Automatic parametrization of age/ sex Leslie matrices for human populations

Abstract

In this paper, we present a technique for parameterizing Leslie transition matrices from simple age and sex population counts, using an implementation of "Wood's Method" [wood]; these matrices can forecast population by age and sex (the "cohort component" method) using simple matrix multiplication and a starting population. Our approach improves on previous methods for creating Leslie matrices in two respects: it eliminates the need to calculate input demographic rates from "raw" data, and our new format for the Leslie matrix more elegantly reveals the population's demographic components of change (fertility, mortality, and migration). The paper is organized around three main themes. First, we describe the underlying algorithm, "Wood's Method," which uses quadratic optimization to fit a transition matrix to age and sex population counts. Second, we use demographic theory to create constraint sets that make the algorithm useable for human populations. Finally, we use the method to forecast 3,120 US counties and show that it holds promise for automating cohort-component forecasts. This paper describes the first published successful application of Wood's method to human populations; it also points to more general promise of constrained optimization techniques in demographic modeling.