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Hahn–Hausman test as a specification test

Listed author(s):
  • Lee, Yoonseok
  • Okui, Ryo

This paper develops a modified version of the Sargan [Sargan, J.D., 1958. The estimation of economic relationships using instrumental variables. Econometrica 26 (3), 393–415] restrictions, and shows that it is numerically equivalent to the test statistic of Hahn and Hausman [Hahn, J., Hausman, J., 2002. A new specification test for the validity of instrumental variables. Econometrica 70 (1), 163–189] up to a sign. The modified Sargan test is constructed such that its asymptotic distribution under the null hypothesis of correct specification is standard normal when the number of instruments increases with the sample size. The equivalence result is useful in understanding what the Hahn–Hausman test detects and its power properties.

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 167 (2012)
Issue (Month): 1 ()
Pages: 133-139

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Handle: RePEc:eee:econom:v:167:y:2012:i:1:p:133-139
DOI: 10.1016/j.jeconom.2011.10.005
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
  2. Yoonseok Lee & Ryo Okui, 2009. "A Specification Test for Instrumental Variables Regression with Many Instruments," Cowles Foundation Discussion Papers 1741, Cowles Foundation for Research in Economics, Yale University.
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  8. Andrews, Donald W.K. & Stock, James H., 2007. "Testing with many weak instruments," Journal of Econometrics, Elsevier, vol. 138(1), pages 24-46, May.
  9. Hausman, Jerry & Stock, James H. & Yogo, Motohiro, 2005. "Asymptotic properties of the Hahn-Hausman test for weak-instruments," Economics Letters, Elsevier, vol. 89(3), pages 333-342, December.
  10. Stanislav Anatolyev & Nikolay Gospodinov, 2008. "Specification Testing in Models with Many Instruments," Working Papers w0124, Center for Economic and Financial Research (CEFIR).
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  12. Harry H. Kelejian & Ingmar R. Prucha, 1999. "On the Asymptotic Distribution of the Moran I Test Statistic with Applications," Electronic Working Papers 99-002, University of Maryland, Department of Economics.
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  14. Morimune, Kimio, 1983. "Approximate Distributions of k-Class Estimators When the Degree of Overidentifiability Is Large Compared with the Sample Size," Econometrica, Econometric Society, vol. 51(3), pages 821-841, May.
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  16. Anderson, T.W. & Kunitomo, Naoto & Matsushita, Yukitoshi, 2010. "On the asymptotic optimality of the LIML estimator with possibly many instruments," Journal of Econometrics, Elsevier, vol. 157(2), pages 191-204, August.
  17. Hasselt, Martijn van, 2010. "Many Instruments Asymptotic Approximations Under Nonnormal Error Distributions," Econometric Theory, Cambridge University Press, vol. 26(02), pages 633-645, April.
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