计量经济学信计111班实验五

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1、word【实验作者】学号： 2011014184 某某： 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软件进展实现；6、 掌握逐步回归法等多重共线性的修正方法，能够利用EViews软件进展实现。【实验内容】1、中国1980-2000年投资总

2、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1980199119811992198219931983199419841995198519961986199719871998198819991989200019901当设定模型为时，是否存在序列相关性？2假如按一阶自相关假设，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19911879896199222871070199329391

3、331199439231746199548542236199655762641199760532834199863072972199965343143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，如此对模型进展适当修正，给出一个比拟合理的模型形式。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19851001986198719881989199019911992199319941995199619971

4、99819992000200120022003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进展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 2000Include

5、d observations: 21VariableCoefficientStd. Errort-StatisticProb.CLOG(X)R-squaredMean dependent varAdjusted R-squaredS.D. dependent varS.E. of regressionAkaike info criterionSum squared residSchwarz criterionLog likelihoodHannan-Quinn criter.F-statisticDurbin-Watson statProb(F-statistic)模型结果为：0.00000.

6、0000R2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，明确存在自相关性。(2) 假如按一阶自相关假设，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:

7、 09:28Sample (adjusted): 1981 2000Included observations: 20 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.CLOG(Y(-1)LOG(X)LOG(X(-1)R-squaredMean dependent varAdjusted R-squaredS.D. dependent varS.E. of regressionAkaike info criterionSum squared residSchwarz criterionLog likelihoodHan

8、nan-Quinn criter.F-statisticDurbin-Watson statProb(F-statistic)因此估计方程为：lntt-1tt-1(0.006) (0.0000) (0.0001) (0.5589)R2然后，将估计的代入差分模型，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:

9、09:31Sample (adjusted): 1981 2000Included observations: 20 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.CLOG(X)-0.610808*LOG(X(-1)R-squaredMean dependent varAdjusted R-squaredS.D. dependent varS.E. of regressionAkaike info criterionSum squared residSchwarz criterionLog likelihoodHan

10、nan-Quinn criter.F-statisticDurbin-Watson statProb(F-statistic)最小二乘估计为lnYtt-1=0.448094+0.90157(lnXtt-1)(0.0055) (0.0000)R2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。对该模型进展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 Seri

11、al Correlation LM Test:F-statisticProb. F(1,17)Obs*R-squaredProb. Chi-Square(1)Test 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-Statistic

12、Prob.CLOG(X)-0.610808*LOG(X(-1)RESID(-1)R-squaredMean dependent varAdjusted R-squaredS.D. dependent varS.E. of regressionAkaike info criterionSum squared residSchwarz criterionLog likelihoodHannan-Quinn criter.F-statisticDurbin-Watson statProb(F-statistic)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

13、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-

14、StatisticProb.CLOG(X)AR(1)R-squaredMean dependent varAdjusted R-squaredS.D. dependent varS.E. of regressionAkaike info criterionSum squared residSchwarz criterionLog likelihoodHannan-Quinn criter.F-statisticDurbin-Watson statProb(F-statistic)Inverted AR Roots.63再通过LM法对模型进展检验，同样在输出窗口中选择“ViewResidualS

15、eriesCorrelationLMTest，在出现的对话框中填入之后“1得到Breusch-Godfrey Serial Correlation LM Test:F-statisticProb. F(1,16)Obs*R-squaredProb. Chi-Square(1)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

16、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.CD(X)R-squaredMean dependent varAdjusted R-squaredS.D. dependent varS.E. of regressionAkaike info criterionS

17、um squared resid37450229Schwarz criterionLog likelihoodHannan-Quinn criter.F-statisticDurbin-Watson statProb(F-statistic)DW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)*

18、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)C(2)C(3)C(4)C(5)C(6)R-squaredMean dependent varAdjusted

19、R-squaredS.D. dependent varS.E. of regressionAkaike info criterionSum squared residSchwarz criterionLog likelihoodHannan-Quinn criter.F-statisticDurbin-Watson statProb(F-statistic)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，(0.4983) () () () ()()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

20、线性由于R2，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，如此对模型进展适当修正，给出一个比拟合理的模型形式下面用Klein判别法进展分析。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，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)X1X2X3X4X5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:

21、Least SquaresDate: 04/08/14 Time: 16:21Sample: 1991 1999Included observations: 9VariableCoefficientStd. Errort-StatisticProb.CX1R-squaredMean dependent varAdjusted R-squaredS.D. dependent varS.E. of regressionAkaike info criterionSum squared residSchwarz criterionLog likelihoodHannan-Quinn criter.F-

22、statisticDurbin-Watson statProb(F-statistic)Lny = + 2062x1() ()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.CX2R-squaredMean dependent varAdjusted R-squaredS.D

23、. dependent varS.E. of regressionAkaike info criterionSum squared residSchwarz criterionLog likelihoodHannan-Quinn criter.F-statisticDurbin-Watson statProb(F-statistic)Lny = x2() ()R2 = 0.9875, F = 555, T = 9Dependent Variable: LOG(Y)Method: Least SquaresDate: 04/08/14 Time: 16:23Sample: 1991 1999In

24、cluded observations: 9VariableCoefficientStd. Errort-StatisticProb.CX3R-squaredMean dependent varAdjusted R-squaredS.D. dependent varS.E. of regressionAkaike info criterionSum squared residSchwarz criterionLog likelihoodHannan-Quinn criter.F-statisticDurbin-Watson statProb(F-statistic)Lny = - + 70.7

25、5213x3() ()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.CX4R-squaredMean dependent varAdjusted R-squaredS.D. dependent varS.E. of regressionAkaike info crite

26、rionSum squared residSchwarz criterionLog likelihoodHannan-Quinn criter.F-statisticDurbin-Watson statProb(F-statistic)Lny = + 0.00559x4() ()R2 = 0.9644, F = 189.7, T = 9Dependent Variable: LOG(Y)Method: Least SquaresDate: 04/08/14 Time: 16:57Sample: 1991 1999Included observations: 9VariableCoefficie

27、ntStd. Errort-StatisticProb.CX5R-squaredMean dependent varAdjusted R-squaredS.D. dependent varS.E. of regressionAkaike info criterionSum squared residSchwarz criterionLog likelihoodHannan-Quinn criter.F-statisticDurbin-Watson statProb(F-statistic)Lny = + 1161x5()R2 = 0.9633, F = 183.5, T = 9根据实验结果明确

28、，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.CX2X3R-squaredMean dependent varAdjusted R

29、-squaredS.D. dependent varS.E. of regressionAkaike info criterionSum squared residSchwarz criterionLog likelihoodHannan-Quinn criter.F-statisticDurbin-Watson statProb(F-statistic)Lny = + x2 x3() (0.4388)R288828, F =, T = 9发现x3不能通过显著性检验，因此采用Lny = x2() ()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De

30、pendent 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)C(2)C(3)R-squaredMean dependent varAdjusted R-squaredS.D. dependent varS.E. of regressionAkaike info criter

31、ionSum squared residSchwarz criterionLog likelihoodHannan-Quinn criter.F-statisticDurbin-Watson statProb(F-statistic)Ln(Yt)=-3.6489+1.796ln(GDPt)-1.2075ln(CPIt)0.0000 0.0000 0.0035R22是否存在多重共线性存在多重共线性3回归分析在Eviews里建立模型得到如下结果：Dependent Variable: LOG(Y)Method: Least SquaresDate: 04/08/14 Time: 20:29Samp

32、le: 1985 2003Included observations: 19LOG(Y)=C(1)+C(2)*LOG(GDP)CoefficientStd. Errort-StatisticProb.C(1)C(2)R-squaredMean dependent varAdjusted R-squaredS.D. dependent varS.E. of regressionAkaike info criterionSum squared residSchwarz criterionLog likelihoodHannan-Quinn criter.F-statisticDurbin-Wats

33、on statProb(F-statistic)0.0000 0.0000R2膨胀因子：Dependent Variable: LOG(Y)Method: Least SquaresDate: 04/08/14 Time: 20:27Sample: 1985 2003Included observations: 19LOG(Y)=C(1)+C(2)*LOG(CPI)CoefficientStd. Errort-StatisticProb.C(1)C(2)R-squaredMean dependent varAdjusted R-squaredS.D. dependent varS.E. of

34、regressionAkaike info criterionSum squared residSchwarz criterionLog likelihoodHannan-Quinn criter.F-statisticDurbin-Watson statProb(F-statistic)0.0008 0.0000R2膨胀因子：Dependent Variable: LOG(GDP)Method: Least SquaresDate: 04/08/14 Time: 20:30Sample: 1985 2003Included observations: 19LOG(GDP)=C(1)+C(2)

35、*LOG(CPI)CoefficientStd. Errort-StatisticProb.C(1)C(2)R-squaredMean dependent varAdjusted R-squaredS.D. dependent varS.E. of regressionAkaike info criterionSum squared residSchwarz criterionLog likelihoodHannan-Quinn criter.F-statisticDurbin-Watson statProb(F-statistic)R2膨胀因子为：根据两个自变量与因变量的回归结果显示，lnCPI与lnGDP对商品进口都是正相关的，然而，当两个自变量同时与因变量进展回归时发现，lnCPI与lnY呈负相关，因而存在矛盾。从经济学意义上解释，当一国消费指数越高，说明改国的货币相对贬值，如此该国处于逆差，因此进口额增加。这在一定程度上说明了GDP与CPI的共线性的存在影响了估计参数1 ,2的准确性。【实验小结】本章内容，主要在于练习序列相关、多重共线性的判断和检验。以与出现序列相关和多重共线性时如何进展修正。而常用的序列相关检验方法为图示法、DW、回归检验法与LM检验法等，多重共线性检验如此有相关系数、VIF法。而对于修正的方法，主要有广义差分法和逐步回归法。15 / 15