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=（y x ）’，则模型为：t t ki i t t z p z A z επ+∆++=∆-=-∑1110其中，'αβπ=如果令1=k ，即滞后项为1，则模型为t t t t z p z A z επ+∆++=∆--1110实际上为两个方程的估计：t t t t t y t x p y p x b y b a y 1112111112111ε+∆+∆+++=∆----t t t t t x t x p y p x b y b a x 2122121122121ε+∆+∆+++=∆----用ols 命令做出的结果：gen t=_ntsset ttime variable: t, 1 to 204gen ly=L.y(1 missing value generated)gen lx=L.x(1 missing value generated)reg D.y ly lx D.ly D.lxSource | SS df MS Number of obs = 202 -------------+------------------------------ F( 4, 197) = 21.07 Model | 37251.2525 4 9312.81313 Prob > F = 0.0000 Residual | 87073.3154 197 441.996525 R-squared = 0.2996 -------------+------------------------------ Adj R-squared = 0.2854 Total | 124324.568 201 618.530189 Root MSE = 21.024------------------------------------------------------------------------------D.y | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+----------------------------------------------------------------ly | .0417242 .0187553 2.22 0.027 .0047371 .0787112 lx | -.0318574 .0171217 -1.86 0.064 -.0656228 .001908 ly |D1. | .1093189 .082368 1.33 0.186 -.0531173 .2717552 lx |D1. | .0792758 .0566966 1.40 0.164 -.0325344 .1910861 _cons | 2.533504 3.757158 0.67 0.501 -4.875909 9.942916 这是t t t t t y t x p y p x b y b a y 1112111112111ε+∆+∆+++=∆----的回归结果，其中y a =2.5335，b 11=0.04172，b 12= -0.03186，p 11=0.10932，p 12=0.07928同理可得t t t t t x t x p y p x b y b a x 2122121122121ε+∆+∆+++=∆----的回归结果，见下 reg D.x ly lx D.ly D.lxSource | SS df MS Number of obs = 202 -------------+------------------------------ F( 4, 197) = 11.18 Model | 36530.2795 4 9132.56988 Prob > F = 0.0000 Residual | 160879.676 197 816.648101 R-squared = 0.1850 -------------+------------------------------ Adj R-squared = 0.1685 Total | 197409.955 201 982.139082 Root MSE = 28.577------------------------------------------------------------------------------D.x | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+----------------------------------------------------------------ly | .037608 .0254937 1.48 0.142 -.0126676 .0878836 lx | -.0307729 .0232732 -1.32 0.188 -.0766694 .0151237 ly |D1. | .4149475 .111961 3.71 0.000 .1941517 .6357434 lx |D1. | -.1812014 .0770664 -2.35 0.020 -.3331825 -.0292203 _cons | 11.20186 5.10702 2.19 0.029 1.130419 21.27331如果用vec 命令vec y x, piVector error-correction modelSample: 3 - 204 No. of obs = 202AIC = 18.29975 Log likelihood = -1839.275 HQIC = 18.35939 Det(Sigma_ml) = 277863.4 SBIC = 18.44715Equation Parms RMSE R-sq chi2 P>chi2----------------------------------------------------------------D_y 4 20.9706 0.6671 396.7818 0.0000D_x 4 28.5233 0.5328 225.8313 0.0000----------------------------------------------------------------------------------------------------------------------------------------------| Coef. Std. Err. z P>|z| [95% Conf. Interval]-------------+----------------------------------------------------------------D_y |_ce1 |L1. | .0418615 .0069215 6.05 0.000 .0282956 .0554273y |LD. | .1091985 .0807314 1.35 0.176 -.0490323 .2674292x |LD. | .0793652 .055411 1.43 0.152 -.0292384 .1879687_cons | -3.602279 3.759537 -0.96 0.338 -10.97084 3.766278-------------+----------------------------------------------------------------D_x |_ce1 |L1. | .0256414 .0094143 2.72 0.006 .0071897 .044093y |LD. | .4254495 .1098075 3.87 0.000 .2102308 .6406683x |LD. | -.1889879 .0753677 -2.51 0.012 -.3367058 -.04127_cons | 5.880993 5.113562 1.15 0.250 -4.141405 15.90339------------------------------------------------------------------------------这里_ce1 L1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。

Cointegrating equations 协整公式Equation Parms chi2 P>chi2-------------------------------------------_ce1 1 853.9078 0.0000-------------------------------------------Identification: beta is exactly identifiedJohansen normalization restriction imposed------------------------------------------------------------------------------beta | Coef. Std. Err. z P>|z| [95% Conf. Interval]-------------+----------------------------------------------------------------_ce1 |y | 1 . . . . .x | -.764085 .0261479 -29.22 0.000 -.8153339 -.7128362 _cons | 146.9988 . . . . .------------------------------------------------------------------------------上表中beta显示的β的估计值。

Impact parametersEquation Parms chi2 P>chi2-------------------------------------------D_y 1 36.57896 0.0000D_x 1 7.418336 0.0065-------------------------------------------------------------------------------------------------------------------------Pi | Coef. Std. Err. z P>|z| [95% Conf. Interval]-------------+----------------------------------------------------------------D_y |y |L1. | .0418615 .0069215 6.05 0.000 .0282956 .0554273x |L1. | -.0319857 .0052886 -6.05 0.000 -.0423512 -.0216203-------------+----------------------------------------------------------------D_x |y |L1. | .0256414 .0094143 2.72 0.006 .0071897 .044093x |L1. | -.0195922 .0071933 -2.72 0.006 -.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。