Small Domain Estimation of Poverty Rates Based on EU Survey on Income and Living Conditions

The aim of this work is to propose a methodology for estimating domains’ poverty rates. SAE model often rely on the normality of the area parameters, but this assumption may be inappropriate for rates. As different rates are obtained by using different, increasing thresholds, we propose a multivariate hierarchical Normal-Logistic-Normal (NLN) model that constraints the estimates to monotonically increase with the thresholds. Moreover, considering that also the assumption of normality of the direct estimators is not satisfying (the distribution of poverty rates is left truncated at 0 and possibly skewed) we introduce, in the univariate context, a Beta sampling models that leads to a Beta-Logistic small area model (BL). Results obtained show both the NLN and the BL models perform considerably better then more ‘usual’ models based on Normality. A Hierarchical Bayesian approach to estimation, where posterior distributions are approximated by means of MCMC computation methods, is adopted.