Directed Search On the Job and the Wage Ladder

Abstract

In this paper we characterize the equilibrium in a labor market where employed workers search on the job and firms direct the search by announcing wages and employment probabilities for the applicants. All workers/jobs are homogeneous and free entry of firms determines the number of jobs. The equilibrium features a wage ladder, with a finite number of rungs. Workers on each particular rung of the ladder choose (optimally) to apply to only the jobs at one level above their current wage, despite that they observe all higher wage offers. Workers choose not to leap several rungs at a time on the wage ladder because the jobs at one level above their current wage provide a significantly higher employment probability, and hence a higher expected surplus, than the jobs at two or more levels above. The wage ladder has the following properties: (i) The gap between two adjacent rungs on the ladder becomes smaller and smaller as wage increases; (ii) A worker s quit rate decreases with wage; (iii)A worker s wage, on average, increases with the employment duration; (iv) The average length of time an unemployed worker will take to return to his previous wage increases with that wage; (v) The density of offer wages decreases with wage; (vi) The density of employed wages can be decreasing, increasing, or hump-shaped. The directed search framework replicates empirical regularities on the wage path of workers and the distribution of offer and employed wages that undirected search cannot.Directed Search, On-the-Job Search, Wage Ladder.