World personal income distribution evolution measured by purchasing power parity exchange rates

TL;DR

This study analyzes the evolution of the world income distribution from 1988 to 2018 using PPP-adjusted incomes and fits multiple statistical distributions. It demonstrates that a bimodal mixture approach (bi-gamma or bi-log-normal) significantly improves fit quality over single-function models, capturing both bulk and tail behavior as the global economy evolves. A key finding is the transition from a bimodal to a more unimodal distribution driven by rapid growth in China and India, with these countries bridging the distribution and masking underlying valley structures. The work highlights the value of multimodal models for interpreting global inequality dynamics and suggests avenues for applying similar analyses to post-pandemic data and richer microdata sources.

Abstract

The evolution of global income distribution from 1988 to 2018 is analyzed using purchasing power parity exchange rates and well-established statistical distributions. This research proposes the use of two separate distributions to more accurately represent the overall data, rather than relying on a single distribution. The global income distribution was fitted to log-normal and gamma functions, which are standard tools in econophysics. Despite limitations in data completeness during the early years, the available information covered the vast majority of the world's population. Probability density function (PDF) curves enabled the identification of key peaks in the distribution, while complementary cumulative distribution function (CCDF) curves highlighted general trends in inequality. Initially, the global income distribution exhibited a bimodal pattern; however, the growth of middle classes in highly populated countries such as China and India has driven the transition to a unimodal distribution in recent years. While single-function fits with gamma or log-normal distributions provided reasonable accuracy, the bimodal approach constructed as a sum of log-normal distributions yielded near-perfect fits.

Figures (46)

• Figure 1: Milanovic income distribution from 1988 to 2018.
• Figure 2: Gamma fit for Milanovic income distribution for year 1988, $R^2=0.69068$
• Figure 3: Gamma fit for year 1993, $R^2=0.73948$
• Figure 4: Gamma fit for year 1998, $R^2=0.72081$
• Figure 5: Gamma fit for year 2003, $R^2=0.73558$