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A comparison of bias approximations for the 2SLS estimator

  • Maurice Bun

    (Institute for Fiscal Studies)

  • Frank Windmeijer


    (Institute for Fiscal Studies and University of Bristol)

We consider the bias of the 2SLS estimator in the linear instrumental variables regression with one endogenous regressor only. By using asymptotic expansion techniques we approximate 2SLS coefficient estimation bias under various scenarios regarding the number and strength of instruments. The resulting approximation encompasses existing bias approximations, which are valid in particular cases only. Simulations show that the developed approximation gives an accurate description of the 2SLS bias in case of either weak or many instruments or both.

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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP07/10.

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Date of creation: 21 Apr 2010
Date of revision:
Handle: RePEc:ifs:cemmap:07/10
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  1. Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-29, October.
  2. John C. Chao & Norman Rasmus Swanson, 2004. "Consistent Estimation with a Large Number of Weak Instruments," Yale School of Management Working Papers ysm374, Yale School of Management.
  3. Hahn, Jinyong & Kuersteiner, Guido, 2002. "Discontinuities of weak instrument limiting distributions," Economics Letters, Elsevier, vol. 75(3), pages 325-331, May.
  4. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  5. Buse, A, 1992. "The Bias of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 60(1), pages 173-80, January.
  6. John C. Chao & Norman Rasmus Swanson, 2004. "Alternative Approximations of the Bias and MSE of the IV Estimator Under Weak Identification with an Application to Bias Correction," Yale School of Management Working Papers ysm375, Yale School of Management.
  7. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
  8. Hahn, Jinyong & Hausman, Jerry, 2002. "Notes on bias in estimators for simultaneous equation models," Economics Letters, Elsevier, vol. 75(2), pages 237-241, April.
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