IDEAS home Printed from https://ideas.repec.org/a/taf/emetrv/v34y2015i6-10p720-733.html
   My bibliography  Save this article

Location Properties of Point Estimators in Linear Instrumental Variables and Related Models

Author

Listed:
  • Keisuke Hirano
  • Jack R. Porter

Abstract

We examine statistical models, including the workhorse linear instrumental variables model, in which the mapping from the reduced form distribution to the structural parameters of interest is singular. The singularity of this mapping implies certain fundamental restrictions on the finite sample properties of point estimators: they cannot be unbiased, quantile-unbiased, or translation equivariant. The nonexistence of unbiased estimators does not rule out bias reduction of standard estimators, but implies that the bias-variance tradeoff cannot be avoided and needs to be considered carefully. The results can also be extended to weak instrument asymptotics by using the limits of experiments framework.

Suggested Citation

  • Keisuke Hirano & Jack R. Porter, 2015. "Location Properties of Point Estimators in Linear Instrumental Variables and Related Models," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 720-733, December.
    • Handle: RePEc:taf:emetrv:v:34:y:2015:i:6-10:p:720-733
    DOI: 10.1080/07474938.2014.956573
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/07474938.2014.956573
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/07474938.2014.956573?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Phillips, Peter C B, 1985. "The Exact Distribution of LIML: II," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(1), pages 21-36, February.
    2. Nelson, Charles R & Startz, Richard, 1990. "Some Further Results on the Exact Small Sample Properties of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 58(4), pages 967-976, July.
    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. Phillips, P C B, 1986. "The Distribution of FIML in the Leading Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 239-243, February.
    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. 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. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    8. Sargan, J D, 1978. "On the Existence of the Moments of 3SLS Estimators," Econometrica, Econometric Society, vol. 46(6), pages 1329-1350, November.
    9. Jerry A. Hausman & Whitney K. Newey & Tiemen Woutersen & John C. Chao & Norman R. Swanson, 2012. "Instrumental variable estimation with heteroskedasticity and many instruments," Quantitative Economics, Econometric Society, vol. 3(2), pages 211-255, July.
    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. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    12. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    13. 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..
    14. 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.
    15. 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.
    16. Kinal, Terrence W, 1980. "The Existence of Moments of k-Class Estimators," Econometrica, Econometric Society, vol. 48(1), pages 241-249, January.
    17. Hillier, Grant H & Kinal, Terrence W & Srivastava, V K, 1984. "On the Moments of Ordinary Least Squares and Instrumental Variables Estimators in a General Structural Equation," Econometrica, Econometric Society, vol. 52(1), pages 185-202, January.
    18. Cattaneo, Matias D. & Crump, Richard K. & Jansson, Michael, 2012. "Optimal inference for instrumental variables regression with non-Gaussian errors," Journal of Econometrics, Elsevier, vol. 167(1), pages 1-15.
    19. Carter, R A L, 1976. "The Exact Distribution of an Instrumental Variables Estimator," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(1), pages 228-233, February.
    20. Ullah, Aman & Nagar, A L, 1974. "The Exact Mean of the Two-Stage Least Squares Estimator of the Structural Parameters in an Equation Having Three Endogenous Variables," Econometrica, Econometric Society, vol. 42(4), pages 749-758, July.
    21. Maasoumi, Esfandiar, 1978. "A Modified Stein-like Estimator for the Reduced Form Coefficients of Simultaneous Equations," Econometrica, Econometric Society, vol. 46(3), pages 695-703, May.
    22. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
    23. Gary Chamberlain, 2007. "Decision Theory Applied to an Instrumental Variables Model," Econometrica, Econometric Society, vol. 75(3), pages 609-652, May.
    24. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
    25. Anderson, T W & Sawa, Takamitsu, 1973. "Distributions of Estimates of Coefficients of a Single Equation in a Simultaneous System and Their Asymptotic Expansions," Econometrica, Econometric Society, vol. 41(4), pages 683-714, July.
    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. Silvia Moler‐Zapata & Richard Grieve & Anirban Basu & Stephen O’Neill, 2023. "How does a local instrumental variable method perform across settings with instruments of differing strengths? A simulation study and an evaluation of emergency surgery," Health Economics, John Wiley & Sons, Ltd., vol. 32(9), pages 2113-2126, September.
    2. Isaiah Andrews & Timothy B. Armstrong, 2017. "Unbiased instrumental variables estimation under known first‐stage sign," Quantitative Economics, Econometric Society, vol. 8(2), pages 479-503, July.
    3. Karthik Rajkumar, 2019. "Ridge regularization for Mean Squared Error Reduction in Regression with Weak Instruments," Papers 1904.08580, arXiv.org.
    4. David M. Kaplan, 2019. "Unbiased Estimation as a Public Good," Working Papers 1911, Department of Economics, University of Missouri.
    5. Roach, Travis & Nath, Saheli, 2023. "Counties with More Vietnam Veterans Have Higher Suicide Rates," Journal of Regional Analysis and Policy, Mid-Continent Regional Science Association, vol. 53(1), April.
    6. Tetsuya Kaji, 2021. "Theory of Weak Identification in Semiparametric Models," Econometrica, Econometric Society, vol. 89(2), pages 733-763, March.

    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. 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.
    2. 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.
    3. Tetsuya Kaji, 2019. "Theory of Weak Identification in Semiparametric Models," Papers 1908.10478, arXiv.org, revised Aug 2020.
    4. Wang, Wenjie & Doko Tchatoka, Firmin, 2018. "On Bootstrap inconsistency and Bonferroni-based size-correction for the subset Anderson–Rubin test under conditional homoskedasticity," Journal of Econometrics, Elsevier, vol. 207(1), pages 188-211.
    5. Guilhem Bascle, 2008. "Controlling for endogeneity with instrumental variables in strategic management research," Post-Print hal-00576795, HAL.
    6. 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.
    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. D. S. Poskitt & C. L. Skeels, 2004. "Approximating the Distribution of the Instrumental Variables Estimator when the Concentration Parameter is Small," Monash Econometrics and Business Statistics Working Papers 19/04, Monash University, Department of Econometrics and Business Statistics.
    9. Chao, John C. & Swanson, Norman R. & Woutersen, Tiemen, 2023. "Jackknife estimation of a cluster-sample IV regression model with many weak instruments," Journal of Econometrics, Elsevier, vol. 235(2), pages 1747-1769.
    10. Mills, Benjamin & Moreira, Marcelo J. & Vilela, Lucas P., 2014. "Tests based on t-statistics for IV regression with weak instruments," Journal of Econometrics, Elsevier, vol. 182(2), pages 351-363.
    11. 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.
    12. 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.
    13. Chao, John C. & Swanson, Norman R. & Hausman, Jerry A. & Newey, Whitney K. & Woutersen, Tiemen, 2012. "Asymptotic Distribution Of Jive In A Heteroskedastic Iv Regression With Many Instruments," Econometric Theory, Cambridge University Press, vol. 28(1), pages 42-86, February.
    14. Guggenberger, Patrik & Ramalho, Joaquim J.S. & Smith, Richard J., 2012. "GEL statistics under weak identification," Journal of Econometrics, Elsevier, vol. 170(2), pages 331-349.
    15. Antoine, Bertille & Lavergne, Pascal, 2023. "Identification-robust nonparametric inference in a linear IV model," Journal of Econometrics, Elsevier, vol. 235(1), pages 1-24.
    16. Isaiah Andrews & Timothy B. Armstrong, 2017. "Unbiased instrumental variables estimation under known first‐stage sign," Quantitative Economics, Econometric Society, vol. 8(2), pages 479-503, July.
    17. Marmer, Vadim & Yu, Zhengfei, 2015. "Efficient Inference in the Classical IV Regression Model with Weak Identification: Asymptotic Power Against Arbitrarily Large Deviations from the Null Hypothesis," Microeconomics.ca working papers vadim_marmer-2015-17, Vancouver School of Economics, revised 02 Sep 2015.
    18. Bertille Antoine & Pascal Lavergne, 2020. "Identification-Robust Nonparametric Interference in a Linear IV Model," Discussion Papers dp20-03, Department of Economics, Simon Fraser University.
    19. Wang, Wenjie, 2021. "Wild Bootstrap for Instrumental Variables Regression with Weak Instruments and Few Clusters," MPRA Paper 106227, University Library of Munich, Germany.
    20. Yukitoshi Matsushita & Taisuke Otsu, 2020. "Jackknife Lagrange multiplier test with many weak instruments," STICERD - Econometrics Paper Series 613, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

    More about this item

    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:taf:emetrv:v:34:y:2015:i:6-10:p:720-733. 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: the person in charge (email available below). General contact details of provider: http://www.tandfonline.com/LECR20 .

    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.