We develop an identification strategy for equilibrium matching models with latent traits and apply it to the 1972 Raising of the School-Leaving Age (RoSLA) reform in England and Wales. Our identification exploits the RoSLA-induced discontinuity in the distribution of qualifications to disentangle the contributions of qualification and ability to marital surplus. Both are valued and are complements in the marital surplus function. Ability increases the probability of ever marrying while basic qualification attainment does not. Hence, the observed gap in marriage rates between basic qualified and unqualified individuals is entirely due to selection on ability. The RoSLA worsened marital prospects of low ability individuals through general equilibrium effects.