Near-Identifiability and the Variances of the Disturbance Terms - Fisher, Franklin M. (Econometrica, 1965)
THE OBSERVATION that large disparity in the variances of the disturbances from different structural equations in a simultaneous system can aid identification is as old as the discovery of the identification problem itself. Thus, in the classic example of E. J. Working [10], it is observed that whereas in the Marshallian cross neither the supply nor the demand curve is identified, this is not the case if one of the curves shifts about a great deal relative to the other. If such shifts do occur, then the relatively stable relationship is approximately traced out by the equilibrium points of intersection. This can, of course, be taken as an early statement of the fact that if one of the equations contains a shifting variable not in the other, the latter equation will be identified by the usual rank condition criterion;2 however, it is clear that even if there is no such explicit variable and all shifts come from the disturbance terms, something is still gained towards the identification of the relatively stable relationship. In other words, the example can be read as implying that information on the variances of the disturbance terms of a multiple equation system can be used for identification of the equation with the smallest disturbance variance.