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Unbiased Instrumental Variables Estimation under Known First-Stage Sign

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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.

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  • Isaiah Andrews & Timothy B. Armstrong, 2015. "Unbiased Instrumental Variables Estimation under Known First-Stage Sign," Cowles Foundation Discussion Papers 1984R, Cowles Foundation for Research in Economics, Yale University, revised Mar 2015.
  • Handle: RePEc:cwl:cwldpp:1984r
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    3. 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).
    4. 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.
    5. Sebastián Amador, 2022. "Hysteresis, endogenous growth, and monetary policy," Working Papers 348, University of California, Davis, Department of Economics.
    6. 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.
    7. Müller, Ulrich K. & Wang, Yulong, 2019. "Nearly weighted risk minimal unbiased estimation," Journal of Econometrics, Elsevier, vol. 209(1), pages 18-34.
    8. 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.
    9. David M. Kaplan, 2019. "Unbiased Estimation as a Public Good," Working Papers 1911, Department of Economics, University of Missouri.
    10. Michael Keane & Timothy Neal, 2021. "A Practical Guide to Weak Instruments," Discussion Papers 2021-05b, School of Economics, The University of New South Wales.
    11. Karthik Rajkumar, 2019. "Ridge regularization for Mean Squared Error Reduction in Regression with Weak Instruments," Papers 1904.08580, arXiv.org.
    12. 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.
    13. 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.
    14. 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).
    15. 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.
    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).

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    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

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