计量经济学经济模型分析

1、我国居民消费水平的变量因素分析2010级工程管理 赵莹201000271120改革开放以来，我国居民收入与消费水平不断提高，居民消费结构升级和消 费需求扩张成为我国经济高速增长的主要动力， 特别是进入20世纪90年代以来， 居民消费需求对国民经济发展的影响不断增大，对国民经济产生了拉动作用。我国经济逐步由短缺经济走向过剩经济、 由卖方市场转向买方市场，社会消费需求 不足，居民消费问题显得更加突出。特别市对于如何启动内需，扩大居民消费变 得越来越重要。因此，及时把握国民经济发展格局中居民消费需求变动趋势，制定符合我国现阶段情况的国民消费政策，对于提高我国经济增长速度和质量都有 重要意义。我选取了

2、全国1990年-2009年居民消费水平及其影响因素的统计资料，详 情如下表所小。年份居民消费水 平居民家庭口支 配收入税收GDP19908332196.52821.86 18667.82 119919322409.22990.1721781.5199211162810.63296.9126923.4819931393P 34994255.3P 35333.921199418334717.25126.8848197.86199523555860.76038.0460793.731996278967656909.8271176.59199730027250.48234.0478973.03 119

3、9831597587.19262.884402.28199933468064.3210682.5889677.05200036328533.412581.5199214.5520013887922615301.38109655.22002414410178.417636.45120332.72003447511094.420017.31135822.8200450321235824165.68159878.32005557313747.928778.54184937.42006626315346.534804.35216314.420077255P 17926.245621.97P 26581

4、0.3 12008834920541.3854223.79314045.42009909822327.8259521.59340506.9、建立回归模型并进行参数估计表1导入数据后得到下表:Equation: UNTITLEDTorkfile: feYHntitled回区Pnt| NairiE|eze| E51nl 日旭 | Foe0 sH 5 tats | Rei i*Dependent Variable YFzlethod Least SquaresDate 12-13/12 Time: 22:19Sample 1990 2009Included observations 20Variab

5、leCoefficientStd Errort StatisticProbX10 4029000 046073Z 7437590.0000X2-0 0231080 016025-1 4420400 1686X30.0044740.0055810 0015930 4345C-78 5498550 62100-1 6S47960 1396R-squared0.999664Mean dependent var3923.300Adjusted F?-squared0 999483S D dependent var2406 042S.E. of regression54.71930Akaike info

6、 criterion11.01317Sum squared resid47907 22Sch.varz Gritericm11 21831Lag likelihood106 1917F-statistic12239.64Curb in-V"： also n stnl0 921749Pro biF-stati stic;0 000000表2由表2可知，模型估计的结果为：Y? 0.403X1 0.023X2 0.004X3 78.550 123(0.046) (0.016) (0.006) (50.521) t= (8.743) (-1.442) (0.802) (-1.555)R20.

7、999564 R20.999483F=12239.64 n=20 D.W.=0.9217、异方差性的检验用怀特检验进行异方差性的检验，得出下表:Equation： UWTULEP Tprkfile；二! ,XViewf| Pt口匚I Obet| 用力"Name：卜 1r232e | EstmaEe Foi eGacr Stats、ESjds|White Heteroskedasticity TestF-3t3tlStlCObs+R-squaii=!d1.45030111 35292Probability0.2316900 2522S1PrubabiliLyTest Equation;

8、Dependent Variable RESIDEMethod Least SquaresDate 12/13/12 Unie 22 39Somplc 1900 2009Included observations 20VariableCoefficientStd. Error bStatisticProb.C-76190.0938527 01-1 9775760 0762X1113 432653.16658 2.1335320 C687-0.0360410,013163 室.7402030的0日xrx2-0 0179260 008845 -2 0267330 0702xrx30 0074900

9、 0029132.5717200 0273X220 733419 9838202。芯4&40 0647X2A2-0 0032600 001745 -1 8681730吧13X2*X30 0022440 0011611 9321200 0Q21X3-10.569114 825719 -2.1901630 0533杼20 0004240 000187 -2.2677390 C467R'Squared0.567646Mean dependent var2395 361Adjusted R-squaredQ.1 侬 26S D dependent ar4137663S.E. cf re

10、gression3795.492Akaike iiM。criterion1a.627B7Sum Gcuarod resid1.44E+03Schwarz criterion20,12573Log likelihood-186 2787F-statistic1 458801Durbin-1-.'at san stat2 777616ProbiF-statistic!0 281690表4由残差图可知，残差的变动有系统模式，连续为正和连续为负，表明残差项 存在一阶正自相关。接下来确定是否存在序列相关性，得出结果如下表：Equation： UMHUED lorkfile:Untitled 伺叵

11、 112s史卡Pr 0二 |Cbecir-irn# F-eszeEt7rtiAtf?| Fo-e«srS：3世EitusSe-ial Coireldliui L(d TesiF-statiaticC：b5*R'Sqiiaf&(l10 39370 F”ba川电3 4U207 Prabahilti0 0041530州3fTast EquationDependent Vaiiabl RESIDUKhod Least SquadsDale 1Z14/12 Tinte 20 53Pressmple mi?s nrj aiu lagged 忖widmlg sat tc zeroV

12、ariableCoefficient Sid Error t-Stai slic Prob.川Q0开招20 043165-1795265。口延X2.0 0275650015114-13230590 0BE2与D,00981D0 0。523g1S512590 0033CJ2.J0340di 7399710160140 3267RESQ 1)07990530 24173433D05,30 0049R'Sc|UaitJ0420710跳川】d叩hiiMiH m -5_2fET3Adjusted R*squared0.266233S.D. dependent var5l21 比7£ E

13、 of regre9sion43.01330Akaike info crlerion1C.57321tunn squared resid2*752.16ychvjsr; crilencn10.8221bLog hlncod.100,7321 F-statistoc27/4"Ddrbln-V'.aisor stat1 727777Probif-statist-c1J69235由表 5 可知 nR28.414207 ,查表可得20.05(1) 3.84 ,22nR 8.414207 > 0.05(1)3.84 ,resid(-i)未通过 5%勺显著Tt检验，表明存回区在一阶

14、序列相关性。 Equation: UNTITLED Vorkf lie: 赵莹Urrt.,sPrint Name =reeie Esnmsrte =orca£t Sts但 ResidsSreusch-Godfrey Serial Correlation LM Test,F-statisticObsftR-squared5 530016Probability8 826830Probability0 0169830 012114Test Equation1Dependent Variable RESIDMei hod Least SquaresDate: 12/14/12 Time 21

15、 06Presainple missing alue lagged residuals set io 7eraVariableCoefficisntStd Errort-StatisticProbX10 0531480056420-0 9589340 3533X2-0 0193310.0191201 0136790 3279X30.0063150.006S091 0007960.3339C27 3181647 335300 5771200 573。RESID。0 8380620 2520013 3256260.0059RESID 52)-0.2197970305682-0 7190380 43

16、35R-squared0441341Mean dependent ar5 21E-13Adjusted R-sqJared0 241321£ D dependent T；ar50 21337S E cf regression43 72297Akaike info criterion10.G3695Sum squared resid26763.78Schwarz critericn10.93667Log likelihood-1003695F-statistic2 21200GDurbin-Watson stat1 &98410PrebfF-statistic)0 111103

17、表6由表 6 可知，nR28.826830 > 20.o5(2)5.99, RESID (-2)未通过 5%的显著性检验，说明不存在二阶序列相关性。Equation: OTTITLED Torkfile:赵莹UTirtiHed 匚1同区，鼻仇| Cbjwut Print Name 叱Est)mat使卜口ssi: | 国己情 | Rwcd5|Dependent Variable YMethod- Least SquaresDate 14"2 Tine: 21:20Sample (adjusted; 1991 2009Included obser73tion5 19 after a

18、djustmetitsCon'/ergence achiie/ed after 56 iterationsVariableCoefficientStd ErrorLStatisticProbX10 3210380 0825483 3691230 Q016X2-0 0385910 028807-1 33S9210 2029X30.0122660 0096501.2710930 2244C36 62573163 73220.2235930 8262AR0 7066G00 2731742 5S6S510 0215R-squared0 999686Mean dependent var4085

19、947Adjusted Rsquared0 999597S D dependent sr2356 3 OSS E of regression47 32352Akaike info criterion10.77233Sum squared resid31353 22Schwarz critenon11 02136Log likelihood-97 34155F-statistic11152 S3D jrbin-V.'atson stat1 454231Prab(F-statistic)0 000000Inverted AR Roots.71表7Y? 0.321X1 0.039X2由表7可

20、知，一阶广义差分的估计结果为0.012X3 36.626 0.707AR(1)(0.083) (0.029)(0.010)(163.732) (0.273)t= (3.889) (-1.336)(1.271)(0.224) (2.587)R20.999686R20.999597D.W.=1.454231由于du 1.40<D.W.< 1- du，判断是不存在序列相关性。 Equation: UNTITLED Torkfile:赵莹，Uirt回国内oc| OfcjKtl pmt-rt?e国 tlma 闾 Fpreca 闺 Stmts | Resids |Breusch-Godfrey

21、 Serial Correlation LM TestF-statisticObs*R-s qua red2 181509 Prababilitv2 730207 Prababil ty0 1634-890 096467Test EquationDependent Variable RESIDMethod Least SquaresDate: 12/14/12 Time: 2144Prasample missing '>alue Igcjged residuals set to 7ero1VariableCoefficientStd Errcrt-StatistiicProb1X

22、1-D. 0073000 079428-0.0929130 9274XS-0.0108850.020703-0 3792440 10GX30.0025980Q0S4320 2754450.7873C61 73289152 6941-0.379442071051AR(1)-0.2330090.306112-07611880 46011RESID-1)0.5M1510.4022711 4769930 16351 R-squared014369SMean dependent ar3 73E-051 Adjusted R*squared-0.185653S.D dependentva41 735421

23、 S.E. of regressiorr45 44474Akaike info criterion10 722961 Suiti squared resid26047 91Sch/yarc criterion11 021201 Log likelihooct,尤明廿双I-statisticU 4JUJU201 irh i! n.sit c mi 仁 tnt1 q 了 nqqjiPrnh I'F.-ctat i&ti r 1 UUI UMI 1八UUI1 3LdLII t U J +1 N LIU (IT Lal liLI L |u 口 11 u表8由表 8 可知，nR22.73

24、0207 < 20.05(1) 3.84, RESID(-1)未通过 5%勺显著性检验，说明不存在一阶序列相关性。Y? 0.321X1 0.039X2此时经过修正后的模型为0.012X3 36.626 0.707AR(1)(0.083) (0.029)t= (3.889) (-1.336)(0.010)(1.271)(163.732) (0.273)(0.224) (2.587)R20.999686R20.999597D.W.=1.454231四、多重共线性的检验由消除序列相关性后的模型可知，t/2(n-k) t0.025(19-5) 2.145,其中X2、和常数的参数估计值未能通过t检

25、验，故认为解释变量间存在多重共线性。计算各解释变量的相关系数表9证实存在多由相关系数矩阵可以看出，个解释变量相互之间相关系数较高, 重共线性。分别作Y对XI、X2、X3的一元回归，结果如下：Equation： UJTTITLED Torkfiloj 赵莹%Unti.- 亘四才Object| PrintM日Estiinate|Fae血t|/tats愀山困Dependent Varisbls YMethod Least SquaresDate 12d4' 12 Tima22 JOSample 1990 2009Included cbaarvation20VariableCoefficien

26、tStd. Error t-StatisticProbXI0.4079910 002506162.79700.0000c2.38520926.08652 -0.0849240.9333R-squar&d0.999321Mean dependent var3S23 300Adjusted R-squared0.999284iS.D. dependent -rarZ4U-： 5ii.h. ot regression64 40003Akaike into criterion11,26274Sum squared resid74652.54Schivarz entenon11.36232Lug

27、 likelihood-110 6274F-stalislic26502 S7Durbin-Watson stat0 66C022ProbF-statistic0 000000Equation： USTITLED TorkfHe:裁量七|pxview Proc| Object Print Name Freeze E&tj(nate| For&cast 与tats|我国tteDependent Variable YMyLhud. Lt5dbl SqiJdiebDate 1214 12 Tima22 42Sample 199口 2009Included ohser/aticns20

28、VariableCoefficientStd Error t-StatisticPratX20 1347620 00065613 655琥0 0000C1414 397172 8863 S 1840240 0000R'gquared0 955481Mean dependent var3923 300Adjusted Rquared0 953007SD dependent var2406 042S E of gg pc二ion621 67G9Ako ike info criterion1E 14623Sum squared resid4896746Sch-.varz criterion1

29、5 54580Lug likelihuud152 4523F-statistic36& 3196Durbin-Watson stat0.137603Prob(F-statistic)0 000000Equati(iT): UBIITLEDToTkfile: VUnlitled | . lfH|XVlewJPrW Object Print| NamFteeje| 里timHteFoHCjst5tats|Resick|Dependent Variable YMethod Least SquaresDate 12/U/12 Time 22 42Sample 1990 2009Included

30、 ohser.ations 20VariableCoefficientStd Error t-StatisticProhX30 0243360 00070035 710220 ooooC821 9839108 6(M77.5685840 OODOR-squared0 &BG031Jean dependent -.ar3923 300Adjust&d R-squared0 9B53O0S D dependent var2406 042S E of regression291 5378Akaike info criterion14 283 54Sum squared resid15

31、30946.Schwarz critefion14 30311Log lik&lihocd-140 0364F-statistic1276.22CDurtin-'/Vatscii stat0 132609noti F-statistic:o aooooo表10由表10可知，R2xiR 2X3R2X2 ,以Xi为基础，顺次加入其他变量逐步回归。结果如下:Equation: UFIITLED Vorkfile:赵童Uirt.一 五回区"iew | Pm匚|Print'的用|中日日££|三5阿日回 E咋冰t| 5:的 R3上Dependent V

32、ariable YMethod Least SquaresDate 121U/12 Time 23 01Sample 1990 2009Included obserations 20VariableCoefficientStd Error t-StatisticProbX104387860 01D73140 663580 0000X2.0 0106070 003645-2.9099610.00&8C-101 26944137955 -2 4473300 0256R-squared0 9S9547esr dependent ar3923 300Adjusted R-squared0 99

33、9494S D dependent、用厂2406 042S E of regression54 14096Akaike infc cjjterian10 95854Sum squared resid49831 15Sch varz criterion11 19QLoy lik&lihood-106 5854F-statistic18753 45Durbin-'atsfln stat1 0C9424ProbiF-statistic:o ooaooo表11由表11可知，XI、X2回归时通过t检验。再加入X3进行检验Equation: UVJIILED Vozkfile:赵童*UnK. 不fBVievv|Prodobjal| P