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

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

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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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  1. Charles R. Nelson & Richard Startz, 1988. "Some Further Results on the Exact Small Sample Properties of the Instrumental Variable Estimator," NBER Technical Working Papers 0068, National Bureau of Economic Research, Inc.
  2. Kinal, Terrence W, 1980. "The Existence of Moments of k-Class Estimators," Econometrica, Econometric Society, vol. 48(1), pages 241-49, January.
  3. Charles R. Nelson & Richard Startz, 1988. "The Distribution of the Instrumental Variables Estimator and Its t-RatioWhen the Instrument is a Poor One," NBER Technical Working Papers 0069, National Bureau of Economic Research, Inc.
  4. Sargan, J D, 1974. "The Validity of Nagar's Expansion for the Moments of Econometric Estimators," Econometrica, Econometric Society, vol. 42(1), pages 169-76, January.
  5. Jinyong Hahn & Jerry Hausman & Guido Kuersteiner, 2004. "Estimation with weak instruments: Accuracy of higher-order bias and MSE approximations," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 272-306, 06.
  6. James G. MacKinnon & Russell Davidson, 2006. "Reply to Ackerberg and Devereux and Blomquist and Dahlberg on 'The case against JIVE'," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(6), pages 843-844.
  7. Christopher F Baum & Mark E Schaffer & Steven Stillman, 2002. "IVREG2: Stata module for extended instrumental variables/2SLS and GMM estimation," Statistical Software Components S425401, Boston College Department of Economics, revised 09 Feb 2015.
  8. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
  9. Kiviet, Jan F. & Phillips, Garry D. A., 1996. "The bias of the ordinary least squares estimator in simultaneous equation models," Economics Letters, Elsevier, vol. 53(2), pages 161-167, November.
  10. Fuller, Wayne A, 1977. "Some Properties of a Modification of the Limited Information Estimator," Econometrica, Econometric Society, vol. 45(4), pages 939-53, May.
  11. Christian Hansen & Jerry Hausman & Whitney Newey, 2006. "Estimation with many instrumental variables," CeMMAP working papers CWP19/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  12. James G. MacKinnon & Russell Davidson, 2006. "The case against JIVE," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(6), pages 827-833.
  13. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  14. 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.
  15. Cheung Ip, Wai & Phillips, Garry D. A., 1998. "The non-monotonicity of the bias and mean squared error of the two stage least squares estimators of exogenous variable coefficients," Economics Letters, Elsevier, vol. 60(3), pages 303-310, September.
  16. Phillips, Garry D. A., 2000. "An alternative approach to obtaining Nagar-type moment approximations in simultaneous equation models," Journal of Econometrics, Elsevier, vol. 97(2), pages 345-364, August.
  17. Sawa, Takamitsu, 1972. "Finite-Sample Properties of the k-Class Estimators," Econometrica, Econometric Society, vol. 40(4), pages 653-80, July.
  18. Mariano, Roberto S, 1972. "The Existence of Moments of the Ordinary Least Squares and Two-Stage Least Squares Estimators," Econometrica, Econometric Society, vol. 40(4), pages 643-52, July.
  19. Phillips, P C B, 1980. "The Exact Distribution of Instrumental Variable Estimators in an Equation Containing n + 1 Endogenous Variables," Econometrica, Econometric Society, vol. 48(4), pages 861-78, May.
  20. Mehmet Caner, 2004. "Testing, Estimation and Higher Order Expansions in GMM with Semi-Weak Instruments," Econometric Society 2004 North American Summer Meetings 128, Econometric Society.
  21. John Chao & Norman Swanson, 2003. "Alternative Approximations of the Bias and MSE of the IV Estimator Under Weak Identification With an Application to Bias Correction," Departmental Working Papers 200315, Rutgers University, Department of Economics.
  22. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  23. Blomquist, Soren & Dahlberg, Matz, 1999. "Small Sample Properties of LIML and Jackknife IV Estimators: Experiments with Weak Instruments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 69-88, Jan.-Feb..
  24. Jinyong Hahn & Jerry Hausman, 2003. "Weak Instruments: Diagnosis and Cures in Empirical Econometrics," American Economic Review, American Economic Association, vol. 93(2), pages 118-125, May.
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