Incomplete self-enforcing labor contracts

We consider a model economy populated by risk-neutral firms with multiple vacancies and risk-averse workers. Following the implicit contract literature, we assume that workers have limited access to the intertemporal trade markets. Following the directed search literature, we assume that unemployed workers choose which firms to visit based on the labor contracts they advertise. Under perfect commitment, the optimal contract between the firm and a worker keeps the worker’s marginal utility constant across dates and states and prescribes that the worker is employed only when employment is ex-post efficient. Also, under perfect commitment, the optimal contract leaves the firm complete discretion to choose the terms of trade offered to future applicants. Therefore, the inflow of new workers is ex-post efficient too. Overall, under perfect commitment, labor contracts create a real wage rigidity that has no allocative effects on labor. Then, we consider an alternative scenario where both firms and workers can leave the employment relationship at any stage and at no cost. Under limited commitment, there is a tension between the goals of insurance provision and recruitment. In those states of the world where the value of the ex-post efficient contract offered to new applicants is lower then the continuation value of the ex-ante optimal contract offered to a senior employee, the firm has an incentive to replace senior with new applicants. The optimal self-enforcing contract efficiently trades-off the goals of insurance and recruitment by prescribing not only what wage the firm should pay its employee at every date and state, but also what contract the firm should offer in the future to new applicants. We show that the optimal self-enforcing contract creates ex-post distortions on the value of the contract offered to new applicants. Most interestingly, we show that for small negative shocks to firm’s productivity, the contract offered to junior and senior employees is identical. The value of this common contract is greater than the value of the ex-post efficient hiring contract. In general equilibrium, this ex-post distortion translates into inefficiently large responses of the unemployment rate to small and negative shocks to aggregate productivity.