计量经济学信计111班实验五.doc

1、计量经济学实验报告纸1【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

2、、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1980 910.9 1996.5 1991 5594.5 8087.11981 961.0 2048.4 1992 8080.1 10284.51982 1230.4 2162.3 1993 13072.3 14143.81983 1430.1 2375.6 1994 17042.1 19359.61984 1832.9 2789.0 1995 20079.3 24718.31985 2543.2 3448.7 1996 22913.5

3、 29082.61986 3120.6 3967.0 1997 22941.1 32412.11987 3791.7 4585.8 1998 28406.2 33387.91988 4753.8 5777.2 1999 29854.7 35087.21989 4410.4 6484.0 2000 32917.7 39570.31990 4517.0 6858.0（1）当设定模型为 时，是否存在序列相关性？01lnlnt ttYX（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ttt原模型；（3）采用差分形式 与 作为新数据，估计模型*1tttX*1ttY，该模型是否存

4、在序列相关性？*01tttYv2、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1X、X计量经济学实验报告纸2年度 （亿元）Y（亿元）1X（亿）23X（元）4（元）5X1991 151.63 52.75 11.5823 0.2637 1879 8961992 226.57 63.67 11.7171 0.2763 2287 10701993 382.45 80.26 11.8517 0.2814 2939 13311994 592.30 95.89 11.9850 0.2862 3923 17461995 875.51 113.34 12.1121 0.2904 4854

5、 22361996 1208.75 133.29 12.2389 0.2937 5576 26411997 1268.95 144.34 12.3626 0.2992 6053 28341998 2264.94 166.28 12.4810 0.3040 6307 29721999 3132.38 198.44 12.5909 0.3089 6534 3143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3X4 5X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

6、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1985 1257.8 8964.4 1001986 1498.3 10202.2 106.51987 1614.2 11962.5 114.31988 2055.1 14928.3 135.81989 2199.9 16909.2 160.21990 2574.3 18547.9 165.21991 3398.7 21617.8 170.81992 4443.3 26638.1 181.71993 5986.2 34634.4 208.4199

7、4 9960.1 46759.4 258.61995 11048.1 58478.1 302.81996 11557.4 67884.6 327.91997 11806.5 74462.6 337.11998 11626.1 78345.2 334.41999 13736.4 82067.5 329.72000 18638.8 89468.1 331.02001 20159.2 97314.8 333.32002 24430.3 105172.3 330.62003 34195.6 117251.9 334.6考虑建立如下的模型计量经济学实验报告纸3012lnlnlt ttYGDPCI（1）利

8、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 011lnlnt ttYGDP012llt ttCI013lnlnt tt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。05,010,015,020,025,030,035,040,010,020,030,040,0XY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

9、 SquaresDate: 04/08/14 Time: 09:27Sample: 1980 2000Included observations: 21计量经济学实验报告纸4Variable Coefficient Std. Error t-Statistic Prob. C 1.430400 0.199492 7.170226 0.0000LOG(X) 0.873297 0.022713 38.44905 0.0000R-squared 0.987311 Mean dependent var 9.031179Adjusted R-squared 0.986643 S.D. dependent

10、 var 1.062296S.E. of regression 0.122773 Akaike info criterion -1.266572Sum squared resid 0.286389 Schwarz criterion -1.167094Log likelihood 15.29901 Hannan-Quinn criter. -1.244983F-statistic 1478.330 Durbin-Watson stat 0.515870Prob(F-statistic) 0.000000模型结果为：Ln=1.4304+0.873297lnx（0.0000） （0.0000）R2

11、=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1ttt型一、Durbin 两步法：估计模型：lnY t=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)Met

12、hod: Least SquaresDate: 04/08/14 Time: 09:28Sample (adjusted): 1981 2000Included observations: 20 after adjustmentsVariable Coefficient Std. Error t-Statistic Prob. C 0.478786 0.151422 3.161934 0.0060LOG(Y(-1) 0.610808 0.084854 7.198352 0.0000LOG(X) 0.425197 0.079033 5.379976 0.0001LOG(X(-1) -0.0679

13、60 0.113837 -0.596995 0.5589R-squared 0.998444 Mean dependent var 9.102781Adjusted R-squared 0.998152 S.D. dependent var 1.036599S.E. of regression 0.044564 Akaike info criterion -3.206903Sum squared resid 0.031776 Schwarz criterion -3.007757Log likelihood 36.06903 Hannan-Quinn criter. -3.168028F-st

14、atistic 3421.366 Durbin-Watson stat 1.143909Prob(F-statistic) 0.000000计量经济学实验报告纸5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(

15、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 adjustmentsVariable Coefficient Std. Error t-Statistic Prob. C 0.448094 0.142255 3.149928 0.0055LOG(X)-0.610808*LOG(X(-1) 0.901570 0.0

16、39947 22.56911 0.0000R-squared 0.965868 Mean dependent var 3.633944Adjusted R-squared 0.963972 S.D. dependent var 0.415141S.E. of regression 0.078798 Akaike info criterion -2.149210Sum squared resid 0.111765 Schwarz criterion -2.049637Log likelihood 23.49210 Hannan-Quinn criter. -2.129772F-statistic

17、 509.3646 Durbin-Watson stat 1.545938Prob(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，d U=1.41，检验值落在（d L，d U）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“ViewRes

18、idual Series Correlation LM Test” ，并在弹出的对话框中输入滞后数“1” ，得到Breusch-Godfrey Serial Correlation LM Test:F-statistic 0.568517 Prob. F(1,17) 0.4612Obs*R-squared 0.647200 Prob. Chi-Square(1) 0.4211Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 04/08/14 Time: 09:32Sample: 1981 2000计量经济学实验报

19、告纸6Included observations: 20Presample missing value lagged residuals set to zero.Variable Coefficient Std. Error t-Statistic Prob. C 0.005122 0.144152 0.035534 0.9721LOG(X)-0.610808*LOG(X(-1) -0.001343 0.040474 -0.033170 0.9739RESID(-1) 0.181551 0.240783 0.754001 0.4612R-squared 0.032360 Mean depend

20、ent var -9.55E-16Adjusted R-squared -0.081480 S.D. dependent var 0.076697S.E. of regression 0.079760 Akaike info criterion -2.082105Sum squared resid 0.108149 Schwarz criterion -1.932745Log likelihood 23.82105 Hannan-Quinn criter. -2.052948F-statistic 0.284259 Durbin-Watson stat 1.854083Prob(F-stati

21、stic) 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20.5()31.40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： ln197lnt tYX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 aft

22、er adjustmentsConvergence achieved after 18 iterationsVariable Coefficient Std. Error t-Statistic Prob. C 1.152717 0.417501 2.760992 0.0134LOG(X) 0.901284 0.045077 19.99411 0.0000AR(1) 0.625297 0.154287 4.052819 0.0008R-squared 0.994529 Mean dependent var 9.102781Adjusted R-squared 0.993885 S.D. dep

23、endent var 1.036599S.E. of regression 0.081059 Akaike info criterion -2.049787Sum squared resid 0.111701 Schwarz criterion -1.900428Log likelihood 23.49787 Hannan-Quinn criter. -2.020631F-statistic 1545.095 Durbin-Watson stat 1.561794Prob(F-statistic) 0.000000计量经济学实验报告纸7Inverted AR Roots .63再通过LM法对模

24、型进行检验，同样在输出窗口中选择“ViewResidual Series Correlation LM Test”，在出现的对话框中填入之后“1”得到Breusch-Godfrey Serial Correlation LM Test:F-statistic 0.905546 Prob. F(1,16) 0.3555Obs*R-squared 1.071301 Prob. 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20.5()31.40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： ln1.57.98ln

25、.62597(1)t tYXAR三、采用差分形式 与 作为新数据，估计模型*1tttX*1ttY，该模型是否存在序列相关性*01tttYv首先选择“QuickEstimate Equation”,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 adjustmentsVariable Coefficie

26、nt Std. Error t-Statistic Prob. C 795.9142 442.5610 1.798428 0.0889D(X) 0.676591 0.189358 3.573073 0.0022R-squared 0.414955 Mean dependent var 1878.690Adjusted R-squared 0.382452 S.D. dependent var 1835.506S.E. of regression 1442.418 Akaike info criterion 17.48067Sum squared resid 37450229 Schwarz c

27、riterion 17.58024Log likelihood -172.8067 Hannan-Quinn criter. 17.50011F-statistic 12.76685 Durbin-Watson stat 1.552885Prob(F-statistic) 0.002174计量经济学实验报告纸8DW 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04801,

28、2,602,402,83,0460810214061802XY 04801,2,602,402,83,01.41.6.812.0.21.42.6XY 04801,2,602,402,83,0.26.27.28.29.30.31X3Y04801,2,602,402,83,01,2,03,04,05,6,07,0XY 04801,2,602,402,83,081,20,602,402,803,2X5Y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：Depend

29、ent 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)*X5Coefficient Std. Error t-Statistic Prob. C(1) 29.54177 38.45207 0.768275 0.4983C(2) 0.021636 0.013523 1.599938 0.2079C(3) -3.034551 3.986712

30、-0.761166 0.5019C(4) 33.71333 32.93943 1.023495 0.3814C(5) 0.001289 0.000834 1.545267 0.2200C(6) -0.002027 0.001664 -1.218014 0.3103R-squared 0.994385 Mean dependent var 6.618673计量经济学实验报告纸9Adjusted R-squared 0.985027 S.D. dependent var 1.018022S.E. of regression 0.124570 Akaike info criterion -1.093

31、179Sum squared resid 0.046553 Schwarz criterion -0.961696Log likelihood 10.91930 Hannan-Quinn criter. -1.376919F-statistic 106.2583 Durbin-Watson stat 3.408677Prob(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)

32、 (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

33、。LOG(Y) X1 X2 X3 X4 X5Log(y) 1.000000 0.983266 0.993755 0.987533 0.982047 0.981460X1 0.983266 1.000000 0.989519 0.970025 0.962777 0.970291X2 0.993755 0.989519 1.000000 0.988234 0.987184 0.988805X3 0.987533 0.970025 0.988234 1.000000 0.967789 0.965389X4 0.982047 0.962777 0.987184 0.967789 1.000000 0.

34、998610X5 0.981460 0.970291 0.988805 0.965389 0.998610 1.000000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: 9Variable Coefficient Std. Error t-Statistic Prob. C 4.216982

35、 0.180703 23.33651 0.0000X1 0.020620 0.001444 14.28009 0.0000R-squared 0.966812 Mean dependent var 6.618673Adjusted R-squared 0.962071 S.D. dependent var 1.018022计量经济学实验报告纸10S.E. of regression 0.198263 Akaike info criterion -0.205312Sum squared resid 0.275158 Schwarz criterion -0.161484Log likelihoo

36、d 2.923903 Hannan-Quinn criter. -0.299892F-statistic 203.9210 Durbin-Watson stat 0.905880Prob(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: 9V

37、ariable Coefficient Std. Error t-Statistic Prob. C -28.65215 1.497494 -19.13339 0.0000X2 2.914366 0.123690 23.56184 0.0000R-squared 0.987548 Mean dependent var 6.618673Adjusted R-squared 0.985769 S.D. dependent var 1.018022S.E. of regression 0.121443 Akaike info criterion -1.185615Sum squared resid

38、0.103239 Schwarz criterion -1.141787Log likelihood 7.335268 Hannan-Quinn criter. -1.280195F-statistic 555.1601 Durbin-Watson stat 1.690478Prob(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 Ti

39、me: 16:23Sample: 1991 1999Included observations: 9Variable Coefficient Std. Error t-Statistic Prob. C -13.85071 1.234534 -11.21938 0.0000X3 70.75213 4.262581 16.59842 0.0000计量经济学实验报告纸11R-squared 0.975222 Mean dependent var 6.618673Adjusted R-squared 0.971682 S.D. dependent var 1.018022S.E. of regres

40、sion 0.171312 Akaike info criterion -0.497534Sum squared resid 0.205434 Schwarz criterion -0.453706Log likelihood 4.238903 Hannan-Quinn criter. -0.592114F-statistic 275.5077 Durbin-Watson stat 2.271547Prob(F-statistic) 0.000001Ln y = - 13.85071 + 70.75213 x3(0.0000) (0.0000)R2 = 0.9752, F = 275.5, T

41、 = 9Dependent Variable: LOG(Y)Method: Least SquaresDate: 04/08/14 Time: 16:55Sample: 1991 1999Included observations: 9Variable Coefficient Std. Error t-Statistic Prob. C 4.114468 0.194259 21.18035 0.0000X4 0.000559 4.05E-05 13.77401 0.0000R-squared 0.964417 Mean dependent var 6.618673Adjusted R-squa

42、red 0.959334 S.D. dependent var 1.018022S.E. of regression 0.205293 Akaike info criterion -0.135626Sum squared resid 0.295017 Schwarz criterion -0.091798Log likelihood 2.610317 Hannan-Quinn criter. -0.230206F-statistic 189.7232 Durbin-Watson stat 1.251489Prob(F-statistic) 0.000003Ln y =4.114468 + 0.

43、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: 9Variable Coefficient Std. Error t-Statistic Prob. 计量经济学实验报告纸12C 4.184633 0.192648 21.72171 0.0000X5 0.001161 8.57E-05 13.54788 0.0000

44、R-squared 0.963263 Mean dependent var 6.618673Adjusted R-squared 0.958015 S.D. dependent var 1.018022S.E. of regression 0.208595 Akaike info criterion -0.103717Sum squared resid 0.304582 Schwarz criterion -0.059890Log likelihood 2.466727 Hannan-Quinn criter. -0.198297F-statistic 183.5451 Durbin-Wats

45、on stat 1.202421Prob(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 Tim

46、e: 17:52Sample: 1991 1999Included observations: 9Variable Coefficient Std. Error t-Statistic Prob. C -25.29657 4.327927 -5.844964 0.0011X2 2.236525 0.827381 2.703137 0.0354X3 16.75681 20.21289 0.829016 0.4388R-squared 0.988828 Mean dependent var 6.618673Adjusted R-squared 0.985104 S.D. dependent var

47、 1.018022S.E. of regression 0.124250 Akaike info criterion -1.071839Sum squared resid 0.092629 Schwarz criterion -1.006097Log likelihood 7.823274 Hannan-Quinn criter. -1.213709F-statistic 265.5225 Durbin-Watson stat 2.089083Prob(F-statistic) 0.000001Ln y = -25.29657 + 2.236525 x2+16.75681 x3(0.0011)

48、 (0.0354) (0.4388)计量经济学实验报告纸13R2 = 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

49、)+C(2)*LOG(GDP)+C(3)*LOG(CPI)Coefficient Std. Error t-Statistic Prob. C(1) -3.648940 0.322308 -11.32129 0.0000C(2) 1.796174 0.180859 9.931363 0.0000C(3) -1.207511 0.353594 -3.414961 0.0035R-squared 0.989725 Mean dependent var 8.771863Adjusted R-squared 0.988441 S.D. dependent var 1.045337S.E. of regression 0.112388 Akaike info criterion -1.389779Sum squared resid 0.202097