The demographic balance equation relates the population growth rate with crude rates of fertility, mortality, and net migration. All these rates refer to changes occurring between two time points, say, t and t + h. However, this fundamental balance equation overlooks the contribution of historical fertility, mortality, and migration in explaining these population counts. Because of this, the balance equation only partially explains a change in growth rate between time t and t + h as it does not include the contribution of historical population trends in shaping the population at time t. The overall population growth rate can also be expressed as the weighted average of age-specific growth rates. In this article, we develop a method to decompose the historical drivers of current population growth by recursively employing the variable-r method on the population's average age-specific growth rates. We illustrate our method by identifying the unique contributions of survival progress, migration change, and fertility decline for current population growth in Denmark, England and Wales, France, and the United States. Our results show that survival progress is mainly having an effect on population growth at older ages, although accounting for indirect historical effects illuminates additional contributions at younger ages. Migration is particularly important in Denmark and England and Wales. Finally, we find that across all populations studied, historical fertility decline plays the largest role in shaping recent reductions in population growth rates.
Keywords: Decomposition; Population dynamics; Population growth; Variable-r.
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