IDEAS home Printed from https://ideas.repec.org/p/rim/rimwps/15-22.html
   My bibliography  Save this paper

A Regularization Approach to Biased Two-Stage Least Squares Estimation

Author

Listed:
  • Nam-Hyun Kim

    (Department of Economics, University of Konstanz, Germany)

  • Winfried Pohlmeier

    (Department of Economics, University of Konstanz, Germany; The Rimini Centre for Economic Analysis, Italy)

Abstract

We propose to apply –norm regularization to address the problem of weak and/or many instruments. We observe that the presence of weak instruments, or weak and many instruments is translated into a nearly singular problem in a control function representation. Hence, we show that mean squares error-optimal -norm regularization with a small sample size reduces the bias and variance of the regularized 2SLS estimators with the presence of weak and/or many instruments. A number of different strategies for choosing a regularization parameter are introduced and compared in a Monte Carlo study.

Suggested Citation

  • Nam-Hyun Kim & Winfried Pohlmeier, 2015. "A Regularization Approach to Biased Two-Stage Least Squares Estimation," Working Paper series 15-22, Rimini Centre for Economic Analysis.
    • Handle: RePEc:rim:rimwps:15-22
    as

    Download full text from publisher

    File URL: http://www.rcea.org/RePEc/pdf/wp15-22.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Donald, Stephen G & Newey, Whitney K, 2001. "Choosing the Number of Instruments," Econometrica, Econometric Society, vol. 69(5), pages 1161-1191, September.
    2. Carrasco, Marine, 2012. "A regularization approach to the many instruments problem," Journal of Econometrics, Elsevier, vol. 170(2), pages 383-398.
    3. Blomquist, Soren & Dahlberg, Matz, 1999. "Small Sample Properties of LIML and Jackknife IV Estimators: Experiments with Weak Instruments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 69-88, Jan.-Feb..
    4. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, December.
    5. Luiz M. Cruz & Marcelo J. Moreira, 2005. "On the Validity of Econometric Techniques with Weak Instruments: Inference on Returns to Education Using Compulsory School Attendance Laws," Journal of Human Resources, University of Wisconsin Press, vol. 40(2).
    6. Fuller, Wayne A, 1977. "Some Properties of a Modification of the Limited Information Estimator," Econometrica, Econometric Society, vol. 45(4), pages 939-953, May.
    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. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    9. Angrist, J D & Imbens, G W & Krueger, A B, 1999. "Jackknife Instrumental Variables Estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 57-67, Jan.-Feb..
    10. Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-529, October.
    11. John C. Chao & Norman R. Swanson, 2005. "Consistent Estimation with a Large Number of Weak Instruments," Econometrica, Econometric Society, vol. 73(5), pages 1673-1692, September.
    12. Jinyong Hahn & Jerry Hausman & Guido Kuersteiner, 2004. "Estimation with weak instruments: Accuracy of higher-order bias and MSE approximations," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 272-306, June.
    13. Hahn, Jinyong & Kuersteiner, Guido, 2002. "Discontinuities of weak instrument limiting distributions," Economics Letters, Elsevier, vol. 75(3), pages 325-331, May.
    14. Hahn, Jinyong & Hausman, Jerry, 2002. "Notes on bias in estimators for simultaneous equation models," Economics Letters, Elsevier, vol. 75(2), pages 237-241, April.
    15. Arel-Bundock, Vincent, 2013. "A solution to the weak instrument bias in 2SLS estimation: Indirect inference with stochastic approximation," Economics Letters, Elsevier, vol. 120(3), pages 495-498.
    16. Bun, Maurice J.G. & Windmeijer, Frank, 2011. "A comparison of bias approximations for the two-stage least squares (2SLS) estimator," Economics Letters, Elsevier, vol. 113(1), pages 76-79, October.
    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. Namhyun Kim & Winfried Pohlmeier, 2016. "A Note on the Regularized Approach to Biased 2SLS Estimation with Weak Instruments," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 78(6), pages 915-924, December.
    2. Arcand, Jean-Louis & Ai, Chunrong & Ethier, Francois, 2007. "Moral hazard and Marshallian inefficiency: Evidence from Tunisia," Journal of Development Economics, Elsevier, vol. 83(2), pages 411-445, July.
    3. Markus Frölich & Michael Lechner, 2004. "Regional treatment intensity as an instrument for the evaluation of labour market policies," University of St. Gallen Department of Economics working paper series 2004 2004-08, Department of Economics, University of St. Gallen.
    4. John C. Chao & Norman R. Swanson, 2005. "Consistent Estimation with a Large Number of Weak Instruments," Econometrica, Econometric Society, vol. 73(5), pages 1673-1692, September.
    5. Daniel A. Ackerberg & Paul J. Devereux, 2009. "Improved JIVE Estimators for Overidentified Linear Models with and without Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 91(2), pages 351-362, May.
    6. Hansen, Christian & Kozbur, Damian, 2014. "Instrumental variables estimation with many weak instruments using regularized JIVE," Journal of Econometrics, Elsevier, vol. 182(2), pages 290-308.
    7. Xuexin WANG, 2021. "Instrumental variable estimation via a continuum of instruments with an application to estimating the elasticity of intertemporal substitution in consumption," Working Papers 2021-11-06, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    8. A. Belloni & D. Chen & V. Chernozhukov & C. Hansen, 2012. "Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain," Econometrica, Econometric Society, vol. 80(6), pages 2369-2429, November.
    9. Guilhem Bascle, 2008. "Controlling for endogeneity with instrumental variables in strategic management research," Post-Print hal-00576795, HAL.
    10. Emma M. Iglesias & Garry D. A. Phillips, 2012. "Almost Unbiased Estimation in Simultaneous Equation Models With Strong and/or Weak Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(4), pages 505-520, June.
    11. Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91(S1), pages 1-24, June.
    12. Antoine, Bertille & Lavergne, Pascal, 2014. "Conditional moment models under semi-strong identification," Journal of Econometrics, Elsevier, vol. 182(1), pages 59-69.
    13. Russell Davidson & James G. MacKinnon, 2006. "The case against JIVE," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(6), pages 827-833, September.
    14. Matsushita, Yukitoshi & Otsu, Taisuke, 2022. "A jackknife Lagrange multiplier test with many weak instruments," LSE Research Online Documents on Economics 116392, London School of Economics and Political Science, LSE Library.
    15. Bun, Maurice J.G. & Windmeijer, Frank, 2011. "A comparison of bias approximations for the two-stage least squares (2SLS) estimator," Economics Letters, Elsevier, vol. 113(1), pages 76-79, October.
    16. Chao, John & Swanson, Norman R., 2007. "Alternative approximations of the bias and MSE of the IV estimator under weak identification with an application to bias correction," Journal of Econometrics, Elsevier, vol. 137(2), pages 515-555, April.
    17. Carrasco, Marine & Tchuente, Guy, 2015. "Regularized LIML for many instruments," Journal of Econometrics, Elsevier, vol. 186(2), pages 427-442.
    18. 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.
    19. Wang, Wenjie & Kaffo, Maximilien, 2016. "Bootstrap inference for instrumental variable models with many weak instruments," Journal of Econometrics, Elsevier, vol. 192(1), pages 231-268.
    20. Mardi Dungey & Vitali Alexeev & Jing Tian & Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91, pages 1-24, June.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:rim:rimwps:15-22. See general information about how to correct material in RePEc.

    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: Marco Savioli (email available below). General contact details of provider: https://edirc.repec.org/data/rcfeait.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.