We introduce on-the-job search frictions in an otherwise standard monetary DSGE New-Keynesian model. Heterogeneity in productivity across jobs generates a job ladder. Firms Bertrand-compete for employed workers, as in the Sequential Auctions protocol of Postel-Vinay and Robin (2002). We study the effects of aggregate shocks to TFP and to monetary policy. The ability of firms to commit to wage contracts, until outside offers arrive and trigger renegotiation, insulates wages from unemployment altogether. Outside job offers to employed workers, when accepted, reallocate employment up the productivity ladder; when declined because matched, they cause sudden increases in production costs and, due to nominal price rigidities, decreases in mark-ups, building inflationary pressure. When employment is concentrated at the bottom of the job ladder, typically after recessions, the reallocation effect prevails; as employment climbs the job ladder, the inflation effect takes over. The model generates endogenous cyclical movements in the labor wedge and in the wage mark-up. The jobto-job transition rate is a better predictor of wage pressure than unemployment, as we showed empirically in previous work. Because this transition rate is low, the economy takes time to absorb cyclical misallocation, hence features strong propagation in the response of job creation, unemployment and wage inflation to aggregate shocks.