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Hi,
I'm running a test to compare using cross sectional random effects versus cross sectional fixed effects. Firstly I want to make sure the correct test to use is the Hausman test, right? (p.s.I'm using panel data)

Secondly when I carry out such a test I get this warning appear: -
** WARNING: estimated cross-section random effects variance is zero.**

What does this mean intuitively?
What implications will it have for my estimations using random effects?

Thanks!

The warning message is pretty clear about what is happening. The estimate of your random effects variance is zero...hence the GLS estimates are equal to the OLS estimates. In general, there's nothing really to do here, except perhaps try a different specification or estimator for the random effects model.