我國私人汽車擁有量分析

1、我國私人汽車擁有量分析 前言：國家統(tǒng)計局最新公布的數(shù)據(jù)顯示，國內(nèi)大城市的私家車擁有量繼續(xù)保持大幅增長的趨勢。截止到年底，在全國十大城市的私家車擁有量排名中，北京私家車的擁有量以多出第二名近萬輛的絕對優(yōu)勢排在了第一位。這十個城市的具體排名分別是：有關(guān)統(tǒng)計資料表明，我國城鎮(zhèn)居民中有3800萬戶（占城鎮(zhèn)居民總戶數(shù)的24.8），有能力承受10萬元左右的汽車消費。從近幾年我國汽車消費的發(fā)展變化來看，汽車消費將成為消費熱點。 從1990年到2000年的10年間，我國民用汽車的保有量由551.36萬輛增加到1608.91萬輛，平均每年增長11.3。其中私人汽車擁有量由1990年的81.62萬輛增加到2000

2、年的625.73萬輛，平均每年增長22.6。私人汽車擁有量占民用汽車的保有量比重從1990年的14.8，上升到2000年的38.9，平均每年上升2.4個百分點。1996年以來，民用汽車擁有量的增加量中，私人汽車增加量的比重均高于57.7，其中最高的是1999年，私人汽車增加量占全部民用汽車增加量的82.5。這說明我國汽車市場結(jié)構(gòu)發(fā)生了根本性的變化，居民個人已經(jīng)成為我國汽車市場的消費主體。隨著我國經(jīng)濟突飛猛進的發(fā)展，人民群眾的收入水平不斷提高，特別是城鎮(zhèn)居民的收入不斷提高，私人汽車擁有量不斷增加，同時銀行的按揭貸款買車等等的一系列推動措施，也促進了私人汽車擁有倆的增加。單從經(jīng)濟方面來說，私人汽車

3、擁有數(shù)量是評判一個國家人民生活水平的重要指標，對它的研究分析是有比較現(xiàn)實的意義的。我國私人汽車擁有量隨時間變化圖如下：數(shù)據(jù)收集：y:我國私人汽車擁有量x1：城鎮(zhèn)居民可支配收入x2：貸款利率x3：燃料、動力類價格指數(shù)（以1990年價格為的定比指數(shù)序列）具體數(shù)據(jù)如下:obsyx1x2（）x319908162001510.29.7210019919604001700.68.64101.9874199211820002026.68.64118.7133199315577002577.410.17162.2811199420542003496.210.98191.49161995249960042831

4、1.52208.1514199628967004838.910.53229.3829199735836005160.38.64250.7155199842365005425.17.08248.4591999533880058545.85250.69522000625330062805.85289.3022200177078006859.65.85289.8808200296898007702.85.31290.17072003121923008472.25.31311.6433普通的多元線性方程形式：y0+1x1+2x2+3x3先對各個變量做平穩(wěn)性檢驗:對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 2003includ

6、ed 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-squared0.9

7、48366 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對x1adf test s

8、tatistic-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 2

9、003included 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對

11、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(adjus

12、ted): 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)-0.3913870.347038-1.1277940.3106c0.1550181.2198420.127

13、0800.9038r-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對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: 09:27sa

15、mple(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)0.0791950.2904280.2726840.7960c101.69563

16、8.342962.6522620.0453r-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(

17、f-statistic)0.151305由此可見，各個變量的隨時間變化是平穩(wěn)的，可以對其直接進行最小二乘估計。對其作普通最小二乘估計：dependent variable: ymethod: least squaresdate: 06/03/05 time: 16:43sample: 1990 2003included observations: 14variablecoefficientstd. errort-statisticprob. c3250054.1725513.1.8835290.0890x12922.028515.06245.6731540.0002x2-214742.9155

18、673.7-1.3794420.1978x3-50492.4814255.54-3.5419550.0053r-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-statistic90.7110

19、8durbin-watson stat1.514620 prob(f-statistic)0.000000樣本回歸模型為: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經(jīng)觀察：各個系數(shù)符合經(jīng)濟意義;從可決系數(shù)看擬合優(yōu)度較好;x2的t檢驗不顯著，而f統(tǒng)計量顯著，效果很好，可以推斷解釋變量可能存在多重共線性。一、多重共線

20、性的檢驗與修正：下面是x1 x2 x3的簡單相關(guān)系數(shù)矩陣:x1x2x3x11-0.738510.975673x2-0.738511-0.66181x30.975673-0.661811可見,各個變量相關(guān)系數(shù)很高, x1 x3尤為突出.我們采用逐步回歸法進行修正：（1）運用ols方法逐一求y對各個解釋變量的回歸，結(jié)合經(jīng)濟意義和統(tǒng)計檢驗出擬合效果最好的一個一元線性回歸方程：方程1：dependent variable: ymethod: least squaresdate: 06/03/05 time: 17:08sample: 1990 2003included observations: 14

21、variablecoefficientstd. 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 cr

22、iterion31.09250log 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. c150419042243778.6.7038280.000

23、0x2-1322763.268920.1-4.9187960.0004r-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 stat

24、0.583287 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 var43549

25、21.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)對比分析，依據(jù)調(diào)整后可決系數(shù)最大原則，選取x1進入回歸模型的第一個解釋變量，形

26、成一元回歸模型:y=-2616509+0.887401x1 (787741.3) (151.6332)t=(-3.321533) (9.724864)adjusted r-squared=0.878018 f=94.57299（3）逐步回歸，將其余變量分別加入模型：dependent variable: ymethod: least squaresdate: 06/03/05 time: 17:13sample: 1990 2003included observations: 14variablecoefficientstd. errort-statisticprob. c2354107.24

27、43622.0.9633680.3561x11164.618197.88255.8854020.0001x2-433834.9204519.4-2.1212410.0574r-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 likeli

28、hood-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.

29、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 s

30、tat1.457294 prob(f-statistic)0.000000由上表可以看出，x3和x1構(gòu)建的模型的擬合值優(yōu)于x2和 x1構(gòu)建的方程的擬合值，且比起y對x1的回歸擬合優(yōu)度更好,t檢驗和f檢驗都更顯著，所以在y=-2616509+0.887401x1的基礎(chǔ)上加入解釋變量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、異方差的檢驗與修正因為時間序列數(shù)據(jù)

31、，樣本個數(shù)較小，所以選用arch檢驗：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-squared0.827082