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Finite sample bias corrected IV estimation for weak and many instruments

Author

Listed:
  • Matthew C. Harding

    (Institute for Fiscal Studies and Stanford University)

  • Jerry Hausman

    () (Institute for Fiscal Studies and MIT)

  • Christopher Palmer

    (Institute for Fiscal Studies)

Abstract

This paper considers the finite sample distribution of the 2SLS estimator and derives bounds on its exact bias in the presence of weak and/or many instruments. We then contrast the behavior of the exact bias expressions and the asymptotic expansions currently popular in the literature, including a consideration of the no-moment problem exhibited by many Nagar-type estimators. After deriving a finite sample unbiased k-class estimator, we introduce a double k-class estimator based on Nagar (1962) that dominates k-class estimators (including 2SLS), especially in the cases of weak and/or many instruments. We demonstrate these properties in Monte Carlo simulations showing that our preferred estimators outperforms Fuller (1977) estimators in terms of mean bias and MSE.

Suggested Citation

  • 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.
  • Handle: RePEc:ifs:cemmap:41/15
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    File URL: https://www.ifs.org.uk/uploads/cemmap/wps/cwp411515.pdf
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    References listed on IDEAS

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    1. 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.
    2. Ullah, Aman, 2004. "Finite Sample Econometrics," OUP Catalogue, Oxford University Press, number 9780198774488.
    3. Richardson, David H & Wu, De-Min, 1971. "A Note on the Comparison of Ordinary and Two-Stage Least Squares Estimators," Econometrica, Econometric Society, vol. 39(6), pages 973-981, November.
    4. Hahn, Jinyong & Hausman, Jerry, 2002. "Notes on bias in estimators for simultaneous equation models," Economics Letters, Elsevier, vol. 75(2), pages 237-241, April.
    5. Srinivasan, T N, 1970. "Approximations to Finite Sample Moments of Estimators Whose Exact Sampling Distributions are Unknown," Econometrica, Econometric Society, vol. 38(3), pages 533-541, May.
    6. D. S. Poskitt & C. L. Skeels, 2009. "Assessing the magnitude of the concentration parameter in a simultaneous equations model," Econometrics Journal, Royal Economic Society, vol. 12(1), pages 26-44, March.
    7. Dwivedi, T. D. & Srivastava, V. K., 1984. "Exact finite sample properties of double k-class estimators in simultaneous equations," Journal of Econometrics, Elsevier, vol. 25(3), pages 263-283, July.
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    Cited by:

    1. Isaiah Andrews & Timothy B. Armstrong, 2015. "Unbiased Instrumental Variables Estimation under Known First-Stage Sign," Cowles Foundation Discussion Papers 1984R5, Cowles Foundation for Research in Economics, Yale University, revised Nov 2016.
    2. Isaiah Andrews & Timothy B. Armstrong, 2015. "Unbiased Instrumental Variables Estimation under Known First-Stage Sign," Cowles Foundation Discussion Papers 1984R4, Cowles Foundation for Research in Economics, Yale University, revised Apr 2016.

    More about this item

    Keywords

    Instrumental variables; weak and many instruments; finite sample; k-class estimators;

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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