While equilibrium allocations in models with incomplete markets are generally not Pareto-efficient, it is often argued that quantitative welfare losses from missing assets are small when time-horizons are long and shocks are transitory. In this paper we use a computational analyses to show that even in the simplest infinite horizon model without aggregate uncertainty welfare losses can be substantial. Furthermore, we show that in this model, welfare losses form incomplete markets to not necessarily disappear when agents become more patient. We identify two scenarios under which this is the case. First, when the economic model is calibrated to higher frequency data, the persistence of negative income shocks must increase as well. In this case, the welfare loss of incomplete markets remains constant even as agents' rate of time preference B>1. Secondly, for a fixed specification of endowment processes, an exogenous decrease of agents' rate of discounting should not affect their abilities to borrow. With exogenous borrowing constraints, the incomplete markets welfare does not converge to complete markets welfare.