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Re: st: constrained least squares, multiple equations


From   Richard Williams <Richard.A.Williams.5@nd.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: constrained least squares, multiple equations
Date   Thu, 04 Mar 2004 22:42:41 -0500

At 07:49 PM 3/4/2004 -0600, Scott Merryman wrote:
I don't believe this is the way to go -- in order to perform cross-equation
tests you would need correlated errors.

From the help on -reg3, ols-

"Note that the covariance of the coefficients between equations is not estimated
under
this option and that cross-equation tests should not be performed after
estimation with
ols. For cross-equation testing, use sureg or 3sls (the default)."
I saw that too. But, since Olena wants to use least squares, the implication seems to be that the covariance between equations should be zero. But like I said originally, maybe 3sls would be more appropriate. We probably need to know more about the substance of the problem here.


Another possible way is pool the data, estimate a single fully interacted model
and test whether or not the coefficient of the interaction term is equal to
zero. However, this does impose the assumption of homoskedasticity across the
model.
If Y1 and Y2 and X1 and X2 stand for the values of Y and X in 2 different populations, then it is fairly straightforward to do this. But, if Y1, Y2, X1 and X2 are 4 different variables in the same population, it gets trickier. I think you'd have to duplicate the data and do various manipulations of the variables. Before going to the trouble of figuring all that out, it would be good to have a better understanding of the problem first.

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