Non-Technical Summary:
In the last decades, the principle of equality of opportunity has been one of the most influential political ideals in public discourse. Two key factors may explain the overwhelming success of this ideal. First, equality of opportunity merges two powerful principles: responsibility and equality. In a world with equal opportunities, all individuals have the same chances to obtain social positions and valuable outcomes. They are free to choose how to behave, and they are held responsible for the consequences of their choices. Second, different understandings of equality of opportunity make it a sufficiently broad principle to gather support from people with very different political leanings.
Moral philosophers and welfare economists have formalized a variety of definitions of equality of opportunity. In particular, in his book “Equality of Opportunity” (1998), John Roemer proposed a theory of equality of opportunity that has triggered a lively economic empirical literature. This literature has attempted to measure to what extent the principle of equal opportunity is violated. A popular approach consists in identifying inequality of opportunity as the share of total inequality that is systematically associated with circumstances beyond individual control, such as gender, race, and socio-economic background.
In this paper, we propose a new method to measure inequality of opportunity taking advantage of two well-known machine learning algorithms: conditional inference regression trees and random forests. Our approach has a number of advantages with respect to existing methods. First, it minimizes the risk of arbitrary and ad-hoc model selection. Second, it provides 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 makes the measurement of inequality of opportunity more easily comprehensible to a larger audience. Importantly, our method is very flexible in terms of model selection. As a consequence it is very suitable for comparing opportunity structures, both over time and across countries.
To illustrate the advantages of our method, we estimate inequality of opportunity in 31 European countries and compare our method with alternative approaches typically adopted in the literature. In particular, we show that the prevalent approaches in the extant literature are subject to structural biases that can be easily handled by using trees and forests. Therefore, trees and forests provide a considerable improvement in terms of the credibility of the estimates. Furthermore, we sketch opportunity trees and provide estimates of circumstance importance for the purpose of comparing differential opportunity structures in Europe.
An updated version of this paper has been published as Brunori, P, Hufe, P and Mahler, D. (2023) The roots of inequality: estimating inequality of opportunity from regression trees and forests. Scandinavian Journal of Economics, 125, 900-932, DOI: 10.1111/sjoe.12530