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Almost Unbiased Estimation in Simultaneous Equations Models with Strong and / or Weak Instruments

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

    ()
    (Cardiff Business School)

Abstract

We propose two simple bias reduction procedures that apply to estimators in a general static simultaneous equation model and which are valid under reatively 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 non-increasing 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 -2 and when implemented for k-class estimators for which k -1 and which 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 larger than 8. Moreover, the combined k-class estimators remain unbiased to order T -1 even if there are redundant variables (including weak instruments) in any part of the simultaneous equation system, and we can allow for any number of endogenous variables. 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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Bibliographic Info

Paper provided by Cardiff University, Cardiff Business School, Economics Section in its series Cardiff Economics Working Papers with number E2011/19.

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Length: 38 pages
Date of creation: Aug 2011
Date of revision:
Handle: RePEc:cdf:wpaper:2011/19

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Keywords: Combined k -class estimators; Bias correction; Weak instruments; Endogenous and exogenous parameter estimators; Permanent Income Hypothesis;

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References

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Cited by:
  1. 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.

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