计量经济学练习题

1、题目：4.4 在本章开始的“引子”提出的“国内生产总值增加会减少财政收入吗？”的例子中，如果所采用的数据如表4.11所示表4.11 1978-2011年财政收入及其影响因素数据年份财政收入(亿元)CZSR财政支出(亿元)CZZC国内生产总值（现价，亿元）GDP税收总额（亿元）SSZE19781132.30 1122.093645.22 519.2819791146.40 1281.794062.58 537.8219801159.90 1228.834545.62 571.719811175.80 1138.414891.56 629.8919821212.30 1229.985323.35

2、700.0219831367.00 1409.525962.65 775.5919841642.90 1701.027208.05 947.3519852004.80 2004.259016.04 2040.7919862122.00 2204.9110275.18 2090.7319872199.40 2262.1812058.62 2140.3619882357.20 2491.2115042.82 2390.4719892664.90 2823.7816992.32 2727.419902937.10 3083.5918667.82 2821.8619913149.48 3386.622

3、1781.50 2990.1719923483.37 3742.226923.48 3296.9119934348.95 4642.335333.92 4255.319945218.10 5792.6248197.86 5126.8819956242.20 6823.7260793.73 6038.0419967407.99 7937.5571176.59 6909.8219978651.14 9233.5678973.03 8234.0419989875.9510798.1884402.28 9262.8199911444.0813187.6789677.05 10682.582000133

4、95.2315886.599214.55 12581.51200116386.0418902.58109655.17 15301.38200218903.6422053.15120332.69 17636.45200321715.2524649.95135822.76 20017.31200426396.4728486.89159878.34 24165.68200531649.2933930.28184937.37 28778.54200638760.240422.73216314.43 34804.35200751321.7849781.35265810.31 45621.97200861

5、330.3562592.66314045.43 54223.79200968518.376299.93340902.81 59521.59201083101.5189874.16401512.80 73210.792011103874.43109247.79472881.56 89738.39(资料来源：中国统计年鉴2008，中国统计出版社2008年版)一、 模型设定及其估计经分析,影响财政收入的主要因素,主要是财政支出、国民生产总值、以及税收等。所以我们只考虑题目中提出的因素，财政支出(CZZC)、国民生产总值(GDP)、税收总额(SSZE),并设定了如下的计量经济模型：利用Eviews软件

6、，生成CZSR、CZZC、GDP、SSZE等数据,并用这些数据对模型进行OLS多元回归，结果如下。Dependent Variable: CZSRMethod: Least SquaresDate: 05/05/14 Time: 12:52Sample: 1978 2011Included observations: 34VariableCoefficientStd. Errort-StatisticProb.  C119.0841107.12491.1116380.2751CZZC0.1223560.0488472.5049000.0179GDP-0.0341040.00

7、5068-6.7290490.0000SSZE1.1811560.06967716.951830.0000R-squared0.999791    Mean dependent var18185.17Adjusted R-squared0.999770    S.D. dependent var26129.67S.E. of regression395.9446    Akaike info criterion14.91056Sum squared resid4703165.

8、    Schwarz criterion15.09013Log likelihood-249.4795    Hannan-Quinn criter.14.97180F-statistic47896.18    Durbin-Watson stat1.025144Prob(F-statistic)0.000000即为：由此可见,该模型的可决系数很高，F检验值为47896.18，明显显著。当时，CZZC，GDP，SSZE的系数t检验都显著。但是GDP的系数符号与预期相反，GD

9、P的系数符号为负表明国内生产总值增加时,财政收入将会减少,然后与实际定性结果相违背,所以该模型有一定的缺陷,很有可能存在严重的多重共线性，为此做进一步分析。二、多重共线性的检测三个解释变量CZZC、GDP、SSZE的相关系数表 1 CZZC、GDP、SSZE的相关系数CZZCGDPSSZECZZC10.991490.99865GDP0.9914910.99387SSZE0.998650.993871由相关系数矩阵可以看出，各解释变量相互之间的相关系数较高，证实确实存在一定的多重共线性。为进一步了解多重共线性的性质，我们做辅助回归，即将每个变量分别作被解释变量对其余的变量进行回归。结果如下：的参

10、数估计结果：Dependent Variable: CZZCMethod: Least SquaresDate: 05/05/14 Time: 12:57Sample: 1978 2011Included observations: 34VariableCoefficientStd. Errort-StatisticProb.  C96.70225393.50660.2457450.8075GDP-0.0188510.018325-1.0286850.3116SSZE1.3124070.10037713.074820.0000R-squared0.997400 &

11、#160;  Mean dependent var19460.41Adjusted R-squared0.997232    S.D. dependent var27672.44S.E. of regression1455.857    Akaike info criterion17.48867Sum squared resid65705105    Schwarz criterion17.62335Log likelihood-294.3075 

12、;   Hannan-Quinn criter.17.53460F-statistic5945.806    Durbin-Watson stat1.368239Prob(F-statistic)0.000000的参数估计Dependent Variable: GDPMethod: Least SquaresDate: 05/05/14 Time: 12:59Sample: 1978 2011Included observations: 34VariableCoefficientStd. Errort-StatisticPr

13、ob.  C13110.882977.7124.4030060.0001CZZC-1.7510431.702216-1.0286850.3116SSZE7.5623762.0620883.6673390.0009R-squared0.988187    Mean dependent var101654.7Adjusted R-squared0.987425    S.D. dependent var125124.3S.E. of regression14031.46  

14、60; Akaike info criterion22.02009Sum squared resid6.10E+09    Schwarz criterion22.15477Log likelihood-371.3415    Hannan-Quinn criter.22.06602F-statistic1296.583    Durbin-Watson stat0.233153Prob(F-statistic)0.000000的参数估计Dependent Vari

15、able: SSZEMethod: Least SquaresDate: 05/05/14 Time: 13:04Sample: 1978 2011Included observations: 34VariableCoefficientStd. Errort-StatisticProb.  C-404.7214266.3939-1.5192590.1388CZZC0.6449960.04933113.074820.0000GDP0.0400110.0109103.6673390.0009R-squared0.998125    Mea

16、n dependent var16214.46Adjusted R-squared0.998004    S.D. dependent var22843.09S.E. of regression1020.617    Akaike info criterion16.77830Sum squared resid32291435    Schwarz criterion16.91298Log likelihood-282.2311    H

17、annan-Quinn criter.16.82423F-statistic8249.980    Durbin-Watson stat1.291261Prob(F-statistic)0.000000表2 辅助回归的值被解释变量可决系数的值方差扩大因子vifCZZC0.997400384.61GDP0.98818784.65SSZE0.998125533.33由于辅助回归的可决系数很高，经验表明扩大因子vif>10时，通常说明该被解释变量与其他解释变量之间有严重的多重共线性，上表中czzc、gdp、ssze方差扩大因子都远大于10，表明存在严重的

18、多重共线性。同时解释变量GDP的回归系数带有负号，与定性分析的结果相违背，则可能存在多重共线性。三、修正多重共线性采用逐步回归的办法，去解决多重共线性问题。分别做czsr对czzc、gdp、ssze的一元回归。Dependent Variable: CZSRMethod: Least SquaresDate: 05/09/15 Time: 11:35Sample: 1978 2011Included observations: 34VariableCoefficientStd. Errort-StatisticProb.  C-169.3819266.7056-0.6350

19、890.5299CZZC0.9431740.007962118.45300.0000R-squared0.997725    Mean dependent var18185.17Adjusted R-squared0.997653    S.D. dependent var26129.67S.E. of regression1265.756    Akaike info criterion17.18175Sum squared resid51268423  

20、;  Schwarz criterion17.27154Log likelihood-290.0897    Hannan-Quinn criter.17.21237F-statistic14031.12    Durbin-Watson stat1.250442Prob(F-statistic)0.000000Dependent Variable: CZSRMethod: Least SquaresDate: 05/09/15 Time: 11:35Sample: 1978 2011Inclu

21、ded observations: 34VariableCoefficientStd. Errort-StatisticProb.  C-2861.490770.4344-3.7141260.0008GDP0.2070410.00482242.937760.0000R-squared0.982939    Mean dependent var18185.17Adjusted R-squared0.982406    S.D. dependent var26129.67S.E. of regres

22、sion3465.891    Akaike info criterion19.19635Sum squared resid3.84E+08    Schwarz criterion19.28614Log likelihood-324.3379    Hannan-Quinn criter.19.22697F-statistic1843.651    Durbin-Watson stat0.151983Prob(F-statistic)

23、0.000000Dependent Variable: CZSRMethod: Least SquaresDate: 05/09/15 Time: 11:36Sample: 1978 2011Included observations: 34VariableCoefficientStd. Errort-StatisticProb.  C-356.3761140.0831-2.5440340.0160SSZE1.1435190.005050226.42530.0000R-squared0.999376    Mean dependent

24、 var18185.17Adjusted R-squared0.999357    S.D. dependent var26129.67S.E. of regression662.7204    Akaike info criterion15.88761Sum squared resid14054348    Schwarz criterion15.97739Log likelihood-268.0893    Hannan-Quinn

25、 criter.15.91823F-statistic51268.43    Durbin-Watson stat0.511014Prob(F-statistic)0.000000结果如下表：表 3 一元回归估计结果解释变量CzzcGdpSsze参数估计值0.9431740.2070411.143519T统计量118.453042.93776226.42530.9977250.9829390.9993760.9976530.9824060.999357其中，加入ssze的方程最大,多以以ssze为基础，顺次加入其它解释变量做逐步回归。Dependent

26、Variable: CZSRMethod: Least SquaresDate: 05/09/15 Time: 13:55Sample: 1978 2011Included observations: 34VariableCoefficientStd. Errort-StatisticProb.  C-356.3761140.0831-2.5440340.0160SSZE1.1435190.005050226.42530.0000R-squared0.999376    Mean dependent var18185.17Adjust

27、ed R-squared0.999357    S.D. dependent var26129.67S.E. of regression662.7204    Akaike info criterion15.88761Sum squared resid14054348    Schwarz criterion15.97739Log likelihood-268.0893    Hannan-Quinn criter.15.91823F-

28、statistic51268.43    Durbin-Watson stat0.511014Prob(F-statistic)0.000000情况1：加入解释变量czzc，再加入gdp的结果如下：Dependent Variable: CZSRMethod: Least SquaresDate: 05/09/15 Time: 11:44Sample: 1978 2011Included observations: 34VariableCoefficientStd. Errort-StatisticProb.  C-328.04851

29、30.9403-2.5053280.0177SSZE0.9232500.09067710.181720.0000CZZC0.1820730.0748522.4324340.0210R-squared0.999476    Mean dependent var18185.17Adjusted R-squared0.999442    S.D. dependent var26129.67S.E. of regression617.0121    Akaike info crite

30、rion15.77175Sum squared resid11801822    Schwarz criterion15.90643Log likelihood-265.1198    Hannan-Quinn criter.15.81768F-statistic29575.82    Durbin-Watson stat0.517163Prob(F-statistic)0.000000Dependent Variable: CZSRMethod: Least Squares

31、Date: 05/09/15 Time: 11:49Sample: 1978 2011Included observations: 34VariableCoefficientStd. Errort-StatisticProb.  C119.0841107.12491.1116380.2751SSZE1.1811570.06967716.951830.0000CZZC0.1223560.0488472.5049000.0179GDP-0.0341040.005068-6.7290490.0000R-squared0.999791    

32、Mean dependent var18185.17Adjusted R-squared0.999770    S.D. dependent var26129.67S.E. of regression395.9446    Akaike info criterion14.91056Sum squared resid4703164.    Schwarz criterion15.09013Log likelihood-249.4795   

33、0;Hannan-Quinn criter.14.97180F-statistic47896.19    Durbin-Watson stat1.025144Prob(F-statistic)0.000000情况2：加入解释变量gdp，再加入czzc的结果如下：Dependent Variable: CZSRMethod: Least SquaresDate: 05/09/15 Time: 11:46Sample: 1978 2011Included observations: 34VariableCoefficientStd. Errort-Stati

34、sticProb.  C130.9162115.76781.1308520.2668SSZE1.3417370.02953045.435880.0000GDP-0.0364100.005391-6.7537310.0000R-squared0.999748    Mean dependent var18185.17Adjusted R-squared0.999731    S.D. dependent var26129.67S.E. of regression428.3063 

35、0;  Akaike info criterion15.04165Sum squared resid5686834.    Schwarz criterion15.17633Log likelihood-252.7081    Hannan-Quinn criter.15.08758F-statistic61395.04    Durbin-Watson stat1.210574Prob(F-statistic)0.000000Dependent Vari

36、able: CZSRMethod: Least SquaresDate: 05/09/15 Time: 11:50Sample: 1978 2011Included observations: 34VariableCoefficientStd. Errort-StatisticProb.  C119.0841107.12491.1116380.2751SSZE1.1811570.06967716.951830.0000GDP-0.0341040.005068-6.7290490.0000CZZC0.1223560.0488472.5049000.0179R-squared0

37、.999791    Mean dependent var18185.17Adjusted R-squared0.999770    S.D. dependent var26129.67S.E. of regression395.9446    Akaike info criterion14.91056Sum squared resid4703164.    Schwarz criterion15.09013Log likelihood

38、-249.4795    Hannan-Quinn criter.14.97180F-statistic47896.19    Durbin-Watson stat1.025144Prob(F-statistic)0.000000我们发现上诉两种情况下，随着新的解释变量加入，模型的都在增大，且各个参数的t检验也是显著的。为此无法判断，于是将CZZC做为基础，再进行一次逐步回归。Dependent Variable: CZSRMethod: Least SquaresDate: 05/09/15 Time: 11:1

39、6Sample: 1978 2011Included observations: 34VariableCoefficientStd. Errort-StatisticProb.  C-169.3819266.7056-0.6350890.5299CZZC0.9431740.007962118.45300.0000R-squared0.997725    Mean dependent var18185.17Adjusted R-squared0.997653    S.D. dependent v

40、ar26129.67S.E. of regression1265.756    Akaike info criterion17.18175Sum squared resid51268423    Schwarz criterion17.27154Log likelihood-290.0897    Hannan-Quinn criter.17.21237F-statistic14031.12    Durbin-Watson stat1

41、.250442Prob(F-statistic)0.000000Dependent Variable: CZSRMethod: Least SquaresDate: 05/09/15 Time: 11:16Sample: 1978 2011Included observations: 34VariableCoefficientStd. Errort-StatisticProb.  C-358.9552330.6697-1.0855400.2861CZZC0.8841970.06123414.439690.0000GDP0.0131550.0135420.9714040.3389