Complementarity and Advantage in the Competing Auctions of Skills

We use a directed search model to develop estimation procedures for the identification of worker and firm rankings from labor market data. These methods allow for a general specification of production complementarities and the possibility that higher ranked workers are not more productive in all firms. We also offer conditions for a positive/negative assortative matching that incorporate the possibility of a stochastic job ladder with on-the-job search. Numerical simulations relate the implications of the model to the implications of fixed effect regressions and give further insights into the performance of our estimation procedures. Finally, we evaluate evidence for Denmark using our methods and we show that workers are highly sorted and that higher type workers are less productive than lower type workers while employed in lower type jobs.