Estimating Income Distributions From Grouped Data: A Minimum Quantile Distance Approach

Abstract

This paper focuses on the estimation of income distribution from grouped data in the form of quantiles. We propose a novel application of the minimum quantile distance (MQD) approach and compare its performance with the maximum likelihood (ML) technique. The estimation methods are applied using three parametric distributions: the generalized beta distribution of the second kind (GB2), the Dagum distribution, and the Singh–Maddala distribution. We provide the density-quantile functions for these distributions, along with reproducible R code. A simulation study is conducted to evaluate the performance of the MQD and ML methods. The proposed methods are then applied to data from 30 European countries, utilizing the aforementioned parametric distributions. To validate the accuracy of the estimates, we compare them with estimates obtained from more detailed and informative microdata sets. The findings confirm the excellent performance of the considered parametric distributions in estimating income distribution. Additionally, the MQD approach is identified as a straightforward and reliable method for this purpose. Notably, the MQD method displays superior robustness in comparison to the ML technique when it comes to selecting suitable starting values for the underlying computation algorithm, specifically when dealing with the GB2 distribution.