SUR and equation weights

[chungrak9]

Hello. I use EViews 8, Enterprise Edition - Jun 18 2014 build (64-bit).
I run it on Windows 7 Professional SP1.

I am confused because the "Cross-section SUR (PCSE)" method of pool estimation yields different results from the "Seemingly Unrelated Regression" method of system estimation. Instead, the pool estimation results are the same as those from the "Weighted L.S. (equation weights)" method of system estimation. Could it be a bug? Or is it just a naming problem such that "Cross-section SUR" is not actually SUR?

Thank you very much.
Rakkoo

[EViews Glenn]

Can you post the workfile with saved versions of the estimated pools in question?

[chungrak9]

In the workfile, there are pairs of pool object and system object. For example, [_rakkoo_t2m1] and [_rakkoo_t2m1_system] have the same results (but slightly different se). You can compare the coefficients, because they are in the same order (while there is no constant in the system). This system estimation was obtained by "Weighted L.S. (equation weights)" method. When I chose "Seemingly Unrelated Regression", the results were different.
Thanks a lot!
Rakkoo

[EViews Gareth]

You realise that you have set the coefficient covariance method to be "Cross-section SUR (PCSE)", which only impacts the coefficient covariance matrix (i.e. the standard errors), and has no impact on the coefficient estimates themselves, right?

[chungrak9]

Correct.

[EViews Gareth]

Then I am confused as to what your question is.

[chungrak9]

Let me clarify my questions:

Is the "Cross-section SUR (PCSE)" method of pool estimation regarded as "Seemingly Unrelated Regression"?

[EViews Gareth]

It is a coefficient covariance estimation method. It is not a method of coefficient estimation. When you choose SUR as a system estimation method you are selecting a coefficient estimation method. You're comparing apples and oranges.

[chungrak9]

Apples and oranges... then your answer to my question is No?

As far as I understand based on the manual, WLS and SUR use different weight matrices. SUR considers heteroskedasticity and contemporaneous correlation in the errors across equations, whereas WLS considers cross-equation heteroskedasticity only. So, I guess I understand that WLS and SUR are apples and oranges.

The source of my confusion is this:
I chose to use the "Cross-section SUR (PCSE)" method because I thought it was SUR. However, it turned out that it did not address contemporaneous correlation in the errors. Does this mean that the "Cross-section SUR (PCSE)" is not SUR, or something else?

[EViews Glenn]

In both of the specified objects, the method is weighted least squares. This can be seen by looking at the options, or at the method in the output.
For the system object, it is "Iterative Weighted Least Squares" and for the Pool, it is "Pooled EGLS (Cross-section weights)".

The Cross-section SUR (PCSE) setting that you choose in the pool is only for the computation of robust standard errors and does not affect the coefficient estimates.

[chungrak9]

I see. I was confused because the word "SUR" was included in the title of "Cross-section SUR (PCSE)" even if it was not SUR.

Then, don't you think the title is misleading? You should re-word "Cross-section SUR" into something else. As you know, "Cross-section SUR" and "Cross-section Weights" are the options for the pool estimation. So I suspected that the former was SUR and the latter WLS. Later, I found that their results were the same (but very slightly different se).

Anyway, I think it's quite clear for me. thank you very much for your help, EViews Glenn and EViews Gareth.

Rakkoo

[EViews Gareth]

It is SUR though. Just not SUR being used as coefficient estimates. Rather SUR being used for covariance estimates.

[chungrak9]

But it does not take into account error correlations across equations, does it?

[Raffalovich]

As I understand this:
Pool uses a weight matrix to calculate parameter estimates (if the equation weight option is selected) and/or to calculate standard errors (if the coefficient covariance method is specified).
WLS and SUR use a weight matrix to calculate both parameter estimates and their standard errors.
Is this correct?
Also, Does the WLS weight matrix include contemporaneous error correlation? Equations 17.13 -17.16 are ambiguous on this point because in 17.16 V is is defined as diagonal.
.

[EViews Glenn]

Weighted least squares does not. Only if using cross-section SUR weights does estimation take into account contemporaneous correlation.

The settings for the standard errors are parallel, but do not affect estimation.