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st: Test coefficients across equations


From   Bersant Hobdari <bh.cees@cbs.dk>
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
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----- 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









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