st: Poolability Test - Fixed Effects, Panel Robust Errors or Roy-Zellner Test

[Carla Müller <csm53@cam.ac.uk>]

Dear all,

I have a panel of 33 countries over 7 periods (7*3 year period 
averages). I am trying to perform a test for poolability.

My restricted model is a fixed effect model with homogeneous slopes, my 
unrestricted model is a fixed effect model with slopes on the variable 
of interest varying across countries (maintaining the assumption that 
the coefficients on all control variables are constant across 
countries).

Following Vaona (2008) ("A quick trick to perform a Roy-Zellner test for 
poolability") I have created 33 interaction terms between the countries 
and the variable of interest and am able to run regressions with these 
33 interaction terms.

My question concerns the testing procedure. Having read previous Stata 
posts on this topic (see e.g.: 
http://hsphsun3.harvard.edu/cgi-bin/lwgate/STATALIST/archives/statalist.0303/Subject/article-391.html) I remain unsure about which of the following approaches is valid:

(1) Run the unrestricted model including all interaction terms using a 
fixed effect estimator, then use an F-test to test the equality of all 
coefficients.

(2) Same procedure as in (1) but using panel robust (clustered) errors 
(or alternatively bootstrapped errors) (having tested for 
autocorrelation, heteroscedasticity and spatial correlation I am using 
these robust errors throughout the whole paper).
Problem: Using cluster robust errors reduces the degrees of freedom and 
as a result I cannot test the equality of all interaction terms 
simultaneously (while I expected the degrees of freedom to be reduced to 
the number of clusters-1, Stata in fact allows me to test only 14 
coefficients at a time (all additional constraints are dropped))

(3) Perform a Roy-Zellner test instead of a Chow test given the presence 
of non-spherical errors (e.g. "Econometrics", Baltagi 2008 ) - how would 
this be different from (2) which is also robust to non-spherical errors?
Problem: How do I perform a Roy-Zellner test in this case?

Thank you for any help and advice,

Best regards,

Carla Müller

Cambridge University

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