A distributional regression approach to income-related inequality of health in Australia

Several studies have confirmed the existence of a significant positive relationship between income and health. Conventional regression techniques such as Ordinary Least Squares only help identify the effect of the covariates on the mean of the health variable. In this way, important information of the income-health relationship could be overlooked. As an alternative, we apply and compare unconventional regression techniques.

We adopt a distributional approach because we want to allow the effect of income on health to vary according to people's health status. We start by analysing the income-health relationship using a distributional regression model that falls into the GAMLSS (Generalized Additive Models for Location, Scale and Shape) framework. We assume a gamma distribution to model the health variable and specify the parameters of this distribution as linear functions of a set of explanatory variables. For comparison, we also adopt a quantile regression analysis. Based on predicted health quantiles, we use both a parametric and a non-parametric approach to estimate the lower tail of the health distribution.

Our data come from Wave 13 of the Household, Income and Labour Dynamics in Australia (HILDA) survey, collected in 2013-2014. According to GAMLSS, we find that the risk of ending up in poor, fair or average health is lower for those who have relatively high incomes ($80,000) than for those who have relatively low incomes ($20,000), for both smokers and non-smokers. In relative terms, the risk-lowering effect of income appears to be the largest for those who are in poor health, again for both smokers and non-smokers. The results obtained on the basis of quantile regression are to a large extent comparable to those obtained by means of GAMLSS regression.

Both distributional regression techniques point in the direction of a non-uniform effect of income on health, and are therefore promising complements to conventional regression techniques as far as the analysis of the income-health relationship is concerned.