# st: Fixed effects decomposition (was xthtaylor)

 From ACavallo@lexecon.com To statalist@hsphsun2.harvard.edu Subject st: Fixed effects decomposition (was xthtaylor) Date Tue, 10 Feb 2004 14:35:28 -0600

```

Mario,

Thanks for your tips - I forgot that these characteristics can be estimated
using a random effects model.

My question about the decomposition still stands though, how do I estimate
g in the model below when using fixed effects.
y(it)=b*x(it) + g*z(i) + a(i) + e(it)
where x(it) are time varying characteristics, z(i) are time invariant
characteristics, and a(i) are the fixed effects.

My proposal is to estimate fixed effects model, predict a(i), then regress
a(i) on z.  I would bootstrap to get the standard errors right on the
auxilliary regression
xtreg y x, fe
predict a, u
by id : keep if _n==1
regress a z

I looked in Greene's "Econometric Analysis" and Baltagi's "Econometric
Analysis of Panel Data" but did not see any explanation.  Does anyone have
references or comments on my proposal?

Regards,

--Alex Cavallo
Lexecon
(312) 322-0208  voice
(312) 322-0218  fax

>Can I use XTHTAYLOR assuming no variables are correlated with a(i)?  In
>other words, is the endog(varlist_endog) option required?  I don't yet
have
>Stata 8 so I can't just try this.

The online help for -xthtaylor- states that the endog() option is required,
http://www.stata.com/help.cgi?xthtaylor

However, the Hausman-Taylor estimator of a model where every variable in X
and Z is assumed to be uncorrelated with the random effect [a(i), or u(i)
in stata's notation] is simply a random-effects model (-xtreg, re- y on X
and Z varlists). I don't have the paper here, but I think this is stated in

Hausman and Taylor (1981) econometrica paper.

>If not, does anyone have a reaction to this proposed method:
>      1.  estimate y(it)=b*x(it) + a(i) + e(it)
>      2.  regress ahat(i) on z(i) to estimate ghat, using bootstrap to get
>standard errors right

Don't trust me much in this, but I think that depending on the procedures
used in steps (1) and (2) (and possibly on the (un)balanced nature of your
panel data set) you could get a "ghat" estimator that would be consistent
but not efficient. If all variables in X and Z are really exogenous,
-xtreg, fe- is both consistent and efficient.

Hope this helps,

Mario F. Rueda Narváez
El Ejido s/n
29013      Málaga  (España)
<http://www.estyeco.uma.es/>http://www.estyeco.uma.es/
Tlf:  +34 952 13 71 90
Fax: +34 952 13 72 62

*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```