Measuring income related inequality in health: standardisation and the partial concentration index

The partial concentration index (PCI) is commonly used as a measure of income related inequality in health after removing the effects of standardising variables such as age and gender which affect health, are correlated with income, but not amenable to policy. Both direct and indirect standardisation have been used to remove the effects of standardising variables. The paper shows that with individual level data direct standardisation is possible using the coefficients from a linear regression of health on income and the standardising variables and yields a consistent estimate of the PCI. Indirect standardisation estimates the effects of the standardising variables on health from a health regression which excludes income. The coefficients on the standardising variables include some of the effects of income on health if income is correlated with the standardising variables. Using these coefficients to remove the effects of the standardising variables also removes some of the effect of income on health and leads to an inconsistent estimate of the PCI. Indirect standardisation underestimates the PCI irrespective of the signs of the correlations of standardising variables and income with each other and with health. An adaptation of the PCI when the marginal effect of income on health depends on the standardising variables is also proposed.