Misallocation inefficiency in partially directed search

We identify a misallocation inefficiency in search models, which is distinct from the aggregate entry distortion emphasized in the previous literature, and arises instead from partially directed search. We consider a framework in which workers differ in whether they can direct their search, and firms are heterogeneous in productivity. The main result is that too many workers apply to high-productivity firms, relative to the social optimum. This occurs because too many firms attract only random searchers, in order to extract more surplus from them. Because it is the low-productivity firms that do so, this induces all the directed searchers to concentrate at the high-productivity firms. A minimum wage can increase employment and welfare by reallocating workers across firms. With endogenous entry by either workers or firms, the misallocation inefficiency coexists with a standard entry externality; in this case, a proper combination of a tax or subsidy and a minimum wage can restore the efficient allocation.