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The Bias of Bootstrapped Versus Conventional Standard Errors in the General Linear and SUR Models

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  • Atkinson, Scott E.
  • Wilson, Paul W.

Abstract

When estimating the seemingly unrelated regression (SUR) model in small samples, the bootstrap feasible generalized least-squares (FGLS) covariance estimator has been widely advocated as less biased than the conventional FGLS covariance estimator obtained by evaluating the asymptotic covariance matrix. Assuming multivariate normal errors and an unbiased estimator of the error covariance, Eaton proves that the conventional estimator is biased downward for a general SUR model. Ignoring terms O ( T –2 ) for this model, we prove that the bootstrap estimator is also biased downward. However, from these results, the relative magnitude of these two biases is indeterminant in general. By ignoring terms O ( T –2 ) for Zellner's two-equation, orthogonal regressor model with bivariate normal errors, we show that the bias of both estimators is downward and that the bootstrap estimator exhibits a smaller bias than the conventional estimator. Monte Carlo simulation results indicate that, in general, neither estimator uniformly dominates the other.

Suggested Citation

  • Atkinson, Scott E. & Wilson, Paul W., 1992. "The Bias of Bootstrapped Versus Conventional Standard Errors in the General Linear and SUR Models," Econometric Theory, Cambridge University Press, vol. 8(02), pages 258-275, June.
  • Handle: RePEc:cup:etheor:v:8:y:1992:i:02:p:258-275_01
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    1. Wanat, Stanisław & Papież, Monika & Śmiech, Sławomir, 2016. "Insurance Market Development and Economic Growth in Transition Countries: Some new evidence based on bootstrap panel Granger causality test," MPRA Paper 69051, University Library of Munich, Germany.
    2. Dufour, Jean-Marie & Khalaf, Lynda, 2002. "Simulation based finite and large sample tests in multivariate regressions," Journal of Econometrics, Elsevier, vol. 111(2), pages 303-322, December.
    3. Léopold Simar & Paul Wilson, 1999. "Some Problems with the Ferrier/Hirschberg Bootstrap Idea," Journal of Productivity Analysis, Springer, vol. 11(1), pages 67-80, February.
    4. Bergström, Pål, 1999. "Bootstrap Methods and Applications in Econometrics - A Brief Survey," Working Paper Series 1999:2, Uppsala University, Department of Economics.
    5. Śmiech, Sławomir & Papież, Monika, 2014. "Energy consumption and economic growth in the light of meeting the targets of energy policy in the EU: The bootstrap panel Granger causality approach," Energy Policy, Elsevier, vol. 71(C), pages 118-129.
    6. Monika Papiez & Slawomir Smiech, 2013. "Economic Growth and Energy Consumption in Post-Communist Countries: a Bootstrap Panel Granger Causality Analysis," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 13, pages 51-68.

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