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RE: st: RE: how to do parameter restrictions in fe, re be models


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: RE: how to do parameter restrictions in fe, re be models
Date   Thu, 19 Nov 2009 00:13:22 -0000

Rup,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Rup Singh
> Sent: 18 November 2009 23:23
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: RE: how to do parameter restrictions in fe, 
> re be models
> 
> thanks Nick
> 
> Let me explain, 
> 
> suppose y is a linear function of a & b. i want to estimate y 
> such that the coefficients of a and b adds to one in panel 
> data methods. can anyone suggest some commands.

Y = aX + bZ + u_i + e_ij

a+b=1

Y = aX + (1-a)Z + u_i + e_ij

Multiply out and rearrange:

(Y-Z) = a(X-Z) + u_i + e_ij

So just regress a new variable V=Y-Z on another new variable W=X-Z:

V = aW + u_i + e_ij

The coefficient on W will be a, and b will be (1-a).  This is an example
of the kind of parameterisation trick Nick was talking about.  As you
can see, it carries through to the panel data case because the u's and
e's are not involved.

Cheers,
Mark

> 
> 
> rgds
> 
> rup
> 
> 
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