Competitive search equilibrium with multidimensional heterogeneity and two-sided ex-ante investments

We analyze a competitive (price-taking) search model where workers and firms make costly investments (e.g. in education and physical capital, respectively) before they enter the labor market. The environment features transferable utility and symmetric information. A key novelty with respect to existing work is that we allow for multidimensional heterogeneity on both sides of the market. The probabilities of finding and filling different jobs and the corresponding wages are determined endogenously in equilibrium. We show that constrained efficient allocations can be determined as optimal solutions to a linear programming problem, whereas the prices supporting these allocations and the associated expected payoffs for workers and firms correspond to the solutions of the ‘dual’ of that linear program. We use this characterization to show that an equilibrium exists and is constrained efficient under very general conditions. The fact that linear programming techniques are used for the structural estimation of frictionless matching models suggests that our framework is potentially useful for empirical studies of labor markets and other markets where search frictions are prevalent.