Estimation of a continuous spatio-temporal population model

In this paper we propose a continuous spatio-temporal model that describes population change in a region in terms of population growth, migration drift towards regions with better economic or climate conditions, and population diffusion from more populated to less populated areas. Finite-differences are used to approximate the space and time derivatives. The model is estimated by using population data from the US census corresponding to the period 1790-1910. People tend to migrate from east to west, and to relocate towards regions with lower precipitation levels and more abundant coal and iron resources. Also population growth tends to be larger in zones with higher precipitation levels and higher temperatures.