请教个模型选择的问题

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stata,FGLS回归

回归一:

Cross-sectional time-series FGLS regression

Coefficients: generalized least squares
Panels: homoskedastic
Correlation: no autocorrelation

Estimated covariances = 1 Number of obs = 700
Estimated autocorrelations = 0 Number of groups = 100
Estimated coefficients = 5 Time periods = 7
Wald chi2(4) = 1952.74
Log likelihood = -922.4935 Prob > chi2 = 0.0000

lnt Coef. Std. Err. z P>z [95% Conf. Interval]

lngdp .1039338 .0029807 34.87 0.000 .0980917 .1097759
lnd -.517205 .0736273 -7.02 0.000 -.6615118 -.3728982
apec .6718755 .104525 6.43 0.000 .4670104 .8767407
lu .5319582 .1361562 3.91 0.000 .265097 .7988194
_cons 21.47754 .6615924 32.46 0.000 20.18084 22.77424

回归二增加了两个变量:

Cross-sectional time-series FGLS regression

Coefficients: generalized least squares
Panels: homoskedastic
Correlation: no autocorrelation

Estimated covariances = 1 Number of obs = 700
Estimated autocorrelations = 0 Number of groups = 100
Estimated coefficients = 7 Time periods = 7
Wald chi2(6) = 2389.42
Log likelihood = -869.1573 Prob > chi2 = 0.0000

lnt Coef. Std. Err. z P>z [95% Conf. Interval]

lngdp .098699 .0028182 35.02 0.000 .0931755 .1042225
lnd -.5550855 .0688252 -8.07 0.000 -.6899805 -.4201906
apec .6710518 .0973144 6.90 0.000 .4803192 .8617844
lu .5567073 .1265311 4.40 0.000 .3087109 .8047036
wto .3978175 .0839592 4.74 0.000 .2332604 .5623745
wtoc .6132775 .0644065 9.52 0.000 .4870431 .739512
_cons 21.3736 .6140994 34.80 0.000 20.16999 22.57721

请教如何判断,

是否回归二要更好一些?

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关键词：模型选择 coefficients correlations correlation coefficient 请教 模型 选择

Basicly, it is hard to say which model is better. if you add two variables, you  will take the risk of missing specification. So first of all, the choosing of variables should base on theories or the empirical results of other guys. If you only want to compare two nonnested models, you can try Cox test or J test.

since the model 2 has two more variables than model 1, this is a comparision of nested models, which should use F-test.

You can treat model one as a restricted model of model two, the restrictions are b5=0 and b6=0

The unrestricted model is always better than restricted model. (see Greene 2002)

"The fit of the restricted least squares coefficients cannot be better than that of the unrestricted solution" (Greene 2002 p101)

But you can use F test to test whether restricted model is statatisticlly not difference with the unrestricted model.

H0: b5=0, b6=0

H1:

If rejected H0, choosing unrestricted model

if do not reject H0, choosing restricted model

Test statistic sees Greene 2002 p102(Fifth Version )

One more thing, this test assumes that disturbances follow normal distribution.

Thanks