We study how individuals match in the workplace or in university when making side payments is costly (non-transferable utility or NTU). In contrast to the transferable utility (TU) benchmark, the pattern of matching will typically be inefficient, involving too much segregation, and provide a possible rationale for "associational redistribution'' such as affirmative action: a social planner who could enforce a matching outcome that differs from the market outcome may raise aggregate social surplus. We show that this static inefficiency due to NTU can be exacerbated in a dynamic environment, in which investments made before the match determine individuals' productive types. In contrast to TU models, which always have an efficient equilibrium, there will typically be investment distortions, with high types over-investing and low types under-investing. We study several forms of associational redistribution, assessing the differential effects of achievement-based and background-based polices.