Competitive Search Equilibrium with Multidimensional Heterogeneity and Two-Sided Ex-ante Investments

We analyze a competitive search environment where heterogeneous workers and firms make costly investments (e.g. in education and physical capital, respectively) before they enter the labor market. A key novelty with respect to existing work is that we allow for multidimensional heterogeneity on both sides of the market. Our environment features transferable utility and symmetric information. As in classical hedonic models, wages depend both on the job's and on the worker's match-relevant characteristics. Yet the presence of search frictions implies that (unlike in those models) markets do not clear. The hedonic wage function and probabilities of finding and filling different jobs are determined endogenously in a competitive search equilibrium. We show that constrained efficient allocations can be determined as optimal solutions to a linear programming problem, whereas the wage function supporting these allocations and 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 a competitive search equilibrium exist and is constrained efficient under very general conditions. Jerez (2014) makes a similar point in the context of a model where all the match-relevant characteristics of the traders are exogenous. Here we extend the analysis to allow for two-sided ex-ante investments which are potentially multidimensional. The fact that linear programming techniques have been used for the structural estimation of frictionless matching models suggests that our framework is potentially useful for empirical studies of labor markets and other hedonic markets (like that for housing) where search frictions are prevalent