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From |
"Nick Cox" <n.j.cox@durham.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: Gravity Model ML estimation |

Date |
Mon, 2 Dec 2002 19:52:56 -0000 |

Julia A Gamas Buentello > > 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. I guess the short answer is No. For those curious about what all this means, the idea is that fluxes T_ij (say of people or of goods or of information) between places i and j in some region are deemed to be driven by characteristics of origins O_i, of destinations D_j, and of the distances d_ij between them. The distance function here is one particular choice. The term "gravity model" here is a historical misnomer based on the fact that some models before this one, which emerged in the late 1960s, used a closer analogue of Newtonian gravitation in which interaction between places was held to be similar to attraction between masses and so governed by an inverse-square law. Of course, as every traveller knows, distance between places, however defined, is not the only measure of the difficulty of interaction. This is all equivalent to an entropy-minimising approach based on statistical mechanics. There is Fortran code in R.S. Baxter's 1976 book which implements that, and I imagine that it would be less work to translate that into Stata than to try to set this up in Stata as a ML problem, unless you particularly want the side results of that as well as the parameter estimates. Or, of course, Fortran compilers continue to exist. Nick n.j.cox@durham.ac.uk * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Gravity Model ML estimation***From:*"Julia A Gamas Buentello" <ardilla@bu.edu>

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