The Kuznets Curve and the Inequality Process

Four economists, Mauro Gallegati, Steven Keen, Thomas Lux, and Paul Ormerod, published a paper after the 2005 Econophysics Colloquium criticizing conservative particle systems as models of income and wealth distribution. Their critique made science news: coverage in a feature article in Nature. A particle system model of income distribution is a hypothesized universal statistical law of income distribution. Gallegati et al. (2006) claim that the Kuznets Curve shows that a universal statistical law of income distribution is unlikely and that a conservative particle system is inadequate to account for income distribution dynamics. The Kuznets Curve is the graph of income inequality (ordinate variable) against the movement of workers from rural subsistence agriculture into more modern sectors of the economy (abscissa). The Gini concentration ratio is the preferred measure of income inequality in economics. The Kuznets Curve has an initial uptick from the Gini concentration ratio of the earned income of a poorly educated agrarian labor force. Then the curve falls in near linear fashion toward the Gini concentration ratio of the earned incomes of a modern, educated labor force as the modern labor force grows. The Kuznets Curve is concave down and skewed to the right. This paper shows that the iconic Kuznets Curve can be derived from the Inequality Process (IP), a conservative particle system, presenting a counter-example to Gallegati et al.’s claim. The IP reproduces the Kuznets Curve as the Gini ratio of a mixture of two IP stationary distributions, one characteristic of the wage income distribution of poorly educated workers in rural areas, the other of workers with an education adequate for industrial work, as the mixing weight of the latter increases and that of the former decreases. The greater purchasing power of money in rural areas is taken into account.