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

Fernanda Peixe (), Alastair Hall and Kostas Kyriakoulis

Econometric Reviews, 2006, vol. 25, issue 1, 117-138

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.

Date: 2006
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DOI: 10.1080/07474930500545488

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