title: The analysis of linkages in demographic theory.
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.
mesh_terms: D000328:Adult; D000367:Age Factors; D000368:Aged; D003710:Demography / Q000379:methods*; D005260:Female; D005298:Fertility; D006801:Humans; D008297:Male; D008433:Mathematics; D008875:Middle Aged; D009026:Mortality; D011157:Population Dynamics; D013223:Statistics as Topic