  # st: Re: coeffs across equations

 From Christopher F Baum To statalist@hsphsun2.harvard.edu Subject st: Re: coeffs across equations Date Fri, 27 Jun 2003 06:25:07 -0400

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

*
* 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/