Arthur W B
Demography. 1984 Feb;21(1):109-28.
Many seemingly different questions that arise in the analysis of population change can be phrased as the same technical question: How, within a given demographic model, would variable y change if the age- or time-specific function f were to change arbitrarily in shape and intensity? At present demography lacks the machinery to answer this question in analytical and general form. This paper suggests a method based on modern functional calculus for deriving closed-form expressions for the sensitivity of demographic variables to changes in input functions or schedules. It uses this "linkage method" to obtain closed-form expressions for the response of the intrinsic growth rate, birth rate, and age composition of a stable population to arbitrary marginal changes in its age patterns of fertility and mortality. It uses it also to obtain expressions for the transient response of the age composition of a nonstable population to time-varying changes in the birth sequence, and to age-specific fertility and mortality patterns that change over time. The problem of "bias" in period vital rates is also looked at.
在人口变化分析中出现的许多看似不同的问题，都可以表述为同一个技术问题：在给定的人口模型中，如果特定年龄或特定时间的函数f在形状和强度上任意变化，变量y将如何变化？目前，人口统计学缺乏以分析性和一般性形式回答这个问题的机制。本文提出了一种基于现代泛函演算的方法，用于推导人口变量对输入函数或时间表变化的敏感性的封闭形式表达式。它使用这种“联系方法”来获得稳定人口的内在增长率、出生率和年龄构成对其生育率和死亡率的年龄模式的任意边际变化的响应的封闭形式表达式。它还使用该方法来获得非稳定人口的年龄构成对出生顺序的随时间变化、以及随时间变化的特定年龄生育率和死亡率模式的瞬态响应的表达式。同时也探讨了时期生命率中的“偏差”问题。
