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Some Properties of Tests for Possibly Unidentified Parameters

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Author Info
G. Forchini ()

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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 < 1/2 concerning possibly unidentified parameters have type II error probability that can be as large as 1 - a.

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File URL: http://www.buseco.monash.edu.au/depts/ebs/pubs/wpapers/2005/wp21-05.pdf
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Publisher Info
Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 21/05.

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Length: 14 pages
Date of creation: Sep 2005
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Handle: RePEc:msh:ebswps:2005-21

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Related research
Keywords: Similar tests; consistent tests; weak instruments; identification;

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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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References listed on IDEAS
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. Hillier, Grant H., 1987. "Classes of Similar Regions and Their Power Properties for Some Econometric Testing Problems," Econometric Theory, Cambridge University Press, vol. 3(01), pages 1-44, February. [Downloadable!]
  2. James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
  3. 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.
  4. Frank Kleibergen, 2005. "Testing Parameters in GMM Without Assuming that They Are Identified," Econometrica, Econometric Society, vol. 73(4), pages 1103-1123, 07. [Downloadable!] (restricted)
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  5. 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)
    Other versions:
  6. Patrik Buggenberger & Richard Smith, 2003. "Generalized empirical likelihood estimators and tests under partial, weak and strong identification," CeMMAP working papers CWP08/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
    Other versions:
  7. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07. [Downloadable!] (restricted)
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