VECM模型實(shí)驗(yàn) ——時(shí)間序列

1、基于VECM模型探究中國(guó)房地產(chǎn)市場(chǎng)對(duì)中國(guó)經(jīng)濟(jì)增長(zhǎng)的影響VECM模型實(shí)驗(yàn)姓名;何毛毛班級(jí)：國(guó)際金融試驗(yàn)班第一部分 實(shí)驗(yàn)背景自1992年中國(guó)逐步確立市場(chǎng)經(jīng)濟(jì)以來(lái)的20多年里，投資，消費(fèi)，出口“三駕馬車”理論對(duì)我國(guó)經(jīng)濟(jì)增長(zhǎng)的巨大作用。政府?dāng)U大了對(duì)基礎(chǔ)設(shè)施建設(shè)的投資，以及中國(guó)的出口保持的高速增長(zhǎng)態(tài)勢(shì)，對(duì)經(jīng)濟(jì)增長(zhǎng)的拉動(dòng)起到了很大的作用。第二部分 實(shí)驗(yàn)分析目的及方法故本文選取了商品房?jī)r(jià)格、居民消費(fèi)指數(shù)以及凈出口三個(gè)變量構(gòu)建VEC模型，進(jìn)行協(xié)整檢驗(yàn)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(guó)現(xiàn)有數(shù)據(jù)現(xiàn)狀進(jìn)行分析，得出房地產(chǎn)市場(chǎng)對(duì)我國(guó)經(jīng)濟(jì)的影響。第三部分 實(shí)驗(yàn)樣本3.1數(shù)據(jù)來(lái)源數(shù)據(jù)來(lái)源于中經(jīng)網(wǎng)統(tǒng)計(jì)數(shù)

2、據(jù)庫(kù)。3.2所選數(shù)據(jù)變量由于國(guó)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(jìn)口額、CPI、房地產(chǎn)開(kāi)發(fā)企業(yè)商品房銷售面積及其銷售額的累積額五個(gè)變量以月為單位的數(shù)據(jù)進(jìn)行一定的處理得到商品房?jī)r(jià)格P、居民消費(fèi)指數(shù)CPI以及凈出口X三個(gè)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?jī)r(jià)格由于商品房?jī)r(jià)格有較強(qiáng)的地域差異，故此處采用了較為簡(jiǎn)單的處理方法。取用房地產(chǎn)開(kāi)發(fā)企業(yè)商品房銷售面積以及房地產(chǎn)開(kāi)發(fā)企業(yè)商品房銷售額的累計(jì)額，而由于我國(guó)不單獨(dú)對(duì)1月份統(tǒng)計(jì)數(shù)據(jù)進(jìn)行調(diào)查，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)，

3、屬于非隨機(jī)、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(bǔ)全數(shù)據(jù)后在每一年度進(jìn)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(guó)內(nèi)市場(chǎng)上商品房的平均價(jià)格序列P。由于序列P有較強(qiáng)的趨勢(shì)性，為了平滑房?jī)r(jià)的變動(dòng)趨勢(shì)，對(duì)P做對(duì)數(shù)化處理記為L(zhǎng)P。4.1.2 凈出口由于現(xiàn)有數(shù)據(jù)僅為出口額、進(jìn)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(jì)量。此外為了平滑凈出口的變動(dòng)趨勢(shì)，對(duì)X同樣也做對(duì)數(shù)化處理記為L(zhǎng)X。4.1.2 CPI由于CPI為相對(duì)數(shù)，為了減少基期的影響以及減少異方差性，對(duì)CPI進(jìn)行對(duì)數(shù)化處理記為L(zhǎng)C。4.2 單位根檢驗(yàn)觀察LC、LX、LP的圖形，如下所示：圖4.1 LC的曲線圖圖

4、4.2 LP的曲線圖圖4.3 LX的曲線圖對(duì)三個(gè)變量選取相應(yīng)的形式進(jìn)行單位根檢驗(yàn).表4.1 各變量單位根檢驗(yàn)結(jié)果變量水平值檢驗(yàn)結(jié)果一階差分檢驗(yàn)結(jié)果檢驗(yàn)形式ADFP檢驗(yàn)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(gè)變量在5%的顯著水平上都不平穩(wěn)，但一階差分平穩(wěn)，因此三個(gè)序列都為一階單整過(guò)程。4.3協(xié)整檢驗(yàn)由于變量LP存在截距和趨勢(shì)，因此選擇

5、第二類形式，且變量無(wú)明顯的時(shí)間特征，因此選擇第三種形式作為協(xié)整檢驗(yàn)形式。根據(jù)信息準(zhǔn)則以及殘差進(jìn)行滯后階數(shù)的確定，當(dāng)滯后階數(shù)為1時(shí)，AIC=-7.137759, SC=-6.790499; 當(dāng)滯后階數(shù)為2時(shí)，AIC= -7.538003, SC= -6.930299; 當(dāng)滯后階數(shù)為3時(shí)，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(jìn)行協(xié)整檢驗(yàn)，檢驗(yàn)結(jié)果如下：表4.2 協(xié)整檢驗(yàn)結(jié)果Date: 12/10/14 Time: 22:06Sample (adjusted): 1999M04 2014M10Included o

6、bservations: 154 after adjustmentsTrend assumption: Linear deterministic trendSeries: LOP LX LC Lags interval (in first differences): 1 to 2Unrestricted Cointegration Rank Test (Trace)HypothesizedTrace0.05No. of CE(s)EigenvalueStatisticCritical ValueProb.*None * 0.151056 33.16842 

7、;29.79707 0.0197At most 1 0.050178 7.948982 15.49471 0.4709At most 2 0.000136 0.021007 3.841466 0.8847 Trace test indicates 1 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level *MacKinnon-Haug-Mic

8、helis (1999) p-valuesUnrestricted Cointegration Rank Test (Maximum Eigenvalue)HypothesizedMax-Eigen0.05No. of CE(s)EigenvalueStatisticCritical ValueProb.*None * 0.151056 25.21943 21.13162 0.0125At most 1 0.050178 7.927975 14.26460 0.3861At most 2 0.000136

9、 0.021007 3.841466 0.8847 Max-eigenvalue 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-values Unrestricted Cointegrating Coefficients (normalized by b'*S11*b=I):

10、 LOPLXLC 3.411003-1.868886 20.02788 1.723127-0.200519-46.26574 3.324745-0.293912 0.064617 Unrestricted Adjustment Coefficients (alpha): D(LOP)-0.014638 0.002027 0.000749D(LX) 0.191633 0.013201 0.001944D(LC) 3.22E-05 0.001393-

11、3.99E-061 Cointegrating Equation(s): Log likelihood 642.0482Normalized cointegrating coefficients (standard error in parentheses)LOPLXLC 1.000000-0.547899 5.871551 (0.06584) (2.89701)Adjustment coefficients (standard error in parentheses)D(LOP)-0.049930 (0.02075)D(

12、LX) 0.653660 (0.13759)D(LC) 0.000110 (0.00176)2 Cointegrating Equation(s): Log likelihood 646.0122Normalized cointegrating coefficients (standard error in parentheses)LOPLXLC 1.000000 0.000000-35.67378 (11.2063) 0.000000 1.000000-75.82659 (

13、21.1778)Adjustment coefficients (standard error in parentheses)D(LOP)-0.046437 0.026950 (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(yàn)和極大特征值檢驗(yàn)結(jié)果均顯示存在一個(gè)協(xié)整關(guān)系。協(xié)整序列的圖形和單位根檢驗(yàn)結(jié)果如下：圖4.4 協(xié)整序列變動(dòng)圖表

14、4.3 協(xié)整序列的單位根檢驗(yàn)結(jié)果Null Hypothesis: COINTEQ01 has a unit rootExogenous: NoneLag Length: 1 (Automatic - based on SIC, maxlag=13)t-Statistic  Prob.*Augmented Dickey-Fuller test statistic-5.020825 0.0000Test critical values:1% level-2.5818275% level-1.94315710% level-1.615178*MacKinnon (199

15、6) 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(dòng)，LX與LP及LX與LC呈現(xiàn)負(fù)向波動(dòng)，即房地產(chǎn)價(jià)格與物價(jià)指數(shù)是正相關(guān)關(guān)系，凈出口與房?jī)r(jià)呈現(xiàn)負(fù)相關(guān)關(guān)系，凈出口與國(guó)內(nèi)物價(jià)水平呈現(xiàn)負(fù)相關(guān)關(guān)系，符合一般的經(jīng)濟(jì)學(xué)理論，故該協(xié)整方程較為合理。4.3 VECM模型的估計(jì)估計(jì)結(jié)果如下：表4.4 VECM模型的估計(jì)結(jié)果 Vector Error Correction Estimates Date: 12/10/14 Time: 22:44 Sam

16、ple (adjusted): 1999M04 2014M10 Included observations: 154 after adjustments Standard errors in ( ) & t-statistics in Cointegrating Eq: CointEq1LC(-1) 1.000000LP(-1) 0.170313 (0.04957) 3.43554LX(-1)-0.093314 (0.01781)-5.23803C-4.731936Error Correction:D(LC)D(LP

17、)D(LX)CointEq1 0.000645-0.293165 3.837997 (0.01032) (0.12185) (0.80788) 0.06244-2.40604 4.75072D(LC(-1) 0.138064 0.168840-12.33234 (0.08462) (0.99882) (6.62253) 1.63161 0.16904-1.86218D(LC(-2) 0.067724 0.101383-2.543282 (0.08694) 

18、(1.02626) (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.

19、266886 (0.00107) (0.01265) (0.08387) 0.13653-2.19159-3.18223D(LX(-2) 0.000433-0.024387 0.011625 (0.00077) (0.00906) (0.06010) 0.56372-2.69065 0.19344C 4.96E-05 0.016137 0.036033 (0.00053) (0.00621) (0.04116) 0.09438 2.59957 0.8754

20、6 R-squared 0.041669 0.352028 0.352984 Adj. R-squared-0.004278 0.320961 0.321963 Sum sq. resids 0.005973 0.832194 36.58429 S.E. equation 0.006396 0.075498 0.500577 F-statistic 0.906886 11.33121 11.37876

21、60;Log likelihood 563.6108 183.4729-107.8418 Akaike AIC-7.215725-2.278869 1.504439 Schwarz SC-7.057961-2.121105 1.662203 Mean dependent 0.000121 0.009293 0.023850 S.D. dependent 0.006382 0.091620 0.607917 Determinant resid co

22、variance (dof adj.) 5.63E-08 Determinant resid covariance 4.80E-08 Log likelihood 642.0482 Akaike information criterion-7.987639 Schwarz criterion-7.4551864.4 VECM模型的檢驗(yàn)下面進(jìn)行殘差的自相關(guān)性的檢驗(yàn)，檢驗(yàn)結(jié)果如下：圖4.5 VECM模型各方程殘差項(xiàng)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(cè)由上圖可以看出VECM基本可以

23、擬合出原序列變動(dòng)趨勢(shì)。4.6 施加約束條件后的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) = 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

24、)*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(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)*

25、D(LP(-2) + C(3,5)*D(LX(-1) + C(3,6)*D(LX(-2) + C(3,7)VAR Model - Substituted Coefficients:=0329193473由于協(xié)整方程中各變量都較為顯著，故此處不加以估計(jì)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(lái)的脈沖響應(yīng)函數(shù)，橫軸表示滯后階數(shù)，由于房地長(zhǎng)行業(yè)的經(jīng)營(yíng)周期較長(zhǎng)，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(shí)線部分為計(jì)算值。圖5.1 脈沖響應(yīng)圖5.2方差分解 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(guó)商品房的銷售價(jià)格與前期

26、的銷售價(jià)格相關(guān)，我國(guó)的CPI、凈出口都是屬于一階單整序列，這符合現(xiàn)實(shí)，在經(jīng)濟(jì)的運(yùn)行過(guò)程中，存在廣泛的時(shí)間滯后效應(yīng)。2. 房地產(chǎn)市場(chǎng)雖然在很大程度上影響了我國(guó)的宏觀經(jīng)濟(jì)，但商品房作為一種投資品，對(duì)居民消費(fèi)影響較小，近期房?jī)r(jià)的頻繁波動(dòng)并未對(duì)我國(guó)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(guó)應(yīng)調(diào)整產(chǎn)業(yè)結(jié)構(gòu)，減少對(duì)房地產(chǎn)市場(chǎng)的依賴程度，特別是減少地方政府的土地財(cái)政的現(xiàn)象。出臺(tái)連續(xù)的穩(wěn)定的政策以調(diào)整房地產(chǎn)市場(chǎng)，減少市場(chǎng)的波動(dòng)，穩(wěn)定消費(fèi)者的預(yù)期，從而使經(jīng)濟(jì)得到穩(wěn)定長(zhǎng)遠(yuǎn)的發(fā)展。附錄原始數(shù)據(jù)指標(biāo)房地產(chǎn)開(kāi)發(fā)企業(yè)商品房銷售面積_累計(jì)房地產(chǎn)開(kāi)發(fā)企業(yè)商品房銷售額_累計(jì)居民消費(fèi)價(jià)格指數(shù)(上年同月=100)_當(dāng)月

27、出口額_當(dāng)月進(jìn)口額_當(dāng)月地區(qū)全國(guó)全國(guó)全國(guó)全國(guó)全國(guó)頻度月月月月月單位萬(wàn)平方米億元-千美元千美元1999-0198.81139260799033271999-02415.0589.8498.71100005387222421999-031025.73207.898.214877936143780271999-041586.54319.597.814804183138374051999-052146.09440.8397.815531943136572171999-062979.41610.6497.915398063145229551999-073633.96745.0398.6173386641

28、39214011999-084287.35871.9298.718325337134464701999-095102.31042.1799.218576263152679991999-106061.591239.9999.418231917137927561999-117062.39144599.119476625169086281999-1213379.352745.549920238657174223922000-0199.816797277152583932000-02636.1144.39100.714775380134286092000-031391.55295.9799.82014

29、6482178135792000-042153.93450.3199.720500392183607952000-052958.13623.65100.120105176169664292000-064073.18844.93100.522192970203014022000-075014.831032.55100.521478509194916282000-086006.881244.7100.323329185207877402000-097088.731460.7410022973290207150342000-108248.81691.7410022799974189164012000

30、-119553.261997.91101.322154881216408812000-1216984.143572101.521986149214142502001-01101.216926471155450072001-02877.96222.4610019198624182256172001-031828.72440.65100.823139003207725262001-042800.78653.78101.622792181218592802001-053795.05898.84101.720813507188087662001-065126.571181.16101.42208103

31、2212515372001-076365.291453.88101.522887692209555002001-087603.851721.1310123540123221615352001-098977.271998.2799.923989367218505982001-1010168.942259.39100.222790526189018092001-1111617.552578.1799.724000007208447712001-1220779.244625.7299.724502579223901052002-019921703291189704172002-02923.75222

32、.8610019137164159184522002-032152.66514.0399.223817766224841452002-043379.57779.7498.726723688257517112002-054564.61045.4998.924644182224331122002-066279.851445.1799.226012762230941422002-077689.71779.9899.129209981269876552002-089300.172157.0399.329437423272049142002-0911129.092635.499.331910755297

33、941392002-1012975.93058.8499.229946376251970372002-1115079.363535.8499.331209190287345982002-1224969.295721.2299.631889489287325822003-01100.429775788310159692003-021560.38392.42100.224455585237796572003-033125.42784.69100.932091277325491242003-044632.511147.4310135617074346012082003-056333.161549.9

34、5100.733842228316041482003-068672.352101.77100.334475859323361762003-0710657.132574.92100.538109608365136662003-0812628.73058.14100.937415036346213672003-0915189.243736.43101.141940698416523362003-1017447.894309.46101.840925906351925022003-1119950.24898.8610341761968368932862003-1232247.247670.9103.

35、248061529423361762004-01103.235712196357366022004-022221.51578.78102.134157738420297442004-034271.161143.3410345847915463878432004-046200.71641.54103.847124115493741852004-058310.092250.27104.444867889427650262004-0611009.882973.5410550496344486526632004-0713426.583657.49105.351003919489722952004-08

36、15595.974287.05105.351400194469105962004-0918201.775053.88105.255803041508109162004-1020681.635703.89104.352523879454335742004-1123725.516545.73102.860925461510297012004-1238231.6410375.71102.463784483527080302005-01101.950755189442611562005-022596.45807.37103.944273164399162222005-035172.671559.331

37、02.760869119551361122005-047194.272141.72101.862151250575601742005-059484.832796.38101.858426919494385352005-0612536.353727.28101.665959601562819782005-0716526.924938.28101.865584266550385202005-0831202.4710027.37101.368399603578066882005-0934725.611313.3100.970185509626231242005-1039352.1912925.891

38、01.268092010560760192005-1143388.2314430.14101.372217762616872162005-1255769.1418080.3101.675412367643960232006-01101.964988815554968282006-025343.891881.93100.954108294516837182006-039458.713192.7100.878045837668571322006-0413560.874615.35101.276948177664913552006-0518136.966270.04101.4731138816010

39、97302006-0622976.627957.48101.581311219668083002006-0727307.989440.0810180337153657135142006-0831384.5910870.72101.390766001719698972006-0935883.3712415.34101.591629488763424742006-1040780.6714053.17101.488127371642975172006-1146113.9316141.36101.995854497729264882006-1260628.1420509.68102.894094055

40、730967502007-01102.286619731707391992007-025371.472247.9102.782095593583393612007-0310600.774050.75103.383424155765527152007-0415765.165997.3210397449955806042082007-05211488059.75103.494065041715908212007-0627904.1510642.83104.4103268286763582172007-0734137.2413142.44105.6107744104833871892007-0840

41、572.8115820.34106.5111354781863807042007-0947369.7118684.77106.2112373049885672062007-1053564.9621286.95106.5107723989806733332007-1160156.8924002.64106.9117620807913395572007-1276192.729603.87106.5114415986917289812008-01107.1109640030901744472008-025144.152154.75108.787367796788131332008-0310449.5

42、64110.53108.3108962891955561422008-0414994.155904.79108.51187710841021026832008-0519633.47837.24107.71204964911002860622008-0625892.6310325.43107.11211795541001799362008-0730453.9612221.17106.31366750461113971472008-0834592.2813813.43104.91348726751061784932008-0940320.7615878.53104.6136432088107065

43、2742008-1044722.9617590.03104128327028930876862008-1149148.3819261.19102.4114987285748974702008-1262088.9424071.41101.2111157222721771862009-0110190453600513442642009-025131.232396.9898.464894649600536582009-0311308.745058.6498.890290547717291122009-0417625.457995.9298.591934722787996872009-0524644.

44、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-

45、1293713.0443994.54101.91307238811122937132010-01101.53109475299953070472010-027155.184115.74102.794522714869103332010-0315360.927976.8102.371121117931193480922010-0423412.1612425.24102.811199206661182394622010-0530189.4315760.19103.061317606631122277492010-0639352.5319819.85102.951373955781173737262

466122885.69103.31455193221167889342010-0852704.4726418.24103.481393022301192661522010-0963150.2331916.58103.611449852851281103042010-1072428.5536992.28104.371359784191088327012010-1182541.2742277.89105.121533257621304359452010-12104349.1152478.72104.591541488951410688332011-01104.91507341

47、511442732102011-028142.955241.61104.9967361271040639642011-0317642.7910151.91105.41521990711520603082011-0424897.9214077.73105.31556840841442630812011-0532931.6418620.1105.51571571911441102232011-0644419.3324589.42106.41619807741397081982011-0752037.1228852.11106.51751280361436444272011-0859854.1833264.4106.21733156971555567392011-0971288.7539311.54106.11696730121551590802011-1079653.1243826.24105.51574907721404576982011-1189593.8849046.86104.21744641231599359952011-12109945.5659119.09104.11747176511581968892012-0