A General Characterization of Consistency Algorithms in Multidimensional Demographic Projection Models

Abstract

Demographic projection models describe the development over time of the population in terms of events. A consistency problem arises if projected numbers of events are required to satisfy certain constraints; the consistency problem can be seen as a generalization of the well-known two-sex problem in nuptiality models. This paper presents a very general characterization of consistency problems, using matrix notation, as well as a slightly less general algorithm to solve them. The preferred specification of the objective function to be minimized by the algorithm leads to a solution that can be interpreted as a generalization of the harmonic-mean approach.