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Identification, Weak Instruments and Statistical Inference in Econometrics

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Author Info
DUFOUR, Jean-Marie

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Abstract

We discuss statistical inference problems associated with identification and testability in econometrics, and we emphasize the common nature of the two issues. After reviewing the relevant statistical notions, we consider in turn inference in nonparametric models and recent developments on weakly identified models (or weak instruments). We point out that many hypotheses, for which test procedures are commonly proposed, are not testable at all, while some frequently used econometric methods are fundamentally inappropriate for the models considered. Such situations lead to ill-defined statistical problems and are often associated with a misguided use of asymptotic distributional results. Concerning nonparametric hypotheses, we discuss three basic problems for which such difficulties occur: (1) testing a mean (or a moment) under (too) weak distributional assumptions; (2) inference under heteroskedasticity of unknown form; (3) inference in dynamic models with an unlimited number of parameters. Concerning weakly identified models, we stress that valid inference should be based on proper pivotal functions —a condition not satisfied by standard Wald-type methods based on standard errors — and we discuss recent developments in this field, mainly from the viewpoint of building valid tests and confidence sets. The techniques discussed include alternative proposed statistics, bounds, projection, split-sampling, conditioning, Monte Carlo tests. The possibility of deriving a finite-sample distributional theory, robustness to the presence of weak instruments, and robustness to the specification of a model for endogenous explanatory variables are stressed as important criteria assessing alternative procedures.

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Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2003-12.

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Length: 39 pages
Date of creation: 2003
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Handle: RePEc:mtl:montde:2003-12

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Keywords: hythesis testing ; confidence set ; confidence interval ; identification ; testability ; asymotic theory ; exact inference ; votal function ; nonrametric model ; Bahadur-Savage ; heteroskedasticity ; serial dendence ; unit root ; simultaneous equations ; structural model ; instrumental variable ; weak instrument ; weak identification ; simultaneous inference ; ojection ; sit-same ; conditional test ; Monte Carlo test ; bootstrap;

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Find related papers by JEL classification:
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Jean-Marie Dufour, 2001. "Logiques et tests d'hypothèses : réflexions sur les problèmes mal posés en économétrie," CIRANO Working Papers 2001s-40, CIRANO. [Downloadable!]
    Other versions:
  2. DUFOUR, Jean-Marie, 2000. "Économétrie, théorie des tests et philosophie des sciences," Cahiers de recherche 2000-14, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  3. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March. [Downloadable!] (restricted)
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  4. Phillips, Peter C B, 1984. "The Exact Distribution of LIML: I," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 249-61, February. [Downloadable!] (restricted)
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  5. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
  6. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September. [Downloadable!] (restricted)
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  7. Dufour, Jean-Marie, 1990. "Exact Tests and Confidence Sets in Linear Regressions with Autocorrelated Errors," Econometrica, Econometric Society, vol. 58(2), pages 475-94, March. [Downloadable!] (restricted)
  8. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07. [Downloadable!] (restricted)
  9. Hahn, Jinyong & Hausman, Jerry, 2002. "Notes on bias in estimators for simultaneous equation models," Economics Letters, Elsevier, vol. 75(2), pages 237-241, April. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Richard Luger, 2004. "Exact Tests of Equal Forecast Accuracy with an Application to the Term Structure of Interest Rates," Working Papers 04-2, Bank of Canada. [Downloadable!]
  2. 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!]
  3. Charlotta Groth & Hashmat Khan, . "Investment adjustment costs: evidence from UK and US industries," Bank of England working papers 332, Bank of England. [Downloadable!]
  4. Mehmet Caner, 2005. "Near Exogeneity and Weak Identification in Generalized Empirical Likelihood Estimators: Fixed and Many Moment Asymptotics," Econometrics 0509018, EconWPA. [Downloadable!]
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  5. Khalaf, Lynda & Kichian, Maral, 2003. "Are New Keynesian Phillips Curved Identified?," Cahiers de recherche 0312, GREEN. [Downloadable!]
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  6. Christopher F Baum & Mark E. Schaffer & Steven Stillman, 2007. "Enhanced routines for instrumental variables/GMM estimation and testing," CERT Discussion Papers 0706, Centre for Economic Reform and Transformation, Heriot Watt University. [Downloadable!]
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  7. Konstantinos Angelopoulos & George Economides, . "Fiscal Policy, Rent Seeking and Growth under Electoral Uncertainty Theory and Evidence from the OECD," Working Papers 2007_28, Department of Economics, University of Glasgow, revised Apr 2008. [Downloadable!]
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  8. Rembert De Blander, 2008. "Which null hypothesis do overidentification restrictions actually test?," Economics Bulletin, Economics Bulletin, vol. 3(76), pages 1-9. [Downloadable!]
  9. BEAULIEU, Marie-Claude & DUFOUR, Jean-Marie & KHALAF, Lynda, 2005. "Exact Multivariate Tests of Asset Pricing Models with Stable Asymmetric Distributions," Cahiers de recherche 2005-04, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  10. Rolf Scheufele, 2008. "Evaluating the German (New Keynesian) Phillips Curve," IWH Discussion Papers 10-08, Halle Institute for Economic Research. [Downloadable!]
  11. Marie-Claude Beaulieu & Lynda Khalaf & Marie-Hélène Gagnon, 2006. "Testing Financial Integration: Finite Sample Motivated Mothods," Computing in Economics and Finance 2006 233, Society for Computational Economics. [Downloadable!]
  12. Sophocles Mavroeidis, 2006. "Testing the New Keynesian Phillips Curve Without Assuming Identification," Working Papers 2006-13, Brown University, Department of Economics. [Downloadable!]
  13. DUFOUR, Jean-Marie & FARHAT, Abdekjelik & HALLIN, Marc, 2005. "Distribution-Free Bounds for Serial Correlation Coefficients in Heteroskedastic Symmetric Time Series," Cahiers de recherche 2005-05, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  14. James M. Nason & Gregor W. Smith, 2008. "The new Keynesian Phillips curve : lessons from single-equation econometric estimation," Economic Quarterly, Federal Reserve Bank of Richmond, issue Fall, pages 361-395. [Downloadable!]
  15. DUFOUR, Jean-Marie & JOUINI, Tarek, 2005. "Finite-Sample Simulation-Based Inference in VAR Models with Applications to Order Selection and Causality Testing," Cahiers de recherche 2005-12, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  16. Lars P. Feld & Justina A.V. Fischer & Gebhard Kirchgässner, 2006. "The Effect of Direct Democracy on Income Redistribution: Evidence for Switzerland," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
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  17. Nihat Aktas & Eric Bodt & Richard Roll, 2004. "European M&A Regulation is Protectionist," University of California at Los Angeles, Anderson Graduate School of Management 1252, Anderson Graduate School of Management, UCLA. [Downloadable!]
  18. Mathias D. Cattaneo & Richard K. Crump & Michael Jansson, 2007. "Optimal Inference for Instrumental Variables Regression with non-Gaussian Errors," CREATES Research Papers 2007-11, School of Economics and Management, University of Aarhus. [Downloadable!]
  19. Jeffry Jacob & Thomas Osang, 2007. "Values, Beliefs and Development," Departmental Working Papers 0705, Southern Methodist University, Department of Economics. [Downloadable!]
  20. 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!]
  21. Kleck, Gary & Kovandzic, Tomislav & Schaffer, Mark E, 2005. "Gun Prevalence, Homicide Rates and Causality: A GMM Approach to Endogeneity Bias," CEPR Discussion Papers 5357, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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