We assess the empirical content of equilibrium models of labor market sorting based on unobserved (to economists) characteristics. In particular, we show theoretically that all parameters of the classic model of sorting based on absolute advantage in Becker, 1973 with search frictions can be nonparametrically identified using only matched employer–employee data on wages and labor market transitions. In particular, these data are sufficient to nonparametrically estimate the output of any individual worker with any given firm. Our identification proof is constructive and we provide computational algorithms that implement our identification strategy given the limitations of the available data sets. Finally, we add on‐the‐job search to the model, extend the identification strategy, and apply it to a large German matched employer–employee data set to describe detailed patterns of sorting and properties of the production function.