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Re: st: RE: suest with large number of fixed effects


From   "Richard Boylan" <rtboylan@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: suest with large number of fixed effects
Date   Wed, 12 Sep 2007 22:23:57 -0500

Thanks so much. There was a typo in what I wrote. I did not mean to
say "more precisely estimated coefficients," but "more precisely
estimated standard errors." See below for an example of suest gives
different standard errors of the regression coefficients.

webuse abdata
reg ys k
est store eq1
reg cap  wage
* here for instance the standard error for wage is .0344861
est store eq2
suest eq1 eq2
* here for instance the standard error for wage is .0430212

Richard

On 9/12/07, Schaffer, Mark E <M.E.Schaffer@hw.ac.uk> wrote:
> Richard,
>
> > -----Original Message-----
> > From: owner-statalist@hsphsun2.harvard.edu
> > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
> > Richard Boylan
> > Sent: Wednesday, September 12, 2007 4:11 PM
> > To: statalist@hsphsun2.harvard.edu
> > Subject: st: suest with large number of fixed effects
> >
> > I would like to estimate several regressions separately, but
> > using suest to obtain more precisely estimate coefficients
> >
> > So, what I would like to do is:
> >
> > xtreg y1 x1, i(id) fe
> > est store eq1
> > xtreg y2 x2, i(id) fe
> > est store eq2
> > xtreg y3 x3, i(id) fe
> > est store eq3
> > suest eq1 eq2 eq3, cluster(id)
> >
> > Given that xtreg does not have a score option, it is
> > discussed in previous postings that one needs to estimate the
> > model using a linear regression with dummy variables.
> >
> > The problem I have is that I have 1000 fixed effects and thus
> > the matrix computed in suest is going to be way too large.
>
> First, there is a misunderstanding here.  -suest- does not give you more
> "precisely estimated coefficients".  They will be *exactly* the same.
> What is different is the SEs, and in particular, the var-cov matrix will
> allow you to test cross-equation restrictions.
>
> To get more efficient estimates of the coefficients, you would need to
> use Zellner's SUR ("seemingly-unrelated regressions") estimator,
> available in Stata as -sureg-.
>
> Second, and somewhat more constructively, since you are in
> fixed-effects-land, you can demean your variables by hand to wipe out
> the fixed effects (the "within" transformation) and then estimate using
> -regress- or -sureg-.  This gives you two options: (a) estimate using
> -regress- and then combine the results with -suest-; (b) estimate using
> -sureg-.
>
> (a) is robust but won't give you more efficient estimates of the
> coefficients.  (b) is more efficient but assumes homoskedasticity.
>
> Moreover, the var-cov estimator in (b) will be wrong, because it won't
> have adjusted for the degrees of freedom lost to the fixed effects.
> Basically, you would need to adjust the vcv matrix by hand, so that
> instead of K being the number of regressors in an eqn, it's the number
> of regressors + number of fixed effects.
>
> Below is some code that compares the two approaches but doesn't do the
> dof adjustment.
>
> Hope this helps.
>
> Cheers,
> Mark
>
> ***** suest vs sureg in a fixed effects model *****
>
> sysuse abdata, clear
> sort id
> * Use Ben Jann's -center- command to demean.
> * Make sure that the estimation sample is consistent ("casewise")
> by id: center ys k n, casewise
> by id: center indoutpt cap emp, casewise
>
> * Compare xtreg,fe and demeaned - should be the same
> xtreg ys k n, i(id) fe
> reg c_ys c_k c_n, nocons
> xtreg indoutpt cap emp, i(id) fe
> reg c_indoutpt c_cap c_emp, nocons
>
> * suest - combine eqns but with same point estimates.  Cluster on firm.
> * Does not require dof adjustment for fixed effects
> qui reg c_ys c_k c_n, nocons
> est store eqn1
> qui reg c_indoutpt c_cap c_emp, nocons
> est store eqn2
> suest eqn1 eqn2, cluster(id)
>
> * sureg - Zellner's seemingly-unrelated eqns estimator.
> * More efficient, different point estimates, but assumes
> homoskedasticity
> * Note SEs are wrong because the dofs don't account for the 140 fixed
> effects
> sureg (c_ys c_k c_n, nocons) (c_indoutpt c_cap c_emp, nocons)
>
> *****************************************************
>
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