Working Papers

Title: The Roots of Inequality: Estimating Inequality of Opportunity from Regression Trees

Authors: Brunori, Paolo / Hufe, Paul / Mahler, Gerszon Daniel


We propose a set of new methods to estimate inequality of opportunity based on conditional inference regression trees. In particular, we illustrate how these methods represent a substantial improvement over existing empirical approaches to measure in equality of opportunity. First, they minimize the risk of arbitrary and ad-hoc model selection. Second, they provide a standardized way of trading off upward and downward biases in inequality of opportunity estimations. Finally, regression trees can be graphically represented; their structure is immediate to read and easy to understand. This will make the measurement of inequality of opportunity more easily comprehensible to a large audience. These advantages are illustrated by an empirical application based on the 2011 wave of the European Union Statistics on Income and Living Conditions.

Title: Model-based Recursive Partitioning to Estimate Unfair Health Inequalities in the United Kingdom Household Longitudinal Study

Authors: Brunori, Paolo / Davillas, Apostolos / Jones, Andrew M. / Scarchilli, Giovanna


We measure unfair health inequality in the UK using a novel data-driven empirical approach. We explain health variability as the result of circumstances beyond individual control and health-related behaviours. We do this using model-based recursive partitioning, a supervised machine learning algorithm. Unlike usual tree-based algorithms, model-based recursive partitioning does identify social groups with different expected levels of health but also unveils the heterogeneity of the relationship linking behaviours and health outcomes across groups. The empirical application is conducted using the UK Household Longitudinal Study. We show that unfair inequality is a substantial fraction of the total explained health variability. This finding holds no matter which exact definition of fairness is adopted: using both the fairness gap and direct unfairness measures, each evaluated at different reference values for circumstances or effort.