  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 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.
