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RMSE Reduction for GMM Estimators of Linear Time Series Models


  • Guido Kuersteiner

    (Massachusetts Institute of Technology)


In this paper we analyze GMM estimators for time series models as advocated by Hayashi and Sims, and Hansen and Singleton. It is well known that these estimators achieve efficiency bounds if the number of lagged observations in the instrument set goes to infinity. A new version of the GMM estimator based on kernel weighted moment conditions is proposed. Higher order asymptotic expansions are used to obtain optimal rates of expansions for the number of instruments to minimize the asymptotic MSE of the estimator. Estimates of optimal bandwidth parameters are then used to construct a fully feasible GMM estimator where the number of lagged instruments are endogenously determined by the data. Expressions for the asymptotic bias of kernel weighted GMM estimators are obtained. It is shown that standard GMM procedures have larger asymptotic biases than kernel weighted GMM. A bias correction for the estimator is proposed. It is shown that the bias corrected version achieves a faster rate of convergence of the higher order terms of the MSE than the uncorrected estimator.

Suggested Citation

  • Guido Kuersteiner, 2000. "RMSE Reduction for GMM Estimators of Linear Time Series Models," Econometric Society World Congress 2000 Contributed Papers 0892, Econometric Society.
  • Handle: RePEc:ecm:wc2000:0892

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    References listed on IDEAS

    1. Andrew Harvey & Chia-Hui Chung, 2000. "Estimating the underlying change in unemployment in the UK," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 163(3), pages 303-309.
    2. Neil Shephard & Michael K Pitt, 1995. "Likelihood analysis of non-Gaussian parameter driven models," Economics Papers 15 & 108., Economics Group, Nuffield College, University of Oxford.
    3. Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 107-160.
    4. Balke, Nathan S, 1993. "Detecting Level Shifts in Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 81-92, January.
    5. Andrew Harvey & Siem Jan Koopman, 2000. "Signal extraction and the formulation of unobserved components models," Econometrics Journal, Royal Economic Society, vol. 3(1), pages 84-107.
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    Cited by:

    1. Mahmoud El-Gamal, 2001. "A Bayesian Interpretation Of Multiple Point Estimates," Econometric Reviews, Taylor & Francis Journals, vol. 20(2), pages 235-245.
    2. Hahn, Jinyong & Hausman, Jerry & Kuersteiner, Guido, 2007. "Long difference instrumental variables estimation for dynamic panel models with fixed effects," Journal of Econometrics, Elsevier, vol. 140(2), pages 574-617, October.
    3. Nour Meddahi, 2003. "ARMA representation of integrated and realized variances," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 335-356, December.
    4. Xu Cheng & Zhipeng Liao, 2012. "Select the Valid and Relevant Moments: A One-Step Procedure for GMM with Many Moments," PIER Working Paper Archive 12-045, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

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