VAR模型的应用

1、VAR模型的应用案例分析的目的一般来说，地区GDP越高，人均收入也越高，居民消费水平也越高， 而反过来，居民消费水平越高，对 GDP的促进作用也越大。那么两者是否 真的存在相互影响呢？本案例将分析居民消费水平与GDP之间的这种联动效应。1.实验数据本实验选取湖北省从1980年到2010年的年度数据。整理如下：表1 GDP总额与居民消费水平年份GDP （万元）居民消费水平X （元）1980199.382011981219.752251982241.552661983262.582931984328.223521985396.264111986442.044931987517.7753319886

2、26.526381989717.087621990824.388131991913.3886919921088.3998619931325.83317123619941700.91746148619952109.384204190819962499.766558232319972856.47035245919983114.015576257919993229.291593254520003545.392517268020013880.533733296220024212.82456326320034757.450974385320045633.24430920056590.1948832006

3、7617.47548020079333.46513200811328.927406200912961.17791201015967.6189773.VAR模型的构建3.1数据平稳性检验因为数据变动趋势较大，本例对数据取对数，其中LGDP表示GDP总额，LX表示居民消费水平。表2将数据取对数调整后的新序列 LGDP与LX年份LGDPLX19805.2952135.30330519815.3924915.416119825.4870765.58349619835.5705565.68017319845.7936845.86363119855.9820716.01859319866.09146.20

4、050919876.2495316.27852119886.4401816.45833819896.5751876.63594719906.7146326.70073119916.8171526.76734319926.9924556.89365619937.1897967.11963619947.4389237.30384319957.6541517.55381119967.8239537.75061519977.9573427.8075119988.0436687.85515719998.0800187.84188620008.1734047.89357220018.2637287.993

5、6220028.3458898.09040220038.4674678.25660720048.636448.36846120058.7933378.49351520068.93828.6088620079.1413558.78155520089.3351148.91004620099.4697088.96072520109.6783189.102421口 Group: UNTITLED Workfile: G:;UntitledVfevv|Prx|object卩riit| NameFree菲 | Sampl已| Sheet|Stats|图1居民消费水平与GDP的对数值的对比图O Series

6、i LX Werkfile: G：:UntitleclTiew | Fnoc Ot宾ct|_Proprtjes PmtwairE 尸re亡Sarglel Gerr| Sheet Graph Stats | dent|Augment&d Dickey-FJller Unit RoalTeston D(LXNull Hypottiesis： D(LX) has a unit rootExogenous: ConstantLag Length: 0 CAutornatlc based on SIC MAXLAG-?)StatisticPrab.*Augmented Dicke t-Fullertes

7、tstatistic-34690 储0.0164Test critical values;1% level SK level 10 level-357 9322-2.967767-2622969MacKinnon 19Q6) one-sided p-values.图2 LX序列的单位根检验结果口 Series; LGDP Workfile; G;Untitled亘亘1Mei-i| FrtM： |Object |Propertes Print rme Freeze Samp-e Genr亡亡tGraphStats I dentAugmented Dickey-Fuller Unit Root T

8、est on D( LG DPNull hypothesis. D(LGDP) has a unit rootExogenous: donstantLag Length: O (Automatic based on SIC, MAXLAG=7t-StatsticProb*Auamented Dickey-Fuller test stall Stic-2 361B330 0623Test criti cal values:1 %)level5% level 10% level-3.675322 -2.967767 -Z 622989MacKinnon (1996) one-sided p-val

9、ues.图4 LGDP序列的单位根检验结果从而LX和LGDP在5%的显著水平上均是平稳序列3.2 VAR模型滞后阶数的选择由于共有31个年度样本数据，选取最大的可能滞后阶数为 3不同判断标准下滞后阶数的选取I II S IViewProc | Object) Print Narnie|Freeze | Estimate (Stats Impulse Resids Van UNTITLED Workfile: G:UntitledVAR Lag OrderSelection Cntena Endogenous variables: LGDP LX Exogenous vanables: CDat

10、e 03/08/12 Time: 19：7Sample: 1980 2010 included observations: 23LagLogLLRFPEAICSCHQ01.176402NA0 0035360.05882001539650.087919195.22144167.93765.66e-06-6.372960-&.0374fi7-&.2856682102.208111.47B10*4.76e-0&-6.5362941-6.110506*-6.44034V3103.443&1.8535965.S9G-0B-6 3S8846-5.722743-B.18&.212* i n di cates

11、 I目q order selected by the criterionLR: sequential modified LR test statistc (each test at 5% level) FPE Final predictiori errorAIC： Aka ike infomation criterionSC; Schwarz information criterionHQ: Hannan-Quinn information criterion从以上分析结果可以看出，FPE, AIC, SC, HQ都得出滞后阶数为2时的 VAR模型为最优的，可得选取的最优滞后阶数为 2，即K=

12、2 。3.3 VAR模型的估计下表是滞后阶数为2时的VAR模型的估计结果VAR（ 2）的估计结果Vector Autoregression EstimatesDate: 05/08/12 Time: 19:07Sample (adjusted): 1982 2010Included observations: 29 after adjustments Standard errors in ( ) & t-statistics in LGDPLXLGDP(-1)1.5165510.954641(0.27898)(0.28720)5.436063.32399LGDP(-2)-0.420999-0.

13、487069(0.25111)(0.25851)-1.67655-1.88416LX(-1)0.0408460.694442(0.23616)(0.24312)0.172952.85637LX(-2)-0.148943-0.245697(0.23483)(0.24174)-0.63427-1.01636C0.1477180.577199(0.17390)(0.17902)0.849463.22423R-squared0.9987400.998174Adj. R-squared0.9985300.997870Sum sq. resids0.0543030.057549S.E. equation0

14、.0475670.048968F-statistic4755.4703280.140Log likelihood49.9177549.07589Akaike AIC-3.097776-3.039717Schwarz SC-2.862035-2.803976Mean dependent7.5911987.440455S.D. dependent1.2405831.060976Determinant resid covariance (dof adj.)3.32E-06Determinant resid covariance2.27E-06Log likelihood106.1169Akaike

15、information criterion-6.628749Schwarz criterion-6.157267从表中可以看出VAR模型的参数估计大多显著3.4 VAR模型的检验VAR模型的检验包括VAR模型的平稳性检验，以及残差的独立性检验。图5平稳性检验结果O Var： LNITTLED Wcrkflle: G:iUntitleJ回 列ViAI Proc | Object| Print | Name FreezeEstjriate Stafe|lmpul5|RidVAR Stability Condition ChckRoots of Charadensfcc Palynomial End

16、ogenous variables: LGDP UC Ecgenous variables: CLag spedTicaflon: i 2Date: 05JO&/12 Time: 19:10RootModulus10090471.0090470 550373-0.25103010 614Q310 550373 *0.251030i0 &140310 .0312000,061200.faming: .Ml east one root outside the unit circle. VAR does not satisthe stability condition.因此VAR模型不满足平稳性的条

17、件所以残差不存在自相关性，满足独立性假设。3.5 VAR模型的预测F面是动态预测结果LGDP.Actuals LGDP (Baselne)-1 | | | | | | | | | | 1 1 1 1 I 1 1 1 1 I 1 1 1 I 1 1 1 1980196519901995200020052010Actuals LX (Baselins)4.VAR模型的应用4.1格兰杰因果检验本例中VAR模型的滞后阶数为2 a口 Group: UNTITLED Workfile: G：iUntitledIm F- Ob- nt N-rr-r =re?-尸 airwise Granger Causal

18、ity TestsDate: 05/06/12 Time 19:17Sample. 1S30 2010Lags： 2Null Hypothesis:Obs F-Staiistic ProbLX does not Granger Cause LGDP290 238420.7897LGDP docs not Granger Cause LX6.094140.0072从中可以看出，LX可能不是LGDP的格兰杰原因，这说明湖北省居民消费水平受地区GDP总额的影响较小，可能湖北省 GDP与投资有更大的关系。4.2脉冲响应脉冲响应函数收到变量顺序的影响，因此其结果与分析的主观因素有关 Var; UNTIT

19、LED Workfile: G:Untitledrnrsii观察第二个图形，GDP对居民消费水平几乎没有影响，这验证了湖北省GDP与居民消费水平的相关关系较小的现实。从时间长短来看， GDP对居民 消费水平的长期影响要大于短期影响，而居民消费水平对 GDP也是长期影响 更显著。4.3方差分解 Van UNTITLED Workfllei Gr:Untftkd|百Vie Ptocgbject卩rit|mrriE ;=rezej Estinn吕怕| $t日号 1讯出1 鸵 |口已列空Va riaice Decompositiancariarice Decomposition of LGDF:PeriodS ELGDPLX10.0+7567100.00900.00000020.