WARNING: estimated coefficient covariance matrix is reduced

[mfb]

I am sometimes getting the following WARNING when doing regression with fixed effects panel data:

Dependent Variable: VC_Y
Method: Panel Least Squares
Date: 21/06/13 Time: 10:01
Sample: 2001 2005
Periods included: 5
Cross-sections included: 18
Total panel (balanced) observations: 90
White cross-section standard errors & covariance (d.f. corrected)
WARNING: estimated coefficient covariance matrix is of reduced rank

What does this WARNING mean? A coefficient covariance matrix should be full rank for it to be ok? What are the consequences of disregarding this WARNING?

Thanks.

[EViews Glenn]

When estimating a White covariance with cross-section correlation, you need at least as many time series observations as cross-sections, otherwise the estimated covariance is not of full rank. From a practical point of view, this simply means that you may get singular matrix errors for selected Wald or similar tests. From a deeper perspective, you *really* don't have enough time series observations to estimate the coefficient covariance in a robust fashion. You are not even close to having the required asymptotics kick in.

[mfb]

Thanks.

'GLS Weights: Cross-section weights' may be helpful in a situation like this?

'Coeff Covariance Method: Cross-section SUR (PCSE)' might help as well?

Those two above seem to be doing what 'White Cross-section' does (accounting for cross-section correlation and cross-section heteroskedasticity), though in different ways?

I am working with 2 different small samples and they both point roughly in the same direction as regards coefficients significance (though the actual values differ).

[EViews Glenn]

The first only accounts for the diagonals, not the off-diagonals.

The second places restrictions on the nature of the cross-section correlation and heteroskedasticity. I do note, however, that it too assumes that there are large numbers of time-series observations. The references to Beck and Katz that we provide in the manual describe the issues in greater detail.