Statistical Estimation of Simultaneous Economic Relations

T HE SAMPLING MODEL of the least squares method. Ever since statisticians began to measure supply and demand curves and other laws of economic behavior from statistical data, the problem of the best method of estimation has been the subject of investigation and discussion. Any statistical method of estimation derives its meaning and area of applicability from the concept of a well-defined sampling model. This is true even if, as in the estimation of economic relations from time series, the sampling is performed by the historical course of economic phenomena, outside the statistician's influence. Even though the available sample is unique, and exist only in our imagination, such commonly used terms as unbiased estimate, bias, standard error of estimate, have a meaning only in relation to such an imagined sampling process. In all studies of methods of estimating economic relations the classical least squares method has been either the starting point, or at least a basis of comparison. This mathematically simple and elegant method requires that from among the variables that enter into a certain relation one is selected as the variable, the remaining ones being called independent variables or variables. The sampling model then specifies that in repeated samples each of the variables would have assumed exactly the same series of values as it has attained in the available sample. The variable equals an unknown function of the determining variables (which remain the same in repeated samples) plus a disturbance which changes from one sample to another in the same way as would random drawings from a specified probability distribution. Difficulties in the choice of the Economists applying this method have again and again felt pangs of conscience when they had to make the choice of the dependent variable. This dilemma was somewhat less oppressive as long as the disturbances in the data which prevent the appearance of a perfect relation were taken to be the results