计量经济学信计111班实验五.doc

计量经济学实验报告纸【实验作者】学号： 2011014184 姓名： 陈乐朋 班级： 信计111班 【实验名称】序列相关、多重共线性的检验与修正【实验目的】1、 理解序列相关的概念，掌握序列相关出现的原因与后果；2、 理解多重共线性的概念，掌握多重共线性出现的原因与后果；3、 掌握序列相关常见的检验方法，包括图示法、DW、回归检验法与LM检验法等；4、 掌握多重共线性常见的检验方法，包括相关系数、VIF法等；5、 掌握广义差分法等序列方差的修正方法，能够利用EViews软件进行实现；6、 掌握逐步回归法等多重共线性的修正方法，能够利用EViews软件进行实现。【实验内容】1、中国1980-2000年投资总额X与工业总产值Y的统计资料如下表所示。年度全社会固定资产投资工业增加值年度全社会固定资产投资工业增加值1980910.91996.519915594.58087.11981961.02048.419928080.110284.519821230.42162.3199313072.314143.819831430.12375.6199417042.119359.619841832.92789.0199520079.324718.319852543.23448.7199622913.529082.619863120.63967.0199722941.132412.119873791.74585.8199828406.233387.919884753.85777.2199929854.735087.219894410.46484.0200032917.739570.319904517.06858.0（1）当设定模型为时，是否存在序列相关性？（2）若按一阶自相关假设，试用Durbin两步法与广义最小二乘法估计原模型；（3）采用差分形式与作为新数据，估计模型，该模型是否存在序列相关性？2、经初步分析，影响电信业务总量的主要因素有邮政业务总量、中国人口数、年度（亿元）（亿元）（亿）（元）（元）1991151.6352.7511.58230.263718798961992226.5763.6711.71710.2763228710701993382.4580.2611.85170.2814293913311994592.3095.8911.98500.2862392317461995875.51113.3412.11210.29044854223619961208.75133.2912.23890.29375576264119971268.95144.3412.36260.29926053283419982264.94166.2812.48100.30406307297219993132.38198.4412.59090.308965343143城镇人口占总人口的比重、人均GDP、全国居民人均消费水平，数据如下表所示（1）试建立关于电信业务总量的多元线性回归模型（2）检验模型是否存在多重共线性。（3）如果存在多重共线性，则对模型进行适当修正，给出一个比较合理的模型形式。3、下表给出了中国商品进口额Y、国内生产总值GDP、消费者价格指数CPI年份商品进口额（亿元）国内生产总值（亿元）消费者价格指数19851257.88964.410019861498.310202.2106.519871614.211962.5114.319882055.114928.3135.819892199.916909.2160.219902574.318547.9165.219913398.721617.8170.819924443.326638.1181.719935986.234634.4208.419949960.146759.4258.6199511048.158478.1302.8199611557.467884.6327.9199711806.574462.6337.1199811626.178345.2334.4199913736.482067.5329.7200018638.889468.1331.0200120159.297314.8333.3200224430.3105172.3330.6200334195.6117251.9334.6考虑建立如下的模型（1）利用表中的数据估计模型中的参数；（2）是否存在多重共线性?（3）进行以下回归根据这些回归，使对数据中的多重共线性的性质作出说明。【结果分析】题一:(1) 是否存在序列相关性首先画出自变量与因变量的散点图，如图1，两者具有较好的线性关系。图 1然后建立模型。将数据输入到Eviews中后，建立模型 ls log(y) c log(x)得到分析结果如下Dependent Variable: LOG(Y)Method: Least SquaresDate: 04/08/14 Time: 09:27Sample: 1980 2000Included observations: 21VariableCoefficientStd. Errort-StatisticProb.C1.4304000.1994927.1702260.0000LOG(X)0.8732970.02271338.449050.0000R-squared0.987311Mean dependent var9.031179Adjusted R-squared0.986643S.D. dependent var1.062296S.E. of regression0.122773Akaike info criterion-1.266572Sum squared resid0.286389Schwarz criterion-1.167094Log likelihood15.29901Hannan-Quinn criter.-1.244983F-statistic1478.330Durbin-Watson stat0.515870Prob(F-statistic)0.000000模型结果为：Ln=1.4304+0.873297lnx（0.0000）（0.0000）R2=0.987 F=1478.33 DW=0.51587在置信度为5%的显著性水平下，各个参数均能通过t检验，但是DW分布在样本量为21的下限临界值为1.22,0.51587小于1.22，表明存在自相关性。(2) 若按一阶自相关假设，试用Durbin两步法与广义最小二乘法估计原模型一、Durbin两步法：估计模型：lnYt=plnYt-1+0(1-p)+ 1(lnXt-plnXt-1)在Eviews中输入：ls log(y) c log(y(-1) log(x) log(x(-1)得到分析结果如下所示：Dependent Variable: LOG(Y)Method: Least SquaresDate: 04/08/14 Time: 09:28Sample (adjusted): 1981 2000Included observations: 20 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C0.4787860.1514223.1619340.0060LOG(Y(-1)0.6108080.0848547.1983520.0000LOG(X)0.4251970.0790335.3799760.0001LOG(X(-1)-0.0679600.113837-0.5969950.5589R-squared0.998444Mean dependent var9.102781Adjusted R-squared0.998152S.D. dependent var1.036599S.E. of regression0.044564Akaike info criterion-3.206903Sum squared resid0.031776Schwarz criterion-3.007757Log likelihood36.06903Hannan-Quinn criter.-3.168028F-statistic3421.366Durbin-Watson stat1.143909Prob(F-statistic)0.000000因此估计方程为：lnt=0.478786+0.610808lnYt-1+0.425197lnXt-0.06796lnXt-1(0.006) (0.0000) (0.0001) (0.5589)R2=0.998 F=3421.366 DW=1.143909然后，将估计的p=0.610808代入差分模型，得到广义模型。在Eviews中输入ls log(y)-0.610808*log(y(-1) c log(x)-0.610808*log(x(-1)得到结果如下所示：Dependent Variable: LOG(Y)-0.610808*LOG(Y(-1)Method: Least SquaresDate: 04/08/14 Time: 09:31Sample (adjusted): 1981 2000Included observations: 20 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C0.4480940.1422553.1499280.0055LOG(X)-0.610808*LOG(X(-1)0.9015700.03994722.569110.0000R-squared0.965868Mean dependent var3.633944Adjusted R-squared0.963972S.D. dependent var0.415141S.E. of regression0.078798Akaike info criterion-2.149210Sum squared resid0.111765Schwarz criterion-2.049637Log likelihood23.49210Hannan-Quinn criter.-2.129772F-statistic509.3646Durbin-Watson stat1.545938Prob(F-statistic)0.000000最小二乘估计为lnYt-0.610808lnYt-1=0.448094+0.90157(lnXt-0.610808lnXt-1)(0.0055) (0.0000)R2=0.965868 F=509.3646 DW=1.545938同理，在5%的显著性水平下，样本容量为20的DW检验的临界值的上下限为dL=1.20，dU=1.41，检验值落在（dL，dU）之外，故不能确定是否存在一阶序列相关。对该模型进行LM法检验，在输出结果窗口中选择“ViewResidualSeriesCorrelationLMTest”，并在弹出的对话框中输入滞后数“1”，得到Breusch-Godfrey Serial Correlation LM Test:F-statistic0.568517Prob. F(1,17)0.4612Obs*R-squared0.647200Prob. Chi-Square(1)0.4211Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 04/08/14 Time: 09:32Sample: 1981 2000Included observations: 20Presample missing value lagged residuals set to zero.VariableCoefficientStd. Errort-StatisticProb.C0.0051220.1441520.0355340.9721LOG(X)-0.610808*LOG(X(-1)-0.0013430.040474-0.0331700.9739RESID(-1)0.1815510.2407830.7540010.4612R-squared0.032360Mean dependent var-9.55E-16Adjusted R-squared-0.081480S.D. dependent var0.076697S.E. of regression0.079760Akaike info criterion-2.082105Sum squared resid0.108149Schwarz criterion-1.932745Log likelihood23.82105Hannan-Quinn criter.-2.052948F-statistic0.284259Durbin-Watson stat1.854083Prob(F-statistic)0.756079检验统计量为0.6472，查询卡方分布，检验值小于临界值，因而不能拒绝原假设，认为模型不存在一阶序列相关。因此估计原模型为：二、广义最小二乘法首先建立模型，在Eviews中输入“log(y) c log(x) AR(1)”AR(1)为随机干扰项。运行结果如下：Dependent Variable: LOG(Y)Method: Least SquaresDate: 04/08/14 Time: 09:33Sample (adjusted): 1981 2000Included observations: 20 after adjustmentsConvergence achieved after 18 iterationsVariableCoefficientStd. Errort-StatisticProb.C1.1527170.4175012.7609920.0134LOG(X)0.9012840.04507719.994110.0000AR(1)0.6252970.1542874.0528190.0008R-squared0.994529Mean dependent var9.102781Adjusted R-squared0.993885S.D. dependent var1.036599S.E. of regression0.081059Akaike info criterion-2.049787Sum squared resid0.111701Schwarz criterion-1.900428Log likelihood23.49787Hannan-Quinn criter.-2.020631F-statistic1545.095Durbin-Watson stat1.561794Prob(F-statistic)0.000000Inverted AR Roots.63再通过LM法对模型进行检验，同样在输出窗口中选择“ViewResidualSeriesCorrelationLMTest”，在出现的对话框中填入之后“1”得到Breusch-Godfrey Serial Correlation LM Test:F-statistic0.905546Prob. F(1,16)0.3555Obs*R-squared1.071301Prob. Chi-Square(1)0.3007同理得检验统计量为1.071301，查询卡方分布，检验值小于临界值，因而不能拒绝原假设，认为模型不存在一阶序列相关。因此估计原模型为：三、采用差分形式与作为新数据，估计模型，该模型是否存在序列相关性首先选择“QuickEstimateEquation”,在出现的对话框中输入“ls y-y(-1) c x-x(-1)”，得到运行结果如下;Dependent Variable: D(Y)Method: Least SquaresDate: 04/08/14 Time: 09:35Sample (adjusted): 1981 2000Included observations: 20 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.C795.9142442.56101.7984280.0889D(X)0.6765910.1893583.5730730.0022R-squared0.414955Mean dependent var1878.690Adjusted R-squared0.382452S.D. dependent var1835.506S.E. of regression1442.418Akaike info criterion17.48067Sum squared resid37450229Schwarz criterion17.58024Log likelihood-172.8067Hannan-Quinn criter.17.50011F-statistic12.76685Durbin-Watson stat1.552885Prob(F-statistic)0.002174DW检验值为1.552885，DW在置信度为5%，样本量为20临界值（1.20,1.41），检验值不在上下限内，因此该模型存在序列相关。题二：（1）试建立关于电信业务总量的多元线性回归模型画出y与x的散点图，发现各个因素与y呈现出对数函数的形式，如下图 从图中可以发现，各个自变量与因变量呈对数函数形式。因此建立模型LOG(Y)=C(1)+C(2)*X1+C(3)*X2+C(4)*X3+C(5)*X4+C(6)*X5输入数据，建立模型得到：Dependent Variable: LOG(Y)Method: Least SquaresDate: 04/08/14 Time: 16:12Sample: 1991 1999Included observations: 9LOG(Y)=C(1)+C(2)*X1+C(3)*X2+C(4)*X3+C(5)*X4+C(6)*X5CoefficientStd. Errort-StatisticProb.C(1)29.5417738.452070.7682750.4983C(2)0.0216360.0135231.5999380.2079C(3)-3.0345513.986712-0.7611660.5019C(4)33.7133332.939431.0234950.3814C(5)0.0012890.0008341.5452670.2200C(6)-0.0020270.001664-1.2180140.3103R-squared0.994385Mean dependent var6.618673Adjusted R-squared0.985027S.D. dependent var1.018022S.E. of regression0.124570Akaike info criterion-1.093179Sum squared resid0.046553Schwarz criterion-0.961696Log likelihood10.91930Hannan-Quinn criter.-1.376919F-statistic106.2583Durbin-Watson stat3.408677Prob(F-statistic)0.001421根据1991-1999年的相关数据所建立的中国电信业务总量计量经济模型如下，Ln y=29.54177+0.021636x13.034551x2 +33.71333x3 +0.001289x4-0.002027x5(0.4983) (0.2079) (0.5019) (0.3814) (0.22) (0.3103)R2 = 0.99, F = 106.3, DW = 3.4, t0.05(3) = 3.18,（2）检验模型是否存在多重共线性由于R2 = 0.99，但每个回归参数的t检验在统计上都不显著（估计量的方差变大所致），这说明模型中存在严重的多重共线性。（3）如果存在多重共线性，则对模型进行适当修正，给出一个比较合理的模型形式下面用Klein判别法进行分析。首先给出解释变量间的简单相关系数矩阵。因为其中有一个简单相关系数大于R2=0.9944，所以根据Klein判别法，模型中存在严重的多重共线性。LOG(Y)X1X2X3X4X5Log(y)1.0000000.9832660.9937550.9875330.9820470.981460X10.9832661.0000000.9895190.9700250.9627770.970291X20.9937550.9895191.0000000.9882340.9871840.988805X30.9875330.9700250.9882341.0000000.9677890.965389X40.9820470.9627770.9871840.9677891.0000000.998610X50.9814600.9702910.9888050.9653890.9986101.000000用逐步回归法筛选解释变量。用每个解释变量分别对被解释变量做简单回归，以可决系数为标准确定解释变量的重要程度，为解释变量排序。发现Dependent Variable: LOG(Y)Method: Least SquaresDate: 04/08/14 Time: 16:21Sample: 1991 1999Included observations: 9VariableCoefficientStd. Errort-StatisticProb.C4.2169820.18070323.336510.0000X10.0206200.00144414.280090.0000R-squared0.966812Mean dependent var6.618673Adjusted R-squared0.962071S.D. dependent var1.018022S.E. of regression0.198263Akaike info criterion-0.205312Sum squared resid0.275158Schwarz criterion-0.161484Log likelihood2.923903Hannan-Quinn criter.-0.299892F-statistic203.9210Durbin-Watson stat0.905880Prob(F-statistic)0.000002Ln y =4.216982 + 0.02062x1(0.0000) (0.0000)R2 = 0.9668, F = 204, T = 9Dependent Variable: LOG(Y)Method: Least SquaresDate: 04/08/14 Time: 16:17Sample: 1991 1999Included observations: 9VariableCoefficientStd. Errort-StatisticProb.C-28.652151.497494-19.133390.0000X22.9143660.12369023.561840.0000R-squared0.987548Mean dependent var6.618673Adjusted R-squared0.985769S.D. dependent var1.018022S.E. of regression0.121443Akaike info criterion-1.185615Sum squared resid0.103239Schwarz criterion-1.141787Log likelihood7.335268Hannan-Quinn criter.-1.280195F-statistic555.1601Durbin-Watson stat1.690478Prob(F-statistic)0.000000Ln y = - 28.65215 2.914366x2 (0.0000) (0.0000)R2 = 0.9875, F = 555, T = 9Dependent Variable: LOG(Y)Method: Least SquaresDate: 04/08/14 Time: 16:23Sample: 1991 1999Included observations: 9VariableCoefficientStd. Errort-StatisticProb.C-13.850711.234534-11.219380.0000X370.752134.26258116.598420.0000R-squared0.975222Mean dependent var6.618673Adjusted R-squared0.971682S.D. dependent var1.018022S.E. of regression0.171312Akaike info criterion-0.497534Sum squared resid0.205434Schwarz criterion-0.453706Log likelihood4.238903Hannan-Quinn criter.-0.592114F-statistic275.5077Durbin-Watson stat2.271547Prob(F-statistic)0.000001Ln y = - 13.85071 + 70.75213 x3 (0.0000) (0.0000)R2 = 0.9752, F = 275.5, T = 9Dependent Variable: LOG(Y)Method: Least SquaresDate: 04/08/14 Time: 16:55Sample: 1991 1999Included observations: 9VariableCoefficientStd. Errort-StatisticProb.C4.1144680.19425921.180350.0000X40.0005594.05E-0513.774010.0000R-squared0.964417Mean dependent var6.618673Adjusted R-squared0.959334S.D. dependent var1.018022S.E. of regression0.205293Akaike info criterion-0.135626Sum squared resid0.295017Schwarz criterion-0.091798Log likelihood2.610317Hannan-Quinn criter.-0.230206F-statistic189.7232Durbin-Watson stat1.251489Prob(F-statistic)0.000003Ln y =4.114468 + 0.00559x4 (0.0000) (0.0000)R2 = 0.9644, F = 189.7, T = 9Dependent Variable: LOG(Y)Method: Least SquaresDate: 04/08/14 Time: 16:57Sample: 1991 1999Included observations: 9VariableCoefficientStd. Errort-StatisticProb.C4.1846330.19264821.721710.0000X50.0011618.57E-0513.547880.0000R-squared0.963263Mean dependent var6.618673Adjusted R-squared0.958015S.D. dependent var1.018022S.E. of regression0.208595Akaike info criterion-0.103717Sum squared resid0.304582Schwarz criterion-0.059890Log likelihood2.466727Hannan-Quinn criter.-0.198297F-statistic183.5451Durbin-Watson stat1.202421Prob(F-statistic)0.000003Ln y = 4.184633 + 0.001161 x5 (0.0000) (0.0000)R2 = 0.9633, F = 183.5, T = 9根据实验结果表明，单个因素x与lny之间的拟合系数都很高，F值也较大，且每个系数P值均小于0.05。因此在模型修改的过程中，采用逐步回归的方法的思想，将拟合值和F值最大的x2最为初始变量，再逐一选取较大的x3，得到Dependent Variable: LOG(Y)Method: Least SquaresDate: 04/08/14 Time: 17:52Sample: 1991 1999Included observations: 9VariableCoefficientStd. Errort-StatisticProb.C-25.296574.327927-5.8449640.0011X22.2365250.8273812.7031370.0354X316.7568120.212890.8290160.4388R-squared0.988828Mean dependent var6.618673Adjusted R-squared0.985104S.D. dependent var1.018022S.E. of regression0.124250Akaike info criterion-1.071839Sum squared resid0.092629Schwarz criterion-1.006097Log likelihood7.823274Hannan-Quinn criter.-1.213709F-statistic265.5225Durbin-Watson stat2.089083Prob(F-statistic)0.000001Ln y = -25.29657 + 2.236525 x2+16.75681 x3 (0.0011) (0.0354) (0.4388)R2 = 0.988828, F =265.5225, T = 9发现x3不能通过显著性检验，因此采用Ln y = - 28.65215 2.914366x2 (0.0000) (0.0000)R2 = 0.9875, F = 555, T = 9题三（1）利用表中的数据估计模型中的参数Dependent Variable: LOG(Y)Method: Least SquaresDate: 04/08/14 Time: 20:19Sample: 1985 2003Included observations: 19LOG(Y)=C(1)+C(2)*LOG(GDP)+C(3)*LOG(CPI)CoefficientStd. Errort-StatisticProb.C(1)-3.6489400.322308-11.321290.0000C(2)1.7961740.1808599.9313630.0000C(3)-1.2075110.353594-3.4149610.0035R-squared0.989725Mean dependent var8.771863Adjusted R-squared0.988441S.D. dependent var1.045337S.E. of regression0.112388Akaike info criterion-1.389779Sum squared resid0.202097Schwarz criterion-1.240657Log likelihood16.20290Hannan-Quinn criter.-1.364542F-statistic770.6017Durbin-Watson stat0.939369Prob(F-statistic)0.000000Ln(Yt)