Transitivity, Spatially Separable Utility Functions, and United States Migration Streams, 1935–1970

The predictions of spatial-interaction models applied to migration systems may be viewed as the outcome of expected-utility maximization in which the average beliefs and preferences at a given origin are spatially separable. This theory indicates that a test of the spatial separability of the utilities may be performed by examining the degree of transitivity in probabilities and gross flows that is predicted by the spatial-interaction models. United States migration data for four periods between 1935 and 1970 were examined for transitivity at three spatial scales of resolution. These flows all exhibited significantly high degrees of transitivity, although for no period or scale of resolution were migration flows completely without some statistically significant intransitivities in either the probabilities or gross flows. The regions involved in intransitivities varied greatly from period to period, and only weak evidence indicated lower degrees of intransitivity for local aggregates of regions. The hypothesis of spatially separable utilities must be rejected for the migration data examined. Theoretical discussion indicates that several causes may lead to intransitivities, which in turn lead to problems in applying spatial-interaction models to migration data.