st: hausman's test with xtivreg2

[Kit Baum <baum@bc.edu>]

Mark said

>
> "One can formalize this evidence against the exogeneity of
> managerial ownership by testing for a correlation between the
> fixed effect and managerial
> ownership. We could use a Hausman (1978) test, but this test
> would tend to
> over-reject the null hypothesis of zero correlation because
> it would tend to reject
> if any of the explanatory variables were correlated with the
> fixed effect.
> To reduce this Type I error, we construct a more precise
> &conditional moment'
> test, which is in the spirit of a Hausman test, but tends to
> reject only if
> managerial ownership is the source of the specification error
> (Greene, 1997, p. 534; Newey, 1985)."

This is very curious.  Do we have the context right?

If I'm not mistaken, the above makes sense if the authors are talking
about the application of a Hausman test to an equation without fixed
effects.  In that case, omission of the fixed effects would generate
omitted variable bias if the explanatory variables are correlated with
the omitted "fixed effects" since they are now in the error term.

But say we apply the Hausman test to a fixed effects estimation done as
a LSDV (least squares dummy variable) estimation.  Then I can't see what
the problem would be.  There's nothing wrong with explanatory variables
being correlated with each other, and the LSDVs that are included as
regressors are just that.


I think what is being confused here is that one could do two Hausman  
tests in a FE context: one for FE vs RE (which does question the  
correlation between regressor and fixed effect) and another, in the  
pure FE context, for endogeneity of regressors. That is, the test of  
OLS vs IV for the LSDV model. The former Hausman test would look at  
the correlation between regressor (mangerial ownership) and the firm- 
specific effect, but if done purely in a OLS/LSDV framework, could be  
weakened if OLS is inappropriate in the first place. But I don't see  
how that critique would apply if the test was done in a IV framework,  
allowing for endogeneity of regressors.



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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