VECM模型实验 ——时间序列

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1、基于VECM模型探究中国房地产市场对中国经济增长的影响VECM模型实验姓名;何毛毛学号：2012300040242班级：国际金融试验班第一部分 实验背景自1992年中国逐步确立市场经济以来的20多年里，投资，消费，出口“三驾马车”理论对我国经济增长的巨大作用。政府扩大了对基础设施建设的投资，以及中国的出口保持的高速增长态势，对经济增长的拉动起到了很大的作用。第二部分 实验分析目的及方法故本文选取了商品房价格、居民消费指数以及净出口三个变量构建VEC模型，进行协整检验和向量误差修正并得到脉冲相应函数和方差分解结果，将中国现有数据现状进行分析，得出房地产市场对我国经济的影响。第三部分 实验样本3.

2、1数据来源数据来源于中经网统计数据库。3.2所选数据变量由于国家在1998年把房地产业定为支柱产业，故本文选取了自1999年1月至2014年10月的出口额、进口额、CPI、房地产开发企业商品房销售面积及其销售额的累积额五个变量以月为单位的数据进行一定的处理得到商品房价格P、居民消费指数CPI以及净出口X三个变量构建VEC模型。 第四部分 模型构建4.1 数据处理4.1.1 商品房价格由于商品房价格有较强的地域差异，故此处采用了较为简单的处理方法。取用房地产开发企业商品房销售面积以及房地产开发企业商品房销售额的累计额，而由于我国不单独对1月份统计数据进行调查，1-2月份数据一起调查，一起发布。所

3、以序列缺少每年一月份的相关数据，属于非随机、不可忽略缺失，在此采用一二月平均值得到一月份的数据。补全数据后在每一年度进行差分处理得到当月量，再把总销售额与总销售面积相除得到国内市场上商品房的平均价格序列P。由于序列P有较强的趋势性，为了平滑房价的变动趋势，对P做对数化处理记为LP。4.1.2 净出口由于现有数据仅为出口额、进口额，故想减得到净出口值，并乘以当月汇率转化成人民币计量。此外为了平滑净出口的变动趋势，对X同样也做对数化处理记为LX。4.1.2 CPI由于CPI为相对数，为了减少基期的影响以及减少异方差性，对CPI进行对数化处理记为LC。4.2 单位根检验观察LC、LX、LP的图形，如

4、下所示：图4.1 LC的曲线图图4.2 LP的曲线图图4.3 LX的曲线图对三个变量选取相应的形式进行单位根检验.表4.1 各变量单位根检验结果变量水平值检验结果一阶差分检验结果检验形式ADFP检验形式ADFPLC（C，0，12）-2.4015630.1428（0，0，11）-6.0470440.0000LP（C，T，12）-2.3274470.4166（0，0，11）-3.6182010.0004LX（C，0，1）-2.7725980.0645（C，0，0）-20.984160.0000综上，三个变量在5%的显著水平上都不平稳，但一阶差分平稳，因此三个序列都为一阶单整过程。4.3协整检验由于

5、变量LP存在截距和趋势，因此选择第二类形式，且变量无明显的时间特征，因此选择第三种形式作为协整检验形式。根据信息准则以及残差进行滞后阶数的确定，当滞后阶数为1时，AIC=-7.137759, SC=-6.790499; 当滞后阶数为2时，AIC= -7.538003, SC= -6.930299; 当滞后阶数为3时，AIC= -7.679420, SC= -6.811272。故此处选择滞后二阶为最优滞后阶数。选择滞后阶数为2，且第三种形式进行协整检验，检验结果如下：表4.2 协整检验结果Date: 12/10/14 Time: 22:06Sample (adjusted): 1999M04 2

6、014M10Included observations: 154 after adjustmentsTrend assumption: Linear deterministic trendSeries: LOP LX LCLags interval (in first differences): 1 to 2Unrestricted Cointegration Rank Test (Trace)HypothesizedTrace0.05No. of CE(s)EigenvalueStatisticCritical ValueProb.*None *0.15105633.1684229.7970

7、70.0197At most 10.0501787.94898215.494710.4709At most 20.0001360.0210073.8414660.8847Trace test indicates 1 cointegrating eqn(s) at the 0.05 level* denotes rejection of the hypothesis at the 0.05 level*MacKinnon-Haug-Michelis (1999) p-valuesUnrestricted Cointegration Rank Test (Maximum Eigenvalue)Hy

8、pothesizedMax-Eigen0.05No. of CE(s)EigenvalueStatisticCritical ValueProb.*None *0.15105625.2194321.131620.0125At most 10.0501787.92797514.264600.3861At most 20.0001360.0210073.8414660.8847Max-eigenvalue test indicates 1 cointegrating eqn(s) at the 0.05 level* denotes rejection of the hypothesis at t

9、he 0.05 level*MacKinnon-Haug-Michelis (1999) p-valuesUnrestricted Cointegrating Coefficients (normalized by b*S11*b=I):LOPLXLC3.411003-1.86888620.027881.723127-0.200519-46.265743.324745-0.2939120.064617Unrestricted Adjustment Coefficients (alpha):D(LOP)-0.0146380.0020270.000749D(LX)0.1916330.0132010

10、.001944D(LC)3.22E-050.001393-3.99E-061 Cointegrating Equation(s):Log likelihood642.0482Normalized cointegrating coefficients (standard error in parentheses)LOPLXLC1.000000-0.5478995.871551(0.06584)(2.89701)Adjustment coefficients (standard error in parentheses)D(LOP)-0.049930(0.02075)D(LX)0.653660(0

11、.13759)D(LC)0.000110(0.00176)2 Cointegrating Equation(s):Log likelihood646.0122Normalized cointegrating coefficients (standard error in parentheses)LOPLXLC1.0000000.000000-35.67378(11.2063)0.0000001.000000-75.82659(21.1778)Adjustment coefficients (standard error in parentheses)D(LOP)-0.0464370.02695

12、0(0.02324)(0.01143)D(LX)0.676407-0.360787(0.15410)(0.07579)D(LC)0.002510-0.000339(0.00192)(0.00094)由上表可知，迹检验和极大特征值检验结果均显示存在一个协整关系。协整序列的图形和单位根检验结果如下：图4.4 协整序列变动图表4.3 协整序列的单位根检验结果Null Hypothesis: COINTEQ01 has a unit rootExogenous: NoneLag Length: 1 (Automatic - based on SIC, maxlag=13)t-StatisticProb

13、.*Augmented Dickey-Fuller test statistic-5.0208250.0000Test critical values:1% level-2.5818275% level-1.94315710% level-1.615178*MacKinnon (1996) one-sided p-values.由上表可知，该协整序列是平稳的，即各变量之间存在协整关系。该协整方程具体为：LC =0.17LP -0.09LX + tLP与LC呈现正向波动，LX与LP及LX与LC呈现负向波动，即房地产价格与物价指数是正相关关系，净出口与房价呈现负相关关系，净出口与国内物价水平呈现负

14、相关关系，符合一般的经济学理论，故该协整方程较为合理。4.3 VECM模型的估计估计结果如下：表4.4 VECM模型的估计结果Vector Error Correction EstimatesDate: 12/10/14 Time: 22:44Sample (adjusted): 1999M04 2014M10Included observations: 154 after adjustmentsStandard errors in ( ) & t-statistics in Cointegrating Eq:CointEq1LC(-1)1.000000LP(-1)0.170313(0.049

15、57) 3.43554LX(-1)-0.093314(0.01781)-5.23803C-4.731936Error Correction:D(LC)D(LP)D(LX)CointEq10.000645-0.2931653.837997(0.01032)(0.12185)(0.80788) 0.06244-2.40604 4.75072D(LC(-1)0.1380640.168840-12.33234(0.08462)(0.99882)(6.62253) 1.63161 0.16904-1.86218D(LC(-2)0.0677240.101383-2.543282(0.08694)(1.02

16、626)(6.80446) 0.77895 0.09879-0.37377D(LP(-1)0.008339-0.579548-1.657204(0.00650)(0.07675)(0.50886) 1.28251-7.55145-3.25673D(LP(-2)0.000560-0.450241-0.344358(0.00699)(0.08251)(0.54704) 0.08012-5.45705-0.62949D(LX(-1)0.000146-0.027722-0.266886(0.00107)(0.01265)(0.08387) 0.13653-2.19159-3.18223D(LX(-2)

17、0.000433-0.0243870.011625(0.00077)(0.00906)(0.06010) 0.56372-2.69065 0.19344C4.96E-050.0161370.036033(0.00053)(0.00621)(0.04116) 0.09438 2.59957 0.87546R-squared0.0416690.3520280.352984Adj. R-squared-0.0042780.3209610.321963Sum sq. resids0.0059730.83219436.58429S.E. equation0.0063960.0754980.500577F

18、-statistic0.90688611.3312111.37876Log likelihood563.6108183.4729-107.8418Akaike AIC-7.215725-2.2788691.504439Schwarz SC-7.057961-2.1211051.662203Mean dependent0.0001210.0092930.023850S.D. dependent0.0063820.0916200.607917Determinant resid covariance (dof adj.)5.63E-08Determinant resid covariance4.80

19、E-08Log likelihood642.0482Akaike information criterion-7.987639Schwarz criterion-7.4551864.4 VECM模型的检验下面进行残差的自相关性的检验，检验结果如下：图4.5 VECM模型各方程残差项的自相关图观察残差自身的自相关图，可以看出均不存在自相关性。4.5 VECM模型的预测- 9 -由上图可以看出VECM基本可以拟合出原序列变动趋势。4.6 施加约束条件后的VECM模型VECM模型的方程形式如下：Estimation Proc:=EC(C,1) 1 2 LC LP LX VAR Model:=D(LC

20、) = A(1,1)*(B(1,1)*LC(-1) + B(1,2)*LP(-1) + B(1,3)*LX(-1) + B(1,4) + C(1,1)*D(LC(-1) + C(1,2)*D(LC(-2) + C(1,3)*D(LP(-1) + C(1,4)*D(LP(-2) + C(1,5)*D(LX(-1) + C(1,6)*D(LX(-2) + C(1,7)D(LP) = A(2,1)*(B(1,1)*LC(-1) + B(1,2)*LP(-1) + B(1,3)*LX(-1) + B(1,4) + C(2,1)*D(LC(-1) + C(2,2)*D(LC(-2) + C(2,3)*D

21、(LP(-1) + C(2,4)*D(LP(-2) + C(2,5)*D(LX(-1) + C(2,6)*D(LX(-2) + C(2,7)D(LX) = A(3,1)*(B(1,1)*LC(-1) + B(1,2)*LP(-1) + B(1,3)*LX(-1) + B(1,4) + C(3,1)*D(LC(-1) + C(3,2)*D(LC(-2) + C(3,3)*D(LP(-1) + C(3,4)*D(LP(-2) + C(3,5)*D(LX(-1) + C(3,6)*D(LX(-2) + C(3,7)VAR Model - Substituted Coefficients:=D(LC)

22、 = 0.000644513086716*( LC(-1) + 0.170312756574*LP(-1) - 0.0933142348512*LX(-1) - 4.73193564637 ) + 0.138063823104*D(LC(-1) + 0.0677239122424*D(LC(-2) + 0.00833863533815*D(LP(-1) + 0.000559987514795*D(LP(-2) + 0.000146302892643*D(LX(-1) + 0.000432856871581*D(LX(-2) + 4.96362755959e-05D(LP) = - 0.2931

23、65434596*( LC(-1) + 0.170312756574*LP(-1) - 0.0933142348512*LX(-1) - 4.73193564637 ) + 0.168839712363*D(LC(-1) + 0.101383062825*D(LC(-2) - 0.579547910079*D(LP(-1) - 0.450240826627*D(LP(-2) - 0.027721572201*D(LX(-1) - 0.0243873548642*D(LX(-2) + 0.0161371977625D(LX) = 3.83799662293*( LC(-1) + 0.170312

24、756574*LP(-1) - 0.0933142348512*LX(-1) - 4.73193564637 ) - 12.3323449379*D(LC(-1) - 2.54328177133*D(LC(-2) - 1.65720417582*D(LP(-1) - 0.344357605774*D(LP(-2) - 0.266886010794*D(LX(-1) + 0.0116247131163*D(LX(-2) + 0.0360329193473由于协整方程中各变量都较为显著，故此处不加以估计施加约束条件的VECM。- 11 - 18 -第五部分 模型应用5.1脉冲响应下图是基于三变量的

25、VECM模型模拟出来的脉冲响应函数，横轴表示滞后阶数，由于房地长行业的经营周期较长，故将滞后阶数设定为60；纵轴表示变量之间的响应程度，图中实线部分为计算值。图5.1 脉冲响应图5.2方差分解 第六部分 结论根据以上结果，我们可以得到以下结论：1. 我国商品房的销售价格与前期的销售价格相关，我国的CPI、净出口都是属于一阶单整序列，这符合现实，在经济的运行过程中，存在广泛的时间滞后效应。2. 房地产市场虽然在很大程度上影响了我国的宏观经济，但商品房作为一种投资品，对居民消费影响较小，近期房价的频繁波动并未对我国居民的生活水平产生较大的影响。由以上结论可以看出，我国应调整产业结构，减少对房地产市

26、场的依赖程度，特别是减少地方政府的土地财政的现象。出台连续的稳定的政策以调整房地产市场，减少市场的波动，稳定消费者的预期，从而使经济得到稳定长远的发展。附录原始数据指标房地产开发企业商品房销售面积_累计房地产开发企业商品房销售额_累计居民消费价格指数(上年同月=100)_当月出口额_当月进口额_当月地区全国全国全国全国全国频度月月月月月单位万平方米亿元-千美元千美元1999-0198.81139260799033271999-02415.0589.8498.71100005387222421999-031025.73207.898.214877936143780271999-041586.54

27、319.597.814804183138374051999-052146.09440.8397.815531943136572171999-062979.41610.6497.915398063145229551999-073633.96745.0398.617338664139214011999-084287.35871.9298.718325337134464701999-095102.31042.1799.218576263152679991999-106061.591239.9999.418231917137927561999-117062.39144599.1194766251690

28、86281999-1213379.352745.549920238657174223922000-0199.816797277152583932000-02636.1144.39100.714775380134286092000-031391.55295.9799.820146482178135792000-042153.93450.3199.720500392183607952000-052958.13623.65100.120105176169664292000-064073.18844.93100.522192970203014022000-075014.831032.55100.521

29、478509194916282000-086006.881244.7100.323329185207877402000-097088.731460.7410022973290207150342000-108248.81691.7410022799974189164012000-119553.261997.91101.322154881216408812000-1216984.143572101.521986149214142502001-01101.216926471155450072001-02877.96222.4610019198624182256172001-031828.72440.

30、65100.823139003207725262001-042800.78653.78101.622792181218592802001-053795.05898.84101.720813507188087662001-065126.571181.16101.422081032212515372001-076365.291453.88101.522887692209555002001-087603.851721.1310123540123221615352001-098977.271998.2799.923989367218505982001-1010168.942259.39100.2227

31、90526189018092001-1111617.552578.1799.724000007208447712001-1220779.244625.7299.724502579223901052002-019921703291189704172002-02923.75222.8610019137164159184522002-032152.66514.0399.223817766224841452002-043379.57779.7498.726723688257517112002-054564.61045.4998.924644182224331122002-066279.851445.1

32、799.226012762230941422002-077689.71779.9899.129209981269876552002-089300.172157.0399.329437423272049142002-0911129.092635.499.331910755297941392002-1012975.93058.8499.229946376251970372002-1115079.363535.8499.331209190287345982002-1224969.295721.2299.631889489287325822003-01100.429775788310159692003

33、-021560.38392.42100.224455585237796572003-033125.42784.69100.932091277325491242003-044632.511147.4310135617074346012082003-056333.161549.95100.733842228316041482003-068672.352101.77100.334475859323361762003-0710657.132574.92100.538109608365136662003-0812628.73058.14100.937415036346213672003-0915189.

34、243736.43101.141940698416523362003-1017447.894309.46101.840925906351925022003-1119950.24898.8610341761968368932862003-1232247.247670.9103.248061529423361762004-01103.235712196357366022004-022221.51578.78102.134157738420297442004-034271.161143.3410345847915463878432004-046200.71641.54103.847124115493

35、741852004-058310.092250.27104.444867889427650262004-0611009.882973.5410550496344486526632004-0713426.583657.49105.351003919489722952004-0815595.974287.05105.351400194469105962004-0918201.775053.88105.255803041508109162004-1020681.635703.89104.352523879454335742004-1123725.516545.73102.86092546151029

36、7012004-1238231.6410375.71102.463784483527080302005-01101.950755189442611562005-022596.45807.37103.944273164399162222005-035172.671559.33102.760869119551361122005-047194.272141.72101.862151250575601742005-059484.832796.38101.858426919494385352005-0612536.353727.28101.665959601562819782005-0716526.92

37、4938.28101.865584266550385202005-0831202.4710027.37101.368399603578066882005-0934725.611313.3100.970185509626231242005-1039352.1912925.89101.268092010560760192005-1143388.2314430.14101.372217762616872162005-1255769.1418080.3101.675412367643960232006-01101.964988815554968282006-025343.891881.93100.95

38、4108294516837182006-039458.713192.7100.878045837668571322006-0413560.874615.35101.276948177664913552006-0518136.966270.04101.473113881601097302006-0622976.627957.48101.581311219668083002006-0727307.989440.0810180337153657135142006-0831384.5910870.72101.390766001719698972006-0935883.3712415.34101.591

39、629488763424742006-1040780.6714053.17101.488127371642975172006-1146113.9316141.36101.995854497729264882006-1260628.1420509.68102.894094055730967502007-01102.286619731707391992007-025371.472247.9102.782095593583393612007-0310600.774050.75103.383424155765527152007-0415765.165997.3210397449955806042082

40、007-05211488059.75103.494065041715908212007-0627904.1510642.83104.4103268286763582172007-0734137.2413142.44105.6107744104833871892007-0840572.8115820.34106.5111354781863807042007-0947369.7118684.77106.2112373049885672062007-1053564.9621286.95106.5107723989806733332007-1160156.8924002.64106.911762080

41、7913395572007-1276192.729603.87106.5114415986917289812008-01107.1109640030901744472008-025144.152154.75108.787367796788131332008-0310449.564110.53108.3108962891955561422008-0414994.155904.79108.51187710841021026832008-0519633.47837.24107.71204964911002860622008-0625892.6310325.43107.1121179554100179

42、9362008-0730453.9612221.17106.31366750461113971472008-0834592.2813813.43104.91348726751061784932008-0940320.7615878.53104.61364320881070652742008-1044722.9617590.03104128327028930876862008-1149148.3819261.19102.4114987285748974702008-1262088.9424071.41101.2111157222721771862009-011019045360051344264

43、2009-025131.232396.9898.464894649600536582009-0311308.745058.6498.890290547717291122009-0417625.457995.9298.591934722787996872009-0524644.4411388.9298.688757886753693562009-0634108.5915799.5798.395411208871595452009-0741754.9819599.5998.2105420240947905832009-0849416.0423463.7498.8103707009879952342

44、009-0958371.0227531.8999.21159379941030058712009-1066368.7331529.1299.5110762383867747492009-1175203.1535987.12100.6113653429945604312009-1293713.0443994.54101.91307238811122937132010-01101.53109475299953070472010-027155.184115.74102.794522714869103332010-0315360.927976.8102.371121117931193480922010

45、-0423412.1612425.24102.811199206661182394622010-0530189.4315760.19103.061317606631122277492010-0639352.5319819.85102.951373955781173737262010-0745818.6122885.69103.31455193221167889342010-0852704.4726418.24103.481393022301192661522010-0963150.2331916.58103.611449852851281103042010-1072428.5536992.28

46、104.371359784191088327012010-1182541.2742277.89105.121533257621304359452010-12104349.1152478.72104.591541488951410688332011-01104.91507341511442732102011-028142.955241.61104.9967361271040639642011-0317642.7910151.91105.41521990711520603082011-0424897.9214077.73105.31556840841442630812011-0532931.641

47、8620.1105.51571571911441102232011-0644419.3324589.42106.41619807741397081982011-0752037.1228852.11106.51751280361436444272011-0859854.1833264.4106.21733156971555567392011-0971288.7539311.54106.11696730121551590802011-1079653.1243826.24105.51574907721404576982011-1189593.8849046.86104.217446412315993

48、59952011-12109945.5659119.09104.11747176511581968892012-01104.51499391131226612272012-027004.154144.58103.21144706931459540142012-0315239.158672.03103.591656581001603107992012-0421561.6612421.09103.371632517121448245242012-0528852.4516932.161031811407621624414402012-0639964.3823314.04102.15180204470

49、1484823652012-0748593.2328699.47101.781769400321517932782012-0857414.8234011.11102.051779732971513127462012-0968441.4140353.67101.911863495091586804802012-1078742.9446300.76101.71755711021435244162012-1191704.9953525.93102.041793807671597474922012-12111303.6564455.79102.521992296821676112452013-0110

50、21873655721582193132013-0210471.147361.33103.221393672351241417752013-0320897.9813991.63102.071821899991830130972013-0429760.5219847.19102.391870614741688999942013-0539118.1325863.98102.11827661161623411582013-0651433.3333376.41102.671743157961471913922013-0761133.2839548.84102.671859913171681733662

51、013-0870841.945723.98102.571906083171620895472013-0984383.3154028.13103.051856435761704263622013-1095930.9961237.63103.211854055761542988642013-11110806.869946103.022022048031684038852013-12130550.5981428.28102.52077424231821015732014-01102.49207132123.5175262820.52014-0210465.627090.42101.95114093694.2137082487.52014-0320111.1813262.96102.38170107988.41624046932014-0427709.2618306.56101.8188540547.9170087976.62014-0536069.623673.64102.48195472920.4159551189.42014-0648365.2331132.81102.34186788536.9155223