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ADMISSIBLE SIGNIFICANCE TESTS IN SIMULTANEOUS EQUATION MODELS

Published online by Cambridge University Press:  21 April 2017

Theodore W. Anderson
Theodore W. Anderson*
Affiliation:
Stanford University
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Abstract

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Consider testing the null hypothesis that a single structural equation has specified coefficients. The alternative hypothesis is that the relevant part of the reduced form matrix has proper rank, that is, that the equation is identified. The usual linear model with normal disturbances is invariant with respect to linear transformations of the endogenous and of the exogenous variables. When the disturbance covariance matrix is known, it can be set to the identity, and the invariance of the endogenous variables is with respect to orthogonal transformations. The likelihood ratio test is invariant with respect to these transformations and is the best invariant test. Furthermore it is admissible in the class of all tests. Any other test has lower power and/or higher significance level. In particular, this likelihood ratio test dominates a test based on the Two-Stage Least Squares estimator.

Type
T.W. ANDERSON MEMORIAL
Information
Econometric Theory , Volume 33 , Issue 3 , June 2017 , pp. 534 - 550
Copyright
Copyright © Cambridge University Press 2017 

Footnotes

The author (deceased, September 17, 2016) thanked Naoto Kunitomo, Graduate School of Economics, University of Tokyo for his generous assistance. An early version of this paper was presented to the James Durbin Seminar sponsored by the London School of Economics and University College, London, on October 29, 2009. This version was presented to the Haavelmo Centennial Symposium, Oslo, on December 14, 2011. Minor editorial changes made by the Editor, December 12, 2016.

References

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