This paper studies the implications of changes in price-setting behavior for the transmission of monetary policy. The analysis is based on a multi-sector menu cost model which is estimated separately for each quarter using Swiss CPI microdata from 2008 to 2022. The impulse responses suggest that the increase in the frequency of price changes revealed by the data has marginally reduced the cumulated response of output to a monetary policy shock. This result is corroborated by evidence from non-linear local projections. Using a time series of the sufficient statistic proposed by Alvarez et al. (2016) to identify states with lower and higher degrees of monetary non-neutrality, we show that the responses of output and inflation to a monetary shock differ as expected between the two regimes.