"A universal long-run elasticity of economic output to population, and its implications for the global economy of 2100
Year: 2026
Type: dataset
Abstract: Complete analysis pipeline, input data, posterior samples and result set for Real output scales sub-proportionally with population, and super-unitary estimates are an artifact of nominal GDP. Let ε be the elasticity of aggregate real output with respect to population. Because output per person is output divided by population, a proportional fall in population changes output per person by (ε − 1) times that fall, so the sign of ε − 1 decides whether depopulation erodes living standards. Fitted to real GDP in constant 2015 US dollars, a three-level hierarchical Bayesian model with penalised cubic B-splines returns a contraction-phase elasticity of 0.652 (95% credible interval 0.594–0.710) under a fixed first-difference spline penalty and 0.806 (0.748–0.863) under adaptive shrinkage, sub-unitary with posterior probability 1.00 under both. Fitted to nominal GDP, the same model on the same panel returns 0.924 and 1.220, straddling unity, because a price-level trend that co-moves with population loads onto the population coefficient. The widely reported super-unitary estimates, including this project's own earlier drafts, are an artifact of measuring output in current prices. A three-level hierarchical model on non-overlapping ten-year changes in the working-age population corroborates the direction on a within-country estimand, returning 0.805 (0.577–1.029) with posterior probability 0.961 of being below one and no evidence of a contraction-regime break. A single projection engine carries that elasticity through United Nations World Population Prospects 2024 medium-variant demography to 2100 for 175 economies. Output per person rises over the century in every one of them, including all 75 whose population falls. The engine asserts before writing that aggregate growth minus per-capita growth equals population growth for every country and every year, that no economy's long-run growth rate is implausible, and that the convergence term behaves as specified; a test suite exercises each assertion, including one case that must abort. This record holds the code repository and seven posterior sample files (about 10 GB). The repository alone reproduces every figure and every reported number; the posteriors are needed only to re-derive a quantity that is not already summarised in results/. All results use a fixed random seed of 42; README.md gives the exact command order.
Institution: Institute of Science Tokyo
Language: English
Subfield: Economics and Econometrics
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7163321265