Hierarchical Bayes multivariate estimation of poverty rates based on increasing thresholds for small domains

A model-based small area method for calculating estimates of poverty rates based on\r\ndifferent thresholds for subsets of the Italian population is proposed. The subsets are\r\nobtained by cross-classifying by household type and administrative region. The suggested\r\nestimators satisfy the following coherence properties: (i) within a given area, rates\r\nassociated with increasing thresholds are monotonically increasing; (ii) interval estimators\r\nhave lower and upper bounds within the interval (0, 1); (iii) when a large domain-specific\r\nsample is available the small area estimate is close to the one obtained using standard\r\ndesign-based methods; (iv) estimates of poverty rates should also be produced for domains\r\nfor which there is no sample or when no poor households are included in the sample.\r\nA hierarchical Bayesian approach to estimation is adopted. Posterior distributions are\r\napproximated by means of MCMC computation methods. Empirical analysis is based on\r\ndata from the 2005 wave of the EU-SILC survey.