An alternative approach to obtaining Nagar-type moment approximations in simultaneous equation models

This paper examines asymptotic expansions for estimation errors expressed explicitly as functions of underlying random variables. Taylor series expansions are obtained from which first and second moment approximations are derived. While the expansions are essentially equivalent to the traditional Nagar type, the terms are expressed in a form which enables moment approximations to be obtained in a particularly straightforward way once the partial derivatives have been found. The approach is illustrated by considering the k-class estimators in a static simultaneous equation model where the disturbances are non-spherical.