st: Gravity Model ML estimation

 From "Julia A Gamas Buentello" To Subject st: Gravity Model ML estimation Date Mon, 2 Dec 2002 14:32:42 -0500

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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.

Julia Gamas
Boston University Center for Transportation Studies

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