Introduction

Richard Stone's work teaches us the importance of identifying the proper intersectoral or interstate flows to enter as numerators in constant-coefficient social accounting models, and of relating these numerators to appropriate denominators measuring stocks. When applied in demographic definitional and structural equations, such procedures lead to correctly specified ‘incidence’ rates and the subpopulations ‘at risk’ of experiencing the changes brought about by these particular rates. In this context, models of the determinants and consequences of migration, for example, that rely on the ‘net migration rate’ are misspecified. So too are models of labour force activity that rely on the ‘labour force participation rate’. In both instances the denominators of the rates do not correspond to the subpopulations that are at risk of experiencing the events represented in the numerators. The result is a confounding of relative propensities with relative population sizes. Demographic innumeracy produces a biased model.

This chapter focusses on demographic innumeracies committed in mathematical representations of demographic processes involving multiple interdependent populations and goes on to show how the demographic accounting principles advocated by Stone (1971) can be used to identify some of the misspecifications that are thereby introduced.

Heterogeneity, selection and the definition of rates

As a population composed of heterogeneous subgroups ages, the members with the highest risks of exit from the population leave first. This differential selection can produce exit patterns for the aggregate population that deviate from those of the constituent subpopulations.