VECM模型實驗——時間序列

1、基于vecM模型探究中國房地產(chǎn)市場對中國經(jīng)濟增長的影響VECM模型實驗姓名 ;何毛毛學(xué)號： 2012300040242班級：國際金融試驗班第一部分 實驗背景自 1992 年中國逐步確立市場經(jīng)濟以來的 20 多年里，投資，消費，出口“三駕馬車”理論對我國 經(jīng)濟增長的巨大作用。政府?dāng)U大了對基礎(chǔ)設(shè)施建設(shè)的投資，以及中國的出口保持的高速增長態(tài)勢，對 經(jīng)濟增長的拉動起到了很大的作用。第二部分 實驗分析目的及方法故本文選取了商品房價格、居民消費指數(shù)以及凈出口三個變量構(gòu)建VEC模型，進行協(xié)整檢驗和向量誤差修正并得到脈沖相應(yīng)函數(shù)和方差分解結(jié)果，將中國現(xiàn)有數(shù)據(jù)現(xiàn)狀進行分析，得出房地產(chǎn)市場對 我國經(jīng)濟的影響。第三

2、部分 實驗樣本3.1 數(shù)據(jù)來源 數(shù)據(jù)來源于中經(jīng)網(wǎng)統(tǒng)計數(shù)據(jù)庫。3.2 所選數(shù)據(jù)變量由于國家在 1998年把房地產(chǎn)業(yè)定為支柱產(chǎn)業(yè)，故本文選取了自1999年1月至 2014年10月的出口額、進口額、CPI、房地產(chǎn)開發(fā)企業(yè)商品房銷售面積及其銷售額的累積額五個變量以月為單位的數(shù)據(jù) 進行一定的處理得到商品房價格 P、居民消費指數(shù)CPI以及凈出口 X三個變量構(gòu)建VEC模型。第四部分 模型構(gòu)建4.1 數(shù)據(jù)處理4.1.1 商品房價格 由于商品房價格有較強的地域差異，故此處采用了較為簡單的處理方法。取用房地產(chǎn)開發(fā)企業(yè)商 品房銷售面積以及房地產(chǎn)開發(fā)企業(yè)商品房銷售額的累計額，而由于我國不單獨對1 月份統(tǒng)計數(shù)據(jù)進行調(diào)查

3、， 1-2 月份數(shù)據(jù)一起調(diào)查，一起發(fā)布。所以序列缺少每年一月份的相關(guān)數(shù)據(jù)，屬于非隨機、不可忽 略缺失，在此采用一二月平均值得到一月份的數(shù)據(jù)。補全數(shù)據(jù)后在每一年度進行差分處理得到當(dāng)月量， 再把總銷售額與總銷售面積相除得到國內(nèi)市場上商品房的平均價格序列P。由于序列P有較強的趨勢性，為了平滑房價的變動趨勢，對P做對數(shù)化處理記為LP。4.1.2 凈出口由于現(xiàn)有數(shù)據(jù)僅為出口額、進口額，故想減得到凈出口值，并乘以當(dāng)月匯率轉(zhuǎn)化成人民幣計量 此外為了平滑凈出口的變動趨勢，對X同樣也做對數(shù)化處理記為 LX。4.1.2 CPI由于CPI為相對數(shù)，為了減少基期的影響以及減少異方差性，對CPI進行對數(shù)化處理記為LC。

4、4.2單位根檢驗觀察LC、LX、LP的圖形，如下所示:LC圖4.1 LC的曲線圖LP圖4.2 LP的曲線圖LX圖4.3 LX 的曲線圖對三個變量選取相應(yīng)的形式進行單位根檢驗表4.1各變量單位根檢驗結(jié)果變量水平值檢驗結(jié)果一階差分檢驗結(jié)果檢驗形式ADFP檢驗形式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綜上，三個變量在5%的顯著水平上都不

5、平穩(wěn)， 但一階差分平穩(wěn)，因此三個序列都為一階單整過程4.3協(xié)整檢驗由于變量LP存在截距和趨勢，因此選擇第二類形式，且變量無明顯的時間特征，因此選擇第三種形式作為協(xié)整檢驗形式。根據(jù)信息準(zhǔn)則以及殘差進行滯后階數(shù)的確定，當(dāng)滯后階數(shù)為1時，AIC=-7.137759,SC=-6.790499;當(dāng)滯后階數(shù)為 2時，AIC=-7.538003, SC= -6.930299;當(dāng)滯后階數(shù)為 3時，AIC=-7.679420, SC= -6.811272。故此處選擇滯后二階為最優(yōu)滯后階數(shù)。選擇滯后階數(shù)為2,且第三種形式進行協(xié)整檢驗，檢驗結(jié)果如下：表4.2協(xié)整檢驗結(jié)果Date: 12/10/14 Time: 22

6、:06Sample (adjusted): 1999M04 2014M10Included observations: 154 after adjustmentsTrend assumption: Linear deterministic trendSeries: LOP LX LCLags interval (in first differences): 1 to 2Unrestricted Cointegration Rank Test (Trace)HypothesizedTraceStatistic0.05Critical ValueProb.*No. of CE(s)Eigenval

7、ueNone *0.15105633.1684229.797070.0197At 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 R

8、ank Test (Maximum Eigenvalue)HypothesizedMax-EigenStatistic0.05Critical ValueProb.*No. of CE(s)EigenvalueNone *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 r

9、ejection of the hypothesis at the 0.05 level*MacKinnon-Haug-Michelis (1999) p-valuesUnrestricted Cointegrating Coefficients (normalized by b*S11*b=l):LOPLXLC3.411003-1.86888620.027881.723127-0.200519-46.265743.324745-0.2939120.064617Unrestricted Adjustment Coefficients (alpha):D(LOP)-0.0146380.00202

10、70.000749D(LX)0.1916330.0132010.001944D(LC)3.22E-050.001393-3.99E-061 Cointegrating Equation(s):Log likelihood642.0482Normalized cointegrating coefficients (standard error in parentheses)LOPLXLC(0.06584)(2.89701)Adjustment coefficients (standard error in parentheses)D(LOP)-0.049930(0.02075)D(LX)0.65

11、3660(0.13759)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

12、.026950(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，跡檢驗和極大特征值檢驗結(jié)果均顯示存在一個協(xié)整關(guān)系。協(xié)整序列的圖形和單位根 檢驗結(jié)果如下：表4.3協(xié)整序列的單位根檢驗結(jié)果Null Hypothesis: COINTEQ01 has a unit rootExogenous: NoneLag Length: 1 (Automatic - based on SIC, maxlag=13)t-StatisticProb.*Augm

13、ented 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，該協(xié)整序列是平穩(wěn)的，即各變量之間存在協(xié)整關(guān)系。該協(xié)整方程具體為：LC =0.17LP -0.09LX + tLP與LC呈現(xiàn)正向波動，LX與LP及LX與LC呈現(xiàn)負(fù)向波動，即房地產(chǎn)價格與物價指數(shù)是正相關(guān)關(guān)系, 凈出口與房價呈現(xiàn)負(fù)相關(guān)關(guān)系，凈出口與國內(nèi)物價水平呈現(xiàn)負(fù)相關(guān)關(guān)系，

14、符合一般的經(jīng)濟學(xué)理論，故 該協(xié)整方程較為合理。4.3 VECM模型的估計估計結(jié)果如下：表4.4 VECM模型的估計結(jié)果Vector Error Correction EstimatesSample (adjusted): 1999M04 2014M10Included observations: 154 after adjustmentsStandard errors in ( ) & t-statistics in Cointegrating Eq:CointEq1LC(-1)LP(-1)LX(-1)C1.0000000.170313(0.04957)3.43554-0.093314(0.0

15、1781)-5.23803-4.731936Error Correction:D(LC)D(LP)D(LX)CointEq10.000645-0.2931653.837997(0.01032)(0.12185)(0.80788)0.06244-2.406044.75072D(LC(-1)0.1380640.168840-12.33234(0.08462)(0.99882)(6.62253)1.631610.16904-1.86218D(LC(-2)0.0677240.101383-2.543282(0.08694)(1.02626)(6.80446)0.778950.09879-0.37377

16、D(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)0.000433-0.0243870.011625(0.00077)(0.009

17、06)(0.06010)0.56372-2.690650.19344C4.96E-050.0161370.036033(0.00053)(0.00621)(0.04116)0.094382.599570.87546R-squared0.0416690.3520280.352984Adj. R-squared-0.0042780.3209610.321963Sum sq. resids0.0059730.83219436.58429S.E. equation0.0063960.0754980.500577F-statistic0.90688611.3312111.37876Log likelih

18、ood563.6108183.4729-107.8418Akaike 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 covariance4.80E-08Log likelihood642.0482Akaike information

19、criterion-7.987639Schwarz criterion-7.4551864.4 VECM模型的檢驗F面進行殘差的自相關(guān)性的檢驗，檢驗結(jié)果如下:Cor(LC 丄 C(-i)Autocorrelations with 2 Std.Err. BoundsCor(LC 丄 P(-i)Cor(LC, LX(-i)圖4.5 VECM模型各方程殘差項的自相關(guān)圖觀察殘差自身的自相關(guān)圖，可以看出均不存在自相關(guān)性。4.5 VECM模型的預(yù)測20002002200420062008201020122014ActualLP (Baseline)LCLXActualLC (Baseline)Actual

20、LX (Baseline)LPActualLP (Baseline)由上圖可以看出VECM基本可以擬合出原序列變動趨勢20184.6 施加約束條件后的 VECM模型VECM模型的方程形式如下：Estimation Proc:14EC(C,1) 1 2 LC LP LX1220002002200420062008201020122014ActualLX (Basel ine)VAR Model:D(LC) = 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

21、(-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) + 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)

22、+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) = 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

23、.000559987514795*D(LP(-2) + 0.000146302892643*D(LX(-1) + 0.000432856871581*D(LX(-2) + 4.96362755959e-05D(LP) = - 0.293165434596*( 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(

24、LP(-2) -0.027721572201*D(LX(-1) - 0.0243873548642*D(LX(-2) + 0.0161371977625D(LX) = 3.83799662293*( LC(-1) + 0.170312756574*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) +

25、 0.0116247131163*D(LX(-2) + 0.0360329193473由于協(xié)整方程中各變量都較為顯著，故此處不加以估計施加約束條件的VECM。第五部分 模型應(yīng)用5.1 脈沖響應(yīng)下圖是基于三變量的 VECM模型模擬出來的脈沖響應(yīng)函數(shù)，橫軸表示滯后階數(shù)，由于房地長行業(yè)的經(jīng)營周期較長，故將滯后階數(shù)設(shè)定為60；縱軸表示變量之間的響應(yīng)程度，圖中實線部分為計算值。LCLPLXResponse of LC to CholeskyOne S.D. InnovationsResponse of LX to CholeskyOne S.D. Innovations.010LC LPLX.6Resp

26、onse of LP to CholeskyOne S.D. Innovations圖e1015202530354045505560p!One S.D. Innovations5.2方差分解.4LCLPLX10080604020010080604020010080604020051015202530354045505560 LC LP LXVarianee Decompositionof LPLC LP LXVarianee Decomposition of LX第六部分結(jié)論根據(jù)以上結(jié)果，我們可以得到以下結(jié)論：1. 我國商品房的銷售價格與前期的銷售價格相關(guān)，我國的CPI、凈出口都是屬于一階單整

27、序列，這符合現(xiàn)實，在經(jīng)濟的運行過程中，存在廣泛的時間滯后效應(yīng)。510152025303540455055602. 房地產(chǎn)市場雖然在很大程度上影響了我國的宏觀經(jīng)濟，但商品房作為一種投資品，對居民消費LCLPLX影響較小，近期房價的頻繁波動并未對我國居民的生活水平產(chǎn)生較大的影響。由以上結(jié)論可以看出，我國應(yīng)調(diào)整產(chǎn)業(yè)結(jié)構(gòu)，減少對房地產(chǎn)市場的依賴程度，特別是減少地方政府的土地財政的現(xiàn)象。出臺連續(xù)的穩(wěn)定的政策以調(diào)整房地產(chǎn)市場，減少市場的波動，穩(wěn)定消費者的預(yù)期，從而使經(jīng)濟得到穩(wěn)定長遠的發(fā)展附錄原始數(shù)據(jù)指標(biāo)房地產(chǎn)開發(fā)企業(yè)商品房銷售面積_累計房地產(chǎn)開發(fā)企業(yè)商品房銷售額累計居民消費價格指數(shù)（上年同月=100）_當(dāng)

28、月出口額_當(dāng)月進口額一當(dāng)月地區(qū)全國全國全國全國全國頻度月月月月月單位萬平方米億元-千美元千美元1999-0198.81139260799033271999-02415.0589.8498.71100005387222421999-031025.73207.898.214877936143780271999-041586.54319.597.814804183138374051999-052146.09440.8397.815531943136572171999-062979.41610.6497.915398063145229551999-073633.96745.0398.617338664

29、139214011999-084287.35871.9298.718325337134464701999-095102.31042.1799.218576263152679991999-106061.591239.9999.418231917137927561999-117062.39144599.119476625169086281999-1213379.352745.549920238657174223922000-0199.816797277152583932000-02636.1144.39100.714775380134286092000-031391.55295.9799.8201

30、46482178135792000-042153.93450.3199.720500392183607952000-052958.13623.65100.120105176169664292000-064073.18844.93100.522192970203014022000-075014.831032.55100.521478509194916282000-086006.881244.7100.323329185207877402000-097088.731460.7410022973290207150342000-108248.81691.741002279997418916401200

31、0-119553.261997.91101.322154881216408812000-1216984.143572101.521986149214142502001-01101.216926471155450072001-02877.96222.4610019198624182256172001-031828.72440.65100.823139003207725262001-042800.78653.78101.622792181218592802001-053795.05898.84101.720813507188087662001-065126.571181.16101.4220810

32、32212515372001-076365.291453.88101.522887692209555002001-087603.851721.1310123540123221615352001-098977.271998.2799.923989367218505982001-1010168.942259.39100.222790526189018092001-1111617.552578.1799.724000007208447712001-1220779.244625.7299.724502579223901052002-019921703291189704172002-02923.7522

33、2.8610019137164159184522002-032152.66514.0399.223817766224841452002-043379.57779.7498.726723688257517112002-054564.61045.4998.924644182224331122002-066279.851445.1799.226012762230941422002-077689.71779.9899.129209981269876552002-089300.172157.0399.329437423272049142002-0911129.092635.499.33191075529

34、7941392002-1012975.93058.8499.229946376251970372002-1115079.363535.8499.331209190287345982002-1224969.295721.2299.631889489287325822003-01100.429775788310159692003-021560.38392.42100.224455585237796572003-033125.42784.69100.932091277325491242003-044632.511147.4310135617074346012082003-056333.161549.

35、95100.733842228316041482003-068672.352101.77100.334475859323361762003-0710657.132574.92100.538109608365136662003-0812628.73058.14100.937415036346213672003-0915189.243736.43101.141940698416523362003-1017447.894309.46101.840925906351925022003-1119950.24898.8610341761968368932862003-1232247.247670.9103

36、.248061529423361762004-01103.235712196357366022004-022221.51578.78102.134157738420297442004-034271.161143.3410345847915463878432004-046200.71641.54103.847124115493741852004-058310.092250.27104.444867889427650262004-0611009.882973.5410550496344486526632004-0713426.583657.49105.351003919489722952004-0

37、815595.974287.05105.351400194469105962004-0918201.775053.88105.255803041508109162004-1020681.635703.89104.352523879454335742004-1123725.516545.73102.860925461510297012004-1238231.6410375.71102.463784483527080302005-01101.950755189442611562005-022596.45807.37103.944273164399162222005-035172.671559.33

38、102.760869119551361122005-047194.272141.72101.862151250575601742005-059484.832796.38101.858426919494385352005-0612536.353727.28101.665959601562819782005-0716526.924938.28101.865584266550385202005-0831202.4710027.37101.368399603578066882005-0934725.611313.3100.970185509626231242005-1039352.1912925.89

39、101.268092010560760192005-1143388.2314430.14101.372217762616872162005-1255769.1418080.3101.675412367643960232006-01101.964988815554968282006-025343.891881.93100.954108294516837182006-039458.713192.7100.878045837668571322006-0413560.874615.35101.276948177664913552006-0518136.966270.04101.473113881601

40、097302006-0622976.627957.48101.581311219668083002006-0727307.989440.0810180337153657135142006-0831384.5910870.72101.390766001719698972006-0935883.3712415.34101.591629488763424742006-1040780.6714053.17101.488127371642975172006-1146113.9316141.36101.995854497729264882006-1260628.1420509.68102.89409405

41、5730967502007-01102.286619731707391992007-025371.472247.9102.782095593583393612007-0310600.774050.75103.383424155765527152007-0415765.165997.3210397449955806042082007-05211488059.75103.494065041715908212007-0627904.1510642.83104.4103268286763582172007-0734137.2413142.44105.6107744104833871892007-084

42、0572.8115820.34106.5111354781863807042007-0947369.7118684.77106.2112373049885672062007-1053564.9621286.95106.5107723989806733332007-1160156.8924002.64106.9117620807913395572007-1276192.729603.87106.5114415986917289812008-01107.1109640030901744472008-025144.152154.75108.787367796788131332008-0310449.

43、564110.53108.3108962891955561422008-0414994.155904.79108.51187710841021026832008-0519633.47837.24107.71204964911002860622008-0625892.6310325.43107.11211795541001799362008-0730453.9612221.17106.31366750461113971472008-0834592.2813813.43104.91348726751061784932008-0940320.7615878.53104.613643208810706

44、52742008-1044722.9617590.03104128327028930876862008-1149148.3819261.19102.4114987285748974702008-1262088.9424071.41101.2111157222721771862009-0110190453600513442642009-025131.232396.9898.464894649600536582009-0311308.745058.6498.890290547717291122009-0417625.457995.9298.591934722787996872009-0524644

45、.4411388.9298.688757886753693562009-0634108.5915799.5798.395411208871595452009-0741754.9819599.5998.2105420240947905832009-0849416.0423463.7498.8103707009879952342009-0958371.0227531.8999.21159379941030058712009-1066368.7331529.1299.5110762383867747492009-1175203.1535987.12100.6113653429945604312009

46、-1293713.0443994.54101.91307238811122937132010-01101.53109475299953070472010-027155.184115.74102.794522714869103332010-0315360.927976.8102.371121117931193480922010-0423412.1612425.24102.811199206661182394622010-0530189.4315760.19103.061317606631122277492010-0639352.5319819.85102.95137395578117373726

47、2010-0745818.6122885.69103.31455193221167889342010-0852704.4726418.24103.481393022301192661522010-0963150.2331916.58103.611449852851281103042010-1072428.5536992.28104.371359784191088327012010-1182541.2742277.89105.121533257621304359452010-12104349.1152478.72104.591541488951410688332011-01104.9150734

48、1511442732102011-028142.955241.61104.9967361271040639642011-0317642.7910151.91105.41521990711520603082011-0424897.9214077.73105.31556840841442630812011-0532931.6418620.1105.51571571911441102232011-0644419.3324589.42106.41619807741397081982011-0752037.1228852.11106.51751280361436444272011-0859854.1833264.4106.21733156971555567392011-0971288.7539311.54106.11696730121551590802011-1079653.1243826.24105.51574907721404576982011-1189593.8849046.86104.21744641231599359952011-12109945.5659119.0