st: Re: coeffs across equations

[Christopher F Baum <baum@bc.edu>]

On Friday, June 27, 2003, at 02:33 AM, Scott wrote in response to 
Bersant:


> Date: Thu, 26 Jun 2003 21:00:53 -0500
> From: "Scott Merryman" <smerryman@kc.rr.com>
> Subject: Re: st: test coefficients across equations [was: Re: sample 
> selection bias]
>
> - ----- 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-.
This is a FAQ on Statalist. One cannot in general test coefficients 
from separate estimations. Pooling the data and estimating a single, 
fully interacted model, as suggested, is probably the most sensible 
approach, although it does then assume homoskedasticity across the 5 
categories, which 5 separate regressions will not. Thus, one may want 
to test for groupwise heteroskedasticity if the est. sigma^2 from the 
category regressions are very different.

The suggestion for sureg relaxes that assumption, and handles the 
separate coefficients (including making it easy to test / constrain 
across equations). However most implementations of SURE will demand 
that there are the same number of observations in each equation (a 
constraint not required by SURE, in that one can calculate consistent 
estimates of the residual covariance matrix from the dot products of 
the residuals, whatever their length). I suspect Bersant may not have 
equal numbers of firms per category.

Kit

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