We study the incentives to enter and to leave homeless shelters. After 2 years of decline, the number of homeless families in new York city's shelters system began rising again in spring 1990 and continued to rise until it his an all time record high in summer 1993. The conventional wisdom about why this happened is that a flood of new families were attracted into shelters by the Dinkins administration's aggressive policy of placement into subsidized housing. We test the conventional wisdom and reject it. Better prospects of subsidized housing increase flows into the shelter system, but this incentive effect is no nearly large enough to offset the first order accounting effect taking families out of the shelters reduces the number of families in them. Why then did the shelter system population grow after spring 1990? A major part of the reason is that the city responded to conventional wisdom and slowed placement in to subsidized housing. Other major factors were higher unemployment (which slowed self initiated exits), greater use of more attractive Tier II shelter instead of hotels, and possibly increasing cocaine use.