Pareto–lognormal distributions: Inequality, poverty, and estimation from grouped income data

The (double) Pareto–lognormal is an emerging parametric distribution for income that has a sound underlying generating process, good theoretical properties, and some limited favorable evidence of its fit to data. We extend existing results for this distribution in 3 directions. (1) We derive closed form formula for its moment distribution functions, and for various inequality and poverty measures. (2) We show how it can be estimated from grouped data using GMM. (3) Using grouped data from ten countries, we compare its performance with that of another leading 4-parameter income distribution, the generalized beta-2 distribution. The results confirm that, when using grouped data, both distributions provide a good fit, with the double Pareto–lognormal distribution outperforming the beta distribution in 4 out of 10 cases.