Classical and Bayesian Inference for Income Distributions using Grouped Data

Abstract

We propose a general framework for Maximum Likelihood (ML) and Bayesian estimation of income distributions based on grouped data information. The asymptotic properties of the ML estimators are derived and Bayesian parameter estimates are obtained by Monte Carlo Markov Chain (MCMC) techniques. A comprehensive simulation experiment shows that obtained estimates of the income distribution are very precise and that the proposed estimation framework improves the statistical precision of parameter estimates relative to the classical multinomial likelihood. The estimation approach is finally applied to a set of countries included in the World Bank database PovcalNet.

The Bayesian approach to poverty measurement

“…This is convenient for reporting income shares as does the World Inequality data base. To each case corresponds a specific statistical problem as surveyed in Eckernkemper and Gribisch (2020). Chotikapanich and Griffiths (2000), Griffiths et al (2005), Chotikapanich and Griffiths (2005), Kakamu (2016), Kakamu and Nishino (2019) contributed also to this field.…”

The arithmetics and politics of domestic resource mobilization for poverty eradication

“…Despite its acknowledged limitations, PovcalNet has been used extensively for distributional analysis (some recent examples include Ravallion, 2020a and 2020b; Dhongde and Minoiu, 2013;Edward, 2006). Additionally, as researchers often only have access to grouped income or consumption data (rather than the original underlying household-level data) for many developing countries, it is a common (if second best) practice to estimate income distributions based on grouped data information (see Eckernkemper and Gribisch, 2021 for an up-to-date review of the literature on the use of grouped data for distributional analysis, with an application to PovcalNet). We are aware that any results reported here, therefore, should be validated by using the underlying microdata whenever available for the analysis.…”