IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v167y2012i1p133-139.html
   My bibliography  Save this article

Hahn–Hausman test as a specification test

Author

Listed:
  • Lee, Yoonseok
  • Okui, Ryo

Abstract

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.

Suggested Citation

  • Lee, Yoonseok & Okui, Ryo, 2012. "Hahn–Hausman test as a specification test," Journal of Econometrics, Elsevier, vol. 167(1), pages 133-139.
  • Handle: RePEc:eee:econom:v:167:y:2012:i:1:p:133-139 DOI: 10.1016/j.jeconom.2011.10.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407611002430
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    3. Chirok Han & Peter C. B. Phillips, 2006. "GMM with Many Moment Conditions," Econometrica, Econometric Society, vol. 74(1), pages 147-192, January.
    4. 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.
    5. Kelejian, Harry H. & Prucha, Ingmar R., 2010. "Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances," Journal of Econometrics, Elsevier, vol. 157(1), pages 53-67, July.
    6. Hasselt, Martijn van, 2010. "Many Instruments Asymptotic Approximations Under Nonnormal Error Distributions," Econometric Theory, Cambridge University Press, vol. 26(02), pages 633-645, April.
    7. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-681, May.
    8. Jinyong Hahn & Jerry Hausman, 2002. "A New Specification Test for the Validity of Instrumental Variables," Econometrica, Econometric Society, vol. 70(1), pages 163-189, January.
    9. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    10. K. Newey, Whitney, 1985. "Generalized method of moments specification testing," Journal of Econometrics, Elsevier, vol. 29(3), pages 229-256, September.
    11. Andrews, Donald W.K. & Stock, James H., 2007. "Testing with many weak instruments," Journal of Econometrics, Elsevier, vol. 138(1), pages 24-46, May.
    12. 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.
    13. Anatolyev, Stanislav & Gospodinov, Nikolay, 2011. "Specification Testing In Models With Many Instruments," Econometric Theory, Cambridge University Press, vol. 27(02), pages 427-441, April.
    14. H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, vol. 104(2), pages 219-257, September.
    15. James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
    16. Hansen, Christian & Hausman, Jerry & Newey, Whitney, 2008. "Estimation With Many Instrumental Variables," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 398-422.
    17. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yoonseok Lee & Mehmet Caner & Xu Han, 2015. "Adaptive Elastic Net GMM Estimation with Many Invalid Moment Conditions: Simultaneous Model and Moment Selection," Center for Policy Research Working Papers 177, Center for Policy Research, Maxwell School, Syracuse University.
    2. Tae-Hwan Kim & Christophe Muller, 2017. "A Robust Test of Exogeneity Based on Quantile Regressions," AMSE Working Papers 1716, Aix-Marseille School of Economics, Marseille, France.
    3. Firmin DOKO TCHATOKA & Jean-Marie DUFOUR, 2016. "Exogeneity Tests, Incomplete Models, Weak Identification and Non-Gaussian Distributions : Invariance and Finite-Sample Distributional Theory," Cahiers de recherche 14-2016, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    4. Tae-Hwan Kim & Christophe Muller, 2013. "A Test for Endogeneity in Conditional Quantiles," Working Papers halshs-00854527, HAL.
    5. Yoonseok Lee & Yu Zhou, 2015. "Averaged Instrumental Variables Estimators," Center for Policy Research Working Papers 180, Center for Policy Research, Maxwell School, Syracuse University.

    More about this item

    Keywords

    Hahn–Hausman test; Sargan test; Many instruments; Overidentifying restrictions test; Specification test;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:167:y:2012:i:1:p:133-139. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.