The Mean Squared Error of the Instrumental Variables Estimator When the Disturbance Has an Elliptical Distribution
将Nagar的有限样本均方误差近似推广到误差服从椭圆分布的情形，允许金融数据中常见的超额峰度，并用于分析工具变量选择对偏差和均方误差的影响。
This paper generalizes Nagar's (1959 Nagar , A. L. ( 1959 ). The bias and moment matrix of the general k-class estimators of the parameters in simultaneous equations . Econometrica 27 : 575 – 595 . [CSA] [Crossref], [Web of Science ®] , [Google Scholar]) 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 Knight , J. L. ( 1985 ). The moments of OLS and 2SLS when the disturbances are non-normal . J. Econometrics 27 : 39 – 60 . [CROSSREF] [CSA] [Crossref], [Web of Science ®] , [Google Scholar]) 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 Buse , A. ( 1992 ). The bias of instrumental variable estimators . Econometrica 60 : 173 – 180 . [CSA] [Crossref], [Web of Science ®] , [Google Scholar]) analysis by considering the impact of additional instruments on both bias and MSE. Second, we evaluate the properties of Andrews's (1999 Andrews , D. W. K. ( 1999 ). Consistent moment selection procedures for generalized method of moments estimation . Econometrica 67 : 543 – 564 . [CROSSREF] [CSA] [Crossref], [Web of Science ®] , [Google Scholar]) selection method in terms of the bias and MSE of the resulting IV estimator.