IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v157y2010i2p191-204.html
   My bibliography  Save this article

On the asymptotic optimality of the LIML estimator with possibly many instruments

Author

Listed:
  • Anderson, T.W.
  • Kunitomo, Naoto
  • Matsushita, Yukitoshi

Abstract

We consider the estimation of the coefficients of a linear structural equation in a simultaneous equation system when there are many instrumental variables. We derive some asymptotic properties of the limited information maximum likelihood (LIML) estimator when the number of instruments is large; some of these results are new as well as old, and we relate them to results in some recent studies. We have found that the variance of the limiting distribution of the LIML estimator and its modifications often attain the asymptotic lower bound when the number of instruments is large and the disturbance terms are not necessarily normally distributed, that is, for the micro-econometric models of some cases recently called many instruments and many weak instruments.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:econom:v:157:y:2010:i:2:p:191-204
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4076(09)00299-1
    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. Anderson, T.W., 2005. "Origins of the limited information maximum likelihood and two-stage least squares estimators," Journal of Econometrics, Elsevier, vol. 127(1), pages 1-16, July.
    2. Kunitomo, Naoto & Matsushita, Yukitoshi, 2009. "Asymptotic expansions and higher order properties of semi-parametric estimators in a system of simultaneous equations," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1727-1751, September.
    3. Donald, Stephen G & Newey, Whitney K, 2001. "Choosing the Number of Instruments," Econometrica, Econometric Society, vol. 69(5), pages 1161-1191, September.
    4. Paul A. Bekker & Jan van der Ploeg, 2005. "Instrumental variable estimation based on grouped data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(3), pages 239-267, August.
    5. Anderson, T W & Kunitomo, Naoto & Sawa, Takamitsu, 1982. "Evaluation of the Distribution Function of the Limited Information Maximum Likelihood Estimator," Econometrica, Econometric Society, vol. 50(4), pages 1009-1027, July.
    6. Hahn, Jinyong, 2002. "Optimal Inference With Many Instruments," Econometric Theory, Cambridge University Press, vol. 18(1), pages 140-168, February.
    7. Andrews,Donald W. K. & Stock,James H. (ed.), 2005. "Identification and Inference for Econometric Models," Cambridge Books, Cambridge University Press, number 9780521844413, October.
    8. Fuller, Wayne A, 1977. "Some Properties of a Modification of the Limited Information Estimator," Econometrica, Econometric Society, vol. 45(4), pages 939-953, May.
    9. Corbae,Dean & Durlauf,Steven N. & Hansen,Bruce E. (ed.), 2006. "Econometric Theory and Practice," Cambridge Books, Cambridge University Press, number 9780521807234, October.
    10. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-681, May.
    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. 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.
    13. 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.
    14. T. W. Anderson & Naoto Kunitomo & Yukitoshi Matsushita, 2006. "A New Light from Old Wisdoms : Alternative Estimation Methods of Simultaneous Equations with Possibly Many Instruments," CIRJE F-Series CIRJE-F-399, CIRJE, Faculty of Economics, University of Tokyo.
    15. Yukitoshi Matsushita, 2007. "t-Tests in a Structural Equation with Many Instruments," CIRJE F-Series CIRJE-F-467, CIRJE, Faculty of Economics, University of Tokyo.
    16. Joshua D. Angrist & Alan B. Keueger, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(4), pages 979-1014.
    17. Anderson, T. W. & Kunitomo, Naoto, 1992. "Asymptotic distributions of regression and autoregression coefficients with martingale difference disturbances," Journal of Multivariate Analysis, Elsevier, vol. 40(2), pages 221-243, February.
    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. Sølvsten, Mikkel, 2020. "Robust estimation with many instruments," Journal of Econometrics, Elsevier, vol. 214(2), pages 495-512.
    2. Naoto Kunitomo, 2012. "An optimal modification of the LIML estimation for many instruments and persistent heteroscedasticity," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 881-910, October.
    3. Bekker, Paul A. & Crudu, Federico, 2015. "Jackknife instrumental variable estimation with heteroskedasticity," Journal of Econometrics, Elsevier, vol. 185(2), pages 332-342.
    4. Carlos Velasco & 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 2024-09-06, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    5. Hausman, Jerry & Lewis, Randall & Menzel, Konrad & Newey, Whitney, 2011. "Properties of the CUE estimator and a modification with moments," Journal of Econometrics, Elsevier, vol. 165(1), pages 45-57.
    6. Michal Kolesár & Raj Chetty & John Friedman & Edward Glaeser & Guido W. Imbens, 2015. "Identification and Inference With Many Invalid Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 474-484, October.
    7. 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.
    8. Dennis Lim & Wenjie Wang & Yichong Zhang, 2022. "A Conditional Linear Combination Test with Many Weak Instruments," Papers 2207.11137, arXiv.org, revised Apr 2023.
    9. Kolesár, Michal, 2018. "Minimum distance approach to inference with many instruments," Journal of Econometrics, Elsevier, vol. 204(1), pages 86-100.
    10. T. W. Anderson & Naoto Kunitomo & Yukitoshi Matsushita, 2008. "On the Asymptotic Optimality of the LIML Estimator with Possibly Many Instruments," CIRJE F-Series CIRJE-F-542, CIRJE, Faculty of Economics, University of Tokyo.
    11. Anderson, T.W. & Kunitomo, Naoto & Matsushita, Yukitoshi, 2011. "On finite sample properties of alternative estimators of coefficients in a structural equation with many instruments," Journal of Econometrics, Elsevier, vol. 165(1), pages 58-69.
    12. Lim, Dennis & Wang, Wenjie & Zhang, Yichong, 2024. "A conditional linear combination test with many weak instruments," Journal of Econometrics, Elsevier, vol. 238(2).
    13. Okui, Ryo, 2011. "Instrumental variable estimation in the presence of many moment conditions," Journal of Econometrics, Elsevier, vol. 165(1), pages 70-86.
    14. 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.
    15. Matsushita, Yukitoshi & Otsu, Taisuke, 2024. "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.
    16. Marine Carrasco & Guy Tchuente, 2016. "Efficient Estimation with Many Weak Instruments Using Regularization Techniques," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1609-1637, December.
    17. Carrasco, Marine & Tchuente, Guy, 2015. "Regularized LIML for many instruments," Journal of Econometrics, Elsevier, vol. 186(2), pages 427-442.
    18. Chao, John C. & Hausman, Jerry A. & Newey, Whitney K. & Swanson, Norman R. & Woutersen, Tiemen, 2014. "Testing overidentifying restrictions with many instruments and heteroskedasticity," Journal of Econometrics, Elsevier, vol. 178(P1), pages 15-21.
    19. 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.
    20. Yukitoshi Matsushita & Taisuke Otsu, 2020. "Second-order refinements for t-ratios with many instruments," STICERD - Econometrics Paper Series 612, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

    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:157:y:2010:i:2:p:191-204. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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.