On Completeness and Consistency in Nonparametric Instrumental Variable Models

• 成果类型: Article
• 署名作者: Freyberger, Joachim
• 署名单位: University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA13304
• 发表日期: 2017
• 页码: 1629-1644
• 关键词: CONDITIONAL MOMENT MODELS; identification; parameter; inference

摘要

This paper provides positive testability results for the identification condition in a nonparametric instrumental variable model, known as completeness, and it links the outcome of the test to properties of an estimator of the structural function. In particular, I show that the data can provide empirical evidence in favor of both an arbitrarily small identified set as well as an arbitrarily small asymptotic bias of the estimator. This is the case for a large class of complete distributions as well as certain incomplete distributions. As a byproduct, the results can be used to estimate an upper bound of the diameter of the identified set and to obtain an easy to report estimator of the identified set itself.