Inequality of Opportunity and Variance Decomposition: A Methodological Insight

This paper introduces a new variance-based measure of inequality of opportunity (EOp) grounded in a decomposition of the Coefficient of Variation (CV). Our approach disentangles overall inequality into a between-group component driven by circumstances beyond individual control (e.g., gender, family background, or region of birth) and a within-group component which captures effort and idiosyncratic heterogeneity. Within this framework, we characterize three increasingly stringent EOp criteria, capturing equality in group means, equality in within-group dispersion, and their joint validity. Using EU-SILC income data, we illustrate the conceptual and empirical relevance of the method data and highlight substantial cross-country heterogeneity in both average outcomes and within-type variability across European countries. The results show that mean-based evaluations alone may fail to capture important differences in outcome dispersion across circumstance groups, underscoring the value of a variance-based approach for the analysis of equality of opportunity.