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The Mean Squared Error of the Instrumental Variables Estimator When the Disturbance Has an Elliptical Distribution

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  • Fernanda Peixe
  • Alastair Hall
  • Kostas Kyriakoulis

Abstract

This paper generalizes Nagar's (1959) approximation to the finite sample mean squared error (MSE) of the instrumental variables (IV) estimator to the case in which the errors possess an elliptical distribution whose moments exist up to infinite order. This allows for types of excess kurtosis exhibited by some financial data series. This approximation is compared numerically to Knight's (1985) formulae for the exact moments of the IV estimator under nonnormality. We use the results to explore two questions on instrument selection. First, we complement Buse's (1992) analysis by considering the impact of additional instruments on both bias and MSE. Second, we evaluate the properties of Andrews's (1999) selection method in terms of the bias and MSE of the resulting IV estimator.

Suggested Citation

  • Fernanda Peixe & Alastair Hall & Kostas Kyriakoulis, 2006. "The Mean Squared Error of the Instrumental Variables Estimator When the Disturbance Has an Elliptical Distribution," Econometric Reviews, Taylor & Francis Journals, vol. 25(1), pages 117-138.
    • Handle: RePEc:taf:emetrv:v:25:y:2006:i:1:p:117-138
    DOI: 10.1080/07474930500545488
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    Cited by:

    1. Alastair R. Hall & Fernanda P. M. Peixe, 2003. "A Consistent Method for the Selection of Relevant Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 22(3), pages 269-287, January.
    2. Alastair Hall & Fernanda Peixe, 2001. "Data mining and the selection of instruments," Journal of Economic Methodology, Taylor & Francis Journals, vol. 7(2), pages 265-277.

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