Heterogeneity and Asymmetry in Cross-Section Gravity Models of Aggregate Migration : The Case of Mexico

The standard empirical gravity model of aggregate migration typically assumes homogeneity, quasi-symmetry, and (log-) linearity in bilateral "migration costs." However, estimation is likely to be plagued with severe mis-specification bias if no attempt is made to control for unobserved migration selectivity and unmeasured spatial heterogeneity. This paper presents an alternative specification of the cross-section gravity model, controlling for unobserved unilateral (origin- and destination-specific) and, most importantly, bilateral (flow-specific) effects. Specifically, individual slopes account for correlated heterogeneity in the bilateral dimension, where linkage factors such as distance and migrant stock (past migration) are allowed to interact separately with bilateral fixed effects. This more general gravity model is applied for an exploratory analysis of inter-state migration in Mexico (1995-2000) and estimated by using the Generalized Maximum Entropy method. The empirical importance of relaxing the standard assumptions is demonstrated by comparing the FE-GME estimates with those obtained from OLS. Furthermore, it is found that the effects of distance and migrant stock jointly account for about 50% of the variation in (the log of) gross migration flows, though the greater part of their contribution is attributable to unobserved bilateral heterogeneity effects (assumed to be largely capturing channeled “herd behavior” in the case of migrant stock), whilst macro socio-economic “push and pull” factors at origins and destinations (unemployment rates, incomes per capita, etc.) have a small explanatory power of no more than about 2%. Finally, it is shown that the inclusion of bilateral fixed-effects interactions in the log form of the gravity model is instrumental in keeping with arbitrary heteroskedasticity