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ADMISSIBLE INVARIANT SIMILAR TESTS FOR INSTRUMENTAL VARIABLES REGRESSION

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

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.

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*Address correspondence to Michael Jansson, Department of Economics, University of California Berkeley, 508-1 Evans Hall #3880, Berkeley, CA 94720-3880, USA; e-mail: mjansson@econ.berkeley.edu.
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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.

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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
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