A simple method for estimating inter-generational replacement based on fertility and migration – some European examples

Chris Wilson, University of St Andrews
Tomas Sobotka, Vienna Institute of Demography
Paul J. Boyle, University of St Andrews
Lee Williamson, University of St Andrews

Concern over unprecedentedly low levels of childbearing in Europe has become increasingly marked among both scientists and policy-makers. In conjunction with the concerns over fertility, there has also been considerable debate on the role migration can play in compensating for fertility below the replacement level. For example, in 2000, the United Nations report Replacement migration: Is it a solution to declining and ageing population? Triggered extensive media comment on the matter. The issue of how to measure inter-generational replacement has been addressed by several scholars in recent years (Smallwood and Chamberlain 2005, Ortega and del Rey 2007, Preston and Wang 2007, Sobotka 2008). In this paper we make use of a very simple method to assess how far migration alters the extent of replacement for a birth cohort as it ages. We term the measure used here the overall replacement ratio (ORR). It is calculated by taking the size of a female birth cohort divided by the size of the cohorts of mothers in the year of birth. For example, we can compare the size of the 1975 cohort over time to the number of women in the main childbearing ages in 1975. Using annual estimates of the size of the 1975 cohort enables us to track the impact of migration on its implied level of replacement. Where immigration is significant, the ratio climbs over time, often reaching the replacement level by the age of 30. The paper presents estimates of the ORR for several European countries demonstrating different replacement regimes. Although extremely simple, the ORR has an intuitive appeal, and helps us see very clearly how a population’s history of fertility, mortality and migration is written into its age structure.