An Equilibrium Model of the Labor Market with Endogenous Capital and Two-Sided Search

In this paper we extend the equilibrium search models of Burdett and Mortensen [1998], Burdett and Vishwanath [1988] and Mortensen and Vishwanath [1994] to allow for endogenous matching and endogenous capital determination. In our model, in order to attract a positive measure of workers, firms must produce a specific hiring effort which is by itself costly (cost of advertising posts, training new employees). Workers then draw firms in proportion to their hiring effort. Moreover, as in the model of Acemoglu and Shimer [1997], upon entering the market firms must choose a determined amount of capital which is then fixed for ever and indexes labour productivity. We characterize the equilibrium and derive expressions for the endogenous equilibrium wage distributions. In particular, we show that with convex or concave hiring costs, the Nash equilibrium of the equilibrium search game is such that all operating firms must choose a different amount of capital from a continuous distribution, and a one-to-one mapping exists between capital and wages. We calibrate the model on French firm data and proceed to various simulations of tax reforms. We thus show that a reform which transfers labour taxes from low wages to high wages, by reducing the monopsony power of large firms, is welfare improving: unemployment is reduced, total output is increased as well as government revenue.