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Re: st: Imposing Parameter Restriction


From   Hung-Jen Wang <hjwang@econ.sinica.edu.tw>
To   Hyeok Jeong <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Imposing Parameter Restriction
Date   Fri, 6 Aug 2004 08:50:31 +0800


Friday, August 6, 2004, 6:03:15 AM, Hyeok Jeong wrote:

> Dear Statalisters:

> I am trying to estimate a nonlinear model using "nl" and this is my first
> time of doing it. Let's say the model is written as "y= f(l;a,b)," where a
> and b are the parameters to be estimated. The model restricts the parameter
> space such that "0 < a < 1" and "b <1".
> Without imposing any restrictions, it turns out that estimates from "nl"
> method violate these restrictions.


If x has a theoretical bound between -1 and +1, then you may
parameterize x as

                exp(y) - exp(-y)
        x = ------------------------------ ,
                exp(y) + exp(-y)

where y is a free, unrestricted parameter. You may also want to see
[R] Heckman for a different parameterization adopted by Stata.

For b<1, I guess you can do

        b = -exp(y) + 1

where y is a free, unrestricted parameter.

Hope it helps.

HJ Wang

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