The Atkinson Inequality Measure and its Sampling Properties : Bayesian and Classical Approaches

This paper examines several Bayesian methods of obtaining posterior probability density functions of the Atkinson inequality measure and its associated social welfare function, in the context of grouped income distribution data. The methods are compared with asymptotic standard errors. The role of the number of income classes is investigated using a simulated distribution. If only a small number of groups is available in published data, there is a clear gain from generating the posterior probability density function when using an explicit income distribution assumption. Even with a small number of groups, the Bayesian approach gives results that are close to the sample values obtained using the corresponding individual observations