计量经济学实验报告1

计量经济学实验报告1《计量经济学》课程实践报告1系部：经济与管理系专业：国际经济与贸易任课教师：李祖辉老师年级班级：2013级2班组员：舒冠、张淑琴、梁湘、冯冬雪税收收入影响因素分析—基于Eviews模型的经济计量分析一、意义1960年以来，中国的经济基本处于高速增长之中。经济增长的高速发展，势必会影响国家财政政策和国家福利水平。而税收作为国家财政收入中最主要的部分对这些政策的实施也会有很大的影响。近些年来，国家的税收也受到多种因素的影响。经济发展水平决定税收收入水平，税收同时也反作用于经济。要实现经济的持续增长，必须要求与经济紧密关联的税收符合其发展的要求，即政府筹集的税收收入应尽可能的满足其实现职能的需求，同时又不至于损害经济的发展。影响未来的需求，我们需要研究影响中国税收收入的主要原因，分析中央和地方税收收入增长的数量规律，从结构上对税收收入的影响做一个很好的了解，对于预测中国税收未来的增长趋势具有重要的作用，对于我国的社会主义现代化建设具有Y=β0+β1X1+β2X2+β3X3+β4X4+u然后将影响因素以某种方式引入模型。（2）数据：对税收收入影响因素的模型分析单位：亿元注：表中数据均来自《中国统计年鉴》3、实证分析：将方程形式设定为二次型Y=β0+β1X1+β2X2+β3X3+β4X4+u（1）、多重共线性EVIEWS的最小二乘估计结果为DependentVariable:YMethod:LeastSquaresDate:11/03/15Time:21:06Sample:19602014Includedobservations:55VariableCoefficientStd.Errort-StatisticProb.

C-3423.7921285.933-2.6624980.0104X1-0.0019670.007001-0.2810290.7798X20.6866520.02093432.801230.0000X332.4841112.435582.6121910.0118X40.0617930.0067479.1586550.0000R-squared0.999720

Meandependentvar16116.57AdjustedR-squared0.999697

S.D.dependentvar29942.14S.E.ofregression521.1390

Akaikeinfocriterion15.43642Sumsquaredresid13579295

Schwarzcriterion15.61890Loglikelihood-419.5015

Hannan-Quinncriter.15.50699F-statistic44552.34

Durbin-Watsonstat1.506966Prob(F-statistic)0.000000

经济意义检验：从回归的结果可以看出，财政支出（X2）、商品零售价格指数（X3）、进出口总额（X4）符号均为正，符合经济意义。国内生产总值（X1）符号为负，不符合经济意义。所以存在某种干扰。统计推断检验。该模型R^2=0.999720,修正的R^2=0.999697，可决系数很高，拟合优度较好，F检验值=44552.34，明显显著。但是当a=0.05时，ta/2(n-k-1)=ta/2(55-4-1)=t0.025(50)=2.009,x1的系数t检验不显著。X1X2X3X4X1

1.000000

0.994288-0.074125

0.987209X2

0.994288

1.000000-0.080662

0.972683X3-0.074125-0.080662

1.000000-0.068631X4

0.987209

0.972683-0.068631

1.000000由相关系数表可以看出，各解释变量之间除了x3之外的相关系数较高，证实确实存在严重的多重共线性。修正多重共线性：运用OLS方法逐一求Y对各个解释变量的回归。结合经济意义和统计检验选出拟合效果最好的一元线性回归方程。DependentVariable:YMethod:LeastSquaresDate:11/03/15Time:21:20Sample:19602014Includedobservations:55VariableCoefficientStd.Errort-StatisticProb.

C-1579.503391.7915-4.0314900.0002X10.1839990.00209287.951270.0000R-squared0.993195

Meandependentvar16116.57AdjustedR-squared0.993067

S.D.dependentvar29942.14S.E.ofregression2493.187

Akaikeinfocriterion18.51620Sumsquaredresid3.29E+08

Schwarzcriterion18.58919Loglikelihood-507.1954

Hannan-Quinncriter.18.54442F-statistic7735.426

Durbin-Watsonstat0.076503Prob(F-statistic)0.000000

DependentVariable:YMethod:LeastSquaresDate:11/03/15Time:21:21Sample:19602014Includedobservations:55VariableCoefficientStd.Errort-StatisticProb.

C214.5864187.42651.1449100.2574X20.8023710.004470179.48440.0000R-squared0.998357

Meandependentvar16116.57AdjustedR-squared0.998326

S.D.dependentvar29942.14S.E.ofregression1224.887

Akaikeinfocriterion17.09477Sumsquaredresid79518466

Schwarzcriterion17.16776Loglikelihood-468.1062

Hannan-Quinncriter.17.12300F-statistic32214.66

Durbin-Watsonstat0.849558Prob(F-statistic)0.000000

DependentVariable:YMethod:LeastSquaresDate:11/03/15Time:21:21Sample:19602014Includedobservations:55VariableCoefficientStd.Errort-StatisticProb.

C55391.2173901.590.7495270.4569X3-380.9575715.7482-0.5322510.5968R-squared0.005317

Meandependentvar16116.57AdjustedR-squared-0.013451

S.D.dependentvar29942.14S.E.ofregression30142.85

Akaikeinfocriterion23.50097Sumsquaredresid4.82E+10

Schwarzcriterion23.57396Loglikelihood-644.2766

Hannan-Quinncriter.23.52920F-statistic0.283291

Durbin-Watsonstat0.027353Prob(F-statistic)0.596777

DependentVariable:YMethod:LeastSquaresDate:11/03/15Time:21:21Sample:19602014Includedobservations:55VariableCoefficientStd.Errort-StatisticProb.

C-915.0621932.0995-0.9817210.3307X40.3796600.01049936.160170.0000R-squared0.961045

Meandependentvar16116.57AdjustedR-squared0.960310

S.D.dependentvar29942.14S.E.ofregression5965.148

Akaikeinfocriterion20.26094Sumsquaredresid1.89E+09

Schwarzcriterion20.33394Loglikelihood-555.1759

Hannan-Quinncriter.20.28917F-statistic1307.558

Durbin-Watsonstat0.287228Prob(F-statistic)0.000000

其中加入x2的方程修正的R^2最大，其方程为：Y=214.5864+0.802371X2(1.144910)(179.4844)修正的R^2=0.998326SE=79518466F=32214.66 所以，以x2为基础，顺次加入其他的自变量逐步回归：当a=0.05时，ta/2(n-k-1)=ta/2(55-4-1)=t0.025(50)=2.009Y=-314.8053+0.583638X2+0.050579X1-2.11601419.932197.513019修正的R^2=0.999182SE=138129403F=32986.08应为x1的引入改进了修正的R^2和F值且其他回归参数的t检验在统计上仍然显著，所以保留x1，方程为：Y=-314.8053+0.583638X2+0.050579X1继续：Y=-3588.465+0.586619X2+0.049981X1+31.73905X3-1.72249720.273907.5168711.575298修正的R^2=0.999205SE=36360185F=22618.10式中X3不显著，删去。继续：Y=-73.73216+0.683414X2+-0.001258X1+0.061678X4-0.74070730.98268-0.1703508.660592修正的R^2=0.999662SE=15432613F=53312.68X4虽然显著，但是它的引入影响了其他回归参数的估计值的数值，使得随机项和x1的回归参数通不过t检验，所以删去x4所以：Y=-314.8053+0.583638X2+0.050579X1-2.11601419.932197.513019修正的R^2=0.999182SE=138129403F=32986.08最小二乘估计为：DependentVariable:YMethod:LeastSquaresDate:11/04/15Time:14:42Sample:19602014Includedobservations:55VariableCoefficientStd.Errort-StatisticProb.

C-314.8053148.7728-2.1160140.0392X10.0505790.0067327.5130190.0000X20.5836380.02928119.932190.0000R-squared0.999212

Meandependentvar16116.57AdjustedR-squared0.999182

S.D.dependentvar29942.14S.E.ofregression856.3047

Akaikeinfocriterion16.39613Sumsquaredresid38129403

Schwarzcriterion16.50562Loglikelihood-447.8936

Hannan-Quinncriter.16.43847F-statistic32986.08

Durbin-Watsonstat1.089983Prob(F-statistic)0.000000

（2）、自相关（序列相关）令e=residDependentVariable:EMethod:LeastSquaresDate:11/04/15Time:14:49Sample(adjusted):19612014Includedobservations:54afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.

C327.0372202.74181.6130730.1132X10.0301700.0120402.5058240.0156X2-0.1111930.044899-2.4765080.0168T1^2-0.9950640.417083-2.3857720.0210E(-1)0.4376820.1284333.4078570.0013R-squared0.293946

Meandependentvar-1.778895AdjustedR-squared0.236309

S.D.dependentvar848.0834S.E.ofregression741.1349

Akaikeinfocriterion16.14226Sumsquaredresid26914768

Schwarzcriterion16.32643Loglikelihood-430.8411

Hannan-Quinncriter.16.21329F-statistic5.099957

Durbin-Watsonstat1.521476Prob(F-statistic)0.001623

LM检验=54*R^2=15.873084>X^2(1)=3.84。然后查看e(-1)的t检验=3.407857>t(50)=2.009，所以，存在一阶自相关。继续：DependentVariable:EMethod:LeastSquaresDate:11/04/15Time:15:08Sample(adjusted):19622014Includedobservations:53afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.

C352.3572208.28231.6917290.0973X10.0257200.0123302.0859130.0424X2-0.0915240.046308-1.9764030.0540T1^2-0.9718900.422199-2.3019680.0258E(-1)0.5253890.1367553.8418180.0004E(-2)-0.2564210.146405-1.7514540.0864R-squared0.337121

Meandependentvar-5.661248AdjustedR-squared0.266602

S.D.dependentvar855.7146S.E.ofregression732.8223

Akaikeinfocriterion16.13795Sumsquaredresid25240341

Schwarzcriterion16.36101Loglikelihood-421.6558

Hannan-Quinncriter.16.22373F-statistic4.780575

Durbin-Watsonstat1.530441Prob(F-statistic)0.001298

LM检验=54*R^2=17.867413>X^2(2)=5.99。然后查看e(-1)e(-2)的t检验，经查表可知e(-2)t值不满足条件，所以，不存在二阶自相关，即存在一阶自相关。自相关的修正：使用迭代法修正得到：DependentVariable:YMethod:LeastSquaresDate:11/04/15Time:15:14Sample(adjusted):19612014Includedobservations:54afteradjustmentsConvergenceachievedafter11iterationsVariableCoefficientStd.Errort-StatisticProb.

C2544.3662273.4391.1191710.2685X10.1889350.01520012.430090.0000X20.0931080.0544351.7104350.0935T1^2-5.7407271.700883-3.3751440.0015AR(1)0.9142670.06474614.120730.0000R-squared0.999710

Meandependentvar16410.75AdjustedR-squared0.999687

S.D.dependentvar30142.96S.E.ofregression533.5896

Akaikeinfocriterion15.48515Sumsquaredresid13951177

Schwarzcriterion15.66932Loglikelihood-413.0991

Hannan-Quinncriter.15.55618F-statistic42271.44

Durbin-Watsonstat1.146070Prob(F-statistic)0.000000InvertedARRoots

.91

DW=1.146070，查表得出上限为1.724，下限为DW=1.146070<1.414，所以存在正相关。再次修正自相关使用迭代法修正得到：DependentVariable:YMethod:LeastSquaresDate:11/04/15Time:15:19Sample(adjusted):19622014Includedobservations:53afteradjustmentsConvergenceachievedafter10iterationsVariableCoefficientStd.Errort-StatisticProb.

C1521.278934.58871.6277510.1103X10.2108320.01191417.696330.0000X2-0.0058670.047559-0.1233700.9023T1^2-5.3034061.080340-4.9090150.0000AR(1)1.4427720.12832011.243560.0000AR(2)-0.5765840.129935-4.4374930.0001R-squared0.999786

Meandependentvar16717.40AdjustedR-squared0.999763

S.D.dependentvar30346.26S.E.ofregression466.9039

Akaikeinfocriterion15.23639Sumsquaredresid10245966

Schwarzcriterion15.45945Loglikelihood-397.7645

Hannan-Quinncriter.15.32217F-statistic43923.39

Durbin-Watsonstat1.883360Prob(F-statistic)0.000000InvertedARRoots

.72+.24i

.72-.24i

DW=1.883360，查表得出上限为1.768，下限为1.374，因为1.768<DW=1.883360<2.232，所以不存在自相关。所以，本文模型估计的结果为：y=1521.278+0.210832x1+-0.005867x21.62775117.69633-0.123370R^2=0.999786DW=1.883360F=43923.39（3）、异方差White检验Y=β0+β1x1+β2X2+uδ^2=α0+α1x1+α2x2+α3(x1)^2+α4(x2)^2+α5(x1*x2)+εDependentVariable:EMethod:LeastSquaresDate:10/14/15Time:15:19Sample:19602014Includedobservations:55VariableCoefficientStd.Errort-StatisticProb.

C127420.1222588.70.5724470.5696X1-70.8442739.79185-1.7803710.0812X2292.6836208.06051.4067230.1658(X1)^20.0023100.0008172.8294090.0067(X2)^20.0375460.0158812.3642820.0221X1*X2-0.0186260.007244-2.5712830.0132R-squared0.560929

Meandependentvar693261.9AdjustedR-squared0.516126

S.D.dependentvar1724521.S.E.ofregression1199595.

Akaikeinfocriterion30.93554Sumsquaredresid7.05E+13

Schwarzcriterion31.15452Loglikelihood-844.7272

Hannan-Quinncriter.31.02022F-statistic12.51985

Durbin-Watsonstat2.686561Prob(F-statistic)0.000000从表中可以看出，nR^2=55*0.560929=30.8511由white检验知，在a=0.05下，查表得知χ^2(5)=11.07，因为nR^2=30.8511>χ^2(5)=11.07，所以拒绝原假设，表明模型中的随机误差存在异方差。修正异方差：使用w=1/abs（resid）作为权数，得出：DependentVariable:YMethod:LeastSquaresDate:11/04/15Time:15:28Sample:19602014Includedobservations:55Weightingseries:1/ABS(RESID)VariableCoefficientStd.Errort-StatisticProb.

C-312.89706.083272-51.435630.0000X10.0513790.00175629.261060.0000X20.5795030.00880265.840110.0000WeightedStatisticsR-squared0.999754

Meandependentvar3107.385AdjustedR-squared0.999744

S.D.dependentvar5593.490S.E.ofregression97.82912

Akaikeinfocriterion12.05732Sumsquaredresid497667.9

Schwarzcriterion12.16681Loglikelihood-328.5764

Hannan-Quinncriter.12.09966F-statistic105637.8

Durbin-Watsonstat0.656664Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.999211

Meandependentvar16116.57AdjustedR-squared0.999181

S.D.dependentvar29942.14S.E.ofregression856.8133

Sumsquaredresid38174711Durbin-Watsonstat1.079339

估计的结果为：y=-312.8970+0.051379x1+0.579503x2（-51.43563）（29.26106）(65.84011)R^2=0.999754DW=0.656664F=105637.8再次做怀特检验：DependentVariable:EMethod:LeastSquaresDate:11/04/15Time:15:34Sample:19602014Includedobservations:55Weightingseries:1/ABS(RESID)VariableCoefficientStd.Errort-StatisticProb.

C119.874631.154373.8477630.0003X10.0214420.0039285.4582490.0000X2-0.1782760.039257-4.5412850.0000X1^2-5.07E-071.87E-07-2.7096590.0093X2^2-1.41E-053.74E-06-3.7746330.0004X1*X25.63E-061.65E-063.4124310.0013WeightedStatisticsR-squared0.394156

Meandependentvar26.71224AdjustedR-squared0.332335

S.D.dependentvar91.44191S.E.ofregression77.76088

Akaikeinfocriterion11.64782Sumsquaredresid296291.0

Schwarzcriterion11.86680Loglikelihood-314.3151

Hannan-Quinncriter.11.73251F-statistic6.375776

Durbin-Watsonstat0.702770Prob(F-statistic)0.000124UnweightedStatisticsR-squared0.379217

Meandependentvar-1.41E-12AdjustedR-squared0.315872

S.D.dependentvar840.2976S.E.ofregression695.0273

Sumsquaredresid23670088Durbin-Watsonstat0.964671

从表中可以看出，nR^2=55*0.394156=21.67858,由white检验知，在a=0.05下，查表得知X^2(5)=11.0705，因为nR^2=21.67858>X^2(5)=11.0705，所以拒绝原假设，表明模型中的随机误差存在异方差。继续修正：使用w=1/（resid）^2作为权数，得出：DependentVariable:YMethod:LeastSquaresDate:11/04/15Time:15:39Sample:19602014Includedobservations:55Weightingseries:1/(RESID)^2VariableCoefficientStd.Errort-StatisticProb.

C-291.44350.512662-568.49020.0000X10.0569050.000157361.72320.0000X20.5375000.000901596.47750.0000WeightedStatisticsR-squared1.000000

Meandependentvar20011.12AdjustedR-squared1.000000

S.D.dependentvar146874.0S.E.ofregression2.481680

Akaikeinfocriterion4.708750Sumsquaredresid320.2543

Schwarzcriterion4.818241Loglikelihood-126.4906

Hannan-Quinncriter.4.751091F-statistic2.56E+09

Durbin-Watsonstat1.307016Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.998561

Meandependentvar16116.57AdjustedR-squared0.998506

S.D.dependentvar29942.14S.E.ofregression1157.354

Sumsquaredresid69652391Durbin-Watsonstat0.559704

估计的结果为：y=-291.4435+0.056905x1+0.537500x2（-568.4902）（361.7232）(596.4775)R^2=1.000000DW=1.307016F=2.56E+09从以上结果可看出存在自相关。同上自相关的修正，最终得DependentVariable:EMethod:LeastSquaresDate:11/04/15Time:15:51Sample(adjusted):19622014Includedobservations:53afteradjustmentsConvergenceachievedafter9