Bayesian Unit-level Quantile Modeling with Application to Wealth Data

Abstract

Modeling wealth quantiles over time and space and across fine-grained demographic classifications is of vital importance to policy makers. However, such data present unique challenges for standard small area estimation methodologies because they are highly skewed and heavy-tailed with both positive and negative values. Traditional area-level modeling and design-based approaches struggle to capture these features. Meanwhile, existing unit-level methodology frequently treats the survey design as ignorable and does not apply to surveys that are repeated over time. Often the analysis is restricted to alternative response variables that are non-negative, such as poverty indicators or income. To overcome these limitations, we propose a Bayesian, asymmetric Laplace pseudolikelihood model that is able to capture the major features of wealth while adjusting for survey weights and accounting for both spatial and temporal dependence. We present a Gibbs sampling algorithm for our model, as well as a variational Bayes algorithm for fast computation. We apply the method to the Survey of Income and Program Participation to characterize geographic, temporal, and demographic variation in the distribution of U.S. household wealth, including for sparsely sampled domains where direct estimates are unavailable or unstable.