Migrants looking for opportunities - On destination size and spatial aggregation in the gravity equation for migration

I consider a RUM model for migration where destination countries or regions are viewed as collections of ‘opportunities’ which are the fundamental units of choice for migrants. The best opportunity for a prospective migrant is more likely to be found in a destination that has many and diverse opportunities. Recent contributions in economics studying migration rather consider entire regions or countries as the fundamental, atomistic, units of choice. The key role of the size of destinations and the diversity within them is therefore often not fully recognised, which may lead to biased inference. I argue that the coefficient on size equals 1 in the ideal RUM model. This is also required for the gravity model for migration to have some intuitive properties: only then migration flows scale proportionally when aggregating destinations, and there is zero net migration between otherwise similar regions of different size. Models omitting size or using a coefficient on size different from 1 violate these properties. Imposing proportional scaling also has implications for how different sets of opportunities should be combined. The approach is showcased in a study of internal migration and urbanisation in Ethiopia.