Abstract
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 language | English (US) |
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Pages (from-to) | 2183-2213 |
Number of pages | 31 |
Journal | Econometrica |
Volume | 84 |
Issue number | 6 |
DOIs | |
State | Published - Nov 1 2016 |
All Science Journal Classification (ASJC) codes
- Economics and Econometrics
Keywords
- Bayes
- Confidence sets
- betting
- conditional coverage
- invariance
- moment inequalities
- nonstandard econometric problems
- recognizable subsets
- unit roots
- weak instruments