Econometrica: May, 1971, Volume 39, Issue 3

The Use of Undersized Samples in the Estimation of Simultaneous Equation Systems

https://doi.org/0012-9682(197105)39:3<455:TUOUSI>2.0.CO;2-V
p. 455-459

James Holmes, P. A. V. B. Swamy

Using a general definition of a generalized inverse of a singular matrix we generalized the k class and three stage least squares procedures so that they can be applied when the sample size, say T, is smaller than the number of exogenous variables, say K, in a system of equations. These generalized k class and three stage least squares estimators, in usual cases, coincide with ordinary least squares and Zellner's [7] efficient estimators respectively as long as T @< K and coincide with the usual k class and three stage least squares estimators respectively as T exceeds K.