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.

Keywords: Equality of opportunity, Machine learning, PhD graduates, Compensation, Reward.

JEL: C38, D31, D63