IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/1984r3.html
   My bibliography  Save this paper

Unbiased Instrumental Variables Estimation under Known First-Stage Sign

Author

Listed:

Abstract

We derive mean-unbiased estimators for the structural parameter in instrumental variables models with a single endogenous regressor where the sign of one or more first stage coefficients is known. In the case with a single instrument, the unbiased estimator is unique. For cases with multiple instruments we propose a class of unbiased estimators and show that an estimator within this class is efficient when the instruments are strong. We show numerically that unbiasedness does not come at a cost of increased dispersion in models with a single instrument: in this case the unbiased estimator is less dispersed than the 2SLS estimator. Our finite-sample results apply to normal models with known variance for the reduced-form errors, and imply analogous results under weak instrument asymptotics with an unknown error distribution.

Suggested Citation

  • Isaiah Andrews & Timothy B. Armstrong, 2015. "Unbiased Instrumental Variables Estimation under Known First-Stage Sign," Cowles Foundation Discussion Papers 1984R3, Cowles Foundation for Research in Economics, Yale University, revised Oct 2015.
  • Handle: RePEc:cwl:cwldpp:1984r3
    Note: Includes Supplemental appendix
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d19/d1984-r3a.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. James J. Heckman & Sergio Urzua & Edward Vytlacil, 2006. "Understanding Instrumental Variables in Models with Essential Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 389-432, August.
    2. Gourieroux, Christian & Holly, Alberto & Monfort, Alain, 1982. "Likelihood Ratio Test, Wald Test, and Kuhn-Tucker Test in Linear Models with Inequality Constraints on the Regression Parameters," Econometrica, Econometric Society, vol. 50(1), pages 63-80, January.
    3. Eleonora Granziera & Hyungsik Roger Moon & Frank Schorfheide, 2018. "Inference for VARs identified with sign restrictions," Quantitative Economics, Econometric Society, vol. 9(3), pages 1087-1121, November.
    4. Donald, Stephen G & Newey, Whitney K, 2001. "Choosing the Number of Instruments," Econometrica, Econometric Society, vol. 69(5), pages 1161-1191, September.
    5. Joshua D. Angrist & Alan B. Krueger, 1993. "Split Sample Instrumental Variables," Working Papers 699, Princeton University, Department of Economics, Industrial Relations Section..
    6. Moreira, Marcelo J., 2009. "Tests with correct size when instruments can be arbitrarily weak," Journal of Econometrics, Elsevier, vol. 152(2), pages 131-140, October.
    7. 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.
    8. Kleibergen, Frank, 2007. "Generalizing weak instrument robust IV statistics towards multiple parameters, unrestricted covariance matrices and identification statistics," Journal of Econometrics, Elsevier, vol. 139(1), pages 181-216, July.
    9. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    10. Angrist, Joshua D & Krueger, Alan B, 1995. "Split-Sample Instrumental Variables Estimates of the Return to Schooling," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(2), pages 225-235, April.
    11. 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.
    12. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    13. Anna Aizer & Joseph J. Doyle, 2015. "Juvenile Incarceration, Human Capital, and Future Crime: Evidence from Randomly Assigned Judges," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 130(2), pages 759-803.
    14. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    15. Frank Kleibergen, 2005. "Testing Parameters in GMM Without Assuming that They Are Identified," Econometrica, Econometric Society, vol. 73(4), pages 1103-1123, July.
    16. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
    17. 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..
    18. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
    19. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    20. Hillier, Grant, 2006. "Yet More On The Exact Properties Of Iv Estimators," Econometric Theory, Cambridge University Press, vol. 22(5), pages 913-931, October.
    21. 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.
    22. Phillips, P.C.B., 1983. "Exact small sample theory in the simultaneous equations model," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 8, pages 449-516, Elsevier.
    23. Keisuke Hirano & Jack R. Porter, 2012. "Impossibility Results for Nondifferentiable Functionals," Econometrica, Econometric Society, vol. 80(4), pages 1769-1790, July.
    24. 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.
    25. Matthew C. Harding & Jerry Hausman & Christopher Palmer, 2015. "Finite sample bias corrected IV estimation for weak and many instruments," CeMMAP working papers CWP41/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    26. Müller, Ulrich K. & Wang, Yulong, 2019. "Nearly weighted risk minimal unbiased estimation," Journal of Econometrics, Elsevier, vol. 209(1), pages 18-34.
    27. Erik Hornung, 2014. "Immigration and the Diffusion of Technology: The Huguenot Diaspora in Prussia," American Economic Review, American Economic Association, vol. 104(1), pages 84-122, January.
    28. 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.
    29. Moreira, Humberto Ataíde & Moreira, Marcelo J., 2013. "Contributions to the Theory of Optimal Tests," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 747, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    30. 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.
    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. Callaway, Brantly & Karami, Sonia, 2023. "Treatment effects in interactive fixed effects models with a small number of time periods," Journal of Econometrics, Elsevier, vol. 233(1), pages 184-208.
    2. Tetsuya Kaji, 2019. "Theory of Weak Identification in Semiparametric Models," Papers 1908.10478, arXiv.org, revised Aug 2020.
    3. Karthik Rajkumar, 2019. "Ridge regularization for Mean Squared Error Reduction in Regression with Weak Instruments," Papers 1904.08580, arXiv.org.
    4. Brassiolo, Pablo & Estrada, Ricardo & Fajardo, Gustavo & Vargas, Juan, 2021. "Self-Selection into corruption: Evidence from the lab," Journal of Economic Behavior & Organization, Elsevier, vol. 192(C), pages 799-812.
    5. Angrist, Joshua & Kolesár, Michal, 2024. "One instrument to rule them all: The bias and coverage of just-ID IV," Journal of Econometrics, Elsevier, vol. 240(2).
    6. Timothy Derdenger & Vineet Kumar, 2019. "Estimating dynamic discrete choice models with aggregate data: Properties of the inclusive value approximation," Quantitative Marketing and Economics (QME), Springer, vol. 17(4), pages 359-384, December.
    7. Matthew C. Harding & Jerry Hausman & Christopher Palmer, 2015. "Finite sample bias corrected IV estimation for weak and many instruments," CeMMAP working papers CWP41/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Sebastián Amador, 2022. "Hysteresis, endogenous growth, and monetary policy," Working Papers 348, University of California, Davis, Department of Economics.
    9. 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.
    10. Müller, Ulrich K. & Wang, Yulong, 2019. "Nearly weighted risk minimal unbiased estimation," Journal of Econometrics, Elsevier, vol. 209(1), pages 18-34.
    11. Khan, Umair & Khalid, Umair & Farooq, Fatima, 2021. "Endogeneity Quagmire Empirical Evidence from Telecommunication Industry of Pakistan," Journal of Accounting and Finance in Emerging Economies, CSRC Publishing, Center for Sustainability Research and Consultancy Pakistan, vol. 7(4), pages 955-967, December.
    12. Bunkanwanicha, Pramuan & Di Giuli, Alberta & Salvade, Federica, 2022. "Bank CEO careers after bailouts: The effects of management turnover on bank risk," Journal of Financial Intermediation, Elsevier, vol. 52(C).
    13. David M. Kaplan, 2019. "Unbiased Estimation as a Public Good," Working Papers 1911, Department of Economics, University of Missouri.
    14. Matthew C. Harding & Jerry Hausman & Christopher Palmer, 2015. "Finite sample bias corrected IV estimation for weak and many instruments," CeMMAP working papers 41/15, Institute for Fiscal Studies.
    15. Michael Keane & Timothy Neal, 2021. "A Practical Guide to Weak Instruments," Discussion Papers 2021-05b, School of Economics, The University of New South Wales.
    16. Tetsuya Kaji, 2021. "Theory of Weak Identification in Semiparametric Models," Econometrica, Econometric Society, vol. 89(2), pages 733-763, March.
    17. Abadie, Alberto & Gu, Jiaying & Shen, Shu, 2024. "Instrumental variable estimation with first-stage heterogeneity," Journal of Econometrics, Elsevier, vol. 240(2).

    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. 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.
    2. 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.
    3. Guilhem Bascle, 2008. "Controlling for endogeneity with instrumental variables in strategic management research," Post-Print hal-00576795, HAL.
    4. Michael P. Murray, 2006. "Avoiding Invalid Instruments and Coping with Weak Instruments," Journal of Economic Perspectives, American Economic Association, vol. 20(4), pages 111-132, Fall.
    5. Dufour, Jean-Marie & Taamouti, Mohamed, 2007. "Further results on projection-based inference in IV regressions with weak, collinear or missing instruments," Journal of Econometrics, Elsevier, vol. 139(1), pages 133-153, July.
    6. Moreira, Humberto & Moreira, Marcelo J., 2019. "Optimal two-sided tests for instrumental variables regression with heteroskedastic and autocorrelated errors," Journal of Econometrics, Elsevier, vol. 213(2), pages 398-433.
    7. 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.
    8. 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.
    9. Manu Navjeevan, 2023. "An Identification and Dimensionality Robust Test for Instrumental Variables Models," Papers 2311.14892, arXiv.org, revised Dec 2024.
    10. 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.
    11. 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.
    12. Donald W.K. Andrews & James H. Stock, 2005. "Inference with Weak Instruments," NBER Technical Working Papers 0313, National Bureau of Economic Research, Inc.
    13. Joel L. Horowitz, 2018. "Non-Asymptotic Inference in Instrumental Variables Estimation," Papers 1809.03600, arXiv.org.
    14. 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.
    15. 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.
    16. Andrews, Donald W.K. & Cheng, Xu & Guggenberger, Patrik, 2020. "Generic results for establishing the asymptotic size of confidence sets and tests," Journal of Econometrics, Elsevier, vol. 218(2), pages 496-531.
    17. 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.
    18. Kolesár, Michal, 2018. "Minimum distance approach to inference with many instruments," Journal of Econometrics, Elsevier, vol. 204(1), pages 86-100.
    19. Horowitz, Joel L., 2021. "Bounding the difference between true and nominal rejection probabilities in tests of hypotheses about instrumental variables models," Journal of Econometrics, Elsevier, vol. 222(2), pages 1057-1082.
    20. 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.

    More about this item

    Keywords

    Weak instruments; Unbiased estimation; Sign restrictions;
    All these keywords.

    JEL classification:

    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • 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:cwl:cwldpp:1984r3. 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: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.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.