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st: Inequality Restrictions with CLogit

From   L S <>
Subject   st: Inequality Restrictions with CLogit
Date   Sat, 2 May 2009 12:24:06 -0700


I am trying to estimate a simple logit binary discrete choice model
using clogit.  For example, utility for person i from option j is
given by

U(ij) = b1*x1(ij) + b2*x2(ij) + e(ij)

where the error e is distributed Type 1 Extreme Value.  Currently, in
my data, I am receiving a nonsensical negative sign on b1—I would like
to restrict the maximum likelihood estimation to have b1 be positive.
I came across the following post on maximum likelihood (ML) estimation
with interval constraints, which seems fairly related:

It seems that, while inequality restrictions are not directly built
into STATA, one can implement them by replacing b1 with exp(c):

U(ij) = exp(c)*x1(ij) + b2*x2(ij) + e(ij)

and then estimating c and b2, as the expression exp(c) will always be

My question is: How would one actually program this in practice using
clogit?  Can one actually use clogit with this, or is it necessary to
use ML?

To get some data to see the issue at hand, one can do:

webuse lowbirth
clogit low lwt smoke, group(pairid)

How could one restrict the coefficient on lwt to be positive?  (I have
no idea for this data if this restriction would make sense.)

Thanks a lot!

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