Accounts and Models for Spatial Demographic Analysis 3: Rates and Life Tables

The paper begins by distinguishing, with the aid of the Lexis diagram that plots age against time, three kinds of demographic rate: age-group rates, period rates, and life-table rates. There are single-region and multiregion versions of those rates. In order to measure multiregional life-table rates, life-table accounts are developed together with an accounts based model that estimates the full accounts matrix from available data. These multiregional rates are then used to construct multiregional life tables akin to those recently proposed by Rogers. It is shown that the calculations involved in measuring the survivorship probabilities of the life table can be succinctly summarized in Stone's fundamental matrix. The detailed connections between life-table accounts and age-group accounts are explored, and the possibility of age-group life tables raised. The conclusion is reached that the age-group accounts are the appropriate ones for generating rates for use in population projection models, and that the life-table accounts are the appropriate ones for generating rates for use in actuarial calculations.