Advanced Search
MyIDEAS: Login

A regularization approach to the many instruments problem

Contents:

Author Info

  • Carrasco, Marine
Registered author(s):

    Abstract

    This paper focuses on the estimation of a finite dimensional parameter in a linear model where the number of instruments is very large or infinite. In order to improve the small sample properties of standard instrumental variable (IV) estimators, we propose three modified IV estimators based on three different ways of inverting the covariance matrix of the instruments. These inverses involve a regularization or smoothing parameter. It should be stressed that no restriction on the number of instruments is needed and that all the instruments are used in the estimation. We show that the three estimators are asymptotically normal and attain the semiparametric efficiency bound. Higher-order analysis of the MSE reveals that the bias of the modified estimators does not depend on the number of instruments. Finally, we suggest a data-driven method for selecting the regularization parameter. Interestingly, our regularization techniques lead to a consistent nonparametric estimation of the optimal instrument.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://www.sciencedirect.com/science/article/pii/S0304407612001248
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Econometrics.

    Volume (Year): 170 (2012)
    Issue (Month): 2 ()
    Pages: 383-398

    as in new window
    Handle: RePEc:eee:econom:v:170:y:2012:i:2:p:383-398

    Contact details of provider:
    Web page: http://www.elsevier.com/locate/jeconom

    Related research

    Keywords: Many instruments; Mean square error; Regularization methods;

    References

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Kuersteiner, Guido M., 2012. "Kernel-weighted GMM estimators for linear time series models," Journal of Econometrics, Elsevier, vol. 170(2), pages 399-421.
    2. Guido M. Kuersteiner, 1999. "Optimal Instrumental Variables Estimation for ARMA Models," Working papers 99-07, Massachusetts Institute of Technology (MIT), Department of Economics.
    3. Yuichi Kitamura & Gautam Tripathi & Hyungtaik Ahn, 2004. "Empirical Likelihood-Based Inference in Conditional Moment Restriction Models," Econometrica, Econometric Society, vol. 72(6), pages 1667-1714, November.
    4. Xiaohong Chen & David T. Jacho-Chávez & Oliver Linton, 2009. "An Alternative Way of ComputingEfficient Instrumental VariableEstimators," STICERD - Econometrics Paper Series /2009/536, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    5. Andersen, Torben G & Sorensen, Bent E, 1996. "GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 328-52, July.
    6. 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.
    7. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2003. "Empirical likelihood estimation and consistent tests with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 117(1), pages 55-93, November.
    8. Gary Chamberlain & Michael Rothschild, 1984. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," NBER Working Papers 0996, National Bureau of Economic Research, Inc.
    9. Manuel A. Domínguez & Ignacio N. Lobato, 2004. "Consistent Estimation of Models Defined by Conditional Moment Restrictions," Econometrica, Econometric Society, vol. 72(5), pages 1601-1615, 09.
    10. Carrasco, Marine & Chernov, Mikhail & Florens, Jean-Pierre & Ghysels, Eric, 2007. "Efficient estimation of general dynamic models with a continuum of moment conditions," Journal of Econometrics, Elsevier, vol. 140(2), pages 529-573, October.
    11. Jushan Bai & Serena Ng, 2000. "Determining the Number of Factors in Approximate Factor Models," Boston College Working Papers in Economics 440, Boston College Department of Economics.
    12. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-62, April.
    13. Angrist, Joshua D & Krueger, Alan B, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, MIT Press, vol. 106(4), pages 979-1014, November.
    14. Linton, Oliver, 2002. "Edgeworth approximations for semiparametric instrumental variable estimators and test statistics," Journal of Econometrics, Elsevier, vol. 106(2), pages 325-368, February.
    15. Doran, Howard E. & Schmidt, Peter, 2006. "GMM estimators with improved finite sample properties using principal components of the weighting matrix, with an application to the dynamic panel data model," Journal of Econometrics, Elsevier, vol. 133(1), pages 387-409, July.
    16. Donald, Stephen G. & Whitney Newey, 1999. "Choosing the Number of Instruments," Working papers 99-05, Massachusetts Institute of Technology (MIT), Department of Economics.
    17. Eastwood, Brian J. & Gallant, A. Ronald, 1991. "Adaptive Rules for Seminonparametric Estimators That Achieve Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 7(03), pages 307-340, September.
    18. Dagenais, Marcel G. & Dagenais, Denyse L., 1997. "Higher moment estimators for linear regression models with errors in the variables," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 193-221.
    19. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, 01.
    20. Carrasco, Marine & Florens, Jean-Pierre, 2000. "Generalization Of Gmm To A Continuum Of Moment Conditions," Econometric Theory, Cambridge University Press, vol. 16(06), pages 797-834, December.
    21. Okui, Ryo, 2011. "Instrumental variable estimation in the presence of many moment conditions," Journal of Econometrics, Elsevier, vol. 165(1), pages 70-86.
    22. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77 Elsevier.
    23. Bai, Jushan & Ng, Serena, 2010. "Instrumental Variable Estimation In A Data Rich Environment," Econometric Theory, Cambridge University Press, vol. 26(06), pages 1577-1606, December.
    24. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, 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 in new window

    Cited by:
    1. Marine Carrasco & Rachidi Kotchoni, 2013. "Efficient Estimation Using the Characteristic Function," Working Papers hal-00867850, HAL.
    2. Guy Tchuente & Marine Carrasco, 2013. "Efficient estimation with many weak instruments using regularization techniques," CIRANO Working Papers 2013s-21, CIRANO.
    3. Kuersteiner, Guido M., 2012. "Kernel-weighted GMM estimators for linear time series models," Journal of Econometrics, Elsevier, vol. 170(2), pages 399-421.
    4. Zhu, Ying, 2013. "Sparse Linear Models and Two-Stage Estimation in High-Dimensional Settings with Possibly Many Endogenous Regressors," MPRA Paper 49846, University Library of Munich, Germany.
    5. Xu Cheng & Zhipeng Liao, 2012. "Select the Valid and Relevant Moments: A One-Step Procedure for GMM with Many Moments," PIER Working Paper Archive 12-045, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    6. Guy Tchuente & Marine Carrasco, 2013. "Regularized LIML for many instruments," CIRANO Working Papers 2013s-20, CIRANO.

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:170:y:2012:i:2:p:383-398. 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: (Zhang, Lei).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 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.