Hierarchical Bayesian estimation of inequality measures with nonrectangular censored survey data with an application to wealth distribution of French households

TL;DR

This paper introduces a Bayesian hierarchical approach to estimate wealth inequality measures from censored survey data, incorporating complex sampling and auxiliary administrative data to improve accuracy.

Contribution

It develops a novel Bayesian hierarchical model with a Gibbs sampler to handle nonrectangular censored survey data and auxiliary information for wealth distribution analysis.

Findings

Effective estimation of wealth inequality measures with confidence intervals.

Improved localization of wealth components using administrative data.

Method applied successfully to French 2004 Wealth Survey.

Abstract

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.