A note on the balancing factors of gravity models

Abstract

Application of the production constrained gravity-type spatial interaction model generally incorporates a “balancing of attractions” procedure to yield the fully constrained condition. Two techniques for balancing a singly constrained gravity model are compared in this note. These are the Federal Highways Administration adjusted attraction factor method and the Furness column and row balancing procedure. This comparison shows firstly that the two techniques are identical, and secondly that the balancing procedure results in an arbitrary distortion of the calibrated distribution function. Furthermore, some empirical results show that the balancing procedure does not necessarily improve the model's predictions on a cell by cell basis. These results indicate that balancing may be an unnecessary as well as undesirable step in the application of the singly constrained gravity model.