MSE dominance of least squares with errors-of-observation

On a criterion of minimum asymptotic coefficient bias, it has been shown recently [McCallum (1972), Wickens (1972)] that faced with a choice of using or discarding a (perhaps poor) proxy for an otherwise relevant independent variable which appears in a multiple regression model, one should always use the proxy. In this paper the analysis is expanded to consider variance in addition to bias in the criterion function. Our major finding is that although inclusion of the proxy is not a superior strategy unequivocally, it is recommended over a broad range of empirical situations.