A Leslie-type urban-rural migration model, and the situation of Germany and Turkey

Harald Schmidbauer, Istanbul Bilgi University
Angi Rösch, FOM University of Applied Sciences

The phenomenon of population ageing is often accompanied by substantial rural-urban migration. It is therefore compelling to analyse the implications of fertility, mortality, and migration patterns together. We introduce a new Leslie-type population model which describes the age structure of urban and rural populations and allows for migration in both directions. This model can project the current population structure into the future and also permits an analysis of the long-run properties of the population such as future urbanisation and age dependency ratio under the assumption that current conditions persist, as well as under assumptions of certain secular trends in demographic phenomena. We show how this model can be transformed into a Markov chain, whose steady-state behaviour is used to derive genealogies in terms of the Markov chain running backward in time. In addition to projecting the future population structure, our model facilitates a plausibility check for age-specific fertility, mortality, migration, and population growth data, which can be crucial in cases where the reliability of data is questionable. Furthermore, it permits an assessment of the difference between the actual population and its stable counterpart, which can be a valuable tool for policy makers. Applying the model to real-world populations, we study the population structures of Germany and Turkey when exposed to their current respective fertility, mortality, and migration patterns. We find that the current extent of German rural depopulation is a transient phenomenon. We also find that the current Turkish population is younger and its urbanisation is higher than those of its stable counterpart. The impact of migration policies on the population structure, in particular growth, urbanisation, and age dependency ratio, is discussed for both countries.