Biases in inequality of opportunity estimates: measures and solutions

In this paper we discuss some limitations of using survey data to measure inequality of opportunity. First, we highlight a link between the two fundamental principles of the theory of equal opportunities -- compensation and reward -- and the concepts of power and confidence levels in hypothesis testing. This connection can be used to address, for example, whether a sample has sufficient observations to appropriately measure inequality of opportunity. Second, we propose a set of tools to normatively assess inequality of opportunity estimates in any type partition. We apply our proposal to Conditional Inference Trees, a machine learning technique that has received growing attention in the literature. Finally, guided by such tools, we suggest that standard tree-based partitions can be manipulated to reduce the risk of compensation and reward principles.Our methodological contribution is complemented with an application using a quasi-administrative sample of Italian PhD graduates. We find a substantial level of labor income inequality among two cohorts of PhD graduates (2012 and 2014), with a significant portion explained by circumstances beyond their control.