We study a model in which firms compete to retain and attract workers searching on the job. A drop in the rate of on-the-job search makes such wage competition less likely, reducing expected labor costs and lowering inflation. This model explains why inflation has remained subdued over the last decade, which is a conundrum for general equilibrium models and Phillips curves. Key to this success is the observed slowdown in the recovery of the employment-to-employment transition rate in the last five years, which is interpreted by the model as a decline in the share of employed workers searching for a job. This fall in the on-the-job search rate is corroborated by the micro data.