Empirical evidence suggests that the pass-through from policy to retail bank rates is asymmetric in the euro area. Bank lending rates adjust more slowly and less completely to Eonia decreases than to increases. We investigate how this downward interest rate rigidity affects the response of the economy to monetary policy shocks. To this end, we introduce asymmetric bank lending rate adjustment costs in a macrofinance dynamic stochastic general equilibrium model. We find that the initial response of GDP to a negative monetary policy shock is 25% lower than its response to a positive shock of similar amplitude. This implies that a central bank would have to decrease its policy rate by 50% to 75% more to obtain a medium-run impact on GDP that would be symmetric to the impact of the positive shock. We also show that downward interest rate rigidity is stronger when policy rates are stuck at their effective lower bound, further disrupting monetary policy transmission. These findings imply that neglecting asymmetry in retail interest rate adjustments may yield misguided monetary policy decisions.