This paper shows that the quantitative predictions of a DSGE model with an endogenous collateral constraint are consistent with key features of the emerging markets' Sudden Stops. Business cycle dynamics produce periods of expansion during which the ratio of debt to asset values raises enough to trigger the constraint. This sets in motion a deflation of Tobin's Q driven by Irving Fisher's debt-deflation mechanism, which causes a spiraling decline in credit access and in the price and quantity of collateral assets. Output and factor allocations decline because the collateral constraint limits access to working capital financing. This credit constraint induces significant amplification and asymmetry in the responses of macro-aggregates to shocks. Because of precautionary saving, Sudden Stops are low probability events nested within normal cycles in the long run.