Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments
AbstractIt 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. Copyright The Econometric Society 2005.
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Bibliographic InfoArticle provided by Econometric Society in its journal Econometrica.
Volume (Year): 73 (2005)
Issue (Month): 4 (07)
Other versions of this item:
- Jean-Marie Dufour & Mohamed Taamouti, 2003. "Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments," CIRANO Working Papers 2003s-39, CIRANO.
- DUFOUR, Jean-Marie & TAAMOUTI, Mohamed, 2003. "Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments," Cahiers de recherche 08-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- DUFOUR, Jean-Marie & TAAMOUTI, Mohamed, 2003. "Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments," Cahiers de recherche 2003-10, Universite de Montreal, Departement de sciences economiques.
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