*pp+c P)*pp(-1)+c (8)*k kp=c(9)+c(10)*xx+c(11 )*xx(-1)+c(12)*aainst wg gg tt aa pp(-1) kk xx(-1) q對聯(lián)立方程進行估計：點擊system 窗口上的estimate 鍵D Syst cb: KLEINIODELTorkfile: CASE?:Case7 目回J PrintJIh

32、l日me 厄已日工已1已5P已已 |5t:at5|R85id0jcc=c(1) +cQ)*pp +c *pK1 )+c(4)*(wp4v/g) ii=c(5)+c (6)*p p+c (7)*p p (-1)+c (6)*k k wp=c(9)+<1 Ofxx+c(11 )*xx(d )+c(12faa inst wg gg tt aa pp(-1) kk xx(-1) c|選才i 2TSLS即兩階段最小二乘估計得到如下Klein聯(lián)立方程的估計結果CoefficientStd. ErrorVStatisticProbC16,554761 46797911,277250.0000C 017

33、3020.1312050.1318720.B956C0.2162340.1192221 8137140,0756C0.8101830 04473518,110690.0000C20 273218.33324924188960.0192C0.15022201925340.7802370.4389C的0.6159440.1809263.4043980,D0T30(B)-0.1577B80.040162-3.929751 ,0003C1 50D2971.2756861 1760700.24500(10)0.4388590.03960311.001560.00000(11)0.14E6740.O431

34、E43.39B0630.00130(12)0 13D3960.0323084.0260010.0002Determinant residualcovariance0.267714Equation: CC=C+0*PP+C陰*PP(-1)+C*(WP+WG)Instruments: WG GG TT AA PP(1) KK XX(-1) CObservations: 21R-squared0.976711Mean dependent var53,99524Adjusted R-squared0,972601S.D dependent var6.860866S.E, of regression1

35、135659Sjm squared resid21 92525Durbin-Watson start1.485072Equation: H=C+Cpj*PP+C(7)*PPf.1)+C(B)*KKInstruments： WG GGTTAAPP(-1) KK XX(-1) CObservations: 21R-squared0.884884Mean dependent var1 266667Adjusted R-squared0.864569S.D. dependent var3,551948S.E. of regression1.307149Sum squared resid29,04636

36、Durbin-Watson stat2.005334Equation: WP=C(9)+C(10)*XX+C(11)*XX(-1)+C(12)*AAInstruments： WG GG R AA PP(-1) KK XX(-1) CObservations: 21R-squaredAdjust白d R-squared S.E. of regression Durbin-Watson stat0.9874140.9851930.7671551.963416Mean dependent varS.D. dependent var Sum squared resid36,36190E.3044011

37、0,00496上述輸出結果與線性單方程分析相同1.對聯(lián)立方程組進行預測聯(lián)立方程的預測是以上述估計結果為基礎進行的。主要分為3步:第1步：建立模型EVies Systea： KLEINBODELforkfile: CASET:C;File Edit Object View Proc uick Otions Window HelpView, (Print Mqm巳JlFrEuzeJ .WEfgETexH歸$匕由引日已區(qū)REd5)£ t- t- UJ s a s E DEstima.te . . s.Make KesidualsEndogenous GrcupSquares行ake Mod

38、elncUpdate Cofs £rmi SystemCoefficient Std. Error t-Statistic Prob.*1/ YJ- -1I 0.pp c c c16,554761.46797911.277250.00000.0173020 1312050.1319720.89560.2162340 1192221.8137140 0756X出現(xiàn)如下對話框 ladel: UNTITLED Tarkfile: CASET: :CaseTYiEwPt0(0bjecH PrinM |FmmB')2日2已函Equations| Vafiabl |Te>!| Eq

39、uations: 3BaselineIS KLEINMCDELEq|1. ccH ii, wp = F( aa, kk, pp, wg, wp, xx )第2步：輸入定義方程由于在設定聯(lián)立方程時沒有輸入定義方程，因此在求解模型時應該加入，否則，模型只識別System中設定的內(nèi)生變量。國回國加入定義方程的方法如下 lodel: UMTITLEB Torkfile: CASET： :CaseT啦之山 "10匚口匕於寸| 陽閨加曰加祈吃的)5Eve 廟uatidns卜圍趾閾強| Equations: 3U KLEINMCDELBaselineEq1Open Link Update Link

40、 Ereak LinkIiiEart. .DeletePasteFraperties.,-kk. pp, wg, wp, kx )輸入需要加入的定義方程Kodel Source EditEikter one rm oreK.s=cc+ii+gg pp-xx-tt-'wp這時模型窗口如下 lodel: UKTITLEB Vorkfile: CASET:Case7%w I '仔、Robjed 【Print Mame FrcBze,150lg EquaHcin5(“白口)匕1 巳弓| T Txt 口巨國Equations: 6Baseline畫畫回圉xx = co + II + gg

41、 "pp = xx - tt - wp 'kk = kk(<1) + ii" KLEINMODELEq1;xx=F(cc, gg( n)Eq2:pp=F(tt, wp( xx)Eq3:kik=F(ii. kk )Eq4.cc,ii,wp= F( aa, kk. pp, wg, wp, xx )第3步：求解模型EH回|ViGwNProcgbjed同ntNameFreezeRigEquationsV白曲bl*Text, del: UUTITLED Vorkfile: CASE?: :CaseTXXTXTMxx = cc + ii + gg "Eq1;xx

42、 = F( cc, gg, ii)m"pp = xx - tt - wp "Eq2:pp = F(tt, wp, xx )m"kk = kk(-l) + ii"Eq3:kk = F(ii, kk)回 KLEINMODELEq4.cc, ii. wp = F( aa, kk( pp. wg. wp. xx)Equations: 6Baseline模型求解窗口如下Kode! Solution以隨機性、靜態(tài)預測為例，其他四個模塊選擇默認狀態(tài)選項完成后，點擊 確定”鍵，各變量的預測均值序列和預測標準差序列自動生成于工作文件中。比如序列XX的預測值序列命名為 XX_0m,預測標準差為 XX_0So 模擬結果如下rkf