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.