Assortative Matching between workers and rms provides evidence of the complementarities or substitutes in production. The presence of complementarities is important for policies that aim to achieve the optimal allocation of resources, for example unemployment insurance. We argue that using wage data alone, it is virtually impossible to identify whether Assortative Matching is positive or negative. 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 rst that the wage for a given worker is non-monotonic in the type of his employer. This is due to the fact that in a sorting model, wages reect the opportunity cost of mismatch. We show analytically that this non-monotonicity prevents standard rm xed eects to correlate with the true type of the rm. We then propose an alternative procedure that measures the strength of sorting in the presence of search frictions. Knowing the strength of sorting facilitates the measurement of the output loss due to mismatch.