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Re: st: Fixed Effect Estimation Results

From   [email protected] (William Gould, Stata)
To   [email protected]
Subject   Re: st: Fixed Effect Estimation Results
Date   Tue, 04 Apr 2006 08:33:17 -0500

Joana Quina <[email protected]> reports, 

    1.  She has estimated the parameters of a model using -xtreg, fe- and 
        that the reported correlation between u_i and X_ij*b is .9249.

    2.  She has estimated the parameters of the same same model on
        the same data.  She then performs a Hausman test that fails to 
        reject random effects.

She writes, 

> It seems counter-intuitive. Any suggestions would be much appreciated.

It certainly does seem counterintuitive.  My first reaction is to suggest
Joana check her work.

Let's first understand just how counterintuitive this is.  The correlation
between u_i and X_ij*b is .9249.  Now let's use an estimation method that
constrains that correlation to be 0.  X_ij is fixed, so the only thing that
can give is b.  The estimated b has got to change.  The Hausman tests basis
its calculation on the change in b, and it reports that the change is small,
relative to variance.

That could could mean is that the variance is large, so large as to suggest
that the model, estimated either way, is not worth much.  But Joana showed us
(1) and the within R^2 was .6385, so let's dimiss that.

However, X_ij is *NOT* necessarily fixed.  Joana could have included extra
variables in the random-effects estimation, variables whose coefficients could
not be estimated by the fixed-effects estimation.  In that case, the result is
not counterintuitive at all.  Omit those variables, as done in the
fixed-effects estimation, and u_i is correlated.  Include them, and the
correlation vanishes.  Said differently, the subset of the b's estimated by
both estimators did not change, and the extra b's estimated by the
random-effects estimator eliminated the correlation.  This is exactly what one
hopes will happen if one has a well-specified model.

Is that what happened?

-- Bill
[email protected]
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