Hierarchical Bayesian estimation of inequalities with non-rectangular censored survey data

We consider the estimation of wealth inequality measures with their confidence interval, based on survey data with interval censoring. We rely on a Bayesian hierarchical model. It consists of a model where, due to survey sampling and unit nonresponse, the summaries of the wealth distribution of households are observed with error; a mixture of multivariate models for the wealth components where groups correspond to portfolios of assets; and a prior on the parameters. A Gibbs sampler is used for numerical purposes to do the inference. We apply this strategy to the French 2004 Wealth Survey. In order to alleviate the nonresponse, the amounts were systematically collected in the form of brackets. Matched administrative data on the liability of the respondents for wealth tax and response to overview questions are used to better localize the wealth components. It implies nonrectangular multidimensional censoring. The variance of the error term in the model for the population inequality measures is obtained using linearization and taking into account the complex sampling design and the various weight adjustments