Mathematical analysis of historical income per capita distributions

TL;DR

This paper analyzes historical income per capita data globally and regionally, demonstrating that growth was monotonically hyperbolic without stagnation or transitions, challenging the core assumptions of Unified Growth Theory.

Contribution

It provides a comprehensive mathematical analysis showing that historical income growth followed hyperbolic patterns, contradicting the idea of Malthusian stagnation and the impact of the Industrial Revolution.

Findings

Income per capita increased monotonically without stagnation.

Growth followed hyperbolic trajectories across regions and time.

Industrial Revolution did not alter growth patterns.

Abstract

Data describing historical growth of income per capita [Gross Domestic Product per capita (GDP/cap)] for the world economic growth and for the growth in Western Europe, Eastern Europe, Asia, former USSR, Africa and Latin America are analysed. They follow closely the linearly-modulated hyperbolic distributions represented by the ratios of hyperbolic distributions obtained by fitting the GDP and population data. Results of this analysis demonstrate that income per capita was increasing monotonically. There was no stagnation and there were no transitions from stagnation to growth. The usually postulated dramatic escapes from the Malthusian trap never happened because there was no trap. Unified Growth Theory is fundamentally incorrect because its central postulates are contradicted repeatedly by data, which were used but never analysed during the formulation of this theory. The large body of readily-available data opens new avenues for the economic and demographic research. They show that certain fundamental postulates revolving around the concept of Malthusian stagnation need to be replaced by the evidence-based interpretations. Within the range of analysable data, which for the growth of population extends down to 10,000 BC, growth of human population and economic growth were hyperbolic. There was no Malthusian stagnation and there were no transitions to distinctly faster trajectories. Industrial Revolution had no impact on changing growth trajectories.