# Re: st: test coefficients across equations [was: Re: sample selection bias]

 From "Scott Merryman" To Subject Re: st: test coefficients across equations [was: Re: sample selection bias] Date Thu, 26 Jun 2003 21:00:53 -0500

```----- 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/
```