私人汽车拥有量的计量分析.docx

影响私人汽车拥有量的计量分析随着我国经济实力的增强，人民生活水平的提高，私人汽车的需求量也是逐年增加。尤其是2002年以来，私人购车占整个市场的份额迅速提升，汽车市场进入私人购车阶段。根据国际通用车价和国内生产总值增长比较系数计算，未来510年中国有购车能力的人口可达5亿，约1.5亿个家庭。未来20年中国有望成为全球第一大汽车市场。正因为私人汽车逐渐占据了汽车消费市场的主导地位，并直接反映了整个汽车行业的现状，所以私人汽车消费市场越来越吸引人们的关注。为了分析私人汽车拥有量的具体影响因素，我选取了一下几个变量进行分析：Y表示私人汽车拥有量，X1表示城镇人口数（万人），X2表示城镇家庭人均可支配收入，X3表示全国汽车产量（万辆），X4表示全国公路里程（万公里），同时预计城镇人口数与私人汽车拥有量呈正相关，城镇家庭人均可支配收入、全国汽车产量及全国公路里程都与私人汽车拥有量呈正相关。表1 私人汽车拥有量相关因素的原始数据YX1X2X3X4198828.4900025094.00739.100043.7200094.24000198934.7100026366.00899.600036.9800096.28000199042.2900027674.001002.20047.1800098.22000199160.4200028661.001181.40064.4700099.96000199273.1200029540.001375.70058.35000101.4300199381.6200030195.001510.20051.40000102.8300199496.0400031203.001700.60071.42000104.11001995118.200032175.002026.600106.6700105.67001996155.770033173.002577.400129.8500108.35001997205.420034169.003496.200136.6900111.78001998249.960035174.004283.000145.2700115.70001999289.670037304.004838.900147.5200118.58002000358.360039449.005160.300158.2500122.64002001423.700041608.005425.100163.0000127.90002002533.900043748.005854.000183.2000135.20002003625.300045906.006280.000207.0000140.30002004770.800048064.006859.600234.2000169.80002005969.000050212.007702.800325.1000176.500020061219.20052376.008472.200444.4000181.000020071481.70054283.009421.600509.1000187.100020081848.10056212.0010493.00570.5000334.500020092333.30057706.0011759.50727.9000345.700020102876.20059379.0013785.80888.9000358.4000基于上述数据，建立的多元线形回归模型可以表示为：Y=0+1X1+2X2+3X3+4X4+根据表1中的数据，利用Eviews对上述所设计的模型进行最小二乘估计。结果为：表2 最小二乘估计结果Dependent Variable: YMethod: Least SquaresDate: 05/31/12 Time: 14:42Sample: 1988 2010Included observations: 23VariableCoefficietStd. Errort-StatisticProb.X10.0028750.0074210.3873720.7030X20.0031860.0300190.1061210.9167X32.5403210.2903488.7492280.0000X42.0191550.5632733.5846820.0021C-396.8791191.8043-2.0691870.0532R-squared0.995198Mean dependent var646.7509Adjusted R-squared0.994130S.D. dependent var796.7598S.E. of regression61.04194Akaike info criterion11.25066Sum squared resid67070.12Schwarz criterion11.49751Log likelihood-124.3826F-statistic932.5459Durbin-Watson stat0.764574Prob(F-statistic)0.000000根据上述结果，可以初步得出的函数为：Y=-396.88+0.0029X1+90.0032X2+2.5403X3+2.0912X4T (-2.0692)(0.3874) (0.1061) (8.7492) (3.5867)R2=0.9952 adjusted R2=0.9941 D.W=0.7646 F=932.5459 经济意义检验：由回归得出的函数结果可以看出X1的系数为0.0029,X2的系数为0.0032,X3的结果为2.5403,X4的结果为2.0912，这四个解释变量的符号与预期相一致，并且其大小在经济理论上也解释得通。 拟合优度检验：从最小二乘估计得出得结果可以看出可决系数R2=0.9952,Adjusted R-squared为0.9941，因此可以得出结论即该模型的解释变量解释了从1988年到2010年间全国私人汽车拥有量变异的99，样本拟合效果比较好。在5显著性水平下，查F分布表得自由度为4和18的临界值为F(4,18)=2.93,而模型的F值为932.5459明显大于临界值2.93，表明整个模型的估计效果显著，X1、X2、X3、X4四个变量联合起来对全国汽车拥有量有显著的影响。 计量经济学检验：在5显著性水平下，查t分布表得自由度为18的临界值为2.101，1，2，3，4的估计值的t统计量分别为0.3874，0.1061，8.7492，3.5867，1和2的t统计量小于t(18)的临界值2.101, 3和4的估计值对应的t统计量则大于临界值，这说明全国的私人汽车拥有量与全国汽车产量和全国公路里程存在明显的线性相关关系，但是对于全国城镇人口数和城镇居民人均可支配收而言却不存在显著的线性相关关系，但这与实际不相符，说明模型可能存在多重共线性。多重共线性检验：根据以上分析，认为模型可能存在严重的多重共线性问题，为了验证是否真实存在，计算解释变量之间的相关系数，得到相关系数矩阵：X1X2X3X4X11.0000000.9824950.9087220.859173X20.9824951.0000000.9542270.907903X30.9087220.9542271.0000000.958364X40.8591730.9079030.9583641.000000 从上面的相关系数矩阵可以看出，各解释变量之间的相关系数很高，证实确实存在多重共线性。 为了修正多重共线性，采用逐步回归法检验和解决多重共线性。分别做Y对X1、X2、X3、X4的一元回归，结果为：VariableCoefficietStd. Errort-StatisticProb.C-1986.12269.1593-7.3791340.0000X10.0658460.00649910.131410.0000R-squared0.830160Mean dependent var646.7509Adjusted R-squared0.822072S.D. dependent var796.7598S.E. of regression336.0854Akaike info criterion14.55555Sum squared resid2372021.Schwarz criterion14.65429Log likelihood-165.388F-statistic102.6455Durbin-Watson stat0.200738Prob(F-statistic)0.000000VariableCoefficietStd. Errort-StatisticProb.C-371.188185.69307-4.3316000.0003X20.2003730.01361814.713500.0000R-squared0.911574Mean dependent var646.7509Adjusted R-squared0.907363S.D. dependent var796.7598S.E. of regression242.5039Akaike info criterion13.90285Sum squared resid1234971.Schwarz criterion14.00159Log likelihood-157.8828F-statistic216.4871Durbin-Watson stat0.128094Prob(F-statistic)0.000000VariableCoefficietStd. Errort-StatisticProb.C-155.23422.50750-6.8970080.0000X33.3838610.06825149.579600.0000R-squared0.991529Mean dependent var646.7509Adjusted R-squared0.991126S.D. dependent var796.7598S.E. of regression75.05654Akaike info criterion11.55730Sum squared resid118303.2Schwarz criterion11.65604Log likelihood-130.900F-statistic2458.136Durbin-Watson stat0.797130Prob(F-statistic)0.000000 VariableCoefficietStd. Errort-StatisticProb.C-814.572889.13548-9.1385920.0000X49.5047050.51488418.459890.0000R-squared0.941952Mean dependent var646.7509Adjusted R-squared0.939187S.D. dependent var796.7598S.E. of regression196.4825Akaike info criterion13.48197Sum squared resid810713.1Schwarz criterion13.58070Log likelihood-153.0426F-statistic340.7675Durbin-Watson stat1.873528Prob(F-statistic)0.000000 其中，加入X3的方程R2的值最大，所以以X3为基础，顺次加入其他变量逐步回归，结果为：VariableCoefficietStd. Errort-StatisticProb.C-232.849107.4047-2.1679020.0424X33.2727950.16530819.798180.0000X10.0025990.0035150.7393620.4683R-squared0.991755Mean dependent var646.7509Adjusted R-squared0.990930S.D. dependent var796.7598S.E. of regression75.88004Akaike info criterion11.61729Sum squared resid115155.6Schwarz criterion11.76540Log likelihood-130.599F-statistic1202.809Durbin-Watson stat0.768221Prob(F-statistic)0.000000VariableCoefficietStd. Errort-StatisticProb.C-170.497430.41258-5.6061480.0000X33.2175680.23056613.955080.0000X20.0107620.0142390.7558340.4586R-squared0.991765Mean dependent var646.7509Adjusted R-squared0.990941S.D. dependent var796.7598S.E. of regression75.83461Akaike info criterion11.61609Sum squared resid115017.8Schwarz criterion11.76420Log likelihood-130.5851F-statistic1204.262Durbin-Watson stat0.744977Prob(F-statistic)0.000000VariableCoefficietStd. Errort-StatisticProb.C-301.436745.35317-6.6464310.0000X32.7349850.19252214.206110.0000X41.9511740.5548103.5168330.0022R-squared0.994766Mean dependent var646.7509Adjusted R-squared0.994243S.D. dependent var796.7598S.E. of regression60.45601Akaike info criterion11.16282Sum squared resid73098.57Schwarz criterion11.31092Log likelihood-125.3724F-statistic1900.595Durbin-Watson stat0.688210Prob(F-statistic)0.000000经过比较，加入X4的方程R2的值为0.994766，是最大的，而且它的t检验显著，所以保留X4，再加入其他新变量逐步回归，结果为：VariableCoefficientStd. Errort-StatisticProb.C-414.242697.44795-4.2509120.0004X32.5577470.23314110.970800.0000X42.0212950.5480703.6880260.0016X10.0036020.002767-1.3018550.2085R-squared0.985195Mean dependent var646.7509Adjusted R-squared0.984436S.D. dependent var796.7598S.E. of regression59.43244Akaike info criterion11.16433Sum squared resid67112.09Schwarz criterion11.36181Log likelihood-124.3898F-statistic1311.647Durbin-Watson stat0.775412Prob(F-statistic)0.000000VariableCoefficientStd. Errort-StatisticProb.C-325.126848.66633-6.6807350.0000X32.5023050.2670779.3692110.0000X42.0037320.5491533.6487660.0017X20.0139280.0112361.2395850.2302R-squared0.994558Mean dependent var646.7509Adjusted R-squared0.994393S.D. dependent var796.7598S.E. of regression59.66100Akaike info criterion11.17200Sum squared resid67629.25Schwarz criterion11.36948Log likelihood-124.4781F-statistic1301.569Durbin-Watson stat0.719800Prob(F-statistic)0.000000在X3，X4的基础上加入X1后的方程R2的值为0.985915，比之前下降了，而且X1的参数为-1.301855，不合理。在X3，X4的基础上加入X2后的方程R2的值为0.994558，较之前有所改善，但它的t检验不显著，这说明是X1，X2引起严重的多重共线性，应予以剔除。最后修正严重多重共线性的回归结果为：Dependent Variable: YMethod: Least SquaresDate: 05/31/12 Time: 14:58Sample: 1988 2010Included observations: 23VariableCoefficietStd. Errort-StatisticProb.C-301.43745.35317-6.6464310.0000X32.7349850.19252214.206110.0000X41.9511740.5548103.5168330.0022R-squared0.994766Mean dependent var646.7509Adjusted R-squared0.994243S.D. dependent var796.7598S.E. of regression60.45601Akaike info criterion11.16282Sum squared resid73098.57Schwarz criterion11.31092Log likelihood-125.374F-statistic1900.595Durbin-Watson stat0.688210Prob(F-statistic)0.000000经过修正多重共线性后得出的函数为：Y=-301.4367+2.7735X3+1.9512X4T (-6.6464) (14.2061) (3.5168)R2=0.9948 adjusted R2=0.9942 D.W=0.6882 F=1900.595 异方差检验：对修正多重共线性后的新函数进行异方差性检验，运用white检验，得到的结果为；White Heteroskedasticity Test:F-statistic0.588700Probability0.708694Obs*R-squared3.394616Probability0.639390 N*R2的结果为3.394616,由white检验可知，在0.05的显著性水平下，自由度为5的卡方临界值为11.0705，远远大于N*R2的值，所以接受原假设，即认为该模型不存在异方差性。 序列相关性检验：由上可知D.W的值为0.688210,且样本容量为23，给定显著性水平为1%,才查D.W表得dL =1.02, dU =1.19，这是有D.WdL， 这表明模型中存在自相关。 用LM检验可知，resid(-1)的伴随概率为0.0009，小于给定的显著性水平5或10，resid(-2)的伴随概率为0.1056,大于给定的显著性水平5或10，由此说明该模型存在一阶序列相关性，而不存在二阶序列相关性Breusch-Godfrey Serial Correlation LM Test:F-statistic9.740089Probability0.001359Obs*R-squared11.95416Probability0.002536Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 06/07/11 Time: 21:24Presample missing value lagged residuals set to zero.VariableCoefficientStd. Errort-StatisticProb.C48.0476336.514961.3158340.2047X30.2632450.1625121.6198550.1227X4-0.7066660.462678-1.5273400.1441RESID(-1)1.0256320.2582843.9709410.0009RESID(-2)-0.4366150.256257-1.7038160.1056R-squared0.519746Mean dependent var6.15E-14Adjusted R-squared0.413023S.D. dependent var57.64254S.E. of regression44.16250Akaike info criterion10.60329Sum squared resid35105.87Schwarz criterion10.85014Log likelihood-116.9378F-statistic4.870044Durbin