A multivariate setting for the estimation of wealth ineaquality indicators applied to Enquête Patrimoine 2004
Survey questions that ask respondents to report financial amounts, particulary assets amounts in household wealth surveys, are subject to high rates of item missing data. A strategy commonly used by survey designers to curb this item non-response rate consist in allowing for bracketed response questions. In return, the resulting measures are a mixture of single valued responses, pre-defined brackets responses, self-defined interval responses and completely missing data. However wealth inequalities analysis requires to complete these coarsened data by way of imputation techniques. This article presents three procedures of estimation of wealth inequality indicators based on different imputation strategies applied to the data the French household wealth survey «Enquête Patrimoine 2004». The imputation techniques all draw on Lollivier and Verger (1989) adaptation of simulated residuals methods, but the estimation prodecures differ in the nature and quantity of information they rely on: the first estimate is based on an aggregate measure of gross wealth collected via a single question and affected by substantial interval censoring in the upper part of the distribution, the second and third estimates are based on coarsened information on more detailed wealth components as well as on additional information whether the household is subject to the wealth tax. The hierarchical approach of the estimation followed gives interval confidence estimates accounting for sampling and total non-response error, as well as simulation error for completed data. The third estimation procedure rely on joint imputation of several wealth components. The joint imputation is achieved in a Bayesian setting, which allow as a by product to produce confidence interval accounting for parameters estimation variance. Simulation in the joint law of components is achieved through Gibbs sampling.