This paper examines the impact of downward wage rigidity (nominal and real) on optimal steady-state inflation. For this purpose, we extend the workhorse model of Erceg, Henderson and Levin (2000) by introducing asymmetric menu costs for wage setting. We estimate the key parameters by simulated method of moments, matching key features of the cross-sectional distribution of individual wage changes observed in the data. We look at five countries (the US, Germany, Portugal, Belgium and Finland). The calibrated heterogeneous agent models are then solved for different steady state rates of inflation to derive welfare implications. We find that, across the European countries considered, the optimal steady-state rate of inflation varies between zero and 2%. For the US, the results depend on the dataset used, with estimates of optimal inflation varying between 2% and 5%.