Flexible Bayesian Models for Time-Varying Income Distributions

TL;DR

This paper introduces flexible Bayesian models that dynamically estimate time-varying income distributions, improving inference stability and accuracy over traditional methods that treat each year independently.

Contribution

It develops Bayesian models with dynamic parameters and shrinkage priors to better analyze income distribution changes over time, especially for small samples.

Findings

Dynamic models yield more precise income distribution estimates.

Proposed approach reduces spurious variation in welfare comparisons.

Application shows improved inference and altered conclusions on distributional dominance.

Abstract

Survey data are widely used to study how income inequality, poverty, and welfare evolve over time. A common practice is to estimate the income distribution separately for each year, treating annual observations as independent cross-sections. For population subgroups with relatively small sample sizes, however, this approach can produce unstable parameter estimates, imprecise inference for inequality and poverty measures, and potentially misleading posterior probabilities of Lorenz and stochastic dominance. This paper develops flexible Bayesian models for time-varying income distributions that borrow strength across adjacent years by allowing the parameters of income distributions to evolve dynamically. We consider a random walk specification and an extended model with shrinkage priors. The proposed framework yields coherent inference for the full income distributions over time, as well as for associated inequality measures, poverty indices, and dominance probabilities. Simulation studies show that, relative to independent year-by-year models, the proposed approach produces substantially more precise and stable inference, while avoiding spurious variation in welfare comparisons. An application to the Aboriginal and residents of the Australian Capital Territory (ACT) population subgroups in the Household, Income and Labour Dynamics in Australia survey shows that the dynamic models deliver improved inference for income distributions and related welfare measures, and can change conclusions about distributional dominance over time.