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Almost Unbiased Estimation in Simultaneous Equation Models With Strong and/or Weak Instruments

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  • Emma M. Iglesias
  • Garry D. A. Phillips

Abstract

We propose two simple bias-reduction procedures that apply to estimators in a general static simultaneous equation model and that are valid under relatively weak distributional assumptions for the errors. Standard jackknife estimators, as applied to 2SLS, may not reduce the bias of the exogenous variable coefficient estimators since the estimator biases are not monotonically nonincreasing with sample size (a necessary condition for successful bias reduction) and they have moments only up to the order of overidentification. Our proposed approaches do not have either of these drawbacks. (1) In the first procedure, both endogenous and exogenous variable parameter estimators are unbiased to order T -super-− 2 and when implemented for k -class estimators for which k > 1, the higher-order moments will exist. (2) An alternative second approach is based on taking linear combinations of k -class estimators for k > 1. In general, this yields estimators that are unbiased to order T -super-− 1 and that possess higher moments. We also prove theoretically how the combined k -class estimator produces a smaller mean squared error than 2SLS when the degree of overidentification of the system is 0, 1, or at least 8. The performance of the two procedures is compared with 2SLS in a number of Monte Carlo experiments using a simple two-equation model. Finally, an application shows the usefulness of our new estimator in practice versus competitor estimators.

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  • 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.
  • Handle: RePEc:taf:jnlbes:v:30:y:2012:i:4:p:505-520
    DOI: 10.1080/07350015.2012.715959
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    Cited by:

    1. Symeonides Spyridon D. & Karavias Yiannis & Tzavalis Elias, 2017. "Size corrected Significance Tests in Seemingly Unrelated Regressions with Autocorrelated Errors," Journal of Time Series Econometrics, De Gruyter, vol. 9(1), pages 1-41, January.
    2. Phillips, Garry D.A. & Liu-Evans, Gareth, 2016. "Approximating and reducing bias in 2SLS estimation of dynamic simultaneous equation models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 734-762.
    3. Phillips, Garry D.A. & Liu-Evans, Gareth, 2011. "The Robustness of the Higher-Order 2SLS and General k-Class Bias Approximations to Non-Normal Disturbances," Cardiff Economics Working Papers E2011/20, Cardiff University, Cardiff Business School, Economics Section.
    4. Peter C. B. Phillips, 2017. "Reduced forms and weak instrumentation," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 818-839, October.
    5. 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.
    6. Liu-Evans, Gareth & Phillips, Garry D.A., 2018. "On the use of higher order bias approximations for 2SLS and k-class estimators with non-normal disturbances and many instruments," Econometrics and Statistics, Elsevier, vol. 6(C), pages 90-105.
    7. Wang, Dandan & Phillips, Garry David Alan, 2019. "Bias assessment and reduction for the 2SLS estimator in general dynamic simultaneous equations models," DES - Working Papers. Statistics and Econometrics. WS 28322, Universidad Carlos III de Madrid. Departamento de Estadística.

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    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
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