Optimal Promotions of Competing Firms in a Frictional Labour Market with Organizational Hierarchies

We study optimal promotion decisions of hierarchical firms, with one junior and one senior managerial position, which interact in a search and matching labor market. Workers acquire experience over time while being employed in a junior position and the firm has to determine the experience level at which the worker receives a promotion which allows her to fill a senior position. Promoted workers move to the senior position in their current firrm, if it is vacant, otherwise they search for senior positions on the market. The promotion cut-offs of the competing firms exhibit strategic complementarity, but we show that generically a unique stable symmetric general equilibrium exists. If workers have homogeneous skills, then an increase in the skill level induces faster promotion. In the presence of two skill levels in the work force an increase of the fraction of high skilled leads to slower promotion of both types of workers, where the promotion threshold for high skilled workers is substantially below that for low skilled workers. This implies earlier promotions of high skill workers compared to the low skilled consistent with available empirical evidence. Finally, we show that inserting pyramidal firms, which have twice as many junior than senior positions, into the market induces all firms to promote later. Pyramidal firms in equilibrium promote substantially later than vertical firms which is supported by the existing empirical findings. The paper also makes a methodological contribution by combining search and matching theory with simulations in order to characterize the general equilibrium promotion cut-offs in a market setting with heterogeneous hierarchical firms.