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1、我国私人汽车拥有量分析前言：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
2、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
3、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
4、.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
5、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 2003Include
6、d 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-squared0.94
7、8366 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 St
8、atistic-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 20
9、03Included 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-
10、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 X
11、2ADF 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(adjust
12、ed): 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)-0.3913870.347038-1.1277940.3106C0.1550181.2198420.1270
13、800.9038R-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)
14、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: 09:27Sam
15、ple(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
16、.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
17、-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. C3250054.1725513.1.8835290.0890X12922.028515.06245.6731540.0002X2-214742.91556
18、73.7-1.3794420.1978X3-50492.4814255.54-3.5419550.0053R-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-statistic90.71108
19、Durbin-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
20、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: 14V
21、ariableCoefficientStd. 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 cri
22、terion31.09250Log 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. C150419042243778.6.7038280.0000
23、X2-1322763.268920.1-4.9187960.0004R-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
24、.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 var435492
25、1.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
26、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. C2354107.244
27、3622.0.9633680.3561X11164.618197.88255.8854020.0001X2-433834.9204519.4-2.1212410.0574R-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 likelih
28、ood-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. C1316764.1047067.1.2575730.2346X13323.203442.20237.5151190.0
29、000X3-58306.1613608.15-4.2846500.0013R-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 st
30、at1.457294 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，
31、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)-3.8674531.37677
32、6-2.8090650.0262E2(-3)1.4041651.1176241.2563840.2493R-squared0.827082 Mean dependent var2.96E+12Adjusted R-squared0.752974 S.D. dependent var3.55E+12S.E. of regression1.76E+12 Akaike info criterion59.51134Sum squared resid2.18E+25 Schwarz criterion59.65603Log likelihood-323.3124 F-statistic11.16052D
33、urbin-Watson stat1.980794 Prob(F-statistic)0.004656计算(n-p) R2 = 6.616656临界值7.81(=0.05),所以接受Ho,表明模型中不存在异方差。三、自相关的检验和修正（1）下面是e与e（-1）的坐标图：（2）DW检验：Durbin-Watson stat :1.980794,靠近2，说明不存在自相关。结论：我们的模型说明我国私人汽车拥有量主要受城镇居民可支配收入的影响，这也是符合经济检验的。从发展来看，我国汽车消费的热点正在逐步形成，汽车有望在未来的5年左右的时间形成我国居民最大的消费热点，在未来的10年左右的时间成为我国最大
34、的经济增长点。近10年来，我国私人汽车的拥有量以20以上的速度增长，即使在经济收缩的19952000年之间，在各地各种限制汽车消费政策的作用之下，我国私人汽车的拥有量仍以20以上的速度增长，这充分说明我国汽车消费增长的巨大潜力。随着经济的发展和居民收入水平的提高，人们对汽车需求的欲望日益增强，在未来的5年甚至10年之内，我国私人汽车的拥有量有望继续以20左右的速度增长。若以2000年625.33万辆的私人汽车保有辆为基数，以20的增长率计算，则到2005年，我国私人汽车的拥有量将达1556.02万辆，2005年当年新增私人汽车259.3万辆，若以每辆车售价10万元计算，则当年居民用于汽车的购买费用就达2593亿元，成为我国居民的最大消费热点；即使每辆汽车按8万元计算，当年仅居民的汽车消费也将达2074.4亿元。汽车有理由成为最大的消费热点从现实来看，我国不但呈现了在短期内形成汽车消费热点的发展趋势，而且已经基本具备了汽车消费热点形成的条件：国民经济的发展为汽车消费的快速增长奠定了基础；我国城市的发展和城市交通的进步，能够支持汽车消费的扩大；加入WTO之后汽车的销售价格将明显下降，更加接近普通居民的购买力。
