Back projection and inverse projection: members of a wider class of constrained projection models.

Constrained by estimated population totals and observed totals of births and deaths, estimates of age-structures from inverse projection have been widely used in historical demography. Back Projection attempted, by using hypothetical constraints on net-migration, to estimate the population totals as well, and has been used to derive ‘censuses’ for England from 1541 to 1871. A wider formulation, called Generalised Inverse Projection, is proposed in this paper, which replaces back-projection and establishes its relation to Inverse Projection more clearly. Under the same assumptions as back projection, but using the new method, the estimates for England are virtually unchanged. This new method is capable of performing population projections, subject to a wide variety of hypothetical and empirical constraints, for contemporary as well as historical data.