Credibility of Confidence Sets in Nonstandard Econometric Problems

• 成果类型: Article
• 署名作者: Muller, Ulrich K.; Norets, Andriy
• 署名单位: Princeton University; Brown University
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA14023
• 发表日期: 2016
• 页码: 2183-2213
• 关键词: instrumental variables regression; PARTIALLY IDENTIFIED PARAMETERS; statistical-inference; weak instruments; EFFICIENT TESTS; time-series; unit-root; intervals; models; coefficients

摘要

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.