Zillmer’s population model: Theory and application

Abstract

August Zillmer (1831–1893) was a German life insurance actuary in Berlin. He is credited for one of the first German textbooks on actuarial mathematics. His name is associated with the Zillmer method of calculating life insurance reserves. In this paper, August Zillmer’s early contribution to demographic analysis, which is virtually unknown, is described and appreciated. In 1863 he published a discrete population model, and produced several age distributions using a given life table and different population growth rates. He showed that the resulting age distributions will eventually become stable. Although the stable model in demography can be traced back to Euler in 1760, Zillmer’s model is the first dynamic analysis of the influence of changes in population growth rates on the age distribution and population parameters such as mean age. His results and conclusions are discussed and compared with modern demographic methods. Finally, Zillmer’s model is considered as a tool for special population forecasts, where new inputs (births) do not depend on the population size of other age-groups.