# st: Test coefficients across equations

 From Bersant Hobdari To statalist@hsphsun2.harvard.edu Subject st: Test coefficients across equations Date Fri, 27 Jun 2003 10:52:03 +0100

```Hi Everyone,

Many thanks to Scott Merryman, David Moore and Mike
Hollis for their comments on my original message. I
however have still some doubts regarding the way I
should follow. I will explain it in more detail taking also into
account comments of Scott, David and Mike.

I am estimating the same specification on different
samples and want to test coefficients equality across the
samples. The main gist of Scott, Davis and Mike
argument was that I introduce ownership dummies and
respective interactions in the pooled sample and then
apply Chow type tests on individual equations. This
however, as they themselves stress, needs sub-samples
to be independent.

I have serious doubts that my sub-samples are
independent. More specifically, I divide the big sample into
smaller ones based on majority ownership. Given that
ownership changes over time a given firm might be
present at different sub-samples over time. I assume this
is enough to state that sub-samples are not independent.
The reason for sample separation is the endogeneity of
ownership structures to the left hand side variable, labor
productivity in this case. If I ignore this problem I will be in
a bigger problem that the one I am trying to solve.

Given non-independence then what is the way to test
coefficient equality across equations. One suggestion
would be to use Zellner's SUR method, suggested by
Scott. To my knowledge however SUR estimates equation
by equation OLS
accounting for cross equation correlation. I however have
used GMM (through ivreg2 procedure) to obtain
estimates. Can SUR be used with GMM?

The big question then becomes: how do I test  coefficients
equality across equations estimated on different samples
when samples are not independent?

Any help is highly appreciated.
Sincerely,
Bersant Hobdari
Content-Type: multipart/alternative; boundary="--=a921961f-c433-46a5-840e-89a84a4a191d"

----=a921961f-c433-46a5-840e-89a84a4a191d
Content-Type: text/plain
Content-Transfer-Encoding: 7bit

****************************************************************************
Denne e-mail er scannet af mailFence fra Sure Solutions (www.suresolutions.dk),
og der er ikke fundet vira.
****************************************************************************

----=a921961f-c433-46a5-840e-89a84a4a191d
Content-Type: text/html
Content-Transfer-Encoding: quoted-printable

<HR>

<DIV align=3Dcenter><FONT face=3DArial size=3D1>Denne e-mail er scannet a=
f mailFence=20
fra Sure Solutions (</FONT><A href=3D"http://www.suresolutions.dk";><FONT =

face=3DArial size=3D1>www.suresolutions.dk</FONT></A><FONT face=3DArial s=
ize=3D1>), og=20
der er ikke fundet vira.</FONT></DIV>
<DIV>
<HR>
</DIV>
</BODY></HTML>

----=a921961f-c433-46a5-840e-89a84a4a191d--
```
```----- Original Message -----
From: "Bersant Hobdari" <bh.cees@cbs.dk>
To: <statalist@hsphsun2.harvard.edu>
Sent: Thursday, June 26, 2003 11:51 AM
Subject: Re: st: Re: sample selection bias

> Hi Everyone,
>
> I had a question on testing coefficient across separately estimated
> samples. The problem is the following: I estimate firm-level production
> function where I divide the sample in 5 sub-samples defined by majority
> owner: I.e., if majority owner is the State I classify the firm in that
> group, if it is a financial institution I classify it in that group and
> so on. After estimating regressions I would like to test the equality of
> coefficients across equations.
>
> Any suggestion how this could be implemented is highly appreciated.
>
> Sincerely,
> Bersant Hobdari

You could create a dummy variable on majority owner then interact it with
your other variables and test the coefficients on the fully interacted model
(see the Stata FAQ on Chow tests).  Example using the auto dataset.

Equation 1:  mpg =  b0 + b1*price  (if domestic)
Equation 2:  mpg  = b0' + b1'*price (if foreign)

Create the interaction term (if you have more categories -xi- comes in
handy)
gen priceXforeign = price *foreign

Regress the full interacted model
regress mpg = price foreign priceXforeign

A test on foreign will compare common intercepts, a test on priceXforeign
will test common slopes, and a test on both foreign and priceXforeign will
test if they are jointly equal to zero, or if equation 2 differs from
equation 1.

However, if you are concerned about correlation across equation (or wish to
test for it), -reshape- your data into a wide data structure and
use -sureg-.

Hope this helps,
Scott

*
*   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/
```
```begin:vcard
n:Hobdari;Bersant
fn:Bersant Hobdari
version:2.1
email;internet:bh.cees@cbs.dk
end:vcard

```