IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v160y2011i2p289-299.html
   My bibliography  Save this article

The Hausman test and weak instruments

Author

Listed:
  • Hahn, Jinyong
  • Ham, John C.
  • Moon, Hyungsik Roger

Abstract

We consider the following problem. There is a structural equation of interest that contains an explanatory variable that theory predicts is endogenous. There are one or more instrumental variables that credibly are exogenous with regard to this structural equation, but which have limited explanatory power for the endogenous variable. Further, there is one or more potentially 'strong' instruments, which has much more explanatory power but which may not be exogenous. Hausman (1978) provided a test for the exogeneity of the second instrument when none of the instruments are weak. Here, we focus on how the standard Hausman test does in the presence of weak instruments using the Staiger-Stock asymptotics. It is natural to conjecture that the standard version of the Hausman test would be invalid in the weak instrument case, which we confirm. However, we provide a version of the Hausman test that is valid even in the presence of weak IV and illustrate how to implement the test in the presence of heteroskedasticity. We show that the situation we analyze occurs in several important economic examples. Our Monte Carlo experiments show that our procedure works relatively well in finite samples. We should note that our test is not consistent, although we believe that it is impossible to construct a consistent test with weak instruments.

Suggested Citation

  • Hahn, Jinyong & Ham, John C. & Moon, Hyungsik Roger, 2011. "The Hausman test and weak instruments," Journal of Econometrics, Elsevier, vol. 160(2), pages 289-299, February.
  • Handle: RePEc:eee:econom:v:160:y:2011:i:2:p:289-299
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4076(10)00189-2
    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. D. W. K. Andrews, 2003. "End-of-Sample Instability Tests," Econometrica, Econometric Society, vol. 71(6), pages 1661-1694, November.
    2. Donald, Stephen G & Newey, Whitney K, 2001. "Choosing the Number of Instruments," Econometrica, Econometric Society, vol. 69(5), pages 1161-1191, September.
    3. Strauss, John & Thomas, Duncan, 1995. "Human resources: Empirical modeling of household and family decisions," Handbook of Development Economics,in: Hollis Chenery & T.N. Srinivasan (ed.), Handbook of Development Economics, edition 1, volume 3, chapter 34, pages 1883-2023 Elsevier.
    4. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 38(2), pages 112-134.
    5. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    6. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-681, May.
    7. Altonji, Joseph G, 1986. "Intertemporal Substitution in Labor Supply: Evidence from Micro Data," Journal of Political Economy, University of Chicago Press, vol. 94(3), pages 176-215, June.
    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. Donald W. K. Andrews & Marcelo J. Moreira & James H. Stock, 2006. "Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression," Econometrica, Econometric Society, vol. 74(3), pages 715-752, May.
    10. Frank Kleibergen, 2000. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Tinbergen Institute Discussion Papers 00-055/4, Tinbergen Institute.
    11. John C. Ham & Kevin T. Reilly, 2002. "Testing Intertemporal Substitution, Implicit Contracts, and Hours Restriction Models of the Labor Market Using Micro Data," American Economic Review, American Economic Association, vol. 92(4), pages 905-927, September.
    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. Laura Di Giorgio & Massimo Filippini & Giuliano Masiero, 2014. "The relationship between costs and quality in nonprofit nursing homes," IdEP Economic Papers 1402, USI Università della Svizzera italiana.
    2. Doko Tchatoka, Firmin, 2012. "On the Validity of Durbin-Wu-Hausman Tests for Assessing Partial Exogeneity Hypotheses with Possibly Weak Instruments," MPRA Paper 40184, University Library of Munich, Germany.
    3. Ruprecht, Benedikt & Entrop, Oliver & Kick, Thomas & Wilkens, Marco, 2013. "Market timing, maturity mismatch, and risk management: Evidence from the banking industry," Discussion Papers 56/2013, Deutsche Bundesbank.
    4. Christian Danne, 2015. "Regional Integration and the Rule of Law," FIW Working Paper series 157, FIW.
    5. James Hansen, 2011. "Does Equity Mispricing Influence Household and Firm Decisions?," RBA Research Discussion Papers rdp2011-06, Reserve Bank of Australia.
    6. Or Levkovich & Jan Rouwendal & Jos van Ommeren, 2017. "The impact of highways on population redistribution: The role of land development restrictions," Tinbergen Institute Discussion Papers 17-109/VIII, Tinbergen Institute.
    7. Seri, Paolo & Zanfei, Antonello, 2013. "The co-evolution of ICT, skills and organization in public administrations: Evidence from new European country-level data," Structural Change and Economic Dynamics, Elsevier, vol. 27(C), pages 160-176.
    8. Kiviet, Jan F. & Pleus, Milan, 2017. "The performance of tests on endogeneity of subsets of explanatory variables scanned by simulation," Econometrics and Statistics, Elsevier, vol. 2(C), pages 1-21.
    9. L. Di Giorgio & M. Filippini & G. Masiero, 2016. "Is higher nursing home quality more costly?," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 17(8), pages 1011-1026, November.
    10. Kinclová Lenka, 2015. "Legitimacy of the “Humanitarian Military Intervention”: An Empirical Assessment," Peace Economics, Peace Science, and Public Policy, De Gruyter, vol. 21(1), pages 111-152, January.
    11. Doko Tchatoka, Firmin, 2011. "Testing for partial exogeneity with weak identification," MPRA Paper 39504, University Library of Munich, Germany, revised Mar 2012.
    12. repec:taf:emetrv:v:36:y:2017:i:6-9:p:928-945 is not listed on IDEAS
    13. Li, Yan & Lyons, Bruce, 2012. "Market structure, regulation and the speed of mobile network penetration," International Journal of Industrial Organization, Elsevier, vol. 30(6), pages 697-707.
    14. Escobal, Javier A. & Cavero, Denice, 2012. "Transaction Costs, Institutional Arrangements and Inequality Outcomes: Potato Marketing by Small Producers in Rural Peru," World Development, Elsevier, vol. 40(2), pages 329-341.
    15. Inoue, Atsushi & Rossi, Barbara, 2011. "Testing for weak identification in possibly nonlinear models," Journal of Econometrics, Elsevier, vol. 161(2), pages 246-261, April.
    16. Bertille Antoine & Eric Renault, 2017. "On the relevance of weaker instruments," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 928-945, October.
    17. Daria Ciriaci & Sandro Montresor & Daniela Palma, 2013. "Do KIBS make manufacturing more innovative? An empirical investigation for four European countries," JRC Working Papers on Corporate R&D and Innovation 2013-04, Joint Research Centre (Seville site).

    More about this item

    Keywords

    Hausman test Weak instruments;

    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:160:y:2011:i:2:p:289-299. 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.