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

Abstract

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 Journal of Economic Literature Classification Numbers: D50, D61, D83.

Unobservable Investments, Trade Efficiency and Search Frictions

“…and the ex ante payoff equals 17 We can verify that function c satisfies all the regularity conditions assumed. 18 Before reaching the steady state, seller entrants randomize between investing c(x) and zero, and the non-investing sellers never trade and stay in the market.…”

“…We are not the first paper to investigate investment incentives and trading outcomes jointly in a dynamic environment with search frictions. A non-exhaustive list includes Masters (1998Masters ( , 2011, Smith (1999), Acemoglu (1996), Acemoglu and Shimer (1999), Charlot, Decreuse and Granier (2005), Charlot and Decreuse (2010), Davis (2001), Kurmann (2014), Flinn and Mullins (2015) and Jerez (2017). What we share in common is that, when participants' types are determined by ex ante investment rather than exogenously given, efficiency cannot be reached under usual conditions.…”

“…In order to see that the two types of equilibrium indeed exist with the right parameters, consider the following example, where c(x) = x 2 − 2x + 1, x 0 = 1, α = 0.1 and β = 0.9. 17 The production cost x equals 1 − 1 3.8 according to (13). Then the condition α(y 0 − x) ≥ c(x) is equivalent to…”

Unobservable investments, trade efficiency and search frictions

“…Mine is not the first paper to investigate investment incentives and trading outcomes jointly in a dynamic environment with search frictions. A non-exhaustive list includes Masters (1998Masters ( , 2011, Smith (1999), Acemoglu (1996), Acemoglu and Shimer (1999), Charlot et al (2005), Charlot and Decreuse (2010), Davis (2001), Kurmann (2014), Flinn and Mullins (2015) and Jerez (2017). What we share in common is that, when participants' types are determined by ex ante investment rather than exogenously given, efficiency cannot be reached under usual conditions.…”

Exponential Income Distribution and Evolution of Unemployment Compensation in the United Kingdom

“…In the literature documenting search models, the unemployment compensation is a wellknown central variable. There is a rich strand of literature dealing with this topic (Moen, 1997;Smith, 1999;Giuseppe and Postel-Vinay, 2013;Kaas and Kircher, 2015;Jerez, 2017;Wright et al, 2019). As our model provides a linear function relationship between and , this potentially bridges the search model and the ADE.…”