Identifying Sorting – In Theory∗ Jan Eeckhout†and Philipp Kircher‡

Assortative Matching between workers and firms provides evidence of the complementarities or substitutes in production. We argue that using wage data alone, it is virtually impossible to identify whether Assortative Matching is positive or negative. For every production function that induces positive sorting we can find a production function that induces negative sorting, whilst generating identical wages. Even though we cannot identify the sign of the sorting, we can identify the strength, i.e., the magnitude of the cross-partial, and the associated welfare loss. We show that a worker’s wages are non-monotonic in firm type. This is due to the fact that in a sorting model, wages reflect the opportunity cost of mismatch. This non-monotonicity allows us to establish analytically that standard fixed effects regressions are not suitable to recover the strength of sorting. We propose an alternative procedure that measures the strength of sorting in the presence of search frictions independent of the sign of the sorting. Knowing the strength of sorting enables us to measure the efficiency loss due to mismatch