Efficiency in a Search and Matching Model with Endogenous Participation

We show that in a search/matching model with endogenous participation in which workers are heterogeneous with respect to market productivity, satisfying the Hosios rule leads to excessive vacancy creation. JEL Codes: D8, J6 Keywords: Search, Matching, Efficiency, Participation, Hosios Rule a Corresponding author: Department of Economics, Georgetown University, Washington, DC 20057, USA, Telephone: 202 687 6105, FAX: 202 687 6102, [email protected] In the standard Pissarides (2000) search/matching model, equilibrium is e¢ cient when wages are determined by Nash bargaining if the worker share of the net surplus of the match equals the elasticity of the matching function with respect to unemployment, i.e., if the Hosios (1990) rule is satis…ed. As discussed in Pissarides (2000, Chapter 8), this result holds more generally. In particular, the Hosios rule implements the e¢ cient outcome when workers are heterogenous with respect to their outside options, e.g., their leisure values, and labor force participation is endogenous. In this note, we also allow for endogenous labor force participation, but assume that workers are heterogeneous with respect to market productivity1 rather than with respect to leisure values. In this setting, the Hosios condition fails because the participation decision a¤ects not only labor market tightness but also the average productivity of matches. This average productivity e¤ect is not present in the Pissarides version of the model with endogenous labor force participation. In our model, an increase in participation causes average match productivity to fall, but the marginal participant does not internalize this e¤ect. As a result, when wages are determined by the Hosios rule, the labor force participation rate is too high. Equivalently, there is excessive vacancy creation. To make our point as simply as possible, we consider a one-period version of the model with a continuum of workers of measure one. Each worker chooses between searching for a job (participating) and engaging in home production (not participating). A nonparticipant receives z with certainty, but a participant’s expected payo¤ depends on his or her type and on labor market tightness. Productivity in market work is distributed across workers according to a continuous distribution function F (y); 0 y 1 and F (0) = 0: All participants search and …nd a job with probability m( ); where is market tightness.2 A worker of type y who …nds a job gets a fraction of the output that he or she produces; a worker who participates but fails to …nd a job gets a payo¤ that is normalized to zero. The expected payo¤ of a participant of type y is thus m( ) y: A worker participates i¤m( ) y z, A similar issue arises in the Albrecht, Navarro and Vroman (2009) model of developing economy labor markets with an informal sector in which workers have di¤erent formalsector productivities. As in Pissarides (2000), the matching function M(v; u) is assumed to have constant returns to scale so it can be written as m( )u: We assume that m( ) is independent of y; i.e., all participants have an equal chance of …nding a job. Our model can be thought of as one in which employers search sequentially for candidates, e.g., an employer hires the …rst worker who applies for the job. Villena-Roldán (2008) considers a model of nonsequential employer search in which a worker’s chance of getting a job depends on his or her productivity.