我国私人汽车拥有量分析.doc

我国私人汽车拥有量分析小组成员: 黎桥(40204090) 部迪 (40204063)尹莉(40204259) 张凌放(40204157) 于兰(40204034) 刘庆庆(40204268)董浩萍（40204032）前言：国家统计局最新公布的数据显示，国内大城市的私家车拥有量继续保持大幅增长的趋势。截止到年底，在全国十大城市的私家车拥有量排名中，北京私家车的拥有量以多出第二名近万辆的绝对优势排在了第一位。这十个城市的具体排名分别是：有关统计资料表明，我国城镇居民中有3800万户（占城镇居民总户数的24.8），有能力承受10万元左右的汽车消费。从近几年我国汽车消费的发展变化来看，汽车消费将成为消费热点。 从1990年到2000年的10年间，我国民用汽车的保有量由551.36万辆增加到1608.91万辆，平均每年增长11.3。其中私人汽车拥有量由1990年的81.62万辆增加到2000年的625.73万辆，平均每年增长22.6。私人汽车拥有量占民用汽车的保有量比重从1990年的14.8，上升到2000年的38.9，平均每年上升2.4个百分点。1996年以来，民用汽车拥有量的增加量中，私人汽车增加量的比重均高于57.7，其中最高的是1999年，私人汽车增加量占全部民用汽车增加量的82.5。这说明我国汽车市场结构发生了根本性的变化，居民个人已经成为我国汽车市场的消费主体。随着我国经济突飞猛进的发展，人民群众的收入水平不断提高，特别是城镇居民的收入不断提高，私人汽车拥有量不断增加，同时银行的按揭贷款买车等等的一系列推动措施，也促进了私人汽车拥有俩的增加。单从经济方面来说，私人汽车拥有数量是评判一个国家人民生活水平的重要指标，对它的研究分析是有比较现实的意义的。我国私人汽车拥有量随时间变化图如下：数据收集：Y:我国私人汽车拥有量X1：城镇居民可支配收入X2：贷款利率X3：燃料、动力类价格指数（以1990年价格为的定比指数序列）具体数据如下:obsYX1X2（）X319908162001510.29.7210019919604001700.68.64101.9874199211820002026.68.64118.7133199315577002577.410.17162.2811199420542003496.210.98191.491619952499600428311.52208.1514199628967004838.910.53229.3829199735836005160.38.64250.7155199842365005425.17.08248.4591999533880058545.85250.69522000625330062805.85289.3022200177078006859.65.85289.8808200296898007702.85.31290.17072003121923008472.25.31311.6433普通的多元线性方程形式：Y0+1x1+2x2+3x3先对各个变量做平稳性检验:对YADF Test Statistic 1.082163 1% Critical Value*-4.3260 5% Critical Value-3.2195 10% Critical Value-2.7557*MacKinnon critical values for rejection of hypothesis of a unit root.Augmented Dickey-Fuller Test EquationDependent Variable: D(ADFY)Method: Least SquaresDate: 06/14/05 Time: 09:21Sample(adjusted): 1994 2003Included observations: 10 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. ADFY(-1)0.3341530.3087821.0821630.3286D(ADFY(-1)-0.1210600.697271-0.1736200.8690D(ADFY(-2)-0.0546060.945213-0.0577720.9562D(ADFY(-3)-0.4094070.879632-0.4654300.6612C-105122.5168342.6-0.6244560.5597R-squared0.948366 Mean dependent var1063460.Adjusted R-squared0.907058 S.D. dependent var710945.9S.E. of regression216741.3 Akaike info criterion27.71765Sum squared resid2.35E+11 Schwarz criterion27.86894Log likelihood-133.5882 F-statistic22.95874Durbin-Watson stat2.080638 Prob(F-statistic)0.002042对X1ADF Test Statistic-0.158912 1% Critical Value*-4.3260 5% Critical Value-3.2195 10% Critical Value-2.7557*MacKinnon critical values for rejection of hypothesis of a unit root.Augmented Dickey-Fuller Test EquationDependent Variable: D(ADFX1)Method: Least SquaresDate: 06/14/05 Time: 09:26Sample(adjusted): 1994 2003Included observations: 10 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. ADFX1(-1)-0.0054770.034465-0.1589120.8800D(ADFX1(-1)0.6644450.4065961.6341620.1632D(ADFX1(-2)-0.3316050.522131-0.6351000.5533D(ADFX1(-3)-0.4146580.416042-0.9966740.3647C609.9278275.29102.2155750.0776R-squared0.746497 Mean dependent var589.4800Adjusted R-squared0.543694 S.D. dependent var229.7711S.E. of regression155.2114 Akaike info criterion13.23431Sum squared resid120452.9 Schwarz criterion13.38560Log likelihood-61.17153 F-statistic3.680899Durbin-Watson stat2.031160 Prob(F-statistic)0.092741对 X2ADF Test Statistic-0.529198 1% Critical Value*-4.3260 5% Critical Value-3.2195 10% Critical Value-2.7557*MacKinnon critical values for rejection of hypothesis of a unit root.Augmented Dickey-Fuller Test EquationDependent Variable: D(ADFX2)Method: Least SquaresDate: 06/14/05 Time: 09:27Sample(adjusted): 1994 2003Included observations: 10 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. ADFX2(-1)-0.0699820.132242-0.5291980.6193D(ADFX2(-1)0.5434260.3211591.6920750.1514D(ADFX2(-2)0.1405350.3683640.3815100.7185D(ADFX2(-3)-0.3913870.347038-1.1277940.3106C0.1550181.2198420.1270800.9038R-squared0.768917 Mean dependent var-0.486000Adjusted R-squared0.584050 S.D. dependent var0.905296S.E. of regression0.583863 Akaike info criterion2.068551Sum squared resid1.704478 Schwarz criterion2.219843Log likelihood-5.342754 F-statistic4.159310Durbin-Watson stat2.443814 Prob(F-statistic)0.075014对X3ADF Test Statistic-2.501558 1% Critical Value*-4.3260 5% Critical Value-3.2195 10% Critical Value-2.7557*MacKinnon critical values for rejection of hypothesis of a unit root.Augmented Dickey-Fuller Test EquationDependent Variable: D(ADFX3)Method: Least SquaresDate: 06/14/05 Time: 09:27Sample(adjusted): 1994 2003Included observations: 10 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. ADFX3(-1)-0.2963260.118457-2.5015580.0544D(ADFX3(-1)-0.3320830.323046-1.0279730.3511D(ADFX3(-2)-0.5925950.256861-2.3070660.0692D(ADFX3(-3)0.0791950.2904280.2726840.7960C101.695638.342962.6522620.0453R-squared0.684768 Mean dependent var14.93622Adjusted R-squared0.432582 S.D. dependent var14.01521S.E. of regression10.55726 Akaike info criterion7.858358Sum squared resid557.2788 Schwarz criterion8.009650Log likelihood-34.29179 F-statistic2.715332Durbin-Watson stat1.902782 Prob(F-statistic)0.151305由此可见，各个变量的随时间变化是平稳的，可以对其直接进行最小二乘估计。对其作普通最小二乘估计：Dependent Variable: YMethod: Least SquaresDate: 06/03/05 Time: 16:43Sample: 1990 2003Included observations: 14VariableCoefficientStd. Errort-StatisticProb. C3250054.1725513.1.8835290.0890X12922.028515.06245.6731540.0002X2-214742.9155673.7-1.3794420.1978X3-50492.4814255.54-3.5419550.0053R-squared0.964556 Mean dependent var4354921.Adjusted R-squared0.953922 S.D. dependent var3498430.S.E. of regression750961.7 Akaike info criterion30.13105Sum squared resid5.64E+12 Schwarz criterion30.31364Log likelihood-206.9174 F-statistic90.71108Durbin-Watson stat1.514620 Prob(F-statistic)0.000000样本回归模型为:y=3250054+2922.028x1-214742.9x2-50492.48x3(1725513) (515.0624) (155673.7) (14255.54)t=(1.883529) (5.673154) (-1.379442) (-3.541955) Adjusted R2-=0.953922 F=90.71108经观察：各个系数符合经济意义;从可决系数看拟合优度较好;X2的T检验不显著，而F统计量显著，效果很好，可以推断解释变量可能存在多重共线性。一、多重共线性的检验与修正：下面是x1 x2 x3的简单相关系数矩阵:x1x2x3x11-0.738510.975673x2-0.738511-0.66181x30.975673-0.661811可见,各个变量相关系数很高, x1 x3尤为突出.我们采用逐步回归法进行修正：（1）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出拟合效果最好的一个一元线性回归方程：方程1：Dependent Variable: YMethod: Least SquaresDate: 06/03/05 Time: 17:08Sample: 1990 2003Included observations: 14VariableCoefficientStd. Errort-StatisticProb. C-2616509.787741.3-3.3215330.0061X11474.612151.63329.7248640.0000R-squared0.887401 Mean dependent var4354921.Adjusted R-squared0.878018 S.D. dependent var3498430.S.E. of regression1221860. Akaike info criterion31.00121Sum squared resid1.79E+13 Schwarz criterion31.09250Log likelihood-215.0085 F-statistic94.57299Durbin-Watson stat0.273300 Prob(F-statistic)0.000000方程2：Dependent Variable: YMethod: Least SquaresDate: 06/03/05 Time: 17:08Sample: 1990 2003Included observations: 14VariableCoefficientStd. Errort-StatisticProb. C150419042243778.6.7038280.0000X2-1322763.268920.1-4.9187960.0004R-squared0.668458 Mean dependent var4354921.Adjusted R-squared0.640830 S.D. dependent var3498430.S.E. of regression2096637. Akaike info criterion32.08113Sum squared resid5.28E+13 Schwarz criterion32.17243Log likelihood-222.5679 F-statistic24.19456Durbin-Watson stat0.583287 Prob(F-statistic)0.000355方程3:Dependent Variable: YMethod: Least SquaresDate: 06/03/05 Time: 17:09Sample: 1990 2003Included observations: 14VariableCoefficientStd. Errort-StatisticProb. C-4659138.1615330.-2.8843250.0137X341472.907074.3335.8624470.0001R-squared0.741202 Mean dependent var4354921.Adjusted R-squared0.719636 S.D. dependent var3498430.S.E. of regression1852398. Akaike info criterion31.83342Sum squared resid4.12E+13 Schwarz criterion31.92472Log likelihood-220.8340 F-statistic34.36829Durbin-Watson stat0.332537 Prob(F-statistic)0.000077(2)对比分析，依据调整后可决系数最大原则，选取X1进入回归模型的第一个解释变量，形成一元回归模型:Y=-2616509+0.887401x1 (787741.3) (151.6332)t=(-3.321533) (9.724864)Adjusted R-squared=0.878018 F=94.57299（3）逐步回归，将其余变量分别加入模型：Dependent Variable: YMethod: Least SquaresDate: 06/03/05 Time: 17:13Sample: 1990 2003Included observations: 14VariableCoefficientStd. Errort-StatisticProb. C2354107.2443622.0.9633680.3561X11164.618197.88255.8854020.0001X2-433834.9204519.4-2.1212410.0574R-squared0.920089 Mean dependent var4354921.Adjusted R-squared0.905560 S.D. dependent var3498430.S.E. of regression1075105. Akaike info criterion30.80114Sum squared resid1.27E+13 Schwarz criterion30.93808Log likelihood-212.6080 F-statistic63.32690Durbin-Watson stat0.449924 Prob(F-statistic)0.000001Dependent Variable: YMethod: Least SquaresDate: 06/03/05 Time: 17:13Sample: 1990 2003Included observations: 14VariableCoefficientStd. Errort-StatisticProb. C1316764.1047067.1.2575730.2346X13323.203442.20237.5151190.0000X3-58306.1613608.15-4.2846500.0013R-squared0.957811 Mean dependent var4354921.Adjusted R-squared0.950141 S.D. dependent var3498430.S.E. of regression781172.8 Akaike info criterion30.16239Sum squared resid6.71E+12 Schwarz criterion30.29933Log likelihood-208.1367 F-statistic124.8664Durbin-Watson stat1.457294 Prob(F-statistic)0.000000由上表可以看出，X3和X1构建的模型的拟合值优于X2和 X1构建的方程的拟合值，且比起y对x1的回归拟合优度更好,t检验和F检验都更显著，所以在Y=-2616509+0.887401x1的基础上加入解释变量x3,得:Y=1316764+3323.203x1-58306.16x3 (1047067) (442.2023) (13608.15)t=(1.257573) (7.515119) (-4.284665)Adjusted R-squared=0.950141 F=124.8664二、异方差的检验与修正因为时间序列数据，样本个数较小，所以选用ARCH检验：Dependent Variable: E2Method: Least SquaresDate: 06/03/05 Time: 18:31Sample(adjusted): 1993 2003Included observations: 11 after adjusting endpointsVariableCoefficientStd. Errort-StatisticProb. C4.33E+111.37E+120.3149420.7620E2(-1)3.4755720.8320874.1769320.0042E2(-2)-3.8674531.376776-2.8090650.0262E2(-3)1.4041651.1176241.2563840.2493R-square