影响我国财政收入因素的统计分析1

第5页共15页R-squared0.999857

Meandependentvar16520.73AdjustedR-squared0.999835

S.D.dependentvar22001.07S.E.ofregression282.4520

Akaikeinfocriterion14.27158Sumsquaredresid2074258.

Schwarzcriterion14.50287Loglikelihood-216.2096

Hannan-Quinncriter.14.34698F-statistic45498.54

Durbin-Watsonstat1.463028Prob(F-statistic)0.000000QUOTE=2231.738+0.000957X1+1.064963X2-0.041868X3+0.022694X4t=（4.038066）（0.131554）（22.30264）（-3.919010）（3.477443）R2=0.999857QUOTE=0.999835F=45498.54DW=1.463028五、模型检验5.1经济检验模型估计结果说明，在假定其他变量不变的情况下，国家财政决算收入中各项税收每增长1%，平均来说国家财政决算收入中各项税收会增长0.096%；在假定其他变量不变的情况下，年末从业人员数增长1%，平均来说国家财政决算收入会增长106.5%;在假定其他变量不变的情况下，全社会固定资产投资总额增长1%，平均来说国家财政决算收入会降低4.19%；在假定其他变量不变的情况下，国内生产总值（现价）增长1%，平均来说国家财政决算收入会增长2.27%。这与理论分析与经验判断相一致。5.2.统计检验1）拟合优度检验由4.4中数据可以得到R2=0.999857，修正的可决系数QUOTE=0.999835，这说明模型对样本的拟合很好。2)变量的显著性检验(t检验)分别针对H0：βj=0（j=1，2，3，4，5），给定显著性水平α=0.05，查t分布表得自由度为n-k=26的临界值tα/2（n-k）=2.056。由3.4中数据可得QUOTE对应t统计量分别为4.038066，0.131554，22.30264，-3.919010，3.477443，其中QUOTE的t统计量绝对值大于2.056，都应当拒绝原假设，QUOTE的t统计量绝对值小于2.056，应该拒绝备择假设，也就是说国家财政决算收入，全社会固定资产投资总额，国内生产总值（现价）分别对被解释变量国家财政决算收入都有显著的影响，而年末从业人员数对被解释变量国家财政决算收入没有显著的影响。3)方程的显著性检验(F检验)针对H0：βj=0（j=2，3，4，5），给定显著性水平α=0.05，在F分布表中查出自由度k-1=4和n-k=26的临界值Fα（4，26）=2.74.由3.4中得到F=45498.54，由于F=45498.54>Fα（4，26）=2.74，应拒绝原假设H0：βj=0（j=2，3，4，5），说明回归方程显著，即国家财政决算收入，年末从业人员数，全社会固定资产投资总额，国内生产总值（现价）等变量联合起来对国家财政决算收入有显著影响。六、多重共线性检验及其修正6.1多重共线性检验从回归结果的系数以及t值我们可以看出模型可能存在多重共线性，下面我们计算出解释变量的相关系数。解释变量的相关系数矩阵如下：变量X1X2X3X4X1

1.000000

0.993302

0.721214

0.979053X2

0.993302

1.000000

0.653618

0.991928X3

0.721214

0.653618

1.000000

0.607997X4

0.979053

0.991928

0.607997

1.000000

由各相关系数值可知,解释变量之间都高度相关，模型存在严重的多重共线性。6.2多重共线性的修正采用逐步回归法，来检验并解决多重共线性问题。分别作y对x1、x2、x3、x4的一元回归一元回归估计结果变量X1X2X3X4参数估计值0.1994561.350621.2392980.314516t统计量40.02286220.13084.46788347.46135R20.9822180.9994020.4077040.9872900.9816040.9993810.3872800.986851可见加入X2的修正可决系数最大，应该以X2为基础，顺次加入其他变量逐步回归。加入新变量的回归结果（一）变量X1X2X3X4X2,X1-0.029179（-4.975477）1.298576（39.24898）0.999660X2,X31.154375（280.8435）-0.050510（-7.188511）0.999775X2,X40.995435（31.40165）0.039243（4.440459）0.999624比较可得，当加入X3时方程的QUOTE改进最大，而且个参数的t检验显著，因此选择保留X3，再继续加入其他新变量逐步回归。加入新变量的回归结果（二）X1X2X3X4X2,x3,x1-0.002932（-0.343420）1.169445（26.52868）-0.046957（-3.735682）0.999767X2,x3,x41.070374（44.93790）-0.040765（-6.268515）0.022562（3.564277）0.999841在加入X2、X3的基础上加入X4后方程的QUOTE有所改善，且各个参数的t检验均显著，所以应当保留X4。加入新变量的回归结果（三）X1X2X3X4X2,x3,x4,x10.000957（0.131554）1.064963（22.30264）-0.041868（-3.919010）0.022694（3.477443）0.999835当加入X1时，QUOTE没有提高，其参数的t检验不显著。因此去除X1最后修正严重多重共线性影响后的回归结果为：QUOTE=2178.690+1.070374X2-0.040765X3+0.022562X4t=（5.872354）（44.93790）（-6.268515）（3.564277）R2=0.999857QUOTE=0.999841F=62956.07DW=1.470169七、异方差检验及其修正7.1异方差检验7.1.1绘制e2对X2、X3、X4的散点图从图上看，散点集中于左下角，模型可能存在异方差。下面我们运用其他方法进一步检验模型的异方差是否存在。7.1.2Goldfeld-Quanadt检验由于n=31删除四分之一的观测值，也就是大约7个观测值，余下部分平分得到两个样本区间：1980~1991和1999~2010，它们的样本个数均为12个，即n1=n2=12。采用OLS进行估计。DependentVariable:YMethod:LeastSquaresDate:05/20/12Time:13:53Sample:19801991Includedobservations:12VariableCoefficientStd.Errort-StatisticProb.

C-787.7499299.0150-2.6344830.0300X20.3704790.0897514.1278680.0033X30.0391310.0075505.1831800.0008X40.0420180.0544560.7715890.4625R-squared0.992545

Meandependentvar1999.403AdjustedR-squared0.989749

S.D.dependentvar697.8872S.E.ofregression70.65790

Akaikeinfocriterion11.61478Sumsquaredresid39940.31

Schwarzcriterion11.77641Loglikelihood-65.68867

Hannan-Quinncriter.11.55494F-statistic355.0346

Durbin-Watsonstat2.502786Prob(F-statistic)0.000000

DependentVariable:YMethod:LeastSquaresDate:05/20/112Time:13:55Sample:19992010Includedobservations:12VariableCoefficientStd.Errort-StatisticProb.

C9743.16214283.100.6821460.5144X21.1196090.05725819.553730.0000X3-0.1504430.200618-0.7498970.4748X40.0124280.0123681.0048180.3444R-squared0.999834

Meandependentvar36910.18AdjustedR-squared0.999771

S.D.dependentvar23848.43S.E.ofregression360.5755

Akaikeinfocriterion14.87448Sumsquaredresid1040118.

Schwarzcriterion15.03612Loglikelihood-85.24689

Hannan-Quinncriter.14.81464F-statistic16037.13

Durbin-Watsonstat2.290085Prob(F-statistic)0.000000有结果计算F统计量：

F=QUOTE=QUOTE=26.04181判断在α=0.05下，分子分母的自由度都是（31-7）/2-4=8，查F分布表得到临界值F0.05（8，8）=3.44，因为F=26.04181>F0.05（8，8）=3.44，所以拒绝原假设，表明模型存在异方差。7.1.3White检验使用EViews得到以下结果：HeteroskedasticityTest:WhiteF-statistic28.71478

Prob.F(9,21)0.0000Obs*R-squared28.67028

Prob.Chi-Square(9)0.0007ScaledexplainedSS22.91936

Prob.Chi-Square(9)0.0064TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:05/20/12Time:16:49Sample:19802010Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.

C-1108436.685409.8-1.6171870.1208X2290.0531148.91161.9478210.0649X2^20.0054150.0022852.3699230.0274X2*X3-0.0046240.002233-2.0707820.0509X2*X4-0.0030380.001238-2.4534210.0230X340.1161126.505721.5134890.1451X3^2-0.0003200.000245-1.3048300.2061X3*X40.0025800.0007543.4230150.0026X4-174.587551.71831-3.3757380.0029X4^20.0004090.0001662.4563110.0228R-squared0.924848

Meandependentvar66956.09AdjustedR-squared0.892640

S.D.dependentvar98811.72S.E.ofregression32376.52

Akaikeinfocriterion23.86395Sumsquaredresid2.20E+10

Schwarzcriterion24.32653Loglikelihood-359.8912

Hannan-Quinncriter.24.01474F-statistic28.71478

Durbin-Watsonstat1.700188Prob(F-statistic)0.000000

从表可看出nR2=28.67028，而在5%的显著性水平下，查表得临界值Χ2（9）=16.919。因为nR2=28.67028>Χ2（9）=16.919,所以，表明模型存在异方差。从上述几种方法检验结果可以看出模型存在异方差性，那么我们将对其进行修正。7.2异方差的修正运用加权最小二乘法估计过程中，我们分别使用权w1=1/x2,w2=1/x2^2,w3=1/sqr(x2)，。经比较发现用权数w3的效果比较好，下面给出权数w1、w2、w3的回归结果DependentVariable:YMethod:LeastSquaresDate:05/20/12Time:14:27Sample:19802010Includedobservations:31Weightingseries:W1VariableCoefficientStd.Errort-StatisticProb.

C1615.115315.38265.1211300.0000X20.6934360.1026986.7521670.0000X3-0.0223090.007573-2.9456940.0066X40.1240560.0305134.0656740.0004WeightedStatisticsR-squared0.990514

Meandependentvar3109.770AdjustedR-squared0.989460

S.D.dependentvar766.5424S.E.ofregression215.2590

Akaikeinfocriterion13.70148Sumsquaredresid1251084.

Schwarzcriterion13.88651Loglikelihood-208.3729

Hannan-Quinncriter.13.76179F-statistic939.7561

Durbin-Watsonstat1.141270Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.998226

Meandependentvar16520.73AdjustedR-squared0.998029

S.D.dependentvar22001.07S.E.ofregression976.8039

Sumsquaredresid25761939Durbin-Watsonstat0.595311DependentVariable:YMethod:LeastSquaresDate:05/20/12Time:14:28Sample:19802010Includedobservations:31Weightingseries:W2VariableCoefficientStd.Errort-StatisticProb.

C269.4737327.91550.8217780.4184X20.3148060.1353052.3266430.0277X30.0122590.0083581.4666910.1540X40.1904840.0599923.1751580.0037WeightedStatisticsR-squared0.935786

Meandependentvar1503.341AdjustedR-squared0.928651

S.D.dependentvar2477.187S.E.ofregression113.5166

Akaikeinfocriterion12.42169Sumsquaredresid347922.4

Schwarzcriterion12.60672Loglikelihood-188.5362

Hannan-Quinncriter.12.48200F-statistic131.1561

Durbin-Watsonstat1.696653Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.973838

Meandependentvar16520.73AdjustedR-squared0.970931

S.D.dependentvar22001.07S.E.ofregression3751.096

Sumsquaredresid3.80E+08Durbin-Watsonstat0.106940

DependentVariable:YMethod:LeastSquaresDate:05/20/12Time:14:29Sample:19802010Includedobservations:31Weightingseries:W3VariableCoefficientStd.Errort-StatisticProb.

C2179.146265.39878.2108390.0000X20.9881290.05366918.411530.0000X3-0.0382880.005657-6.7687660.0000X40.0452640.0153362.9513900.0065WeightedStatisticsR-squared0.999006

Meandependentvar6966.490AdjustedR-squared0.998895

S.D.dependentvar4843.265S.E.ofregression255.0939

Akaikeinfocriterion14.04105Sumsquaredresid1756968.

Schwarzcriterion14.22609Loglikelihood-213.6363

Hannan-Quinncriter.14.10137F-statistic9043.425

Durbin-Watsonstat1.238294Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.999781

Meandependentvar16520.73AdjustedR-squared0.999756

S.D.dependentvar22001.07S.E.ofregression343.5156

Sumsquaredresid3186080.Durbin-Watsonstat1.099033

经比较可知，用权数w3的效果最好，修正后的模型为：QUOTE=2179.146+0.988129X2-0.038288X3+0.045264X4t=（8.210839）（18.41153）（-6.768766）（2.951390）R2=0.999006QUOTE=0.998895F=9043.425DW=1.238294八、自相关的检验及其修正8.1自相关的检验1%的显著性水平，查DW统计表可知，dL=0.960dU1.510。此模型DW值为1.238294。为无法判断的区域。此时只能改用图示法来检验。通过EViews软件得出该模型的残差图如下上图表明模型显然存在自相关。在这里我们使用广义差分法进行弥补。8.2自相关修正DependentVariable:EMethod:LeastSquaresDate:05/20/12Time:14:47Sample(adjusted):19812010Includedobservations:30afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.

E(-1)0.4206670.2216801.8976300.0677R-squared0.110457

Meandependentvar0.114935AdjustedR-squared0.110457

S.D.dependentvar331.4580S.E.ofregression312.6166

Akaikeinfocriterion14.36060Sumsquaredresid2834145.

Schwarzcriterion14.40730Loglikelihood-214.4090

Hannan-Quinncriter.14.37554Durbin-Watsonstat1.188304

QUOTE=0.420667et-1由此可知QUOTE=0.420667，对原模型进行广义差分，得到广义差分方程为：Yt-0.420667Yt-1=β0(1-0.420667)+β2(X2t-0.420667X2t-1)+β3(X3t-0.420667X3t-1)+β4(X4t-0.420667X4t-1)对广义差分方程进行回归DependentVariable:Y-0.420667*Y(-1)Method:LeastSquaresDate:05/20/12Time:15:10Sample(adjusted):19812010Includedobservations:30afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.

C984.5681399.38722.4651970.0206X2-0.420667*X2(-1)1.0599670.02996835.369500.0000X3-0.420667*X3(-1)-0.0322150.011536-2.7926470.0097X4-0.420667*X4(-1)0.0239500.0077583.0871770.0048R-squared0.999671