Competitive or Random Search?

We set up a search model with on-the-job search that spans random and competitive search as well as intermediate cases with partially directed search. Firms are heterogeneous in terms of productivity, and firms with different productivities are in different submarkets, with all firms in the same submarket being identical. Workers are identical, still a worker's optimal search behavior, that is, the optimal submarket for her to visit, depends on the productivity of the current employer. The higher is the productivity of the current employer, the higher is the productivity of the firm it is optimal for the worker to target her search at. We use a discrete choice framework to model the workers' choice of submarkets, with a single noise parameter \mu governing the degree to which search is directed. As \mu goes to zero, search becomes fully directed, while it becomes random as \mu goes to infinity. We derive the equilibrium of the model, and simulate the equilibrium allocation. We also show how the parameter \mu can be identified using a maximum likelihood approach where submarkets are identified via the Bagger and Lentz (2016) poaching rank, or in a classification step as in Lentz, Piyapromdee and Robin (2017). Alternatively, we use a simulated method of moments approach. We will identify \mu on Danish and/or Norwegian matched employer-employee data.