The problem of statistical estimation of the parameters of Leontief and other linear models is discussed. The discussion is based on the assumptions that in such interdependent models there is one variable which may be regarded more or less as exogenous and that the random errors may be effectively described by means of a normal probability distribution. It is found that in certain circumstances the least squares method of estimation when applied directly to these models gives rise to a large bias and underestimation of the random variation. Furthermore, the results differ the more from those obtained by maximum likelihood estimation the larger the degree of interdependence and the larger the relative importance of the residual variation in the models. The analysis assumes certain results of the theory of Leontief models and of simultaneous equations methods of estimation in particular and of the theory of statistical estimation and regression in general.