Search, Screening and Sorting

We investigate the effect of search frictions on labor market sorting by constructing a model which is in line with recent evidence that employers collect a pool of applicants before interviewing a subset of them. In this environment, we derive the necessary and sufficient conditions for sorting in applications as well as matches. We show that positive sorting is obtained when production complementarities outweigh a force against sorting measured by a quality-quantity elasticity. Interestingly, we find that the required degree of production complementarity for positive sorting is increasing in the number of interviews: it ranges from square-root-supermodularity if each firm can interview a single applicant to log-supermodularity if each firm can interview all its applicants.