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st: Gravity Model ML estimation


From   "Julia A Gamas Buentello" <ardilla@bu.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Gravity Model ML estimation
Date   Mon, 2 Dec 2002 14:32:42 -0500

______________________________________________

 Hi,

 Does anybody have a subroutine that will solve the following problem?:

 I have a gravity model of the form:

 Tij = Ai *Oi* Bj* Dj * (d to the minus beta), where

Ai = Sumation over i of [Bj* Dj * (d to the minus beta)]

and

 Bj = Summation over j of [Ai Oi * (d to the minus beta)]

 The purpose is to find beta using non-linear maximum likelihood.  The Ai
and Bj are balancing factors that "guarantee" that two constraints are met.
I want to estimate it using maximum likelihood.  The procedure is to start
with a beta=1, then use it to iterate Ai and Bj until Ai and Bj no longer
change, then to go back and check that a constraint equation is met.  The
constraint equation is:

 estimated sum over i and j of Tij ln(dij) = the "real" sum over i and j of
Tij ln(dij)

Does Stata have a subroutine that already does this?  I am hoping to save
some graduate student hours and not have to write up the program from
scratch.

 Thank you for any help you can give me.

Julia Gamas
Boston University Center for Transportation Studies


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