What does the data say about wage setting and job search?

Do current wages depend on past labour market conditions? Wage posting models suggest so, Nash bargaining models do not, Bertrand competition between employers is somewhere in between. Recent evidence suggests Nash bargaining to be an adequate description of the data. We re-evaluate this evidence, using a more precise analytical framework and more efficient estimation techniques. Our evidence is easily squared with wage posting, but not with Nash bargaining, while Bertrand competition is clearly rejected. In wage posting models firms can pay hiring and retention premiums. Our evidence is consistent retention premiums, but it is more difficult to square with hiring premiums. Finally, our methodology allows two important side conclusions. First, we find strong support for the general class of models with on-the-job search. Second, the estimation results suggest the productivity distribution to have an fat tailed upper support, which is hard to square with pure sorting models.