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Re: st: Unknown number in constraints


From   Maarten buis <maartenbuis@yahoo.co.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Unknown number in constraints
Date   Tue, 10 Mar 2009 08:31:16 +0000 (GMT)

--- On Tue, 10/3/09, jjc.li@utoronto.ca <jjc.li@utoronto.ca> wrote:
> I have to regress the translog cost function with
> parametric restrictions. One of the restrictions is
> 
> a11= -d11^2+a1-a1^2
> a12= -d11d21-a2a1
> .................
> a33= -d31^2-d32^2-d33^2+a3-a3^2
> 
> a11 to a33 are all parameters appeared in the cost function
> and other constraints, but d11 to d33 are all unknown
> numbers. So how to define the constrain above in stata?

I see to difficulties here (all solvable, but not easily): First, the
constraints are non-linear (they include a square term). Second, they contain numbers that apperently need to be estimated (the d-s). Both problems rule out using the -constraint- command, which would be the easy way of including constraints. What might be possible is to rewrite this model as a nonlinear least squares problem, in which case you can use -nl- to estimate this model. If that is not possible then you can define your own likelihood function which has these constraints hard coded in. The way to do that in Stata is to use the -ml- command. If you choose to go that way then you will probably need access to this book 
http://www.stata-press.com/books/ml.html

Hope this helps,
Maarten

-----------------------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://home.fsw.vu.nl/m.buis/
-----------------------------------------





      

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