Bayesian State-Space Modeling and Model-Based Counterfactual Analysis of Dynamic Income Distributions from Grouped Data

Abstract

Grouped income data contain only limited information about the evolution of income distributions over time. This paper develops a Bayesian state-space model for the generalized beta distribution of the second kind (GB2) to estimate dynamic income distributions using repeated grouped income data. By borrowing information across adjacent periods through the latent GB2 parameters, the proposed framework improves estimation precision relative to independent cross-sectional estimation. Building on the estimated latent-state dynamics, we further construct a model-based counterfactual framework that quantifies the contribution of demographic covariates while preserving the estimated evolution of the remaining model components. Using Japanese household income data from 1969--2007, we find that population aging and declining household size affect different parts of the income distribution through distinct channels, with population aging becoming an increasingly important driver of income inequality after around 2000. More generally, the proposed framework provides a unified Bayesian approach to dynamic distributional analysis and model-based counterfactual inference using repeated grouped income data.