A random walk stochastic volatility model for income inequality

•Assuming the lognormal, we estimate income distributions using Japanese quintile income data.•We estimate the dynamic model including income inequality by SV model and random-walk SV model.•The model comparison by marginal likelihood shows that the SV model is supported.•The SV model implies the persistent income inequality.•It supports the previous result more firmly.

This paper develops dynamic models that include income inequality from grouped income data to investigate persistent inequality. After we check that the lognormal distribution is adequately fitted to Japanese income data, by the asymptotic theorem of selected order statistics we construct an approximate linear model, which is extended to dynamic models, including a stochastic volatility (SV) model and a random-walk SV model. We can thus estimate the parameter of inequality directly. Both models are estimated using Japanese income data with the Markov chain Monte Carlo (MCMC) method and a model comparison is made. The SV model is better fitted than the random-walk SV model. We can capture the changing Gini coefficients for Japan using the SV model.