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Some Properties of Tests for Possibly Unidentified Parameters

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  • G. Forchini

Abstract

It is well known that confidence intervals for weakly identified parameters are unbounded with positive probability (e.g. Dufour, Econometrica 65, pp. 1365-1387 and Staiger and Stock, Econometrica 65, pp. 557-586), and that the asymptotic risk of their estimators is unbounded (Pötscher, Econometrica 70, pp.1035-1065). In this note we extend these "impossibility results" and show that uniformly consistent tests for weakly identified parameters do not exist. We also show that all similar tests of size a

Suggested Citation

  • 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.
    • Handle: RePEc:msh:ebswps:2005-21
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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2005/wp21-05.pdf
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    References listed on IDEAS

    as
    1. Faust, Jon, 1996. "Near Observational Equivalence and Theoretical size Problems with Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 12(4), pages 724-731, October.
    2. Guggenberger, Patrik & Smith, Richard J., 2005. "Generalized Empirical Likelihood Estimators And Tests Under Partial, Weak, And Strong Identification," Econometric Theory, Cambridge University Press, vol. 21(4), pages 667-709, August.
    3. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    4. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
    5. Frank Kleibergen, 2005. "Testing Parameters in GMM Without Assuming that They Are Identified," Econometrica, Econometric Society, vol. 73(4), pages 1103-1123, July.
    6. Hillier, Grant H., 1987. "Classes of Similar Regions and Their Power Properties for Some Econometric Testing Problems," Econometric Theory, Cambridge University Press, vol. 3(1), pages 1-44, February.
    7. James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
    8. 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.
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    Cited by:

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    2. Sriananthakumar, Sivagowry, 2013. "Testing linear regression model with AR(1) errors against a first-order dynamic linear regression model with white noise errors: A point optimal testing approach," Economic Modelling, Elsevier, vol. 33(C), pages 126-136.

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    More about this item

    Keywords

    Similar tests; consistent tests; weak instruments; identification;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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