Some Impossibility Theorems in Econometrics With Applications to Structural and Dynamic Models

General characterizations of valid confidence sets and tests in problems which involve locally almost unidentified (LAU) parameters are provided and applied to several econometric models. Two types of inference problems are studied: (1) inference about parameters which are not identifiable on certain subsets of the parameter space, and (2) inference about parameter transformations with discontinuities. When a LAU parameter or parametric function has an unbounded range, it is shown under general regularity conditions that any valid confidence set with level 1 − α for this parameter must be unbounded with probability close to 1−α in the neighborhood of nonidentification subsets and will have a non-zero probability of being unbounded under any distribution compatible with