This paper provides positive testability results for the identification condition in a nonparametric instrumental variable model, known as completeness, and it links the outcome of the test to properties of an estimator of the structural function. In particular, I show that the data can provide empirical evidence in favor of both an arbitrarily small identified set as well as an arbitrarily small asymptotic bias of the estimator. This is the case for a large class of complete distributions as well as certain incomplete distributions. As a byproduct, the results can be used to estimate an upper bound of the diameter of the identified set and to obtain an easy to report estimator of the identified set itself.

This study provides a structural analysis of detailed, alternating‐offer bargaining data from eBay, deriving bounds on buyers and sellers private value distributions and the gains from trade using a range of assumptions on behavior and the informational environment. These assumptions range from weak (assuming only that acceptance and rejection decisions are rational) to less weak (e.g., assuming that bargaining offers are weakly increasing in players' private values). We estimate the bounds and show what they imply for consumer negotiation behavior and inefficient breakdown. For the median product, bargaining ends in impasse in 37% of negotiations even when the buyer values the good more than the seller.