This paper compares two different models in a common environment. The first model has liquidity constraints in that consumers save a single asset that they cannot sell short. The second model has debt constraints in that consumers cannot borrow so much that they would want to default, but is otherwise a standard complete markets model. Both models share the features that individuals are unable to completely insure against idiosyncratic shocks and that interest rates are lower than subjective discount rates. In a stochastic environment, the two models have quite different dynamic properties, with the debt constrained model exhibiting simple stochastic steady states, while the liquidity constrained model has greater persistence of shocks.