stata-误差修正模型讲解.doc

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：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：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.lx Source | 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reg D.x ly lx D.ly D.lx Source | 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 = 202 AIC = 18.29975Log likelihood = -1839.275 HQIC = 18.35939Det(Sigma_ml) = 277863.4 SBIC = 18.44715Equation Parms RMSE R-sq chi2 Pchi2-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 .0554273 y | LD. | .1091985 .0807314 1.35 0.176 -.0490323 .2674292 x | 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 .044093 y | LD. | .4254495 .1098075 3.87 0.000 .2102308 .6406683 x | 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的估计值，上述结果没有的估计，而是在下面的表格中。Cointegrating equations 协整公式Equation Parms chi2 Pchi2-_ce1 1 853.9078 0.0000-Identification: beta is exactly identified Johansen 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显示的的估计值。Impact parametersEquation Parms chi2 Pchi2-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 .0554273 x | L1. | -.0319857 .0052886 -6.05 0.000 -.0423512 -.0216203-+-D_x | y | L1. | .0256414 .0094143 2.72 0.006 .0071897 .044093 x | L1. | -.0195922 .0071933 -2.72 0.006 -.0336908 -.0054935命令pi 显示的估计值，上表中显示，在第一个方程中协整向量中，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，vecrank y x Johanson协整检验 Johansen tests for cointegration Trend: constant Number of obs = 202Sample: 3 - 204 Lags = 2- 5%maximum trace critical rank parms LL eigenvalue statistic value 0 6 -1856.3997 . 34.5784 15.41 1 9 -1839.2746 0.15596 0.3282* 3.76 2 10 -1839.1105 0.00162-trace statistic 表明拒绝rank（）=0的假设，但是不能拒绝rank（）=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）vec y x, alal显示的估计值，即速度调整参数的估计Adjustment parametersEquation Parms chi2 Pchi2-D_y 1 36.57896 0.0000D_x 1 7.418336 0.0065- alpha | Coef. Std. Err. z P|z| 95% Conf. Interval-+-D_y | _ce1 | L1. | .0418615 .0069215 6.05 0.000 .0282956 .0554273-+-D_x | _ce1 | L1. | .0256414 .0094143 2.72 0.006 .0071897 .044093而矩阵的估计为：- 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 . . . . .-即146.9988+y-0.764085 x=0而即为，即=（0.0418615 0.0256414），=（1 -0.764085），的第一行即为第一个方程中的的估计值（0.0418615 -0.0319857）其中，0.0418615*（-0.764085）= -0.0319857的第二行即为第二个方程中的的估计值（0.0256414 -0.0195922）- Pi | Coef. Std. Err. z P|z| 95% Conf. Interval-+-D_y | y | L1. | .0418615 .0069215 6.05 0.000 .0282956 .0554273 x | L1. | -.0319857 .0052886 -6.05 0.000 -.0423512 -.0216203-+-D_x | y | L1. | .0256414 .0094143 2.72 0.006 .0071897 .044093 x | L1. | -.0195922 .0071933 -2.72 0.006 -.0336908 -.0054935此时虽然矩阵的估计中有截距项，但在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，则截距项出现在中，而误差修正模型中没有截距项。vec y x, t(rc) pi alVector error-correction modelSample: 3 - 204 No. of obs = 202 AIC = 18.30856Log likelihood = -1841.164 HQIC = 18.36157Det(Sigma_ml) = 283111.1 SBIC = 18.43958Equation Parms RMSE R-sq chi2 Pchi2-D_y 3 20.9329 0.6666 395.9259 0.0000D_x 3 28.5972 0.5280 221.5231 0.0000- | Coef. Std. Err. z P|z| 95% Conf. Interval-+-D_y | _ce1 | L1. | .041464 .0045894 9.03 0.000 .0324688 .0504591 y | LD. | .1128688 .0801805 1.41 0.159 -.044282 .2700196 x | LD. | .0765203 .054746 1.40 0.162 -.0307799 .1838205-+-D_x | _ce1 | L1. | .0386104 .0062698 6.16 0.000 .0263218 .050899 y | LD. | .4012721 .1095377 3.66 0.000 .1865822 .6159621 x | LD. | -.1705861 .0747907 -2.28 0.023 -.3171732 -.0239991-Cointegrating equationsEquation Parms chi2 Pchi2-_ce1 1 924.1123 0.0000-Identification: beta is exactly identified Johansen normalization restriction imposed- beta | Coef. Std. Err. z P|z| 95% Conf. Interval-+-_ce1 | y | 1 . . . . . x | -.773902 .025458 -30.40 0.000 -.8237986 -.7240053 _cons | 105.6838 81.37255 1.30 0.194 -53.8035 265.171-Adjustment parametersEquation Parms chi2 Pchi2-D_y 1 81.62498 0.0000D_x 1 37.92271 0.0000- alpha | Coef. Std. Err. z P|z| 95% Conf. Interval-+-D_y | _ce1 | L1. | .041464 .0045894 9.03 0.000 .0324688 .0504591-+-D_x | _ce1 | L1. | .0386104 .0062698 6.16 0.000 .0263218 .050899-Impact parametersEquation Parms chi2 Pchi2-D_y 1 81.62498 0.0000D_x 1 37.92271 0.0000- Pi | Coef. Std. Err. z P|z| 95% Conf. Interval-+-D_y | y | L1. | .041464 .0045894 9.03 0.000 .0324688 .0504591 x | L1. | -.032089 .0035518 -9.03 0.000 -.0390504 -.0251277 _cons | 4.382067 .4850288 9.03 0.000 3.431428 5.332706-+-D_x | y | L1. | .0386104 .0062698 6.16 0.000 .0263218 .050899 x | L1. | -.0298806 .0048522 -6.16 0.000 -.0393908 -.0203705 _cons | 4.080489 .6626169 6.16 0.000 2.781784 5.379194-此时在的矩阵估计中，有截距项，但是在误差修正模型中没有截距项。如果用t(rt)命令，在协整向量中有趋势项的估计（即对时间t的系数的估计），而在整个误差修正模型中没有趋势项，但是有截距项的估计。在的估计中，只有趋势项，没有截距项，因为截距项的估计已经包含在误差修正模型中了。vec y x, t(rt) pi alVector error-correction modelSample: 3 - 204 No. of obs = 202 AIC = 18.2926Log likelihood = -1837.553 HQIC = 18.35887Det(Sigma_ml) = 273167.6 SBIC = 18.45638Equation Parms RMSE R-sq chi2 Pchi2-D_y 4 20.8735 0.6702 400.296 0.0000D_x 4 28.0435 0.5484 239.2424 0.0000- | Coef. Std. Err. z P|z| 95% Conf. Interval-+-D_y | _ce1 | L1. | .0769485 .01239 6.21 0.000 .0526645 .1012325 y | LD. | .0861433 .0819685 1.05 0.293 -.0745121 .2467986 x | LD. | .0989288 .0554018 1.79 0.074 -.0096569 .2075144 _cons | -2.443936 3.5442 -0.69 0.490 -9.390441 4.502569-+-D_x | _ce1 | L1. | .0632409 .016646 3.80 0.000 .0306153 .0958664 y | LD. | .3552693 .1101247 3.23 0.001 .1394288 .5711098 x | LD. | -.1724981 .0744324 -2.32 0.020 -.3183828 -.0266133 _cons | 2.973666 4.761634 0.62 0.532 -6.358965 12.3063-Cointegrating equationsEquation Parms chi2 Pchi2-_ce1 1 143.3685 0.0000-Identification: beta is exactly identified Johansen normalization restriction imposed- beta | Coef. Std. Err. z P|z| 95% Conf. Interval-+-_ce1 | y | 1 . . . . . x | -1.093286 .0913076 -11.97 0.000 -1.272