Distortions of Asymptotic Confidence Size in Locally Misspecified Moment Inequality Models

• 成果类型: Article
• 署名作者: Bugni, Federico A.; Canay, Ivan A.; Guggenberger, Patrik
• 署名单位: Duke University; Northwestern University; University of California System; University of California San Diego
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA9604
• 发表日期: 2012
• 页码: 1741-1768
• 关键词: inference; parameters; set; intervals; regions; hybrid

摘要

This paper studies the behavior, under local misspecification, of several confidence sets (CSs) commonly used in the literature on inference in moment (in)equality models. We propose the amount of asymptotic confidence size distortion as a criterion to choose among competing inference methods. This criterion is then applied to compare across test statistics and critical values employed in the construction of CSs. We find two important results under weak assumptions. First, we show that CSs based on subsampling and generalized moment selection (Andrews and Soares (2010)) suffer from the same degree of asymptotic confidence size distortion, despite the fact that asymptotically the latter can lead to CSs with strictly smaller expected volume under correct model specification. Second, we show that the asymptotic confidence size of CSs based on the quasi-likelihood ratio test statistic can be an arbitrary small fraction of the asymptotic confidence size of CSs based on the modified method of moments test statistic.