The Analysis of Causal Linkages in Demographic Theory

Arthur, W.B. (1980). The Analysis of Causal Linkages in Demographic Theory. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-80-110

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Abstract

Many seemingly different questions that interest, demographers 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 "causal linkage method" on three bodies of theory: stable population analysis, non-stable or transient population analysis, and demographic incomplete-data estimation techniques.

In stable theory closed-form expressions are obtained for the response of the intrinsic growth rate, birth rate and age composition to arbitrary marginal changes in the fertility and mortality age patterns.

In non-stable theory, expressions are obtained for the transient response of the age composition to time-varying changes in the birth sequence, and to changing age-specific fertility and mortality patterns. The problem of bias in period vital rates is also looked at.

In incomplete data analysis a general format for robustness or error analysis is suggested; this is applied to a standard Brass estimation technique.

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