For the regression equation C = A,B + e where A is a p x q stochastic matrix whose elements are independently distributed and contemporaneously correlated with the elements of 8, the lth moment of the least squares estimator of (3 exists if and only if l < p - q + 1. In particular, this implies that the lth moment of the k-class estimator of the coefficients of the G1 -1 non-normalizing endogenous variables of an equation with K1 included and K2 excluded exogenous variables in a simultaneous system with N observations exists if and only if 1 < M where

[In the context of regression models with stochastic explanatory variables, the exact sampling distribution of the omitted variable (OV) estimator is derive. We show that stochastic regressors present the problem of larger variance for the OV estimator than in the nonstochastic case, and derive conditions under which omission may be better under a minimum mean square error criterion. Since the errors-in-variables problem can be interpreted as a specification error problem with stochastic regressors, we also consider the issue of MSE dominance of the proxy-variable estimator over the OV estimator.]