Equality of opportunity and luck: Definitions and testable conditions, with an application to income in France

We offer a model of equality of opportunity that encompasses different conceptions expressed in the public and philosophical debates. In addition to circumstances whose effect on outcome should be compensated and effort which represents a legitimate source of inequality, we introduce a third factor, luck, that captures the random factors whose impact on outcome should be even-handed for equality of opportunity to be satisfied. Then, we analyze how the various definitions of equality of opportunity can be empirically identified, given data limitations and provide testable conditions. Definitions and conditions resort to standard stochastic dominance tools. Lastly, we develop an empirical analysis of equality of opportunity for income acquisition in France over the period 1979-2000 which reveals that the degree of inequality of opportunity tends to decrease and that the degree of risk of income distributions, conditional on social origin, appears very similar across all groups of social origins.