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We introduce liquidity frictions into an otherwise standard DSGE model with nominal and real rigidities, explicitly incorporating the zero bound on the short-term nominal interest rate. Within this framework, we ask: Can a shock to the liquidity of private paper lead to a collapse in short-term nominal interest rates and a recession like the one associated with the 2008 U.S. financial crisis? Once the nominal interest rate reaches the zero bound, what are the effects of interventions in which the government exchanges liquid government assets for illiquid private paper? We find that the effects of the liquidity shock can be large, and we show some numerical examples in which the liquidity facilities prevented a repeat of the Great Depression in 2008-09.