Credibility of Confidence Sets in Nonstandard Econometric Problems

Ulrich K. Müller, Andriy Norets

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


Confidence intervals are commonly used to describe parameter uncertainty. In nonstandard problems, however, their frequentist coverage property does not guarantee that they do so in a reasonable fashion. For instance, confidence intervals may be empty or extremely short with positive probability, even if they are based on inverting powerful tests. We apply a betting framework and a notion of bet-proofness to formalize the “reasonableness” of confidence intervals as descriptions of parameter uncertainty, and use it for two purposes. First, we quantify the violations of bet-proofness for previously suggested confidence intervals in nonstandard problems. Second, we derive alternative confidence sets that are bet-proof by construction. We apply our framework to several nonstandard problems involving weak instruments, near unit roots, and moment inequalities. We find that previously suggested confidence intervals are not bet-proof, and numerically determine alternative bet-proof confidence sets.

Original languageEnglish (US)
Pages (from-to)2183-2213
Number of pages31
Issue number6
StatePublished - Nov 1 2016

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics


  • Bayes
  • Confidence sets
  • betting
  • conditional coverage
  • invariance
  • moment inequalities
  • nonstandard econometric problems
  • recognizable subsets
  • unit roots
  • weak instruments


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