Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments

Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments

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 confidenc...

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Veröffentlicht in:Econometrica. - Wiley. - 73(2005), 4, Seite 1351-1365
1. Verfasser: Dufour, Jean-Marie (VerfasserIn)
Weitere Verfasser: Taamouti, Mohamed
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 2005
Zugriff auf das übergeordnete Werk:Econometrica
Schlagworte:Simultaneous equations Structural model Instrumental variable Weak instrument Confidence interval Testing Projection Quadric Exact inference Asymptotic theory mehr... Mathematics Economics Behavioral sciences Information science Philosophy
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520 |a 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. 
540 |a Copyright 2005 Econometric Society 
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