Introduction

Measurement of parameters occurring in theoretical equation systems is one of the most important problems of econometrics. If our equations were exact in the observable economic variables involved, this problem would not be one of statistics, but a purely mathematical one of solving a certain system of ‘observational’ equations, having the parameters in question as unknowns. This might itself present complicated and interesting problems, such as the problem of whether or not there is a one-to-one correspondence between each system of values of the parameters and the corresponding set of all values of the variables satisfying the equation system. For example, if we have, simultaneously, a demand curve and a supply curve, the set of possible observations might be just one single intersection point, and knowing that only would not, in general, permit us to draw any inference regarding the slope of either curve.

Real statistical problems arise if the equations in question contain certain stochastical elements (‘unexplained residuals’), in addition to the variables that are given or directly observable. And some such element must, in fact, be present in any equation which shall be applicable to actual observations (unless the equation in question is a trivial identity). In other words, if we consider a set of related economic variables, it is, in general, not possible to express any one of the variables as an exact function of the other variables only.