title: Population momentum: A wider definition.
abstract: Summary   Keyfitz has derived an elegant formula for estimating the ultimate size of an initially stable, growing population that abruptly reduces its fertility to replacement level. Reduction of fertility is achieved by the rather unrealistic device of dividing the original age schedule nffertility rates by the net reproduction rate. Only the inertia of the age distribution is thus accounted for, but not that of the fertility schedule. The key idea of an abrupt imposition of a fixed regimen capable in the long run of generating zero population growth may be retained, but the regimen made more realistic. By elaborating the population setting, such disparate ZPG regimens as reduction of marital fertility by contraception, delayed and/or less universal marriage, raised mortality risks, or permanent net out-migration may be formulated. Convergence of the populaton to stationarity becomes a two-phase process: a primary adjustment period of changing fertility rates followed by a period of age adjustment.   The present paper treats what happens when a fixed ZPG sterilization regimen, defined by a minimum age of sterilization γ and constant continuous risk φ of sterilization among unsterilized wives aged γ to β, is imposed abruptly (or else progressively over an interval T) upon an initially stable, growing population. Additional sources of residual growth are: (1) the nine-month lag in sterilization effect owing to pregnancy: (2) the more youthful pattern of child-bearing under sterilization: (3) the extra adjustment period (of length β-γ-0.75) of changing fertility rates; and (4) any delays in exposing elements of the population to the sterilization regimen.   Two questions are pursued. First, how important are the additional sources of residual growth? Secondly, how do their relative sizes vary as a function of the characteristics of the initial population?
authors.forename: R G
authors.initials: RG
authors.lastname: Potter
authors.forename: O
authors.initials: O
authors.lastname: Wolowyna
authors.forename: P M
authors.initials: PM
authors.lastname: Kulkarni