Credible evidence of sex discrimination using instrumental inequality

In their 1975 analysis of UC Berkeley admissions data, Bickel et al. argued that quantifying sex discrimination requires isolating the direct effect of sex on an outcome of interest (e.g., admission) from the indirect effect through acceptable mechanisms (e.g., department choice). This approach faces a significant challenge: direct effects cannot be identified without the implausible assumption of no mediator–outcome confounding. We sidestep this identification problem by exploiting the instrumental inequality, a causal constraint inherent in instrumental variables. This method has the advantage of not requiring functional forms, distributional assumptions, or even the assumption of no mediator–outcome confounding. We further derive bounds on the direct effect using a polynomial programming approach, which allows us to characterize the direction and magnitude of discrimination. Applying the proposed approach to two contentious cases in South Korea, we provide credible evidence of sex discrimination against women.