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• W2122480349 abstract "General characterizations of valid confidence sets and tests in problems which involve locally almost unidentified (LAU) parameters are provided and applied to several econo- metric models. Two types of inference problems are studied: (i) inference about parame- ters which are not identifiable on certain subsets of the parameter space, and (ii) 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 - a for this parameter must be unbounded with probability close to 1 - a in the neighborhood of nonidentification subsets and will have a nonzero probability of being unbounded under any distribution compatible with the model: no valid confidence set which is almost surely bounded does exist. These properties hold even if identifying restrictions are imposed. Similar results also obtain for parameters with bounded ranges. Consequently, a confidence set which does not satisfy this characterization has zero coverage probability (level). This will be the case in particular for Wald-type confidence intervals based on asymptotic errors. Furthermore, Wald-type statistics for testing given values of a LAU parameter cannot be pivotal functions (i.e., they have distributions which depend on unknown nuisance param- eters) and even cannot be usefully bounded over the space of the nuisance parameters. These results are applied to several econometric problems: inference in simultaneous equations (instrumental variables (IV) regressions), linear regressions with autoregressive errors, inference about long-run multipliers and cointegrating vectors. For example, it is shown that asymptotically justified confidence intervals based on IV estimators (such as two-stage least squares) and the associated standard errors have zero coverage probability, and the corresponding t statistics have distributions which cannot be bounded by any finite set of distribution functions, a result of interest for interpreting IV regressions with weak instruments. Furthermore, expansion methods (e.g., Edgeworth expansions) and bootstrap techniques cannot solve these difficulties. Finally, in a number of cases where Wald-type methods are fundamentally flawed (e.g., IV regressions with poor instruments), it is observed that likelihood-based methods (e.g., likelihood-ratio tests and confidence sets) combined with projection techniques can easily yield valid tests and confidence sets." @default.
• W2122480349 created "2016-06-24" @default.
• W2122480349 creator A5031632775 @default.
• W2122480349 date "1997-11-01" @default.
• W2122480349 modified "2023-10-18" @default.
• W2122480349 title "Some Impossibility Theorems in Econometrics With Applications to Structural and Dynamic Models" @default.
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• W2122480349 doi "https://doi.org/10.2307/2171740" @default.
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