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We show that a model with imperfectly forecastable changes in future productivity and an occasionally-binding collateral constraint can match a set of stylized facts about Sudden Stop events. "Good" news about future productivity raises leverage during times of expansions, increasing the probability that the constraint binds, and a Sudden Stop occurs, in future periods. During the Sudden Stop, the nonlinear effects of the constraint induce output, consumption and investment to fall substantially below trend, as they do in the data. Also consistent with data, the economy exhibits a boom period prior to the Sudden Stop, with output, consumption, and investment all above trend.