A receiver wants to learn multidimensional information from a sender, and she has the capacity to verify just one dimension. The sender's payoff depends on the belief he induces, via an exogenously given monotone function. We show that by using a randomized verification strategy, the receiver can learn the sender's information fully in many cases. We characterize exactly when it is possible to do so. In particular, when the exogenous payoff function is submodular, we can explicitly describe a full‐learning mechanism; when it is (strictly) supermodular, full learning is not possible. In leading cases where full learning is possible, it can be attained using an indirect mechanism in which the sender chooses the probability of verifying each dimension.

We model and test two school-based peer cultures: one that stigmatizes effort and one that rewards ability. The model shows that either may reduce participation in educational activities when peers can observe participation and performance. We design a field experiment that allows us to test for, and differentiate between, these two concerns. We find that peer pressure reduces takeup of an SAT prep package virtually identically across two very different high school settings. However, the effects arise from very distinct mechanisms: a desire to hide effort in one setting and a desire to hide low ability in the other.