There exists a large literature analyzing the effects of search frictions in the labor market. In this literature, firms are typically modeled in a parsimonious way, with exogenous output per worker. In particular, agency problems between workers and firms are ignored. The focus is thus solely on the effects of search frictions on the flows into and out of employment.
In the present paper, we allow a firm’s output to depend on the wage contracts firms offer their workers. A worker’s output depends on both her effort and a match-specific component. The firm observes total output, but cannot disentangle output into its different components. The firm acts as a principal and chooses a wage contract that maximizes profits given the information constraints. Our aim is to analyze the interplay between search frictions in the market place and agency problems created by workers’ private information. The search frictions and agency problems interact through the amount of "rents" that accrue to the worker.
A worker’s private information gives her an information rent, which is larger the closer the wage is linked to her output. Without search frictions, a firm, when setting the wage contract, trades off incentives for the worker to provide effort and rent extraction from the worker. This trade-off is also present when there are search frictions in the labor market. However, with search frictions, rents that accrue to the worker have an additional effect. More rents to the worker when hired also benefit the firm in the recruiting process, as it speeds up the hiring rate. Hence, it is less costly for a firm to provide workers with incentives when it operates in a competitive, frictional market than in a frictionless market.
We show that the resulting search equilibrium, which we refer to as generalized competitive search equilibrium, has a simple form. The agency problem and the wage posting problem can be disentangled into two separate maximization problems. The solution to the firms’ problem satisfies a modified Hosios rule, which determines constrained efficient resource allocation. When the information constraints are tight in a well-defined sense, the optimal wage contract prescribes that a large share of the match surplus is allocated to the employees. As a result, profits will be lower, and fewer resources are used to create new vacancies as compared to the equilibrium without agency problems. We also show that macroeconomic variables influence the tightness of the information constraints, and hence the optimal contracts. In particular, high search frictions tend to increase the incentive power of the wage contracts, while a higher value of leisure /unemployment benefit tends to reduce it.
We then analyze the effect of private information on the responsiveness of the unemployment rate to productivity changes, motivated by findings in Shimer (2005) and Hall (2004). They document that fluctuations in the unemployment rate predicted by the standard Diamond-Mortensen-Pissarides (DMP) model (Diamond 1982, Mortensen 1986, Pissarides 1985) in response to observed productivity shocks are much smaller than actual fluctuations in the unemployment rate, as wages in the model absorb much of the shock.
