計(jì)量經(jīng)濟(jì)學(xué)報(bào)告

計(jì)量經(jīng)濟(jì)學(xué)報(bào)告PAGEPAGE2計(jì)量經(jīng)濟(jì)學(xué)報(bào)告計(jì)量經(jīng)濟(jì)學(xué)報(bào)告課程名稱(chēng)計(jì)量經(jīng)濟(jì)學(xué)班級(jí)與班級(jí)代碼專(zhuān)業(yè)國(guó)際經(jīng)濟(jì)與貿(mào)易任課教師學(xué)號(hào)：姓名：日期：年月日研究?jī)?chǔ)蓄額與GDP之間的關(guān)系中國(guó)儲(chǔ)蓄存款總額（Y，億元）與GDP（億元）數(shù)據(jù)如下表。表1年GDP儲(chǔ)蓄(Y)年GDP儲(chǔ)蓄(Y)19722518.1105.2198711962.53081.419732720.9121.2198814928.33822.219742789.9136.5198916909.25196.419752997.3149.6199018547.97119.819762943.7159.1199121617.89141.619773201.9181.6199226638.11175819783624.1210.6199334634.415203.519794038.2281199446759.421518.819804517.8399.5199558478.129662.319814862.4523.7199667884.638520.819825294.7675.4199774462.646279.819835934.5892.5199878345.253407.5198471711214.7199982067.4659621.819858964.41622.6200089442.264332.4198610202.22238.5200195933.373762.4第一步，散點(diǎn)圖（圖1）圖1第二步，建立數(shù)學(xué)模型由經(jīng)濟(jì)理論知，中國(guó)儲(chǔ)蓄存款總額受GDP的影響，當(dāng)GDP增加時(shí)，中國(guó)儲(chǔ)蓄存款總額也隨著增加，它們之間具有正向的同步變動(dòng)趨勢(shì)。中國(guó)儲(chǔ)蓄存款總額除受GDP的影響外，還受到其他一些變量的影響及隨機(jī)因素的影響，將其他變量及隨機(jī)變量的影響均歸并到隨機(jī)變量u中，根據(jù)GDP與Y的樣本數(shù)據(jù)，作GDP與Y之間的散點(diǎn)圖可以看出，它們的變化趨勢(shì)是線性的，由此建立中國(guó)儲(chǔ)蓄存款總額Y與GDP之間的一元線性回歸模型：第三步，估計(jì)參數(shù)樣本回歸模型為：下面是Eviews的估計(jì)結(jié)果（表2）：表2DependentVariable:YMethod:LeastSquaresDate:12/13/11Time:12:27Sample:19722001Includedobservations:30CoefficientStd.Errort-StatisticProb.

C-4366.305932.1408-4.6841690.0001GDP0.7185770.02291831.354660.0000R-squared0.972308

Meandependentvar15044.68AdjustedR-squared0.971319

S.D.dependentvar22537.94S.E.ofregression3816.918

Akaikeinfocriterion19.39661Sumsquaredresid4.08E+08

Schwarzcriterion19.49003Loglikelihood-288.9492

Hannan-Quinncriter.19.42650F-statistic983.1150

Durbin-Watsonstat0.206704Prob(F-statistic)0.000000(-4.68)(31.35),R2=0.9723，DW=0.206704，T=30第四步，統(tǒng)計(jì)檢驗(yàn)擬合優(yōu)度樣本可決系數(shù)為R-squared=0.972308修正樣本可決系數(shù)為：AdjustedR-squared=0.971319即R2=0.972308，2=0.971319計(jì)算結(jié)果表明，估計(jì)的樣本回歸方程較好地?cái)M合了樣本觀測(cè)值?；貧w系數(shù)估計(jì)值的顯著性檢驗(yàn)——t檢驗(yàn)提出檢驗(yàn)的原假設(shè)為：得t統(tǒng)計(jì)量為的t-Statistic=-4.684169的t-Statistic=31.35466對(duì)于給出顯著性水平α=0.05，查自由度v=30-2=28的t分布表，得臨界值t0.025（28）=2.05，|t0|=4.684169＞t0.025（28）=2.05，t1=31.35466＞t0.025（28）=2.05，故回歸系數(shù)均顯著不為零，回規(guī)模型中應(yīng)包含常數(shù)項(xiàng)，GDP對(duì)Y有顯著影響。從以上的評(píng)價(jià)可以看出，此模型是比較好的。F檢驗(yàn)提出檢驗(yàn)的原假設(shè)為：-=0對(duì)立假設(shè)為：至少有一個(gè)不等于零(i=1,2)F-statistic=983.1150對(duì)于給定的顯著性水平α=0.05，查出分子自由度為2，分母自由度為27的F分布上側(cè)分位數(shù)F0.05（2，27）=3.35因?yàn)镕=983.1150＞3.35,所以否定H0，總體回歸方程是顯著的，即在中國(guó)儲(chǔ)蓄存款總額Y與GDP之間存在顯著的線性性。第五步，檢驗(yàn)異方差(-4.68)(31.35),R2=0.9723，DW=0.206704，T=301．利用殘差圖判斷。建立殘差關(guān)于GDP的散點(diǎn)圖，如圖5.1，可以發(fā)現(xiàn)隨著GDP增加，殘差呈現(xiàn)不斷增大的趨勢(shì)，即存在遞增性的異方差。圖22．用White方法檢驗(yàn)是否存在異方差，得表3HeteroskedasticityTest:WhiteF-statistic10.36874

Prob.F(2,27)0.0005Obs*R-squared13.03220

Prob.Chi-Square(2)0.0015ScaledexplainedSS13.06975

Prob.Chi-Square(2)0.0015TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:12/15/11Time:21:15Sample:19722001Includedobservations:30CoefficientStd.Errort-StatisticProb.

C-57307.365222451.-0.0109730.9913GDP650.9958433.64191.5012290.1449GDP^2-0.0023760.004863-0.4885350.6291R-squared0.434407

Meandependentvar13597608AdjustedR-squared0.392511

S.D.dependentvar20985874S.E.ofregression16356723

Akaikeinfocriterion36.15282Sumsquaredresid7.22E+15

Schwarzcriterion36.29294Loglikelihood-539.2922

Hannan-Quinncriter.36.19764F-statistic10.36874

Durbin-Watsonstat1.029242Prob(F-statistic)0.000456因?yàn)橹缓幸粋€(gè)解釋變量，所以White檢驗(yàn)輔助回歸式中應(yīng)該包括兩個(gè)解釋變量。輔助回歸式估計(jì)結(jié)果如下：(-0.011)(1.50)(-0.49)R2=0.4344,T=30TR2=30*0.4344=13.03220＞，所以結(jié)論是該回歸模型中存在異方差?？朔惙讲町惙讲钚拚缦拢罕?DependentVariable:YMethod:LeastSquaresDate:12/14/11Time:16:27Sample:19722001Includedobservations:30Weightingseries:1/GDPCoefficientStd.Errort-StatisticProb.

C-1584.144176.6377-8.9683210.0000GDP0.5256390.03388215.513990.0000WeightedStatisticsR-squared0.895788

Meandependentvar2121.702AdjustedR-squared0.892066

S.D.dependentvar1703.101S.E.ofregression880.7714

Akaikeinfocriterion16.46381Sumsquaredresid21721230

Schwarzcriterion16.55723Loglikelihood-244.9572

Hannan-Quinncriter.16.49370F-statistic240.6838

Durbin-Watsonstat0.082459Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.890189

Meandependentvar15044.68AdjustedR-squared0.886267

S.D.dependentvar22537.94S.E.ofregression7600.750

Sumsquaredresid1.62E+09Durbin-Watsonstat0.075333再進(jìn)行White檢驗(yàn)：表5HeteroskedasticityTest:WhiteF-statistic2.453316

Prob.F(2,27)0.1050Obs*R-squared4.613428

Prob.Chi-Square(2)0.0996ScaledexplainedSS2.426664

Prob.Chi-Square(2)0.2972得=0.1050大于0.05，所以認(rèn)為已經(jīng)消除了回歸模型的異方差性。得輸出結(jié)果，整理后得到回歸式為：t(-8.97)(15.51)R2=0.895788,DW=0.082459第六步，檢驗(yàn)誤差項(xiàng)ut是否存在自相關(guān)已知DW=0.082459，若給定α=0.05，查表可得DW檢驗(yàn)臨界值dL=1.35，dU=1.49。因?yàn)镈W=0.082459＜1.35，依據(jù)判別規(guī)則，認(rèn)為誤差項(xiàng)ut存在嚴(yán)重的正自相關(guān)。圖3殘差分布圖2.用LM檢驗(yàn)判斷是否存在自相關(guān)設(shè)定滯后期為一階，得到LM檢驗(yàn)結(jié)果表6Breusch-GodfreySerialCorrelationLMTest:F-statistic195.2096

Prob.F(1,27)0.0000Obs*R-squared26.35479

Prob.Chi-Square(1)0.0000TestEquation:DependentVariable:RESIDMethod:LeastSquaresDate:12/14/11Time:16:39Sample:19722001Includedobservations:30Presamplemissingvaluelaggedresidualssettozero.Weightseries:1/GDPCoefficientStd.Errort-StatisticProb.

C-90.4259463.03508-1.4345340.1629GDP0.0175370.0120921.4502230.1585RESID(-1)1.1382960.08147113.971740.0000WeightedStatisticsR-squared0.878493

Meandependentvar-3.18E-13AdjustedR-squared0.869493

S.D.dependentvar865.4524S.E.ofregression312.6517

Akaikeinfocriterion14.42270Sumsquaredresid2639280.

Schwarzcriterion14.56282Loglikelihood-213.3404

Hannan-Quinncriter.14.46752F-statistic97.60479

Durbin-Watsonstat1.384248Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.971780

Meandependentvar2429.691AdjustedR-squared0.969690

S.D.dependentvar7047.859S.E.ofregression1227.018

Sumsquaredresid40650455Durbin-Watsonstat0.089874然后，設(shè)定滯后期為二階，得到LM檢驗(yàn)結(jié)果表7Breusch-GodfreySerialCorrelationLMTest:F-statistic95.66349

Prob.F(2,26)0.0000Obs*R-squared26.41094

Prob.Chi-Square(2)0.0000TestEquation:DependentVariable:RESIDMethod:LeastSquaresDate:12/14/11Time:16Sample:19722001Includedobservations:30Presamplemissingvaluelaggedresidualssettozero.Weightseries:1/GDPCoefficientStd.Errort-StatisticProb.

C-78.2202066.55056-1.1753500.2505GDP0.0152650.0127361.1986450.2415RESID(-1)1.2639890.2136115.9172470.0000RESID(-2)-0.1649420.258630-0.6377550.5292WeightedStatisticsR-squared0.880365

Meandependentvar-3.18E-13AdjustedR-squared0.866561

S.D.dependentvar865.4524S.E.ofregression316.1443

Akaikeinfocriterion14.47384Sumsquaredresid2598628.

Schwarzcriterion14.66067Loglikelihood-213.1076

Hannan-Quinncriter.14.53361F-statistic63.77566

Durbin-Watsonstat1.610521Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.972780

Meandependentvar2429.691AdjustedR-squared0.969639

S.D.dependentvar7047.859S.E.ofregression1228.054

Sumsquaredresid39211044Durbin-Watsonstat0.106734據(jù)值判斷拒絕原假設(shè)，所以BG（LM）檢驗(yàn)結(jié)果也說(shuō)明本式存在自相關(guān)。用廣義最小乘數(shù)估計(jì)回歸參數(shù)方法一：首先，估計(jì)自相關(guān)系數(shù)=1-DW/2=1-0.082459/2=0.9588對(duì)原變量做廣義差分變換。令GDYt=Yt-0.9588Yt-1GDGDPt=GDPt-0.9588GDPt-1以GDYt、GDGDPt，（1972~2001）為樣本再次回歸，得圖8DependentVariable:GDYMethod:LeastSquaresDate:12/14/11Time:17:05Sample(adjusted):19732001Includedobservations:29afteradjustmentsCoefficientStd.Errort-StatisticProb.

C-268.1692444.0470-0.6039210.5509GDGDP0.7894960.07254810.882350.0000R-squared0.814338

Meandependentvar3076.325AdjustedR-squared0.807462

S.D.dependentvar3933.489S.E.ofregression1725.983

Akaikeinfocriterion17.81145Sumsquaredresid80433503

Schwarzcriterion17.90575Loglikelihood-256.2661

Hannan-Quinncriter.17.84099F-statistic118.4255

Durbin-Watsonstat0.879545Prob(F-statistic)0.000000得到回歸式（-0.604）（10.88）R2=0.814338，DW=0.879545，T=30根據(jù)圖7得，*=-268.17=*/(1-)=-268.17/(1-0.9588)=-6508.98則原模型的廣義最小二乘估計(jì)結(jié)果是回歸方程擬合得效果比較好，且DW=0.879545。通過(guò)查表，得dL=1.35，dU=1.49。因?yàn)镈W=0.879545＞1.35，依據(jù)判別規(guī)則，誤差項(xiàng)還沒(méi)消除自相關(guān)，所以使用方法二消除自相關(guān)。圖4殘差圖方法二1.首先，引進(jìn)ar(1)，消除自相關(guān)，建立模型如下：表9DependentVariable:YMethod:LeastSquaresDate:12/15Sample(adjusted):19732001Includedobservations:29afteradjustmentsConvergenceachievedafter32iterationsCoefficientStd.Errort-StatisticProb.

C-3399.4591818.546-1.8693280.0729GDP0.3833810.1239753.0924090.0047AR(1)1.1871060.05195822.847450.0000R-squared0.996806

Meandependentvar15559.83AdjustedR-squared0.996560

S.D.dependentvar22756.41S.E.ofregression1334.663

Akaikeinfocriterion17.32844Sumsquaredresid46314443

Schwarzcriterion17.46989Loglikelihood-248.2624

Hannan-Quinncriter.17.37274F-statistic4056.981

Durbin-Watsonstat1.070551Prob(F-statistic)0.000000InvertedARRoots

1.19EstimatedARprocessisnonstationary得到回歸式（-1.869）（3.092）R2=0.996806，DW=1.070551回歸方程中的DW=1.070551，通過(guò)查表，得dL=1.35，dU=1.49。因?yàn)镈W=1.070551＜1.35，依據(jù)判別規(guī)則，誤差項(xiàng)還沒(méi)有消除自相關(guān)，說(shuō)明誤差項(xiàng)存在二階及以上的自相關(guān)。2.接著，引進(jìn)ar(1)、ar(2)，消除自相關(guān)，得出模型表10DependentVariable:YMethod:LeastSquaresDate:12/15Sample(adjusted):19742001Includedobservations:28afteradjustmentsConvergence