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.
Highlights
The empirical analysis of welfare, income inequality and poverty requires precise estimates of the distribution of income
This performance appears to be robust against varying data generating process (DGP), parameterizations, sample sizes and numbers of income groups
Our results indicate significant improvements over the conventional multinomial Maximum Likelihood (ML) approach and we obtain accurate parameter estimates which come close to those obtained for individual income data
Summary
The empirical analysis of welfare, income inequality and poverty requires precise estimates of the distribution of income. The traditional and most frequently applied method is ML based on sample proportions using a multinomial likelihood function (see e.g. McDonald, 1984, and Bandourian et al, 2003) This approach is inefficient in the majority of practical applications since it neglects the information content of observed group means and does not account for unknown group boundaries. While Chotikapanich and Griffiths (2000) employ the standard multinomial likelihood of McDonald (1984), the recent contributions of Kakamu (2016) and Kakamu and Nishino (2019) employ the joint likelihood of a set of order statistics as proposed by Nishino and Kakamu (2011), which is – – appropriate for quantile-data only Both Bayesian settings do not account for unknown group boundaries and ignore the information of observed group mean incomes. Note that the multinomial ML method of McDonald (1984) remains inefficient since the informational content of the group-specific mean incomes is not exploited
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