Heterogeneity and asymmetry in cross-section gravity models of aggregate migration

The standard gravity model of aggregate migration erroneously assumes homogeneity, quasi-symmetry, and (log) linearity. As a result, estimation of the model using, say, the convenient OLS estimator is plagued by omitted-variables and misspecification biases. This paper, therefore, presents estimates for a cross-section gravity model controlling for unobserved unilateral (origin-/destination-specific) and bilateral (flow-specific) effects. Individual slopes on the bilateral linkage factors have been included to account for potentially correlated heterogeneity in the bilateral dimension that is distinctively related to distance, contiguity, and previous migration (migrant stock), respectively. To implement the model, I use a novel "three-way" fixed-effects type of Generalized Maximum Entropy estimator (FE-GME). The importance of fixed effects is demonstrated by comparing the FE-GME results with those obtained from OLS. The model is applied for an exploratory analysis of cross-sectional data on inter-state migration in Mexico during the period 1995-2000. It is found that accounting for unobserved heterogeneity in all three dimensions results in appreciably lower magnitudes of all coefficients (except the one on distance!), while most of them retain their statistical significance. Moreover, including bilateral fixed-effects is found to be instrumental in keeping with arbitrary heteroskedasticity, even if the gravity model is specified in its conventional double-log form.