stata误差修正模型讲解.docx
《stata误差修正模型讲解.docx》由会员分享，可在线阅读，更多相关《stata误差修正模型讲解.docx（18页珍藏版）》请在冰豆网上搜索。
stata误差修正模型讲解
误差修正模型：
如果用两个变量，人均消费y和人均收入x（从格林的数据获得）来研究误差修正模型。
令z=（yx）’，则模型为：
其中，
如果令
，即滞后项为1，则模型为
实际上为两个方程的估计：
用ols命令做出的结果：
gent=_n
tssett
timevariable:
t,1to204
genly=L.y
（1missingvaluegenerated）
genlx=L.x
（1missingvaluegenerated）
regD.ylylxD.lyD.lx
Source|SSdfMSNumberofobs=202
-------------+------------------------------F（4,197）=21.07
Model|37251.252549312.81313Prob>F=0.0000
Residual|87073.3154197441.996525R-squared=0.2996
-------------+------------------------------AdjR-squared=0.2854
Total|124324.568201618.530189RootMSE=21.024
------------------------------------------------------------------------------
D.y|Coef.Std.Err.tP>|t|[95%Conf.Interval]
-------------+----------------------------------------------------------------
ly|.0417242.01875532.220.027.0047371.0787112
lx|-.0318574.0171217-1.860.064-.0656228.001908
ly|
D1.|.1093189.0823681.330.186-.0531173.2717552
lx|
D1.|.0792758.05669661.400.164-.0325344.1910861
_cons|2.5335043.7571580.670.501-4.8759099.942916
这是
的回归结果，其中
=2.5335，b11=0.04172，b12=-0.03186，p11=0.10932，p12=0.07928
同理可得
的回归结果，见下
regD.xlylxD.lyD.lx
Source|SSdfMSNumberofobs=202
-------------+------------------------------F（4,197）=11.18
Model|36530.279549132.56988Prob>F=0.0000
Residual|160879.676197816.648101R-squared=0.1850
-------------+------------------------------AdjR-squared=0.1685
Total|197409.955201982.139082RootMSE=28.577
------------------------------------------------------------------------------
D.x|Coef.Std.Err.tP>|t|[95%Conf.Interval]
-------------+----------------------------------------------------------------
ly|.037608.02549371.480.142-.0126676.0878836
lx|-.0307729.0232732-1.320.188-.0766694.0151237
ly|
D1.|.4149475.1119613.710.000.1941517.6357434
lx|
D1.|-.1812014.0770664-2.350.020-.3331825-.0292203
_cons|11.201865.107022.190.0291.13041921.27331
如果用vec命令
vecyx,pi
Vectorerror-correctionmodel
Sample:
3-204No.ofobs=202
AIC=18.29975
Loglikelihood=-1839.275HQIC=18.35939
Det（Sigma_ml）=277863.4SBIC=18.44715
EquationParmsRMSER-sqchi2P>chi2
----------------------------------------------------------------
D_y420.97060.6671396.78180.0000
D_x428.52330.5328225.83130.0000
----------------------------------------------------------------
------------------------------------------------------------------------------
|Coef.Std.Err.zP>|z|[95%Conf.Interval]
-------------+----------------------------------------------------------------
D_y|
_ce1|
L1.|.0418615.00692156.050.000.0282956.0554273
y|
LD.|.1091985.08073141.350.176-.0490323.2674292
x|
LD.|.0793652.0554111.430.152-.0292384.1879687
_cons|-3.6022793.759537-0.960.338-10.970843.766278
-------------+----------------------------------------------------------------
D_x|
_ce1|
L1.|.0256414.00941432.720.006.0071897.044093
y|
LD.|.4254495.10980753.870.000.2102308.6406683
x|
LD.|-.1889879.0753677-2.510.012-.3367058-.04127
_cons|5.8809935.1135621.150.250-4.14140515.90339
------------------------------------------------------------------------------
这里_ce1L1显示的是速度调整参数α的估计值，上述结果没有π的估计，而是在下面的表格中。
Cointegratingequations协整公式
EquationParmschi2P>chi2
-------------------------------------------
_ce11853.90780.0000
-------------------------------------------
Identification:
betaisexactlyidentified
Johansennormalizationrestrictionimposed
------------------------------------------------------------------------------
beta|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显示的β的估计值。
Impactparameters
EquationParmschi2P>chi2
-------------------------------------------
D_y136.578960.0000
D_x17.4183360.0065
-------------------------------------------
------------------------------------------------------------------------------
Pi|Coef.Std.Err.zP>|z|[95%Conf.Interval]
-------------+----------------------------------------------------------------
D_y|
y|
L1.|.0418615.00692156.050.000.0282956.0554273
x|
L1.|-.0319857.0052886-6.050.000-.0423512-.0216203
-------------+----------------------------------------------------------------
D_x|
y|
L1.|.0256414.00941432.720.006.0071897.044093
x|
L1.|-.0195922.0071933-2.720.006-.0336908-.0054935
命令pi显示π的估计值，上表中显示，在第一个方程中协整向量π中，y的L1（滞后一期）的估计值为0.0418615，x的L1（滞后一期）的估计值为-0.0319857，这与ols估计的b11=0.04172，b12=-0.03186很类似；在第二个方程中协整向量π的估计与ols估计的有些差别，可能暗示第二个方程对均衡误差没有反应。
检验协整向量的秩，
vecrankyxJohanson协整检验
Johansentestsforcointegration
Trend:
constantNumberofobs=202
Sample:
3-204Lags=2
-------------------------------------------------------------------------------
5%
maximumtracecritical
rankparmsLLeigenvaluestatisticvalue
06-1856.3997.34.578415.41
19-1839.27460.155960.3282*3.76
210-1839.11050.00162
-------------------------------------------------------------------------------
tracestatistic表明拒绝rank（π）=0的假设，但是不能拒绝rank（π）=1的假设，所以人均消费和人均收入的模型中，协整向量的秩为1。
也表明人均消费和人均收入符合误差修正模型。
（不在第一个上就说明至少有一个协整关系）
vecyx,al
al显示α的估计值，即速度调整参数的估计
Adjustmentparameters
EquationParmschi2P>chi2
-------------------------------------------
D_y136.578960.0000
D_x17.4183360.0065
-------------------------------------------
------------------------------------------------------------------------------
alpha|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β矩阵的估计为：
------------------------------------------------------------------------------
beta|Coef.Std.Err.zP>|z|[95%Conf.Interval]
-------------+----------------------------------------------------------------
_ce1|
y|1.....
x|-.764085.0261479-29.220.000-.8153339-.7128362
_cons|146.9988.....
------------------------------------------------------------------------------
即146.9988+y-0.764085x=0
而αβ’即为π，即α’=（0.04186150.0256414），β’=（1-0.764085），
π的第一行即为第一个方程中的π的估计值（0.0418615-0.0319857）
其中，0.0418615*（-0.764085）=-0.0319857
π的第二行即为第二个方程中的π的估计值（0.0256414-0.0195922）
------------------------------------------------------------------------------
Pi|Coef.Std.Err.zP>|z|[95%Conf.Interval]
-------------+----------------------------------------------------------------
D_y|
y|
L1.|.0418615.00692156.050.000.0282956.0554273
x|
L1.|-.0319857.0052886-6.050.000-.0423512-.0216203
-------------+----------------------------------------------------------------
D_x|
y|
L1.|.0256414.00941432.720.006.0071897.044093
x|
L1.|-.0195922.0071933-2.720.006-.0336908-.0054935
此时虽然β矩阵的估计中有截距项，但在π的显示结果中没有截距项，此时截距项被放在误差修正模型中了。
如果用t（rc）命令，则截距项出现在π中，而误差修正模型中没有截距项。
vecyx,t（rc）pial
Vectorerror-correctionmodel
Sample:
3-204No.ofobs=202
AIC=18.30856
Loglikelihood=-1841.164HQIC=18.36157
Det（Sigma_ml）=283111.1SBIC=18.43958
EquationParmsRMSER-sqchi2P>chi2
----------------------------------------------------------------
D_y320.93290.6666395.92590.0000
D_x328.59720.5280221.52310.0000
----------------------------------------------------------------
------------------------------------------------------------------------------
|Coef.Std.Err.zP>|z|[95%Conf.Interval]
-------------+----------------------------------------------------------------
D_y|
_ce1|
L1.|.041464.00458949.030.000.0324688.0504591
y|
LD.|.1128688.08018051.410.159-.044282.2700196
x|
LD.|.0765203.0547461.400.162-.0307799.1838205
-------------+----------------------------------------------------------------
D_x|
_ce1|
L1.|.0386104.00626986.160.000.0263218.050899
y|
LD.|.4012721.10953773.660.000.1865822.6159621
x|
LD.|-.1705861.0747907-2.280.023-.3171732-.0239991
------------------------------------------------------------------------------
Cointegratingequations
EquationParmschi2P>chi2
-------------------------------------------
_ce11924.11230.0000
-------------------------------------------
Identification:
betaisexactlyidentified
Johansennormalizationrestrictionimposed
------------------------------------------------------------------------------
beta|Coef.Std.Err.zP>|z|[95%Conf.Interval]
-------------+----------------------------------------------------------------
_ce1|
y|1.....
x|-.773902.025458-30.400.000-.8237986-.7240053
_cons|105.683881.372551.300.194-53.8035265.171
------------------------------------------------------------------------------
Adjustmentparameters
EquationParmschi2P>chi2
-------------------------------------------
D_y181.624980.0000
D_x137.922710.0000
------------------------------------------------------------------------------
alpha|Coef.Std.Err.zP>|z|[95%Conf.Interval]
-------------+----------------------------------------------------------------
D_y|
_ce1|
L1.|.041464.00458949.030.000.0324688.0504591
-------------+----------------------------------------------------------------
D_x|
_ce1|
L1.|.0386104.00626986.1
升级会员 