Skip to main content
    • Aa
    • Aa


  • Victor Chernozhukov (a1), Christian Hansen (a2) and Michael Jansson (a3)

This paper studies a model widely used in the weak instruments literature and establishes admissibility of the weighted average power likelihood ratio tests recently derived by Andrews, Moreira, and Stock (2004, NBER Technical Working Paper 199). The class of tests covered by this admissibility result contains the Anderson and Rubin (1949, Annals of Mathematical Statistics 20, 46–63) test. Thus, there is no conventional statistical sense in which the Anderson and Rubin (1949) test “wastes degrees of freedom.” In addition, it is shown that the test proposed by Moreira (2003, Econometrica 71, 1027–1048) belongs to the closure of (i.e., can be interpreted as a limiting case of) the class of tests covered by our admissibility result.

Corresponding author
*Address correspondence to Michael Jansson, Department of Economics, University of California Berkeley, 508-1 Evans Hall #3880, Berkeley, CA 94720-3880, USA; e-mail:
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

T.W. Anderson & H. Rubin (1949) Estimation of the parameters of a single equation in a complete set of stochastic equations. Annals of Mathematical Statistics 20, 4663.

D.W.K Andrews . (1996) Admissibility of the likelihood ratio test when the parameter space is restricted under the alternative. Econometrica 64, 705718.

D.W.K. Andrews & W. Ploberger (1995) Admissibility of the likelihood ratio test when a nuisance parameter is present only under the alternative. Annals of Statistics 23, 16091629.

G Chamberlain . (2007) Decision theory applied to an instrumental variables model. Econometrica 75, 609652.

J.-M. Dufour (1997) Some impossibility theorems in econometrics with applications to structural and dynamic models. Econometrica 65, 13651387.

J.-M. Dufour (2003) Identification, weak instruments, and statistical inference in econometrics. Canadian Journal of Economics 36, 767808.

J. Hahn & J. Hausman (2003) Weak instruments: Diagnosis and cures in empirical econometrics. American Economic Review 93, 118125.

F Kleibergen . (2002) Pivotal statistics for testing structural parameters in instrumental variables regression. Econometrica 70, 17811803.

M.J Moreira . (2003) A conditional likelihood ratio test for structural models. Econometrica 71, 10271048.

R.J Muirhead . (1982) Aspects of Multivariate Statistical Theory. Wiley.

D. Staiger & J.H. Stock (1997) Instrumental variables estimation with weak instruments. Econometrica 65, 557586.

J.H. Stock , J.H. Wright , & M. Yogo (2002) A survey of weak instruments and weak identification in generalized method of moments. Journal of Business & Economic Statistics 20, 518529.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 10 *
Loading metrics...

Abstract views

Total abstract views: 124 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 24th September 2017. This data will be updated every 24 hours.