Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-14T17:33:29.506Z Has data issue: false hasContentIssue false
  • English
  • Français

ADMISSIBLE INVARIANT SIMILAR TESTS FOR INSTRUMENTAL VARIABLES REGRESSION

Published online by Cambridge University Press:  01 June 2009

Victor Chernozhukov ,
Christian Hansen  and
Michael Jansson
Get access Rights & Permissions [Opens in a new window]

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.

Type
Research Article
Information
Econometric Theory , Volume 25 , Issue 3 , June 2009 , pp. 806 - 818
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

The authors thank Jim Powell, Paul Ruud, a co-editor, and (in particular) two referees for very valuable comments.

References

REFERENCES

Anderson, T.W. & Rubin, H. (1949) Estimation of the parameters of a single equation in a complete set of stochastic equations. Annals of Mathematical Statistics 20, 46–63.10.1214/aoms/1177730090CrossRefGoogle Scholar
Andrews, D.W.K. (1996) Admissibility of the likelihood ratio test when the parameter space is restricted under the alternative. Econometrica 64, 705–718.10.2307/2171868CrossRefGoogle Scholar
Andrews, D.W.K., Moreira, M.J., & Stock, J.H. (2004) Optimal Invariant Similar Tests for Instrumental Variables Regression. NBER Technical Working Paper 299.10.3386/t0299CrossRefGoogle Scholar
Andrews, D.W.K. & Ploberger, W. (1995) Admissibility of the likelihood ratio test when a nuisance parameter is present only under the alternative. Annals of Statistics 23, 1609–1629.10.1214/aos/1176324316CrossRefGoogle Scholar
Andrews, D.W.K. & Stock, J.H. (2007) Inference with weak instruments. In Blundell, R., Newey, W.K., & Persson, T. (eds.), Advances in Economics and Econometrics: Theory and Applications, Ninth World Congress, vol. III, pp. 122–173. Cambridge University Press.Google Scholar
Chamberlain, G. (2007) Decision theory applied to an instrumental variables model. Econometrica 75, 609–652.10.1111/j.1468-0262.2007.00764.xCrossRefGoogle Scholar
Dufour, J.-M. (1997) Some impossibility theorems in econometrics with applications to structural and dynamic models. Econometrica 65, 1365–1387.10.2307/2171740CrossRefGoogle Scholar
Dufour, J.-M. (2003) Identification, weak instruments, and statistical inference in econometrics. Canadian Journal of Economics 36, 767–808.10.1111/1540-5982.t01-3-00001CrossRefGoogle Scholar
Ferguson, T.S. (1967) Mathematical Statistics: A Decision Theoretic Approach. Academic Press.Google Scholar
Hahn, J. & Hausman, J. (2003) Weak instruments: Diagnosis and cures in empirical econometrics. American Economic Review 93, 118–125.10.1257/000282803321946912CrossRefGoogle Scholar
Kleibergen, F. (2002) Pivotal statistics for testing structural parameters in instrumental variables regression. Econometrica 70, 1781–1803.10.1111/1468-0262.00353CrossRefGoogle Scholar
Lehmann, E.L. & Romano, J.P. (2005) Testing Statistical Hypotheses, 3rd ed. Springer-Verlag.Google Scholar
Moreira, M.J. (2001) Tests with Correct Size When Instruments Can Be Arbitrarily Weak. CLE Working paper 37, University of California Berkeley.Google Scholar
Moreira, M.J. (2003) A conditional likelihood ratio test for structural models. Econometrica 71, 1027–1048.10.1111/1468-0262.00438CrossRefGoogle Scholar
Muirhead, R.J. (1982) Aspects of Multivariate Statistical Theory. Wiley.10.1002/9780470316559CrossRefGoogle Scholar
Staiger, D. & Stock, J.H. (1997) Instrumental variables estimation with weak instruments. Econometrica 65, 557–586.10.2307/2171753CrossRefGoogle Scholar
Stock, J.H., Wright, J.H., & Yogo, M. (2002) A survey of weak instruments and weak identification in generalized method of moments. Journal of Business & Economic Statistics 20, 518–529.10.1198/073500102288618658CrossRefGoogle Scholar