# st: Re: fixed effects and SUR

 From "Kit Baum, Faculty Micro Resource Center" To statalist@hsphsun2.harvard.edu Subject st: Re: fixed effects and SUR Date Tue, 22 Oct 2002 10:56:39 -0400

```--On Tuesday, October 22, 2002 2:33 -0400 Jeremy wrote:

```
```Hi Everybody,

Could anybody give me some idea how to estimate SUR with fixed effects
using Stata? I'm new to Stata. All I know at this point is that I could
use XTREG to estimate a single equation with fixed effects, and SUREG to
estimate a system of equations. I've no idea how to proceed from here.
For your information, I'm trying to use Stata to "cross-check" some
appreciated.

Jeremy Z.

```
```and cb23 responded
```
```Just in case no-one comes up with a correct answer on this, I would try
the following :-

I think I am right in saying that the xtreg fixed effects model is just
a standard OLS model with dummies for the groups with one alteration: in
OLS we choose a baseline dummy for which we set the coefficient to zero
and in fixed effects we sum the dummy coefficients on all groups to
zero.  This means that the coefficients on the other Xs should be the
same in fixed effects and the dummy variable approach, and the only
difference will be in the coefficients of the constant and the group
dummies/effects.  You should try this to make sure it works.  You can
even try to choose the baseline dummy such that the coefficients on the
other dummies are close to summing to zero.

Than, having realised we can roughly write a fixed effect model as a
standard equation, you could then rewrite your fixed effect equations in
a dummy variable form and stick them in to a SUR model.
```

I find this quite confused. Note that if we start with the most general (infeasible) model of panel data, in which every i and t has its own coefficient vector, we can define special cases:

a) all slopes constant over i and t, s^2 constant over i and t, intercept varies over i

b) intercept, slopes, and s^2 all have an i subscript, but are constant over t

The former case is one-way (individual) fixed effects, aka LSDV (dummy var) model, which may be estimated by xtreg, fe or areg. Note that normalisation of the intercepts makes no difference here; no matter whether you include a constant and (n-1) dummies, or express data as demeaned by individual, you will get the same estimates in terms of significance.

The latter case is Zellner SUR, estimable via sureg. This is a 'fixed effect' model, in that each individual has his/her own equation (thus N < T for standard SUR), with his/her own intercept, set of slopes, and s^2. One can consider special cases of SUR in which further constraints are imposed (e.g. common slopes over units) which, since SUR is a GLS estimator, takes you back very close to individual fixed effects (except that SUR allows for s^2_i, whereas
IFE imposes a single s^2 on the entire panel).

So I don't know what it means to estimate SUR with fixed effects; if you're using SUR, you are already estimating individual fixed effects, and more.

Kit
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Kit Baum, Faculty Micro Resource Center fmrc@bc.edu
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