Despite the critical analysis of Pagan (1984) and several subsequent applied studies, empirical models characterized by expectations are often estimated with "generated regressor" proxies that are treated as ordinary nonstochastic regressors. This paper offers a Generalized Least Squares estimator designed to cope with the nonscalar disturbance matrix precipitated by generated regressors. The approach is designed as a natural extension of Pagan's analysis and the author demonstrates how it may be applied to multi-equation models. Experimentation with numerical examples reveals the potential severity of ignoring the problem. These results also suggest an easily calculated indicator of potential inference distortion in models that fail to account for "generated regressors."