Citation

Arthur WB. Demography 1984; 21(1): 109-128.

Copyright

(Copyright © 1984, Population Association of America, Publisher Holtzbrinck Springer Nature Publishing Group)

DOI

unavailable

PMID

unavailable

Abstract

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.