st: RE: Re: fixed effects and SUR

 From baum To Nick Winter , StataList Subject st: RE: Re: fixed effects and SUR Date Tue, 22 Oct 2002 11:30:03 -0400

Nick,

If you take a panel and reshape wide by i, you can estimate the same model on sureg, right? In my mind sureg is a panel data estimator.

. use http://fmwww.bc.edu/ec-p/data/Greene2000/TBL15-1

. tsset firm year
panel variable: firm, 1 to 5
time variable: year, 1935 to 1954

. xtreg i f c,fe

Fixed-effects (within) regression Number of obs = 100
Group variable (i) : firm Number of groups = 5

R-sq: within = 0.8003 Obs per group: min = 20
between = 0.7699 avg = 20.0
overall = 0.7782 max = 20

F(2,93) = 186.40
corr(u_i, Xb) = -0.1359 Prob > F = 0.0000

---------------------------------------------------------------------------
---
i | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+-------------------------------------------------------------
---
f | .1059799 .015891 6.67 0.000 .0744236 .1375363
c | .3466596 .0241612 14.35 0.000 .2986803 .3946388
_cons | -62.59438 29.44191 -2.13 0.036 -121.0602 -4.128578
-------------+-------------------------------------------------------------
---
sigma_u | 120.02194
sigma_e | 69.117977
rho | .75095637 (fraction of variance due to u_i)
---------------------------------------------------------------------------
---
F test that all u_i=0: F(4, 93) = 58.96 Prob > F = 0.0000

. reshape wide i f c,i(year) j(firm)
(note: j = 1 2 3 4 5)

Data long -> wide
---------------------------------------------------------------------------
--
Number of obs. 100 -> 20
Number of variables 5 -> 16
j variable (5 values) firm -> (dropped)
xij variables:
i -> i1 i2 ... i5
f -> f1 f2 ... f5
c -> c1 c2 ... c5
---------------------------------------------------------------------------
--

. forv i=1/5 {
2. local rhs "`rhs' ( i`i' f`i' c`i') "
3. }

. di "`rhs'"
( i1 f1 c1) ( i2 f2 c2) ( i3 f3 c3) ( i4 f4 c4) ( i5 f5 c5)

. sureg `rhs'

Seemingly unrelated regression
----------------------------------------------------------------------
Equation Obs Parms RMSE "R-sq" chi2 P
----------------------------------------------------------------------
i1 20 2 84.94729 0.9207 261.3219 0.0000
i2 20 2 12.36322 0.9119 207.2128 0.0000
i3 20 2 26.46612 0.6876 46.88498 0.0000
i4 20 2 9.742303 0.7264 59.14585 0.0000
i5 20 2 95.85484 0.4220 14.9687 0.0006
----------------------------------------------------------------------

---------------------------------------------------------------------------
---
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+-------------------------------------------------------------
---
i1 |
f1 | .120493 .0216291 5.57 0.000 .0781007 .1628853
c1 | .3827462 .032768 11.68 0.000 .318522 .4469703
_cons | -162.3641 89.45922 -1.81 0.070 -337.7009 12.97279
-------------+-------------------------------------------------------------
---
i2 |
f2 | .0695456 .0168975 4.12 0.000 .0364271 .1026641
c2 | .3085445 .0258635 11.93 0.000 .2578529 .3592362
_cons | .5043112 11.51283 0.04 0.965 -22.06042 23.06904
-------------+-------------------------------------------------------------
---
i3 |
f3 | .0372914 .0122631 3.04 0.002 .0132561 .0613268
c3 | .130783 .0220497 5.93 0.000 .0875663 .1739997
_cons | -22.43892 25.51859 -0.88 0.379 -72.45443 27.57659
-------------+-------------------------------------------------------------
---
i4 |
f4 | .0570091 .0113623 5.02 0.000 .0347395 .0792788
c4 | .0415065 .0412016 1.01 0.314 -.0392472 .1222602
_cons | 1.088878 6.258805 0.17 0.862 -11.17815 13.35591
-------------+-------------------------------------------------------------
---
i5 |
f5 | .1014782 .0547837 1.85 0.064 -.0058958 .2088523
c5 | .3999914 .1277946 3.13 0.002 .1495186 .6504642
_cons | 85.42324 111.8774 0.76 0.445 -133.8525 304.6989
---------------------------------------------------------------------------
---

If you impose constraints that the slopes are common across equations of the SUR, you're going to be very close to a xtreg,fe model.

Kit

--On Tuesday, October 22, 2002 11:10 -0400 Nick Winter <nwinter@policystudies.com> wrote:

```Kit,

I'm confused by your mentioning of -sureg- in relation to panel models.
How does sureg estimate what you describe?  I thought of -sureg- as
estimating different models on the same cases; not the same models on
different sets of cases?

But maybe I'm just missing something obvious?

Thanks
Nick

-----------------------------------------------------------
Nicholas Winter, Ph.D.                     P 202.939.5343
Policy Studies Associates                  F 202.939.5732
1718 Connecticut Avenue, NW     nwinter@policystudies.com
Washington, DC 20009-1148           www.policystudies.com
-----------------------------------------------------------

```
```-----Original Message-----
From: Kit Baum, Faculty Micro Resource Center [mailto:fmrc@bc.edu]
Sent: Tuesday, October 22, 2002 10:57 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: Re: fixed effects and SUR

--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
be gratefully
> 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
--------------------------------------------------------------------
Kit Baum, Faculty Micro Resource Center                  fmrc@bc.edu
Academic Technology Services, Boston College   http://www.bc.edu/ats
http://fmwww.bc.edu/FMRC/                http://fmwww.bc.edu/GStat/
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