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Kernel-weighted GMM estimators for linear time series models

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  • Kuersteiner, Guido M.

Abstract

This paper analyzes the higher-order asymptotic properties of generalized method of moments (GMM) estimators for linear time series models using many lags as instruments. A data-dependent moment selection method based on minimizing the approximate mean squared error is developed. In addition, a new version of the GMM estimator based on kernel-weighted moment conditions is proposed. It is shown that kernel-weighted GMM estimators can reduce the asymptotic bias compared to standard GMM estimators. Kernel weighting also helps to simplify the problem of selecting the optimal number of instruments. A feasible procedure similar to optimal bandwidth selection is proposed for the kernel-weighted GMM estimator.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 170 (2012)
Issue (Month): 2 ()
Pages: 399-421

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Handle: RePEc:eee:econom:v:170:y:2012:i:2:p:399-421

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Time series; Feasible GMM; Number of instruments; Kernel weights; Higher-order MSE; Bias reduction;

References

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  1. Kenneth D. West & David W. Wilcox, 1994. "A Comparison of Alternative Instrumental Variables Estimators of Dynamic Linear Model," Macroeconomics 9410001, EconWPA.
  2. Carrasco, Marine, 2012. "A regularization approach to the many instruments problem," Journal of Econometrics, Elsevier, vol. 170(2), pages 383-398.
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  4. West,K.D. & Wong,K.-F. & Anatolyev,S., 2001. "Instrumental variables estimation of heteroskedastic linear models using all lags of instruments," Working papers 20, Wisconsin Madison - Social Systems.
  5. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, 01.
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  7. Hansen, Lars Peter, 1985. "A method for calculating bounds on the asymptotic covariance matrices of generalized method of moments estimators," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 203-238.
  8. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-80, July.
  9. Kuersteiner, Guido M., 2001. "Optimal instrumental variables estimation for ARMA models," Journal of Econometrics, Elsevier, vol. 104(2), pages 359-405, September.
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  11. Atsushi Inoue, 2006. "A bootstrap approach to moment selection," Econometrics Journal, Royal Economic Society, vol. 9(1), pages 48-75, 03.
  12. Newey, Whitney K & West, Kenneth D, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," Review of Economic Studies, Wiley Blackwell, vol. 61(4), pages 631-53, October.
  13. Hansen, Lars Peter & Singleton, Kenneth J, 1996. "Efficient Estimation of Linear Asset-Pricing Models with Moving Average Errors," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 53-68, January.
  14. 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.
  15. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2009. "Choosing instrumental variables in conditional moment restriction models," Journal of Econometrics, Elsevier, vol. 152(1), pages 28-36, September.
  16. Kuersteiner, Guido M., 2005. "Automatic Inference For Infinite Order Vector Autoregressions," Econometric Theory, Cambridge University Press, vol. 21(01), pages 85-115, February.
  17. Magnus, J.R. & Neudecker, H., 1979. "The commutation matrix: Some properties and applications," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153207, Tilburg University.
  18. Canay, Ivan A., 2010. "Simultaneous selection and weighting of moments in GMM using a trapezoidal kernel," Journal of Econometrics, Elsevier, vol. 156(2), pages 284-303, June.
  19. Guido Kuersteiner & Ryo Okui, 2010. "Constructing Optimal Instruments by First-Stage Prediction Averaging," Econometrica, Econometric Society, vol. 78(2), pages 697-718, 03.
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  22. Kuersteiner, Guido M., 2002. "Efficient Iv Estimation For Autoregressive Models With Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 18(03), pages 547-583, June.
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Cited by:
  1. Carrasco, Marine, 2012. "A regularization approach to the many instruments problem," Journal of Econometrics, Elsevier, vol. 170(2), pages 383-398.

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