Efficiency of two sided investments in an equilibrium unemployment framework

This paper investigates the efficiency of investments by firms and workers in a matching model with high- and low-productivity jobs. Search is sector specific and random within sectors. Search frictions and ex-post bargaining imply that wage inequality arises as a result of the difference in investment costs between the sectors. The efficiency properties of the equilibrium are analyzed under the particular division in bargaining proposed by Hosios (1990). The conclusion is that the equilibrium is inefficient, with a too low fraction of workers and a too high vacancy-unemployment ratio in the high-productivity sector. The opposite happens in the low-productivity sector.