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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.

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.

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).

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.