A functional approach to small area estimation of the relative median poverty gap

We consider the estimation of the relative median poverty gap (RMPG) at the level of Italian provinces by using data from the European Union Survey on Income and Living Conditions. The overall sample size does not allow reliable estimation of income-distribution-related parameters at the provincial level; therefore, small area estimation techniques must be used. The specific challenge in estimating the RMPG is that, as it summarizes the income distribution of the poor, samples for estimating it for small subpopulations are even smaller than those available in other parameters. We propose a Bayesian strategy where various parameters summarizing the distribution of income at the provincial level are modelled by means of a multivariate small area model. To estimate the RMPG, we relate these parameters to a distribution describing income, namely the generalized beta distribution of the second kind. Posterior draws from the multivariate model are then used to generate draws for the distribution's area-specific parameters and then of the RMPG defined as their functional.