We introduce a model of two-sided statistical discrimination in which worker and firm beliefs are complementary. Firms try to infer whether workers have made investments required for them to be productive, and simultaneously, workers try to deduce whether firms have made investments necessary for them to thrive. When multiple equilibria exist, group differences are sustained by both sides of the interaction – workers and firms. Strategic complementarity complicates both empirical analysis designed to detect discrimination and policy meant to alleviate it. Affirmative action is much less effective than in traditional statistical discrimination models. More generally, we demonstrate the futility of policies that are designed to correct gender and racial disparities but do not address both sides of the coordination problem. We propose a two-sided version of “investment insurance” – a policy in which the government (after observing a noisy version of the employer’s signal) offers to hire any worker who it believes to be qualified and whom the employers does not offer a job – and show that it (weakly) dominates any alternative. The paper concludes by proposing a way to identify statistical discrimination by employers when beliefs are complements.