A note on the undercover relationship between the Chotikapanich Lorenz curve and the Pareto distribution.

Abstract We study the relationship between the Chotikapanich (1993) Lorenz curve and the Pareto distribution. First, we show that the Chotikapanich Lorenz curve is generated by a log-uniform distribution. Second, we show that the log-uniform distribution is a limiting case of a truncated Pareto distribution. Given this, we propose a mixture Lorenz curve model to estimate the scale parameter of the Pareto distribution, thus allowing us to identify at which point of the distribution incomes become Pareto-distributed. This model assumes that the bottom part of the income distribution is drawn from a log-uniform distribution, and the upper part as a classical Pareto distribution. Using Montecarlo simulations, we show that our model can accurately recover the threshold. With this, we estimate this model for 181 countries using data from the World Income Inequality Database. We find a negative relationship between the aggregate level of inequality (measured through the Gini coefficient) and the point where the Pareto distribution starts. JEL Classification: D3, H8.