TY - JOUR

T1 - A generative model of income distribution

T2 - Formalization with iterated investment game

AU - Hamada, Hiroshi

PY - 2003/10

Y1 - 2003/10

N2 - The purpose of this paper is to formalize a simple model that theoretically connects individuals' rational choice at the micro level to income distribution, which is subject to the Gibrat's law empirically, as social structure at macro level. We use an iterated investment game as a baseline model in which a player has a binary choice between investing and not investing. Given parameters which prescribe the 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 investigate changes in the Gini coefficient and skewness of the total 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, 10. As a result of analysis, we derive the implication that the Gini coefficient increases up to critical point, where 0 ≤ γ ≤ 1/(R + 1), then decreases as prize density increases, where 1/(R - 1) < γ ≤ 1. Furthermore, we show that our model, with cumulative effect, generates a lognormal distribution under the condition that 1/(R + 1) < γ ≤ 1.

AB - The purpose of this paper is to formalize a simple model that theoretically connects individuals' rational choice at the micro level to income distribution, which is subject to the Gibrat's law empirically, as social structure at macro level. We use an iterated investment game as a baseline model in which a player has a binary choice between investing and not investing. Given parameters which prescribe the 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 investigate changes in the Gini coefficient and skewness of the total 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, 10. As a result of analysis, we derive the implication that the Gini coefficient increases up to critical point, where 0 ≤ γ ≤ 1/(R + 1), then decreases as prize density increases, where 1/(R - 1) < γ ≤ 1. Furthermore, we show that our model, with cumulative effect, generates a lognormal distribution under the condition that 1/(R + 1) < γ ≤ 1.

KW - Gini coefficient

KW - Income distribution

KW - Inequality

KW - Relative deprivation

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U2 - 10.1080/00222500390240939

DO - 10.1080/00222500390240939

M3 - Article

AN - SCOPUS:0242510869

SN - 0022-250X

VL - 27

SP - 279

EP - 299

JO - Journal of Mathematical Sociology

JF - Journal of Mathematical Sociology

IS - 4

ER -