Dynamics in a Model of On-the-Job Search

Recent papers have argued that standard theories of the labor market, e.g. the Mortensen and Pissarides (1994) matching model, cannot generate significant movements in unemployment and vacancies in response to shocks of a plausible magnitude (Hall 2003, Shimer 2003). This paper shows that introducing on-the-search in the manner of Burdett and Mortensen (1998) and Postel-Vinay and Robin (2002) may help to reconcile labor market theories with empirical evidence by substantially amplifying and propagating shocks to the economy. The driving force in this paper is cyclical changes in the composition of the searching population. By paying a fixed cost, a firm may contact one worker, randomly selected from the searching population, which consists of both unemployed and employed workers. Firms prefer to contact unemployed workers because they can be attracted at a lower wage; hiring an employed worker requires outbidding the incumbent employer. Now consider an aggregate shock that raises the present value of output from all matches, e.g. an increase in productivity or a decline in the exogenous separation rate. This raises the profit from contacting a worker, inducing firms to create job vacancies. In standard labor market models, this would have two effects, both of which reduce profits and mitigate the amount of job creation: wages increase and it becomes harder for firms to contact workers. For reasons discussed below, neither of these occur in this model. Instead, equilibrium is restored through a worsening of the composition of the searching population, i.e. an increase in the conditional likelihood of contacting an employed worker. Crucially, a small change in the composition of the searching population may be achieved only through a large change in the rate at which searching workers find jobs. Therefore, even a small increase in the present value of output causes a large decrease in the unemployment rate, amplifying the original shock. There are several important elements in this model. The first, borrowed directly from