Identification, weak instruments, and statistical inference in econometrics

We discuss statistical inference problems associated with identification and testability in econometrics. We consider inference in non-parametric models and weakly identified structural models (weak instruments). We point out that many ill-defined statistical problems, such as non-testable hypotheses, occur in these areas and are typically associated with asymptotic approximations. In non-parametric models, such problems include testing moments and inference under heteroscedasticity or serial dependence of unknown form. For weakly identified structural models, difficulties are typically associated with improper pivots, and we review recent developments aimed at proposing more reliable procedures, including alternative proposed statistics, bounds, projection, split-sampling, conditioning, Monte Carlo tests.