IDEAS home Printed from https://ideas.repec.org/p/bri/cmpowp/13-315.html
   My bibliography  Save this paper

A Weak Instrument F-Test in Linear IV Models with Multiple Endogenous Variables

Author

Listed:
  • Eleanor Sanderson
  • Frank Windmeijer

Abstract

We consider testing for weak instruments in a model with multiple endogenous variables. Unlike Stock and Yogo (2005), who considered a weak instruments problem where the rank of the matrix of reduced form parameters is near zero, here we consider a weak instruments problem of a near rank reduction of one in the matrix of reduced form parameters. For example, in a two-variable model, we consider weak instrument asymptotics of the form π1=δ π2 +c/√n where π1 and π2 are the parameters in the two reduced-form equations, c is a vector of constants and n is the sample size. We investigate the use of a conditional first-stage F-statistic along the lines of the proposal by Angrist and Pischke (2009) and show that, unless δ = 0, the variance in the denominator of their F-statistic needs to be adjusted in order to get a correct asymptotic distribution when testing the hypothesis H0: π1=δ π2. We show that a corrected conditional F-statistic is equivalent to the Cragg and Donald (1993) minimum eigenvalue rank test statistic, and is informative about the maximum total relative bias of the 2SLS estimator and the Wald tests size distortions. When δ = 0 in the two-variable model, or when there are more than two endogenous variables, further information over and above the Cragg-Donald statistic can be obtained about the nature of the weak instrument problem by computing the conditional first-stage F-statistics.

Suggested Citation

  • Eleanor Sanderson & Frank Windmeijer, 2013. "A Weak Instrument F-Test in Linear IV Models with Multiple Endogenous Variables," The Centre for Market and Public Organisation 13/315, The Centre for Market and Public Organisation, University of Bristol, UK.
  • Handle: RePEc:bri:cmpowp:13/315
    as

    Download full text from publisher

    File URL: http://www.bristol.ac.uk/cmpo/publications/papers/2013/wp315.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Kleibergen, Frank & Paap, Richard, 2006. "Generalized reduced rank tests using the singular value decomposition," Journal of Econometrics, Elsevier, vol. 133(1), pages 97-126, July.
    2. Rothenberg, Thomas J., 1984. "Approximating the distributions of econometric estimators and test statistics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 15, pages 881-935, Elsevier.
    3. Andrews,Donald W. K. & Stock,James H. (ed.), 2005. "Identification and Inference for Econometric Models," Cambridge Books, Cambridge University Press, number 9780521844413.
    4. Cragg, John G. & Donald, Stephen G., 1993. "Testing Identifiability and Specification in Instrumental Variable Models," Econometric Theory, Cambridge University Press, vol. 9(2), pages 222-240, April.
    5. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
    6. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    7. José Luis Montiel Olea & Carolin Pflueger, 2013. "A Robust Test for Weak Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 358-369, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mikusheva, Anna, 2013. "Survey on statistical inferences in weakly-identified instrumental variable models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 29(1), pages 117-131.
    2. Stimpfle, Alexander & Stadelmann, David, 2015. "The Impact of Fundamental Development Factors on Different Income Groups: International Evidence," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113128, Verein für Socialpolitik / German Economic Association.
    3. Murray Michael P., 2017. "Linear Model IV Estimation When Instruments Are Many or Weak," Journal of Econometric Methods, De Gruyter, vol. 6(1), pages 1-22, January.
    4. Fernando Broner & Daragh Clancy & Aitor Erce & Alberto Martin, 2022. "Fiscal Multipliers and Foreign Holdings of Public Debt [When Should You Adjust Standard Errors for Clustering?]," Review of Economic Studies, Oxford University Press, vol. 89(3), pages 1155-1204.
    5. Wong, Siang Leng & Chang, Youngho & Chia, Wai-Mun, 2013. "Energy consumption, energy R&D and real GDP in OECD countries with and without oil reserves," Energy Economics, Elsevier, vol. 40(C), pages 51-60.
    6. Per G. Fredriksson & Khawaja A. Mamun, 2014. "Tobacco Politics and Electoral Accountability in the United States," Public Finance Review, , vol. 42(1), pages 4-34, January.
    7. Wenjie Wang & Yichong Zhang, 2021. "Wild Bootstrap for Instrumental Variables Regressions with Weak and Few Clusters," Papers 2108.13707, arXiv.org, revised Nov 2022.
    8. Gergely Ganics & Atsushi Inoue & Barbara Rossi, 2021. "Confidence Intervals for Bias and Size Distortion in IV and Local Projections-IV Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(1), pages 307-324, January.
    9. Coutinho, Leonor & Georgiou, Dimitrios & Heracleous, Maria & Michaelides, Alexander & Tsani, Stella, 2022. "Limiting fiscal procyclicality: Evidence from resource-dependent countries," Economic Modelling, Elsevier, vol. 106(C).
    10. Itzhak Ben-DAVID & Francesco A. FRANZONI & Rabih MOUSSAWI & John SEDUNOV III, 2015. "The Granular Nature of Large Institutional Investors," Swiss Finance Institute Research Paper Series 15-67, Swiss Finance Institute, revised Apr 2016.
    11. Giorgio d’Agostino & John Paul Dunne & Luca Pieroni, 2019. "Military Expenditure, Endogeneity and Economic Growth," Defence and Peace Economics, Taylor & Francis Journals, vol. 30(5), pages 509-524, July.
    12. Antoine, Bertille & Renault, Eric, 2020. "Testing identification strength," Journal of Econometrics, Elsevier, vol. 218(2), pages 271-293.
    13. Firat Bilgel, 2021. "Infant mortality in Turkey: Causes and effects in a regional context," Papers in Regional Science, Wiley Blackwell, vol. 100(2), pages 429-453, April.
    14. Christopher F Baum & Mark E. Schaffer & Steven Stillman, 2007. "Enhanced routines for instrumental variables/GMM estimation and testing," Boston College Working Papers in Economics 667, Boston College Department of Economics, revised 05 Sep 2007.
    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. Quinn A. W. Keefer, 2019. "Do sunk costs affect expert decision making? Evidence from the within-game usage of NFL running backs," Empirical Economics, Springer, vol. 56(5), pages 1769-1796, May.
    17. Emek Basker & Lucia Foster & Shawn Klimek, 2017. "Customer‐employee substitution: Evidence from gasoline stations," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 26(4), pages 876-896, December.
    18. Hadjiyiannis, Costas & Heracleous, Maria S. & Tabakis, Chrysostomos, 2016. "Regionalism and conflict: Peace creation and peace diversion," Journal of International Economics, Elsevier, vol. 102(C), pages 141-159.
    19. Jorge Gonzalez Chapela, 2011. "Recreation, home production, and intertemporal substitution of female labor supply: evidence on the intensive margin," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 14(3), pages 532-548, July.
    20. Michael Keane & Timothy Neal, 2021. "A New Perspective on Weak Instruments," Discussion Papers 2021-05a, School of Economics, The University of New South Wales.

    More about this item

    Keywords

    weak instruments; multiple endogenous variables; F-test;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

    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:bri:cmpowp:13/315. 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: . General contact details of provider: https://edirc.repec.org/data/cmbriuk.html .

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (email available below). General contact details of provider: https://edirc.repec.org/data/cmbriuk.html .

    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.