st: re: test of coefficients across OLS and fixed effect regressions

[Kit Baum <baum@bc.edu>]

Jackie wants to compare the coefficients on X1 in these two models:

reg Y X1 X2
xtreg Y X1 X2, fe i(id)

If the F-statistic at the foot of the -xtreg, fe- output rejects its  
null (that there are no fixed effects) then the OLS form of the  
equation is misspecified, and its coefficient should not be compared  
with anything. On the other hand if the F-statistic fails to reject  
that null H, you're wasting lots of d.f. by fitting a fixed effects  
model, and for more efficient estimates you should constrain the FE  
to zero (i.e. use OLS). The FE coefficient is unbiased and consistent  
but inefficient. So it makes little sense to think of comparing these  
coefficients, particularly in the former case where unobserved  
heterogeneity renders OLS inconsistent.

Kit

Kit Baum, Boston College Economics and DIW Berlin
http://ideas.repec.org/e/pba1.html
An Introduction to Modern Econometrics Using Stata:
http://www.stata-press.com/books/imeus.html


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