Linkages of intrinsic to age-specific rates

For more about the East-West Center, see http://www.eastwestcenter.org/We know that changes in birth rates at particular ages of women affect the overall increase of a population, its age distribution, and other features. Our object here is to ascertain the amount of the effect. For example, a fall in the age-specific birth rate of women aged 40-44 will tend to raise the mean age of the population; the paper finds an expression for the fraction of a year by which the mean age is raised by a given alteration in the birth rate to women aged x. We implicitly compare two populations, the same in all other respects but the age under study, in which fertility and mortality remain constant for a long period of time. The formulas show by how much the long-term projections differ if births differ at one age of women only and deaths are identical.The effects of changes in death rates at particular ages are more pervasive, because mortality acts through the life table numbers surviving to the several ages, and a change in the age specific rate at a particular age thus affects all subsequent ages. The paper finds expressions for the effects of changes in death rates analogous to those for the changes in birth rates. The Appendix Table presents the results in one place for births and deaths.To illustrate and verify some of the formulas a computer program was run, projecting the population of Mexico 1966 with observed rates, and with an increase in the deaths at ages 25-29 and 50-54