我国居民汽车消费量的计量经济分析

1、我国居民汽车消费量的计量经济分析摘要：随着我国经济的持续、快速的增长，以及加入世界贸易组织后对外开放程度的不断加深，市场上对各种商品的需求也在与日俱增。汽车作为高档消费品，也随着市场经济的不断发展逐步走进了普通大众的生活。然而，中国的汽车需求量到底有多大，汽车消费量和影响因素的关系到底是怎么样的。希望通过此次研究，能对我国的汽车需求量有更深入的认识，以解释以上提出的问题。 Keywords最小二乘法 多重共线性 自相关 异方差分析过程：由于研究的汽车需求量是一个时间序列数据，为此我们对其进行了平稳性检验，并利用最小二乘估计、多重共线、异方差及自相关等计量经济学的检验方法，对模型进行了进一步的检

2、验和调整，最后并对模型进行了评价和推广，以提高模型估计的可靠性，进而满足模型预测的需要。模型检验经济理论实际经济活动估计参数 搜集统计数据模型检验变量选取和具体数据：因变量 Y 我国的汽车拥有量（单位：万辆）自变量 X1 国内生产总值（元）X2 居民消费水平（人均）（元）X3 公路通车历程（单位：万公里）X4 人均能源消费情况（千克）具体数据如下：（表 1）年份居民汽车拥有量国内生产总值居民消费水平公路通车里程人均能源消费情况198973.1216992.3788101.43139.3199081.6218667.8833102.83139.2199196.0421781.5932104.11

3、138.11992118.226923.51116105.67133.41993155.7735333.91393108.35130.61994205.4248197.91833111.78129.31995249.9660793.72355115.7130.81996289.6771176.62789118.58145.51997358.67789733002122.64133.11998423.6584402.33159127.85115.91999533.8889677.13346135.17121.42000625.3399214.63632140.27126.42001770.781

4、09655.23869169.8130.32002968.98120332.74106176.52136.920031219.23135822.84411180.98153.920041481.66159878.34925187.07164.220051848.07183084.85439193.05179.4资料来源于中国统计年鉴（资料数据是从 1989 年到 2005 年）建立模型：设定模型为Y=C+1X1+2X2+3X3+4X4+ +U 模型的参数估计、检验及修正1. 我们首先对中的数据，利用 EVIEWS 软件，运用最小二乘法估计，得到以下输出框：Dependent Variable:

5、 Y Method: Least SquaresDate: 06/25/07Time: 16:00 Sample: 1989 2005Included observations: 17VariableCoefficientStd. Errort-StatisticProb.C-375.8803213.8440-1.7577310.1042X10.0244400.0026789.1256230.0000X2-0.5662930.076587-7.3940710.0000X33.6392290.9651363.7706890.0027X40.5938421.1961070.4964790.6285

6、R-squared0.997142Mean dependent var558.8265Adjusted R-squared0.996189S.D. dependent var533.4785S.E. of regression32.93195Akaike info criterion10.06669Sum squared resid13014.16Schwarz criterion10.31175Log likelihood-80.56688F-statistic1046.685Durbin-Watson stat1.709336Prob(F-statistic)0.0000002.很明显可以

7、看到，X2 的系数的符号为负，首先从经济意义上是说不通的，居民消费水平汽车需求成负相关关系;这与我们实际生活中的情况是不相符合的。同时还可以看出，X2、X4 的 t 值都不显著，则说明解释变量之间有可能存在多重共线性。因此接下来我们来一一的检验。2.计量经济学检验和修正（1）多重共线性检验和修正用 EVIEWS 软件，得相关系数矩阵表：（表 4）X1X2X3X4X11.0000000.9904150.9611210.577850X20.9904151.0000000.9410970.478188X30.9611210.9410971.0000000.586115X40.5778500.4781

8、880.5861151.000000从上表可见，解释变量之间存在高度线性相关。下面利用逐步回归法（向上回归）进行修正首先运用 OLS 方法逐一求 Y 对各个解释变量的回归YX1Dependent Variable: Y Method: Least SquaresDate: 06/25/07Time: 16:13 Sample: 1989 2005Included observations: 17VariableCoefficientStd. Errort-StatisticProb.C-260.815266.70809-3.9097990.0014X10.0102390.00071114.39

9、0900.0000R-squared 0.932462Mean dependent var558.8265Adjusted R-squared 0.927960S.D. dependent var533.4785S.E. of regression 143.1873Akaike info criterion12.87631Sum squared resid 307539.0Schwarz criterion12.97434Log likelihood-107.4487F-statistic207.0981Durbin-Watson stat 0.195109Prob(F-statistic)0

10、.000000YX2Dependent Variable: YMethod: Least SquaresDate: 06/25/07Time: 16:15Sample: 1989 2005Included observations: 17VariableCoefficientStd. Errort-StatisticProb.C-373.2180113.3823-3.2916770.0049X20.3305950.0357969.2354870.0000R-squared 0.850440Mean dependent var558.8265Adjusted R-squared 0.840469

11、S.D. dependent var533.4785S.E. of regression 213.0782Akaike info criterion13.67133Sum squared resid 681034.5Schwarz criterion13.76935Log likelihood-114.2063F-statistic85.29422Durbin-Watson stat 0.193835Prob(F-statistic)0.000000YX3Dependent Variable: YMethod: Least SquaresDate: 06/25/07Time: 16:16Sam

12、ple: 1989 2005Included observations: 17VariableCoefficientStd. Errort-StatisticProb.C-1560.595157.8209-9.8883900.0000X315.653041.13465313.795430.0000R-squared0.926941Mean dependent var558.8265Adjusted R-squared0.922071S.D. dependent var533.4785S.E. of regression148.9250Akaike info criterion12.95489S

13、um squared resid332679.8Schwarz criterion13.05292Log likelihood-108.1166F-statistic190.3140Durbin-Watson stat0.736231Prob(F-statistic)0.000000YX4Dependent Variable: Y Method: Least SquaresDate: 06/25/07Time: 16:17 Sample: 1989 2005Included observations: 17VariableCoefficientStd. Errort-StatisticProb

14、.C-2863.457844.1530-3.3921070.0040X424.781206.0761954.0784080.0010R-squared0.525818Mean dependent var558.8265Adjusted R-squared0.494206S.D. dependent var533.4785S.E. of regression379.4057Akaike info criterion14.82522Sum squared resid2159231.Schwarz criterion14.92325Log likelihood-124.0144F-statistic

15、16.63341Durbin-Watson stat0.260384Prob(F-statistic)0.000989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。经分析在五个一元回归模型中汽车需求量 Y 对国内生产总值 X1 的线性关系强，拟合效果好，即Y= 260.8152+0.010239 X1(66.70809)(0.000711)R2=0.932462S.E.= 143.1873F=207.0981逐步回归（向上回归）以 X1 为基础将其余解释变量逐一代入上式Y C X1 X2Dependent Variable: Y Method: Least SquaresDate:

16、 06/25/07Time: 16:28 Sample: 1989 2005Included observations: 17VariableCoefficientStd. Errort-StatisticProb.C43.8907533.447161.3122410.2105X10.0290600.00162317.907480.0000X2-0.6425030.054866-11.710360.0000R-squared0.993744Mean dependent var558.8265Adjusted R-squared0.992850S.D. dependent var533.4785

17、S.E. of regression45.10981Akaike info criterion10.61486Sum squared resid28488.53Schwarz criterion10.76190Log likelihood-87.22632F-statistic1111.876Durbin-Watson stat0.818191Prob(F-statistic)0.000000可以看见 X2 的系数为负，即居民消费水平和汽车消费量负相关，这与实际的情况是不相符合的，则可以剔除 X2Y C X1 X3Dependent Variable: Y Method: Least Squa

18、resDate: 06/25/07Time: 16:31 Sample: 1989 2005Included observations: 17VariableCoefficientStd. Errort-StatisticProb.C-891.0252311.0446-2.8646220.0125X10.0056030.0023352.3998940.0309X37.3949273.5802272.0654910.0579R-squared0.948236Mean dependent var558.8265Adjusted R-squared0.940842S.D. dependent var

19、533.4785S.E. of regression129.7554Akaike info criterion12.72796Sum squared resid235710.4Schwarz criterion12.87500Log likelihood-105.1877F-statistic128.2300Durbin-Watson stat0.403106Prob(F-statistic)0.000000Y C X1 X4Dependent Variable: Y Method: Least SquaresDate: 06/25/07Time: 16:34 Sample: 1989 200

20、5Included observations: 17VariableCoefficientStd. Errort-StatisticProb.C-1321.981225.6176-5.8593900.0000X10.0087010.00055615.662960.0000X48.5752321.7905494.7891650.0003R-squared0.974401Mean dependent var558.8265Adjusted R-squared0.970744S.D. dependent var533.4785S.E. of regression91.24825Akaike info

21、 criterion12.02383Sum squared resid116567.4Schwarz criterion12.17087Log likelihood-99.20255F-statistic266.4479Durbin-Watson stat0.745247Prob(F-statistic)0.000000可以看见加入 X4 后 R 变化最明显，则以 X1 X4 为基础再加入 X3 得Dependent Variable: Y Method: Least SquaresDate: 06/25/07Time: 16:39 Sample: 1989 2005Included obse

22、rvations: 17VariableCoefficientStd. Errort-StatisticProb.C-1751.028239.0337-7.3254420.0000X10.0051300.0013453.8147680.0021X48.0069691.4772565.4201610.0001X35.8596162.0772062.8209120.0144R-squared0.984121Mean dependent var558.8265Adjusted R-squared0.980456S.D. dependent var533.4785S.E. of regression7

23、4.57931Akaike info criterion11.66393Sum squared resid72306.96Schwarz criterion11.85998Log likelihood-95.14338F-statistic268.5618Durbin-Watson stat1.144836Prob(F-statistic)0.000000经过比较后发现加入 X3 后可决系数 R 有改进且各变量的 T 检验都显著则剔除变量以后的模型为Y= 1751.028+0.005130X1+5.859616X3+8.006969X4（239.0337）（0.001345）（1.477256

24、）（2.077206）T=(-7.325442)(3.814768)(5.420161)(2.820912)R2=0.984121R 2 =0.980456F=268.5618df=15（2）异方差检验和修正运用 White 检验方法对模型检验异方差，结果如下：White Heteroskedasticity Test:F-statistic6.978791Probability0.003943Obs*R-squared13.72275Probability0.032891Test Equation:Dependent Variable: RESID2 Method: Least Square

25、sDate: 06/25/07Time: 18:09 Sample: 1989 2005Included observations: 17VariableCoefficientStd. Errort-StatisticProb.C197845.8249214.40.7938780.4457X10.3715210.3774290.9843470.3482X12-7.57E-062.35E-06-3.2215500.0092X35680.0782596.3022.1877570.0535X32-17.039978.402082-2.0280650.0700X4-10411.853225.793-3

26、.2276860.0091X4243.6099512.339773.5340960.0054R-squared0.807221Mean dependent var4253.350Adjusted R-squared0.691553S.D. dependent var8067.932S.E. of regression4480.769Akaike info criterion19.94588Sum squared resid2.01E+08Schwarz criterion20.28897Log likelihood-162.5400F-statistic6.978791Durbin-Watso

27、n stat2.914372Prob(F-statistic)0.003943从上面可以看出，nR2=13.72275，由 white 检验知，在=0.05 的情况下查临界值c的 20.05（9）=16.9190，因为 nR2=13.72275<2c0.05（9）=16.9190,表明模型不存在异方差。（3）自相关检验和修正经过异方差检验和修正后，模型为:Y= 1751.028+0.005130X1+5.859616X3+8.006969X4（239.0337）（0.001345）（1.477256）（2.077206）T=(-7.325442)(3.814768)(5.420161)(

28、2.820912)R2=0.984121 R 2 =0.980456F=268.5618df=15DW=1.144836从模型设定来看，没有违背 D-W 检验的假设条件，因此可以用 D-W 检验来检验模型是否存在一阶自相关。D-W 检验：由回归结果得 DW=1.144836，给定显著性水平 =0.05，样本容量为 17，K=3 查 DW 表的下限临界值 0.897，上限临界值为 1.710。可见 DW=1.144836 Du= 1.710，所以无法判断是否存在子相关，需要采用广义差分法对模型进行修正：得到回归方程et =0.412119 et -1对原模型进行广义差分，得到如下结果修正的模型回归结果为：Dependent Variable: Y Method: Least SquaresDate: 06/25/07Time: 21:55 Sample(adjusted): 1995 2005Included observations: 11 after adjusting endpoints Convergence achieved after 5 iterationsVariableCoefficientStd. Errort-StatisticProb.C-983.0565566.6927-1.7347260.1335X1