While some notable market crashes have occurred in a single day, in other cases a collapse may occur over several months.9 To model this, our second extension of the Blanchard and Watson model allows the expected value of the bubble, conditional on collapse, to be non-zero, thereby allowing for partial collapses. We assume that the expected size of a bubble in state C, which we define as utPt, depends on the relative size of the bubble in the previous period, so that