Compare methods

	Inverse Projection	Historical GDP Back-Projection
Field	Historical Demography	Economic History
Family	Process / pipeline	Process / pipeline
Year of origin	1981	2001
Originator	Ronald Lee; E. A. Wrigley and R. S. Schofield; generalized by Jim Oeppen	Angus Maddison; with indicator methods from Robert Allen, Paolo Malanima, and Jan Luiten van Zanden
Type	Demographic reconstruction from aggregate flows	descriptive-extrapolation
Seminal source	Wrigley, E. A., & Schofield, R. S. (1981). The Population History of England 1541-1871: A Reconstruction. Edward Arnold / Harvard University Press. ISBN: 9780674690073	Maddison, A. (2007). Contours of the World Economy 1-2030 AD: Essays in Macro-Economic History. Oxford University Press. ISBN: 9780199227204
Aliases	Back projection, Generalized inverse projection, Demographic back-projection, Lee-Wrigley-Schofield projection	Maddison back-projection, Indicator-based GDP estimation, Retrospective GDP extrapolation, Benchmark-and-interpolation GDP
Related	4	3
Summary	Inverse projection, and its more flexible successor generalized inverse projection, reconstructs the demographic history of a population from the outside in. Where conventional cohort-component projection runs a known population forward using assumed rates, inverse projection runs the logic backward: starting from a population of known size and age structure at one date, and given annual totals of births and deaths, it infers the population sizes, age distributions, mortality levels, life expectancies and fertility rates that must have prevailed in earlier years. The technique was devised by Ronald Lee and applied by Wrigley and Schofield to their English aggregative series, allowing three centuries of population history to be recovered without any direct census before 1801. Jim Oeppen's generalization relaxed restrictive assumptions about migration and closed populations. The method is the bridge that turns raw counts of vital events into a fully articulated demographic regime.	Historical GDP back-projection estimates long-run income for periods too thinly documented for full national accounting. Rather than rebuilding sectoral value-added year by year, it anchors to a handful of relatively secure benchmark estimates and fills the gaps between and before them using indirect indicators that move with income, chiefly the share of population living in towns, real wages of building labourers, agricultural productivity, and population density. The logic, associated above all with Angus Maddison and developed further by Allen, Malanima, and van Zanden, is that these indicators bear a stable, theoretically grounded relationship to per-capita output, so their movements can proxy GDP growth where direct measurement is impossible. The method has produced the multi-century per-capita income series that frame debates about pre-modern stagnation, Malthusian dynamics, and the European Little Divergence, while remaining explicitly more uncertain than bottom-up accounts.