An alternative functional form for the Lorenz curve with empirical applications

Given that the Lorenz curve is widely used for analyzing income distribution and inequality, this study introduces an alternative functional form for the Lorenz curve that is constructed based on the weighted average of the exponential function and the functional form implied by Pareto distribution. Using the data on the Gini index and the decile income shares of Thailand and other 4 countries with different income inequality, socioeconomic, and regional backgrounds, this study shows that the alternative functional form meets required criteria for a good functional form suggested by Dagum (1977). Moreover, this study compares the performance of the alternative functional form to that of Kakwani (1980). The results show that the performance of the alternative functional form is comparable to that of Kakwani (1980). However, the alternative functional form has an advantage in that the Gini index can be conveniently computed since it has an explicit mathematical solution whereas, for the Kakwani (1980)’s functional form, the Gini index is computed by using the numerical integration since its closed-form expression does not exist. Furthermore, this study finds that when the values of cumulative normalized rank of income are low, the Kakwani (1980)’s functional form does not always satisfy the monotonic increasing condition for the Lorenz curve. Thus, when applying any functional form for the Lorenz curve to analyze and formulate policy at the lower tail of income distribution, the shape of the estimated Lorenz curve should be considered together with the values of goodness-of-fit statistics and the estimated Gini index.