The Momentum of Real Population Under Linear Fertility Transition

Population momentum is the ratio of a population's ultimate size after a demographic transition to its initial size before the transition. For stable population and instantaneous drop to replacement fertility, Keyfitz found a simple formula for the momentum. Although Keyfitz's formula has been extended to cover gradual demographic transitions, the stable initial population, however, is still an obstacle to approaching reality. Using the solution of the Lotka equation with time-varying vital rates and extending it to negative values of time, exact and accurate formulae for the momentum of any initial population that undergoes a linear fertility transition are expressed. Examples using the data from the United Nations indicate that the accurate formula works well for the age structures that are far from stable such as the more and less developed regions, as well as that close to stable such as the least developed region.