Projection-based statistical inference in linear structural models with possibly weak instruments

• 成果类型: Article
• 署名作者: Dufour, JM; Taamouti, M
• 署名单位: Universite de Montreal; Universite de Montreal; Universite de Montreal
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.1111/j.1468-0262.2005.00618.x
• 发表日期: 2005
• 页码: 1351-1365
• 关键词: VARIABLES REGRESSION; confidence sets; identification; parameters

摘要

It is well known that standard asymptotic theory is not applicable or is very unreliable in models with identification problems or weak instruments. One possible way out consists of using a variant of the Anderson-Rubin ((1949), AR) procedure. The latter allows one to build exact tests and confidence sets only for the full vector of the coefficients of the endogenous explanatory variables in a structural equation, but not for individual coefficients. This problem may in principle be overcome by using projection methods (Dufour (1997), Dufour and Jasiak (2001)). At first sight, however, this technique requires the application of costly numerical algorithms. In this paper, we give a general necessary and sufficient condition that allows one to check whether an AR-type confidence set is bounded. Furthermore, we provide an analytic solution to the problem of building projection-based confidence sets from AR-type confidence sets. The latter involves the geometric properties of quadrics and can be viewed as an extension of usual confidence intervals and ellipsoids. Only least squares techniques are needed to build the confidence intervals.