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

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Author Info
Jean-Marie Dufour
Mohamed Taamouti

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Abstract

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. Copyright The Econometric Society 2005.

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File URL: http://hdl.handle.net/10.1111/j.1468-0262.2005.00618.x
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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 73 (2005)
Issue (Month): 4 (07)
Pages: 1351-1365
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Handle: RePEc:ecm:emetrp:v:73:y:2005:i:4:p:1351-1365

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  1. Aviv Nevo & Adam Rosen, 2008. "Identification with imperfect instruments," CeMMAP working papers CWP16/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
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  2. Jean-Marie Dufour & Lynda Khalaf & Maral Kichian, 2005. "Inflation Dynamics and the New Keynesian Phillips Curve: an Identification Robust Econometric Analysis," CIRANO Working Papers 2005s-30, CIRANO. [Downloadable!]
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  3. James M. Nason & Gregor W. Smith, 2008. "Identifying the new Keynesian Phillips curve," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(5), pages 525-551. [Downloadable!]
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  4. Jean-Marie Dufour & Lynda Khalaf & Maral Kichian, 2009. "Structural Inflation Models with Real Wage Rigidities: The Case of Canada," Working Papers 09-21, Bank of Canada. [Downloadable!]
  5. Eric Zivot & Saraswata Chaudhuri, 2008. "A Comment on Weak Instrument Robust Tests in GMM and the New Keynesian Phillips Curve," Working Papers UWEC-2008-23, University of Washington, Department of Economics. [Downloadable!]
  6. Saraswata Chaudhuri & Eric Zivot, 2008. "A new method of projection-based inference in GMM with weakly identified nuisance parameters," Working Papers UWEC-2008-26, University of Washington, Department of Economics. [Downloadable!]
  7. Mehmet Caner, 2005. "Boundedly Pivotal Structural Change Tests in Continuous Updating GMM with Strong, Weak Identification and Completely Unidentified Cases," Econometrics 0509016, EconWPA. [Downloadable!]
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  8. Khalaf, Lynda & Kichian, Maral, 2003. "Are New Keynesian Phillips Curved Identified?," Cahiers de recherche 0312, GREEN. [Downloadable!]
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  9. Richard Startz & Charles Nelson & Eric Zivot, 1999. "Improved Inference for the Instrumental Variable Estimator," Working Papers 0039, University of Washington, Department of Economics. [Downloadable!]
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  10. Yilmazkuday, Hakan, 2009. "Is there a Role for International Trade Costs in Explaining the Central Bank Behavior?," MPRA Paper 15951, University Library of Munich, Germany. [Downloadable!]
  11. Jean-Marie Dufour & Abderrahim Taamouti, 2008. "Exact optimal and adaptive inference in regression models under heteroskedasticity and non-normality of unknown forms," Economics Working Papers we086027, Universidad Carlos III, Departamento de Economía. [Downloadable!]
  12. Denis Bolduc & Lynda Khalaf & Clément Yélou, 2005. "Identification Robust Confidence Sets Methods for Inference on Parameter Ratios and their Application to Estimating Value-of-Time," Computing in Economics and Finance 2005 48, Society for Computational Economics. [Downloadable!]
  13. Donald W.K. Andrews & James H. Stock, 2005. "Inference with Weak Instruments," Cowles Foundation Discussion Papers 1530, Cowles Foundation, Yale University. [Downloadable!]
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