The Inequality Process vs. The Saved Wealth Model. Two Particle Systems of Income Distribution; Which Does Better Empirically?

The Inequality Process (IP) is a stochastic particle system in which particles are randomly paired for wealth exchange. A coin toss determines which particle loses wealth to the other in a randomly paired encounter. The loser gives up a fixed share of its wealth, a positive quantity. That share is its parameter, ω_ψ, in the ψth equivalence class of particles. The IP was derived from verbal social science theory that designates the empirical referent of (1-ω_ψ) as worker productivity, operationalized as worker education. Consequently, the stationary distribution of wealth of the IP in which particles can have different values of ω (like workers with different educations) is obliged to fit the distribution of labor income conditioned on education. The hypothesis is that when a) the stationary distribution of wealth in the ψth equivalence class of particles is fitted to the distribution of labor income of workers at the ψth level of education, and b) the fraction of particles in the ψth equivalence class equals the fraction of workers at the ψth level of education, then c) the model's stationary distributions fit the corresponding empirical distributions, and d) estimated (1-ω_ψ) increases with level of education. The Saved Wealth Model (SW) was proposed as a modification of the particle system model of the Kinetic Theory of Gases (KTG). The SW is isomorphic to the IP up to the stochastic driver of wealth exchange between particles. The present paper shows that 1) the stationary distributions of both particle systems pass test c): they fit the distribution of U.S. annual wage and salary income conditioned on education over four decades, 2) the parameter estimates of the fits differ by particle system, 3) both particle systems pass test d), but 4) the IP's overall fits are better than the SW's because 5) the IP's stationary distribution conditioned on larger (1-ω_ψ) has a heavier tail than the SW's fitting the distribution of wage income of the more educated better, and 6) since the level of education in the U.S. labor force rose, the IP's fit advantage increased over time.