st: H0 for xttest0 and the like

[Kit Baum <baum@bc.edu>]

Nicola said

Despite reading some statistics manual and original papers I am still  
not sure to have understood correctly the use and the alternative  
hypotheses for several tests to be used after -xtreg-.
Command -xttest0- is referred to as "the Breusch and Pagan Lagrange- 
multiplier test for random effects, a test that Var(v_i)=0". I argue  
that if the test is significant, the model is better estimated  
through -regress-. Am I right?

No, you have it backwards. The null for xttest0 is var(u) = 0. If  
that was the case then there are no random effects. A significant  
result rejects var(u)=0 in favor of var(u) > 0, in which case the  
pooled OLS model that assumes that the error process has vce =  
\sigma^2 I_{NT}  is not the appropriate model. So a rejection  
(significant test result) implies that you should NOT use OLS.


The Hausman test for FE vs RE has the null that both FE and RE are  
consistent estimators because X \perp u, and since RE is more  
efficient, it is to be preferred to FE. Under the null the  
coefficient vectors from FE and RE should not differ significantly  
for the common coefficients. Under the alternative X is correlated  
with u, RE is inconsistent and you should use FE. So a significant  
Hausman test statistic implies FE, as you state.


Kit Baum, Boston College Economics
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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