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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.

Suggested Citation

  • 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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    1. Russell Davidson & James G. MacKinnon, 2006. "The case against JIVE," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(6), pages 827-833, September.
    2. 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.
    3. Nelson, Charles R & Startz, Richard, 1990. "Some Further Results on the Exact Small Sample Properties of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 58(4), pages 967-976, July.
    4. 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 10 May 2022.
    5. 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..
    6. 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.
    7. Fuller, Wayne A, 1977. "Some Properties of a Modification of the Limited Information Estimator," Econometrica, Econometric Society, vol. 45(4), pages 939-953, May.
    8. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-681, May.
    9. Nelson, Charles R & Startz, Richard, 1990. "The Distribution of the Instrumental Variables Estimator and Its t-Ratio When the Instrument Is a Poor One," The Journal of Business, University of Chicago Press, vol. 63(1), pages 125-140, January.
    10. Chao, John & Swanson, Norman R., 2007. "Alternative approximations of the bias and MSE of the IV estimator under weak identification with an application to bias correction," Journal of Econometrics, Elsevier, vol. 137(2), pages 515-555, April.
    11. 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 861-878, May.
    12. 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.
    13. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    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 518-529, October.
    15. 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, June.
    16. Sawa, Takamitsu, 1972. "Finite-Sample Properties of the k-Class Estimators," Econometrica, Econometric Society, vol. 40(4), pages 653-680, July.
    17. 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.
    18. Owen, A D, 1976. "A Proof That Both the Bias and the Mean Square Error of the Two-Stage Least Squares Estimator Are Monotonically Non-Increasing Functions of Sample Size," Econometrica, Econometric Society, vol. 44(2), pages 409-411, March.
    19. Kinal, Terrence W, 1980. "The Existence of Moments of k-Class Estimators," Econometrica, Econometric Society, vol. 48(1), pages 241-249, January.
    20. Sargan, J D, 1974. "The Validity of Nagar's Expansion for the Moments of Econometric Estimators," Econometrica, Econometric Society, vol. 42(1), pages 169-176, January.
    21. Hansen, Christian & Hausman, Jerry & Newey, Whitney, 2008. "Estimation With Many Instrumental Variables," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 398-422.
    22. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    23. Ullah, Aman, 2004. "Finite Sample Econometrics," OUP Catalogue, Oxford University Press, number 9780198774488.
    24. Hahn, Jinyong & Hausman, Jerry, 2002. "Notes on bias in estimators for simultaneous equation models," Economics Letters, Elsevier, vol. 75(2), pages 237-241, April.
    25. 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.
    26. 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.
    27. 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 643-652, July.
    28. 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.
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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. Peter C. B. Phillips, 2017. "Reduced forms and weak instrumentation," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 818-839, October.
    3. 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.
    4. Phillips, Garry David Alan & Wang, Dandan, 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.
    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. 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.
    7. 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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    • 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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