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

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  • Jean-Marie Dufour

Abstract

General characterizations of valid confidence sets and tests in problems involving (locally almost) unidentified (LAU) parameters are presented. In particular, any valid confidence set for an unbounded LAU parameter must be unbounded with positive probability. Consequently, almost surely bounded confidence sets, like Wald-type confidence sets, have zero coverage probability and Wald-type test statistics cannot be pivotal functions. The results are applied to simultaneous equations (weak instruments), regressions with autoregressive errors, long-run multipliers, and cointegrating vectors. For such models, Wald-type procedures are not recommended while LR procedures can be shown to be valid.

Suggested Citation

  • Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
  • Handle: RePEc:ecm:emetrp:v:65:y:1997:i:6:p:1365-1388
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