Evaluation and extension of the radiation model for internal migration

Human migration is often studied using gravity models. These models, however, have known limitations, including analytic inconsistencies and a dependence on empirical data to calibrate multiple parameters for the region of interest. Overcoming these limitations, the radiation model has been proposed as an alternative, universal approach to predicting different forms of human mobility, but has not been adopted for studying migration. Here we show, using data on within-country migration from the USA and Mexico, that the radiation model systematically underpredicts long-range moves, while the traditional gravity model performs well for large distances. The universal opportunity model, an extension of the radiation model, shows an improved fit of long-range moves compared to the original radiation model, but at the cost of introducing two additional parameters. We propose a more parsimonious extension of the radiation model that introduces a single parameter. We demonstrate that it fits the data over the full distance spectrum and also—unlike the universal opportunity model—preserves the analytical property of the original radiation model of being equivalent to a gravity model in the limit of a uniform population distribution.

Figure 1

Observed (tax return based) and model data for internal migration in the USA on a county level [22]. Panels (a) and (b) show the distribution of migrant flows over travel distance (in 20-km bins; $y$ axis indicates share of total migrant flow), for distances below (a) and above 200 km (b). Analogously, panels (c) and (d) display the distribution of migrant flows over destination population size. Panels (e)–(h) display the Sørensen-Dice coefficient for each model as a function of traveled distance (150-km bins) and origin population size (33 333-inhabitant bins). Panels (j)–(m) compare the census and the model value of each individual flow. The orange line is the identity line. Black circles indicate the average, and error bars indicate the 25th and 75th percentile, across a range of different size classes.

Figure 2

As Fig. 1 but for Mexico, with observations based on microcensus data [23]. Binning distance in (a) and (b) is 20 km. Sørensen-Dice coefficients in panels (e)–(h) are shown for 100 km and 100 000 inhabitants bins.

Figure 3

Observed migration flow density in (a) the USA (IRS) and (b) Mexico (IPUMS), in terms of traveled distance and origin population population size. The colorbar indicates the number of migrants.

Figure 4

Observed and model data for inter- and intrastate migration originating in (a) Texas and (b) San Luis Potos. Observed flows were taken from census data [23, 24]. Panels A–E display the spatial distribution of arriving intrastate migrants and panels F–K display the distribution of arriving interstate migrants.