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Testing Parameters in GMM Without Assuming that They Are Identified

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Frank Kleibergen

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Abstract

We propose a generalized method of moments (GMM) Lagrange multiplier statistic, i.e., the K statistic, that uses a Jacobian estimator based on the continuous updating estimator that is asymptotically uncorrelated with the sample average of the moments. Its asymptotic χ-super-2 distribution therefore holds under a wider set of circumstances, like weak instruments, than the standard full rank case for the expected Jacobian under which the asymptotic χ-super-2 distributions of the traditional statistics are valid. The behavior of the K statistic can be spurious around inflection points and maxima of the objective function. This inadequacy is overcome by combining the K statistic with a statistic that tests the validity of the moment equations and by an extension of Moreira's (2003) conditional likelihood ratio statistic toward GMM. We conduct a power comparison to test for the risk aversion parameter in a stochastic discount factor model and construct its confidence set for observed consumption growth and asset return series. Copyright The Econometric Society 2005.

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File URL: http://hdl.handle.net/10.1111/j.1468-0262.2005.00610.x
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Publisher Info
Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 73 (2005)
Issue (Month): 4 (07)
Pages: 1103-1123
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Handle: RePEc:ecm:emetrp:v:73:y:2005:i:4:p:1103-1123

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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. Sophocles Mavroeidis, 2006. "Testing the New Keynesian Phillips Curve Without Assuming Identification," Working Papers 2006-13, Brown University, Department of Economics. [Downloadable!]
  3. Pål Boug, Ådne Cappelen and Anders Rygh Swensen, 2007. "The New Keynesian Phillips Curve revisited," Discussion Papers 500, Research Department of Statistics Norway. [Downloadable!]
  4. G. Forchini, 2005. "Some Properties of Tests for Possibly Unidentified Parameters," Monash Econometrics and Business Statistics Working Papers 21/05, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  5. Paul Levine & Luis F. Martins & Vasco J. Gabriel, 2006. "Robust Estimates of the New Keynesian Phillips Curve," Department of Economics Discussion Papers 0206, Department of Economics, University of Surrey. [Downloadable!]
  6. Mehmet Caner, 2005. "Higher Order Expansions in GMM with Nearly Weak and Many Nearly Weak Instruments," Working Papers 209, University of Pittsburgh, Department of Economics, revised Jan 2005. [Downloadable!]
  7. Maurice J.G. Bun & Frank Windmeijer, 2007. "The Weak Instrument Problem of the System GMM Estimator in Dynamic Panel Data Models," Bristol Economics Discussion Papers 07/595, Department of Economics, University of Bristol, UK. [Downloadable!]
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  8. 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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  9. 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!]
  10. Yukitoshi Matsushita, 2007. "t-Tests in a Structural Equation with Many Instruments," CIRJE F-Series CIRJE-F-467, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  11. 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!]
  12. Rolf Scheufele, 2008. "Evaluating the German (New Keynesian) Phillips Curve," IWH Discussion Papers 10-08, Halle Institute for Economic Research. [Downloadable!]
  13. 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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  14. Angelica Gonzalez, 2007. "Empirical Likelihood Estimation in Dynamic Panel Models," ESE Discussion Papers 168, Edinburgh School of Economics, University of Edinburgh. [Downloadable!]
  15. Leandro M. Magnusson, 2008. "Inference in Limited Dependent Variable Models Robust to Weak Identification," Working Papers 0801, Tulane University, Department of Economics, revised Apr 2009. [Downloadable!]
  16. Leandro M. Magnusson, 2008. "Tests in Censored Models when the Structural Parameters Are Not Identified," Working Papers 0802, Tulane University, Department of Economics. [Downloadable!]
  17. Vasco Gabriel & Paul Levine & Christopher Spencer & Bo Yang, 2008. "On the (ir)relevance of direct supply-side effects of monetary policy," Department of Economics Discussion Papers 0408, Department of Economics, University of Surrey. [Downloadable!]
  18. Mehmet Caner, 2005. "Exponential Tilting With Weak Instruments," Working Papers 208, University of Pittsburgh, Department of Economics, revised Jan 2005. [Downloadable!]
  19. Whitney Newey & Frank Windmeijer, 2005. "GMM with many weak moment conditions," CeMMAP working papers CWP18/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  20. Mehmet Caner, 2006. "Near Exogeneity and Weak Identification in Generlized Empirical Likelihood estimators : Fixed and Many Moment Asymptotics," Working Papers 212, University of Pittsburgh, Department of Economics, revised Jan 2006. [Downloadable!]
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  21. Richard Smith, 2005. "Weak instruments and empirical likelihood: a discussion of the papers by DWK Andrews and JH Stock and Y Kitamura," CeMMAP working papers CWP13/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
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