Immigration into a Population with Fertility below Replacement Level – The Case of Germany

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Abstract
In this paper stable population theory is used to study the demographic effects of a steady stream of immigrants into a population with fertility below replacement level. It is assumed that the fertility of foreigners (persons born outside the country) is higher than that of the native-born. We present a discrete-time Leslie-type model and analyse its asymptotic stationary behaviour. We prove that the asymptotic ratio between foreign-born and native-born does not depend on the size of the immigration flow, but solely on the relative fertility of the two groups, the sex ratio, and age distribution of the immigrants. In contrast to the continuous-time approach in which deep results of renewal theory have been used to establish this result, our proof is elementary. The analytical model is supplemented by numerical simulations with German data which show the effects of continuous immigration on the size of the population and on the ratio of foreign-born citizens in the united Germany under different demographic regimes.

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