我國居民汽車消費量的計量經(jīng)濟分析

1、我國居民汽車消費量的計量經(jīng)濟分析摘要：隨著我國經(jīng)濟的持續(xù)、快速的增長，以及加入世界貿(mào)易組織后對外開放程度的不斷加深，市場上對各種商品的需求也在與日俱增。汽車作為高檔消費品，也隨著市場經(jīng)濟的不斷發(fā)展逐步走進了普通大眾的生活。然而，中國的汽車需求量到底有多大，汽車消費量和影響因素的關(guān)系到底是怎么樣的。希望通過此次研究，能對我國的汽車需求量有更深入的認識，以解釋以上提出的問題。 Keywords最小二乘法 多重共線性 自相關(guān) 異方差分析過程：由于研究的汽車需求量是一個時間序列數(shù)據(jù)，為此我們對其進行了平穩(wěn)性檢驗，并利用最小二乘估計、多重共線、異方差及自相關(guān)等計量經(jīng)濟學(xué)的檢驗方法，對模型進行了進一步的檢

2、驗和調(diào)整，最后并對模型進行了評價和推廣，以提高模型估計的可靠性，進而滿足模型預(yù)測的需要。模型檢驗經(jīng)濟理論實際經(jīng)濟活動估計參數(shù) 搜集統(tǒng)計數(shù)據(jù)模型檢驗變量選取和具體數(shù)據(jù)：因變量 Y 我國的汽車擁有量（單位：萬輛）自變量 X1 國內(nèi)生產(chǎn)總值（元）X2 居民消費水平（人均）（元）X3 公路通車歷程（單位：萬公里）X4 人均能源消費情況（千克）具體數(shù)據(jù)如下：（表 1）年份居民汽車擁有量國內(nèi)生產(chǎn)總值居民消費水平公路通車里程人均能源消費情況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資料來源于中國統(tǒng)計年鑒（資料數(shù)據(jù)是從 1989 年到 2005 年）建立模型：設(shè)定模型為Y=C+1X1+2X2+3X3+4X4+ +U 模型的參數(shù)估計、檢驗及修正1. 我們首先對中的數(shù)據(jù)，利用 EVIEWS 軟件，運用最小二乘法估計，得到以下輸出框：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.很明顯可以

7、看到，X2 的系數(shù)的符號為負，首先從經(jīng)濟意義上是說不通的，居民消費水平汽車需求成負相關(guān)關(guān)系;這與我們實際生活中的情況是不相符合的。同時還可以看出，X2、X4 的 t 值都不顯著，則說明解釋變量之間有可能存在多重共線性。因此接下來我們來一一的檢驗。2.計量經(jīng)濟學(xué)檢驗和修正（1）多重共線性檢驗和修正用 EVIEWS 軟件，得相關(guān)系數(shù)矩陣表：（表 4）X1X2X3X4X11.0000000.9904150.9611210.577850X20.9904151.0000000.9410970.478188X30.9611210.9410971.0000000.586115X40.5778500.4781

8、880.5861151.000000從上表可見，解釋變量之間存在高度線性相關(guān)。下面利用逐步回歸法（向上回歸）進行修正首先運用 OLS 方法逐一求 Y 對各個解釋變量的回歸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結(jié)合經(jīng)濟意義和統(tǒng)計檢驗選出擬合效果最好的一元線性回歸方程。經(jīng)分析在五個一元回歸模型中汽車需求量 Y 對國內(nèi)生產(chǎn)總值 X1 的線性關(guān)系強，擬合效果好，即Y= 260.8152+0.010239 X1(66.70809)(0.000711)R2=0.932462S.E.= 143.1873F=207.0981逐步回歸（向上回歸）以 X1 為基礎(chǔ)將其余解釋變量逐一代入上式Y(jié) 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可以看見 X2 的系數(shù)為負，即居民消費水平和汽車消費量負相關(guān)，這與實際的情況是不相符合的，則可以剔除 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可以看見加入 X4 后 R 變化最明顯，則以 X1 X4 為基礎(chǔ)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經(jīng)過比較后發(fā)現(xiàn)加入 X3 后可決系數(shù) R 有改進且各變量的 T 檢驗都顯著則剔除變量以后的模型為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）異方差檢驗和修正運用 White 檢驗方法對模型檢驗異方差，結(jié)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從上面可以看出，nR2=13.72275，由 white 檢驗知，在=0.05 的情況下查臨界值c的 20.05（9）=16.9190，因為 nR2=13.72275<2c0.05（9）=16.9190,表明模型不存在異方差。（3）自相關(guān)檢驗和修正經(jīng)過異方差檢驗和修正后，模型為: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從模型設(shè)定來看，沒有違背 D-W 檢驗的假設(shè)條件，因此可以用 D-W 檢驗來檢驗?zāi)Ｐ褪欠翊嬖谝浑A自相關(guān)。D-W 檢驗：由回歸結(jié)果得 DW=1.144836，給定顯著性水平 =0.05，樣本容量為 17，K=3 查 DW 表的下限臨界值 0.897，上限臨界值為 1.710。可見 DW=1.144836 Du= 1.710，所以無法判斷是否存在子相關(guān)，需要采用廣義差分法對模型進行修正：得到回歸方程et =0.412119 et -1對原模型進行廣義差分，得到如下結(jié)果修正的模型回歸結(jié)果為：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