Grouped data estimation and testing of Gini coefficients using lognormal distributions

Assuming that income is lognormal distributed, we obtain the estimator of the parameter explicitly based on selected order statistics from grouped data, and having the Gini coefficient from it. The estimator from grouped data is useful because grouped data are simply treated and available also in developing countries. It can be used in a similar way as the maximum likelihood estimator. The paper proposes a test statistic which is derived by using the asymptotic normality of the estimator, and a likelihood ratio test based on the maximum likelihood estimator, in order to test the change in inequality. We finally apply these estimations and tests to Japanese data.