A Generative Model of Income Distribution :

Formalization with Iterative Investment Game

Abstract

     The purpose of this paper is to formalize a simple model that theoretically connects individuals' rational choice at micro level to income distribution, which is according to the Gibrat's law empirically, as social structure at macro level. We employ iterative investment game as a baseline model in which player has a binary choice between investing and not investing. Given parameters which prescribe payoff structure of the game are the prize density γ and the rate of return R . Method of analysis is a simulation with computation.
     We investigated changes in Gini coefficient and skewness of the gross profit distribution, as the parameters varied as follows : 0≦γ≦1, R={0.5,1,2,3}, and n (the number of times that the game is repeated) = 5 or 10. As a result of analysis, we derived the implication that Gini coefficient increases up to critical point, where γ≦1/(R+1), then decreases as prize density increases, where γ>1/(R+1).
     Furthermore, we show that our model, with cumulative effect, generates a lognormal distribution under condition that γ>1/(R+1).