8 - Reconstitution and inverse projection

Summary

This volume is the second of a pair which, from the beginning, were viewed as part of a single enterprise. It is important, therefore, to consider whether the evidence taken from parish reconstitutions agrees with that derived from aggregative data. The conversion of aggregative data into demographic estimates was originally carried out by using a method called back projection (BP), which has now been superseded by a more flexible and refined method known as generalised inverse projection (GIP), which belongs to a family of statistical techniques whose properties are better understood.

The estimates of fertility, mortality, and nuptiality which were published in the Population history of England were in principle open to correction and improvement in each of three different ways. First, the change from BP to GIP might produce different demographic estimates, even with unchanged input data and input parameters (that is, such matters as the assumptions made about the age structure of cohort migration). Second, the new knowledge gained from reconstitution might make it appear that different input data were to be preferred to those used earlier. And, third, reconstitution data might suggest that the input parameters should be altered to reflect, say, a revised view about changes in the age structure of mortality in the past. It is convenient to consider each of these points in turn.

Generalised inverse projection and back projection

In 1974 Lee achieved a breakthrough by developing a technique which he christened inverse projection (IP) to generate estimates of the demographic characteristics of a population from long-run aggregative data.