Social optimum in a model with hierarchical firms and endogenous promotion time

This paper develops a search and matching model with hierarchical firms, human capital accumulation, internal promotions and on-the-job search. At the time of their market entry firms maximize present value of profits with respect to their promotion rule. Workers who are eligible for promotion but cannot be promoted because the senior position in the firm is taken start searching on-the-job. The decentralized equilibrium is then compared to the socially optimal one. The welfare analysis is conducted in two steps: in the first one fixed firm entry is assumed, while in the second firm entry is determined by a free-entry condition. Under fixed firm entry, the social planner can induce aprrox. 5% welfare gain by imposing earlier promotion timing compared to the one firms choose in the decentralized equilibrium. The inefficiency of the decentralized equilibrium is caused by strategic complementarity in firms' promotion choices. If a firm delays internal promotions it creates a negative externality on all other firms by reducing the pool of potential candidates to the high productivity senior jobs. However, due to strategic complementarity the competitors respond by also increasing their promotion requirement. Imposing a free-entry condition further reveals that in the decentralized equilibrium firm entry is biased downwards which exacerbates the allocative inefficiency in the economy.