Econometrica: Jul, 1972, Volume 40, Issue 4

Finite-Sample Properties of the k-Class Estimators

https://doi.org/0012-9682(197207)40:4<653:FPOTKE>2.0.CO;2-5
p. 653-680

Takamitsu Sawa

This paper is concerned with the so-called k-class estimators of structural parameters in a simultaneous system. The structural equation being estimated is assumed, as is common in other small-sample investigations, to consist of two endogenous variables; and the number of the exogenous variables (included or excluded) as well as the number of equations in the system are arbitrary so long as the identifiability condition of the estimated equation is satisfied. Moreover, we assume that the system contains no lagged endogenous variables and disturbance terms of each period are independently distributed as multivariate normal. The exact finite-sample moments of the k-class estimators are evaluated for 0 @< k < 1. For k > 1 it is proved that the estimator does not possess even the first-order moment. The exact moment functions are expanded in terms of the inverse of the noncentrality (or concentration) parameter. This expansion sheds more light on the comparative study of alternative k-class estimators. Numerical calculations of the mean square error and the bias for some specific cases are also given for illustrative purposes.