This paper shows that the problem of testing hypotheses in moment condition models without any assumptions about identification may be considered as a problem of testing with an infinite‐dimensional nuisance parameter. We introduce a sufficient statistic for this nuisance parameter in a Gaussian problem and propose conditional tests. These conditional tests have uniformly correct asymptotic size for a large class of models and test statistics. We apply our approach to construct tests based on quasi‐likelihood ratio statistics, which we show are efficient in strongly identified models and perform well relative to existing alternatives in two examples.

We consider how a firm dynamically allocates business among several suppliers to motivate them in a relational contract. The firm chooses one supplier who exerts private effort. Output is non-contractible, and each supplier observes only his own relationship with the principal. In this setting, allocation decisions constrain the transfers that can be promised to suppliers in equilibrium. Consequently, optimal allocation decisions condition on payoff-irrelevant past performance to make strong incentives credible. We construct a dynamic allocation rule that attains first-best whenever any allocation rule does. This allocation rule performs strictly better than any rule that depends only on payoff-relevant information.