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Finite Sample BIAS Corrected IV Estimation for Weak and Many Instruments

In: Essays in Honor of Aman Ullah

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  • Matthew Harding
  • Jerry Hausman
  • Christopher J. Palmer

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 unbiasedk-class estimator, we introduce a double-k-class estimator based on Nagar (1962) that dominatesk-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 outperform Fuller (1977) estimators in terms of mean bias and MSE.

Suggested Citation

  • Matthew Harding & Jerry Hausman & Christopher J. Palmer, 2016. "Finite Sample BIAS Corrected IV Estimation for Weak and Many Instruments," Advances in Econometrics, in: Essays in Honor of Aman Ullah, volume 36, pages 245-273, Emerald Group Publishing Limited.
    • Handle: RePEc:eme:aecozz:s0731-905320160000036016
    DOI: 10.1108/S0731-905320160000036016
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    Citations

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    Cited by:

    1. Yong Bao & Aman Ullah, 2021. "Analytical Finite Sample Econometrics: From A. L. Nagar to Now," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 17-37, December.
    2. Bai Huang & Tae-Hwy Lee & Aman Ullah, 2017. "A combined estimator of regression models with measurement errors," Indian Economic Review, Springer, vol. 52(1), pages 73-91, December.
    3. Guy Tchuente, 2021. "A Note on the Topology of the First Stage of 2SLS with Many Instruments," Papers 2106.15003, arXiv.org.

    More about this item

    Keywords

    Instrumental variables; weak and many instruments; finite sample; k-class estimators; C31; C13; C15;
    All these keywords.

    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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