Total system (balanced) observations

[cel]

If, for example, you estimate a system of 3 equations in eviews with 35 data points eviews writes:

Included observations: 35
Total system (balanced) observations 105

the last part is clearly 3*35. But why does e-views declare this. is it suggesting that estimating in a system is increasing your degrees of freedom?

[EViews Glenn]

In unbalanced cases, it may be useful to know how many actual data points you have. And in the rare cases where there is homogeneity across equations, some calculations in the stacked representation use the total number of data points.

[cel]

Thanks Glenn. Just one contextual follow up.

I ask because replicating a paper where there's 21 data points and 5 estimable parameters and cross-quation parameter constraints. To me this appears to have a mere 21-5=16 dof! However the author says that since he’s estimating a system of 3 equations he’s actually using 3*21-5= 58 dof.

I thought actually this information piece that e-views was producing was somehow alluding to this too (namely the potentially higher degrees of freedom under system estimation).

[EViews Glenn]

There's an ambiguity in interpretation of d.f. that comes up in this context.

Suppose you have a three equation linear model with no cross-equation restrictions, k regressors, and T observations. Ignoring cross-correlations, You can estimate equation by equation with T-k d.f.

Now suppose you stack the same three equations and estimate in a single equation with 3T observations. If you were to estimate this specification in any software package, you'd see 3T-3K as the reported d.f. In one sense that is absolutely correct since you have a stacked single equation representation, but as is your instinct, in a deeper sense, you still only have T observations identifying each set of K coefficients.

But now suppose that one of the coefficients has a cross-equation restrictions across all three equations. In that case, the three equations are no longer separable, and the stacked representations 3T-2*(K-1)-1 is probably what you'd want.

I think you see the issues involved. For what it's worth, I generally think in terms of the stacked representation as did the author, but find d.f. to be possibly misleading concept in the stacked framework when there are no cross-equation restrictions.

Note that I said the stacked d.f. is only of interest in rare cases of homogeneity in my earlier post -- I was thinking about variance restrictions -- but it is true that when there are cross-equation coefficient restrictions the alternate d.f. has some meaning. Note however, that the standard estimator of the coefficient variances does not use the stacked d.f. unless you impose the homogeneous variance restriction. So that's the reason I rarely worry about d.f. in the system setting.

[cel]

great answer, many thanks.