Theoretical Underpinnings of the Gravity Hypothesis

Various theoretical rationalizations of the gravity hypothesis for spatial interaction are examined. Deterministic utility theory cannot account for variability in individual behavior. Choice models based on Luce's axiom contain some inconsistencies. Random utility theory provides a probabilistic formulation that is internally consistent, and also solves the aggregation problem. However, investigation reveals that, although this provides a theoretical justification for gravity-like behavior, the assumptions made are sufficiently unrealistic to cast doubt on the empirical validity of the gravity hypothesis.     

Gravity Parameter Estimation

The question of whether ordinary least-squares (OLS) regression provides unbiased estimates for parameters of the gravity model is investigated. Holding attractiveness constant and looking only at the location of destinations, OLS is shown to give unbiased estimates if underlying behavior conforms to the gravity hypothesis. Johnston's conjectures on this are examined and found to explain only partially observed variations in distance exponents. Allowing attractiveness to vary, spatial autocorrelation in attractiveness is shown to lead to bias in OLS estimation due to misspecification, even where behavior conforms to the gravity hypothesis. Deterministic and stochastic illustrations are provided.