Firms select not only how many, but also which workers to hire. Yet, in standard search models of the labor market, all workers have the same probability of being hired. We argue that selective hiring crucially affects welfare analysis. Our model is isomorphic to a search model under random hiring but allows for selective hiring. With selective hiring, the positive predictions of the model change very little, but the welfare costs of unemployment are much larger because unemployment risk is distributed unequally across workers. As a result, optimal unemployment insurance may be higher and welfare is lower if hiring is selective.