Panel data, ‘GLS Weights’, ‘Coef Covariance Method’

[mfb]

Concerning panel data, Eviews has the following ‘GLS Weights’ and ‘Coef Covariance Method’ options on the Quick/Equation Estimation/Panel Options tab:
1) GLS Weights: No weights, Cross-section weights, Cross-section SUR, Period weights,
Period SUR.
2) Coef Covariance Method: Ordinary, White cross-section, White period, White (diagonal), Cross-section SUR (PCSE), Cross-section weights (PCSE), Period SUR (PCSE), Period weights (PCSE).

My question is this: is it legitimate to just pick and choose the best combination of ‘GLS Weights’ and ‘Coef Covariance Method’ (in terms of lowest coefficients Standard Errors for maximum coefficients statistical significance) and just report the coefficients and standard errors thus selected?
That is, could I just pick, for example, ‘No weights’ and ‘White cross-section’, or ‘Cross-section weights’ and Period SUR (PCSE), just because one of these yields the lowest Standard Errors and maximum coefficient statistical significance?

Thanks,
Mfb

[startz]

No. In general you should pick the method with the largest standard errors. In particular, your method (2) is more general than your method (1).

[mfb]

You say that I should pick the method with the largest standard errors? I want my explanatory variables to be statistically significant, meaning they should have high t-statistics. A t-stat is obtained by dividing the coefficient value by its standard error. Therefore, I should have standard errors as small as possible. Isn't it? Efficient estimation means low standard errors, is it not?

[startz]

You say that I should pick the method with the largest standard errors? I want my explanatory variables to be statistically significant, meaning they should have high t-statistics. A t-stat is obtained by dividing the coefficient value by its standard error. Therefore, I should have standard errors as small as possible. Isn't it? Efficient estimation means low standard errors, is it not?

That's what you want of course. But in most of these cases low standard errors does not mean more efficient estimation, it means a more flexible method of calculating standard errors. So the lower standard errors are probably wrong.

[mfb]

I see what you mean. If I pick a combination of (1) Weights and (2) Method that gives the lowest standard errors, and if the coefficients are still statistically significant, then I am on the safe side: whatever the correct combination of (1) Weights and (2) Method, the model is validated. But then a problem arises (as far as I can see with the regressions that I have been running) in that it is always possible to find a combination of (1) Weights and (2) Method where the coefficients are not statistically significant (meaning I can not reject the null of the coefficients being zero). If this happens, how do I go about choosing a correct combination of (1) Weights and (2) Method?

[startz]

I see what you mean. If I pick a combination of (1) Weights and (2) Method that gives the lowest standard errors, and if the coefficients are still statistically significant, then I am on the safe side: whatever the correct combination of (1) Weights and (2) Method, the model is validated.

It depends what you mean by safe. Usually safe means avoiding a false positive, so if anything you want a method with the highest standard errors.

[mfb]

Sorry, I meant to say 'highest', not 'lowest'; I repeat with correction:
I see what you mean. If I pick a combination of (1) Weights and (2) Method that gives the highest standard errors, and if the coefficients are still statistically significant, then I am on the safe side: whatever the correct combination of (1) Weights and (2) Method, the model is validated. But then a problem arises (as far as I can see with the regressions that I have been running) in that it is always possible to find a combination of (1) Weights and (2) Method where the coefficients are not statistically significant (meaning I can not reject the null of the coefficients being zero). If this happens, how do I go about choosing a correct combination of (1) Weights and (2) Method?

[startz]

The answer is a little complicated, and perhaps somewhat more art than science. Some methods for getting the standard errors are simply more general and it's hard to ignore these if they give larger standard errors. On the weighting schemes however, one may be right and another may be wrong.

So there's not a general answer. You have to think about which methods to look at based on what they're designed to do more than by looking at the results you get.

[mfb]

Does it make sense to use together (1) GLS Cross-section Weights with (2) Cross-section weights (PCSE)?
Or (1) GLS Period Weights with (2) Period weights (PCSE)?
Or (1) GLS Cross-section SUR with (2) Cross-section SUR (PCSE)?
Or (1) GLS Period SUR with (2) Period SUR (PCSE)?

Meaning that, when I pick one of the (1) GLS options, I should also pick the corresponding (2) PCSE option?

[startz]

I don't think there is a general answer. It depends on the model you're estimating. But perhaps someone else here might want to chime in.

[mfb]

Does it make sense in Eviews to use both GLS and Robust Standard Errors in the same go?

Also, it might be useful to be able to look at a residuals covariance matrix to check whether there is heteroskedasticity or contemporaneous correlations or serial correlation cross-wise or period-wise. One would then be in a better position to choose among the various options. But the panel estimation output does not appear to supply us with a residual covariance matrix after performing simple fixed or random effects estimation.

Is there any easy way to check the residual covariance matrix and do tests on it to see what kind of GLS or robustification we should use? Or would we need to build it from the RESID output?