A wide class of models with On-the-Job Search (OJS) predicts that workers gradually select into better-paying jobs, until lay-off occurs, when this selection process starts over from scratch. We develop a simple methodology to test these predictions. Our inference uses two sources of identification to distinguish between returns to experience and the gains from OJS: (i) time-variation in job-finding rates and (ii)the time since the last lay-off. Conditional on the termination date of the job, job duration should be distributed uniformly. Using extreme value theory, we can infer the shape of the wage-offer distribution from the effect of the time since the last lay-off on wages. This methodology is applied to the NLSY 79. We find remarkably strong support for all implications. The offer distribution is Gumbel, which has an unbounded support, which is inconsistent with pure sorting models. The standard deviation of wage offers is 7 to 15% (depending on educational level and urbanisation). OJS accounts for 30% of the experience profile and 9% of total wage dispersion. The average wage loss after lay-off is 11%.