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Re: st: Unknown number in constraints


From   jjc.li@utoronto.ca
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Unknown number in constraints
Date   Tue, 10 Mar 2009 09:43:45 -0400

Thanks Maarten,

So you mean use -nl to treat all those a system of nonlinear equations, don't you?

I forgot to tell you that what I am donig is seemingly unrelated regression (-sureg-). Does it affect the -nl- method?

For example, there are total 4 functions (1 cost functions together with 3 cost share equations), 5 normal constraints and 2 constrains with the unknown numbers. Then I can get all the parameters and unknown numbers by solving the 11 equations system like following:

    f1(a1,...,an) = 0
    f2(a1,...,an) = 0
    .
    .
    .
    f11(a1,...,an) = 0


Jingjing




引用 Maarten buis <maartenbuis@yahoo.co.uk>:


--- 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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