stata-誤差修正模型講解

Axt=aAxt=a+byx21t—1+bx+pAy22t—121t—1+pAx22t—1+82t誤差修正模型：如果用兩個(gè)變量，人均消費(fèi)y和人均收入x（從格林的數(shù)據(jù)獲得）來研究誤差修正模型。令z=（yx）'，則模型為：Az=A+兀z+壬pAz+￡t0t—1it—1ti=1其中，兀=ap'如果令k=1，即滯后項(xiàng)為1,則模型為Az=A+兀z+pAz+8t0t—11t—1t實(shí)際上為兩個(gè)方程的估計(jì)：Ayt=a+by+bxy11t—1Ayt=a+by+bxy11t—112t—111t—112t—11t用ols命令做出的結(jié)果：gent=_ntssetttimevariable:t,1to204genly=L.y(1missingvaluegenerated)genlx=L.x(1missingvaluegenerated)regD.ylylxD.lyD.lxSource|SSdfMSModel|37251.2525Residual|87073.315449312.81313197441.996525Source|SSdfMSModel|37251.2525Residual|87073.315449312.81313197441.996525-+Total|124324.568201618.530189Numberofobs=202F(4,197)=21.07

Prob>F=0.0000R-squared=0.2996AdjR-squared=0.2854RootMSE=21.024D.y|_l_Coef.Std.Err.tP>|t|[95%Conf.Interval]1ly|.0417242.01875532.220.027.0047371.0787112lx|-.0318574.0171217-1.860.064-.0656228.001908ly|D1.|.1093189.0823681.330.186-.0531173.2717552lx|D1.|.0792758.05669661.400.164-.0325344.1910861cons12.5335043.7571580.670.501-4.8759099.942916這是Ay=a+by+bty11t—112x+pAyt—111t—1+p12Ax+8t—11t的回歸結(jié)果，其中a=2.5335y

b11=0.04172，b12=-0.03186，p11=0.10932，p12=0.07928同理可得Ax=a+by+bx+pAy+pAx+s的回歸結(jié)果，見下tx21t-122t121t-122t-12tregD.xlylxD.lyD.lxSource|SSdfMSNumberofobs=202_l__F(4,197)=11.181Model|36530.279549132.56988Prob>F=0.0000Residual|160879.676197816.648101R-squared=0.1850_l__AdjR-squared=0.16851Total|197409.955201982.139082RootMSE=28.577D.x|Coef.Std.Err.tP>|t|[95%Conf.Interval]1ly|.037608.02549371.480.142-.0126676.0878836lx|-.0307729.0232732-1.320.188-.0766694.0151237ly|D1.|.4149475.1119613.710.000.1941517.6357434lx|D1.|-.1812014.0770664-2.350.020-.3331825-.0292203cons|11.201865.107022.190.0291.13041921.27331如果用vec命令vecyx,piVectorerror-correctionmodelSample:3-204R-sqNo.ofobs=AICHQICSBIC202=18.29975=18.35939=18.44715Loglikelihood=-1839.275RMSEDet(Sigma_ml)=Equation277863.4Parmschi2P>chi2D_y420.97060.6671396.78180.0000D_x428.52330.5328225.83130.0000|Coef.Std.Err.zP>|z|[95%Conf.Interval]D_y1|_ce1|L1.|.0418615.00692156.050.000.0282956.0554273y|LD.|VI.1091985.08073141.350.176-.0490323.2674292x|LD.|.0793652.0554111.430.152-.0292384.1879687_cons|-3.6022793.759537-0.960.338-10.970843.766278D_x1|_ce1|L1.|.0256414.00941432.720.006.0071897.044093y|LD.|vI.4254495.10980753.870.000.2102308.6406683x|LD.|-.1889879.0753677-2.510.012-.3367058-.04127_cons|5.8809935.1135621.150.250-4.14140515.90339這里_celL1顯示的是速度調(diào)整參數(shù)a的估計(jì)值，上述結(jié)果沒有n的估計(jì)，而是在下面的表格中。Cointegratingequations協(xié)整公式EquationParmschi2P>chi2_ce11853.90780.0000Identification:betaisexactlyidentifiedJohansennormalizationrestrictionimposedbeta|Coef.Std.Err.zP>|z|[95%Conf.Interval]+_ce1|y|1....x|-.764085.0261479-29.220.000-.8153339-.7128362_cons|146.9988....上表中beta顯示的B的估計(jì)值。ImpactparametersEquationParmschi2P>chi2D_y136.578960.0000D_x17.4183360.0065D_y136.578960.0000D_x17.4183360.0065Pi|Coef.Std.Err.zP>|z|[95%Conf.Interval]+D_y|y|L1.|vI.0418615.00692156.050.000.0282956.0554273x|L1.|-.0319857.0052886-6.050.000-.0423512-.0216203D_x|y|L1.|VI.0256414.00941432.720.006.0071897.044093x|L1.|-.0195922.0071933-2.720.006-.0336908-.0054935命令pi顯示n的估計(jì)值，上表中顯示，在第一個(gè)方程中協(xié)整向量n中，y的L1（滯后一期）的估計(jì)值為0.0418615,x的L1（滯后一期）的估計(jì)值為-0.0319857，這與ols估計(jì)的b]]=0.04172,b12=-0.03186很類似；在第二個(gè)方程中協(xié)整向量n的估計(jì)與ols估計(jì)的有些差別，可能暗示第二個(gè)方程對(duì)均衡誤差沒有反應(yīng)。

檢驗(yàn)協(xié)整向量的秩vecrankyxTrend:constantSample:檢驗(yàn)協(xié)整向量的秩vecrankyxTrend:constantSample:3-204JohansentestsforcointegrationNumberofobs=202Lags=25%maximumtracecriticalrankparmsLLeigenvaluestatisticvalue06-1856.3997.34.578415.4119-1839.27460.155960.3282*3.76210-1839.11050.00162tracestatistic表明拒絕rank(n)=0的假設(shè)，但是不能拒絕rank(n)=1的假設(shè)，所以人均消費(fèi)和人均收入的模型中，協(xié)整向量的秩為1。也表明人均消費(fèi)和人均收入符合誤差修正模型。(不在第一個(gè)上就說明至少有一個(gè)協(xié)整關(guān)系)vecyx,alal顯示a的估計(jì)值，即速度調(diào)整參數(shù)的估計(jì)AdjustmentparametersD_y136.578960.0000D_x17.4183360.0065EquationParmschi2P>chi2D_y136.578960.0000D_x17.4183360.0065alpha|Coef.Std.Err.zP>|z|[95%Conf.Interval]+D_y|_ce1|L1.|.0418615.00692156.050.000.0282956.0554273+D_x|_ce1|L1.|.0256414.00941432.720.006.0071897.044093而B矩陣的估計(jì)為:beta|Coef.Std.Err.zP>|z|[95%Conf.Interval]_ce11|y|1x|-.764085.0261479-29.220.000-.8153339-.7128362_cons|146.9988即146.9988+y-0.764085x=0而aB'即為n，即a'=(0.04186150.0256414),B'=(1-0.764085),n的第一行即為第一個(gè)方程中的n的估計(jì)值(0.0418615-0.0319857)其中，0.0418615*(-0.764085)=-0.0319857n的第二行即為第二個(gè)方程中的n的估計(jì)值(0.0256414-0.0195922)Pi|Coef.Std.Err.zP>|z|[95%Conf.Interval]+D_y|y|L1.|vI.0418615.00692156.050.000.0282956.0554273x|L1.|-.0319857.0052886-6.050.000-.0423512-.0216203D_x|y|L1.|VI.0256414.00941432.720.006.0071897.044093x|L1.|-.0195922.0071933-2.720.006-.0336908-.0054935此時(shí)雖然B矩陣的估計(jì)中有截距項(xiàng)，但在n的顯示結(jié)果中沒有截距項(xiàng)，此時(shí)截距項(xiàng)被放在誤差修正模型中了。如果用t(rc)命令，則截距項(xiàng)出現(xiàn)在n中，而誤差修正模型中沒有截距項(xiàng)。vecyx,t(rc)pialVectorerror-correctionmodelSample:3-204No.ofobs=202如果用t(rc)命令，則截距項(xiàng)出現(xiàn)在n中，而誤差修正模型中沒有截距項(xiàng)。vecyx,t(rc)pialVectorerror-correctionmodelSample:3-204No.ofobs=202Loglikelihood=-1841.164Det(Sigma_ml)=283111.1AICHQICSBIC=18.30856=18.36157=18.43958EquationParmsRMSER-sqchi2P>chi2D_y3D_x320.93290.6666395.92590.000028.59720.5280221.52310.0000|Coef.Std.Err.zP>|z|[95%Conf.Interval]+D_y|_ce1|L1.|"1.041464.00458949.030.000.0324688.0504591y|LD.|vI.1128688.08018051.410.159-.044282.2700196x|LD.|.0765203.0547461.400.162-.0307799.1838205D_x|_ce1|L1.|"1.0386104.00626986.160.000.0263218.050899y|LD.|vI.4012721.10953773.660.000.1865822.6159621x|LD.|-.1705861.0747907-2.280.023-.3171732-.0239991CointegratingequationsEquationParmschi2P>chi2_ce11924.11230.0000Identification:betaisexactlyidentifiedJohansennormalizationrestrictionimposedbeta|Coef.Std.Err.zP>|z|[95%Conf.Interval]+_ce1|y|1....x|-.773902.025458-30.400.000-.8237986-.7240053_cons|105.683881.372551.300.194-53.8035265.171AdjustmentparametersEquationParmschi2P>chi2D_y181.624980.0000D_x137.922710.0000alpha|Coef.Std.Err.zP>|z|[95%Conf.Interval]+D_y|_ce1|L1.|.041464.00458949.030.000.0324688.0504591+D_x|_ce1|L1.|.0386104.00626986.160.000.0263218.050899ImpactparametersEquationParmschi2P>chi2D_y181.624980.0000D_x137.922710.0000D_y181.624980.0000D_x137.922710.0000Pi|Coef.Std.Err.zP>|z|[95%Conf.Interval]D_y1|y|L1.|VI.041464.00458949.030.000.0324688.0504591x|L1.|-.032089.0035518-9.030.000-.0390504-.0251277_cons|4.382067.48502889.030.0003.4314285.332706

+D_x|y|L1.|VI.0386104.00626986.160.000.0263218.050899x|L1.|-.0298806.0048522-6.160.000-.0393908-.0203705_cons|4.080489.66261696.160.0002.7817845.379194此時(shí)在n的矩陣估計(jì)中，有截距項(xiàng)，但是在誤差修正模型中沒有截距項(xiàng)。如果用t(rt)命令，在協(xié)整向量B中有趨勢(shì)項(xiàng)的估計(jì)(即對(duì)時(shí)間t的系數(shù)的估計(jì))，而在整個(gè)誤差修正模型中沒有趨勢(shì)項(xiàng)，但是有截距項(xiàng)的估計(jì)。在T的估計(jì)中，只有趨勢(shì)項(xiàng)，沒有截距項(xiàng)，因?yàn)榻鼐囗?xiàng)的估計(jì)已經(jīng)包含在誤差修正模型中了。vecyx,t(rt)pialVectorerror-correctionmodelSample:3-204No.ofobs=202AIC=18.2926Loglikelihood=-1837.553HQIC=18.35887Det(Sigma_ml)=273167.6SBIC=18.45638EquationParmsRMSER-sqchi2P>chi2D_y420.87350.6702400.2960.0000D_x428.04350.5484239.24240.0000|Coef.Std.Err.zP>|z|[95%Conf.Interval]1D_y|_ce1|L1.|.0769485.012396.210.000.0526645.1012325y|LD.|vI.0861433.08196851.050.293-.0745121.2467986x|LD.|.0989288.05540181.790.074-.0096569.2075144_cons|-2.4439363.5442-0.690.490-9.3904414.5025691D_x|_ce1|L1.|.0632409.0166463.800.000.0306153.0958664y|LD.|VI.3552693.11012473.230.001.1394288.5711098x|LD.|-.1724981.0744324-2.320.020-.3183828-.0266133_cons|2.9736664.7616340.620.532-6.35896512.3063CointegratingequationsEquationParmschi2P>chi2_ce11143.36850.0000

Identification:betaisexactlyidentifiedJohansennormalizationrestrictionimposedbeta|Coef.Std.Err.zP>|z|[95%Conf.Interval]1_ce1|y|1....x|-1.093286.0913076-11.970.000-1.272246-.9143263_trend|6.9237132.4147372.870.0042.19091511.65651_cons|265.9482AdjustmentparametersEquationParmschi2P>chi2D_y138.570540.0000D_x114.433640.0001D_y138.570540.0000D_x114.433640.0001alpha|Coef.Std.Err.zP>|z|[95%Conf.Interval]+D_y|_ce1|L1.|.0769485.012396.210.000.0526645.1012325D_x1|_ce1|L1.|.0632409.0166463.800.000.0306153.0958664

ImpactparametersEquationParmschi2P>chi2D_y138.570540.0000D_x114.433640.0001D_y138.570540.0000D_x114.433640.0001Pi|Coef.Std.Err.zP>|z|[95%Conf.Interval]D_y1|y|L1.|VI.0769485.012396.210.000.0526645.1012325x|L1.|-.0841267.0135458-6.210.000-.110676-.0575773_trend|.5327692.0857856.210.000.3646337.7009046D_x1|y|L1.|vI.0632409.0166463.800.000.0306153.0958664x|L1.|-.0691403.0181988-3.800.000-.1048094-.0334713_trend|.4378615.11525213.800.000.2119715.6637515如果用t(t)命令，在協(xié)整向量B中有趨勢(shì)項(xiàng)和截距項(xiàng)的估計(jì)，在誤差修正模型中也有趨勢(shì)項(xiàng)和截距項(xiàng)的估計(jì)，但在n的估計(jì)中沒有趨勢(shì)項(xiàng)和截距項(xiàng)的估計(jì)vecyx,t(t)pialVectorerror-correctionmodelSample:3-204No.ofobs=202AIC=18.28006Loglikelihood=-1835.286HQIC=18.35295Det(Sigma_ml)=267103.3SBIC=18.46021EquationParmsRMSER-sqchi2P>chi2D_y521.06720.6657392.3350.0000D_x527.70990.5613252.07890.0000|Coef.Std.Err.zP>|z|[95%Conf.Interval]+D_y|_ce1|L1.|"1.0571242.02451162.330.020.0090823.105166y|LD.|7I.1223172.08141531.500.133-.0372539.2818883x|LD.|.087465.05742441.520.128-.0250847.2000147_trend|.0903107.04149892.180.030.0089743.1716471_cons|-.46461323.478827-0.130.894-7.2829896.3537631D_x|_ce1|L1.|"1.1193333.03224033.700.000.0561435.182523y|LD.|7I.3340591.1070863.120.002.1241744.5439439x|LD.|-.1378621.0755306-1.830.068-.2858994.0101751_trend|-.0432312.0545838-0.790.428-.1502134.063751_cons|1.6335194.5757210.360.721-7.3347310.60177CointegratingequationsEquationParmschi2P>chi2EquationParmschi2P>chi2_ce1_ce11249.03470.0000Identification:betaisexactlyidentifiedJohansennormalizationrestrictionimposedbeta|Coef.Std.Err.zP>|z|[95%Conf.Interval]-+_ce1|y|1....x|-1.226905.0777465-15.780.000-1.379285-1.074525_trend|9.62045....._cons|341.1097....AdjustmentparametersEquationParmschi2P>chi2D_y15.4311990.0198D_x113.700170.0002D_y15.4311990.0198D_x113.700170.0002alpha|Coef.Std.Err.zP>|z|[95%Conf.Interval]+D_y|_ce1|L1.|.0571242.02451162.330.020.0090823.105166D_x1|_ce1|L1.|.1193333.03224033.700.000.0561435.182523ImpactparametersEquationParmschi2P>chi2D_y15.4311990.0198D_x113.700170.0002Pi|Coef.Std.Err.zP>|z|[95%Conf.Interval]+D_y|y|L1.|.0571242.02451162.330.020.0090823.105166x|L1.|-.0700859.0300734-2.330.020-.1290287-.0111431+D_x|y|L1.|VI.1193333.03224033.700.000.0561435.182523x|L1.|-.1464106.0395557-3.700.000-.2239384-.0688827?usehttp：//www.stat^^/data/rlO/lutkepohL2(QuarterlySAWestGermanmacrodata,BilDMtfroiaLutkepohl1993TableE.1).vardln_invdla_incdln.coiisuinpifqtr<=tq(19?3q4),dfksmall(outputomifted).vargrangerGrangercausalityWaldte?tsEquationExcludedFdfProb>Fdln.invdln^inc-048472660.9527dln^invdln.consunip1.50042660.2306dln_invALL1.59174660-1869dln^incdln.inv1.76832660.1786dln.inc◎JLn^consump1.71342660.1873dln^incALL1?94664660.1130.dln_conBiimpdln^inv?971472660.3839--dln_consumpdin.inc6r146S2660.0036din.consuinpALL3.7746466o.ooaoSincetheestimates()optionwasnotspecified,vargrangerusedtEieactivee()results.Considertheresultsofthethreetestsforthefirstequalion.ThefirstisaWaldtestthatthecoefficientsonthetwolagsofdln.?incthatappearintheequationfordln_invarejointlyzero.Thenullhypothesisthatdln-incdoesnotGranger-causedlu_invcannotberejected,Similarly,wecannotrejectthenullhypothesisthatthecoefficientsonthetwolagsofdln^consumpintheequationfordln^invarejointlyzero,sowecannotrejectthehypothesisthatdln_consumpdoesnotGranger-causedln_inv.ThethirdtestiswiLhrespecttothenullhypothesis(hatthecoefficientsonthetwolagsofailtheotherendogenousvariablesarejointlyzero.Sincethiscannotberejected,wecannotrejectthenul]hypothesisthatdInlineanddln_consump,jointly,donotGranger-causedln_inv.Sincewefailed[orejectmostofthesenullhypotheses,wemightbeinterestedinimposingsomeconstraintsonthecoefficients.See[T5]varformoreonfittingVARmodelswithconstraintson5hecoefficients.:<1>Example2:UsingtestinsteadofvargrangerWecouldhaveusedtesttocomputetheseWaldtests,butvargrangersavesagreatdealoftyping.Still,seeinghowtousetesttoobtaintheresultsreportedbyvargrangerisuseful..test[dln?invjL.dln_iuc[dln_inv]L2.dln^inc[dln.inv]L-dln_inc=0[dln_inv]L2?dln_inc=0F(2,66)=0.05Prob>F=0.9527?test[dla_inv]L,dln^consttmp[din.丘v]L2；d1n_cm3ujiip，accanulate[dljn_inv]L.d]ji?inc0Edlu_inv]L2.dln?inq百qC3)CdIninuJL.dln_consump=0(4)Cdln_iliv)L2.dln_consiinip=0TOC\o"1-5"\h\zF<4.66}=1,59Prob>F=0+1869-切毗[din.,inv]L.din.inv￡dln_inv]L2.dlu_in?faccumulate.C1)[dln.inv]Lndln?iiic=0-..[din^l^vHS-dln?inc*0-[dln_inv]L.dlo_consump=o<4)tSTdin^cpusump=o^.￡5)[dln^icv]L.dln.inv=0.<6)Ldln-invns.dlu^inv=0F<6t66)R1.62Prob>F=0.1547.-.Thefirsttwocallstotestshowhowvargrangerobtainsiuresults.ThefirsttestreproducesthefirstleEtreportedforthedln^invequation.Thesecond[eslreproduces[heALLentryforth