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We analyse a version of Spence's job market signalling model in which firms can make job offers before workers complete their education. Workers cannot commit to turning down such offers. Offers are private, so that workers are unable to use one firm's offer in an attempt to elicit better offers from other firms. In the unique sequential equilibrium outcome of the model with unproductive education, there is no wasteful education. When education is productive, the standard model predicts that more able individuals become overeducated to separate themselves from less able workers. In our model, less able workers become overeducated to (partially) pool with more able workers. The pooling mutes the incentives of high ability workers, who in consequence actually choose to become undereducated. We examine the robustness of our result to modifications to the basic model.

We consider large double auctions with private values. Values need be neither symmetric nor independent. Multiple units may be owned or desired. Participation may be stochastic. We introduce a very mild notion of "a little independence." We prove that all nontrivial equilibria of auctions that satisfy this notion are asymptotically efficient. For any alpha>0, inefficiency disappears at rate (1/n)^(2 alpha). Copyright The Econometric Society 2006.

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