weighting matrix SUR

[lukeroom]

Hello, I am trying to understand what weighting matrix Eviews is using in estimating a SUR system.
My Eviews results do not match with results from other softwares, therefore, I need to understand exacty what weighting matrix Eviews is using.

All the details of the estimation are comparable (one step estimation... ecc...), OLS results are the same, but SUR estimation is different.

Is it possible to get the weighting matrix that Eviews is using?
Thank you for your help, Luca

[EViews Glenn]

https://www.eviews.com/help/helpintro.h ... %23ww37465

[edit]

My guess is that it is the d.f. correction. Also keep in mind that the residual covariance is computed assuming mean zero, so, for example, the diagonals are just the average of the squared residuals.

Oh, I almost forgot that you can get the covariance matrix used to form the weights using the estcov view, or using the @estcov data member. In the SUR case, you'll want the inverse. Then depending on how you represent the system specificaiton, that inverse covariance may need to be fed into a Kronecker product.

https://www.eviews.com/help/helpintro.h ... 23ww232614
https://www.eviews.com/help/helpintro.h ... ystem.html#ww230608

[lukeroom]

Thank you for your very competent answer.
Now I understand what's going on...
My panel is unbalanced.

This is what Eviews is doing (which does not seem to be correct, but anyway...):
1. for the balanced part of the panel, it computes the correct variances and covariances.
2. for the unbalanced part of the panel, let's suppose that the length of the balanced part is T and the unbalanced part is t. The variances of the residuals of the unbalanced part are computed dividing by t (which seems to be the correct way to go: there are t residuals), the covariances between the balanced and the unbalanced part are computed dividing by T (which does not seem to be the correct thing to do. Basically, it assumes that the residuals associated to the points which are not present in the unbalanced part are equal to zero). This clearly divides the sum of products of the residuals of the balanced and unbalanced part by a too big of a number, T as opposed to t.

Do you think I am right?
Thank you for your help.
Luca

[EViews Glenn]

I now understand the issue you are seeing.

In the unbalanced case, EViews divides by the max of the two counts, which as you correctly point out is equivalent to assuming that the "missing observation residuals" are equal to zero. This was a deliberate choice that downward biases the estimator for that term. Note that this estimator of a covariance is asymptotically valid so long as the number of pairwise missings becomes insignificant relative to the increasing sample size.

The alternative estimator would divide by the actual number of pairwise obsevations, which produces "better" covariances, but also produces a covariance matrix that is more sensitive in small samples and is not guaranteed to be PSD. It has been some time, but my recollection is that there was a deliberate decision to trade off the small sample properties (downward bias) of the covariance estimators for the overall stability of the covariance matrix used in SUR. This is, I believe, somewhat like setting presample values of residuals to 0 in the serial correlation LM testing, which has been shown to have better small sample properties.

I can't say for certain which has better properties in this case as I don't believe that there has been a comprehensive analysis, but our determination was that the small sample stability was to be prioritized, and to rely on asymptotics for theoretical correctness. That said, I would certainly be happy to look at any evidence arguing for the contrary. At the very least, we did make certain to document how the covariances are computed in the unbalanced case.

Which brings us here. I hope that this answers your question. If you have further questions or evidence related to the choice of covariance estimation, I'd very much look forward to additional discussion.