A Comparison of Single and Simultaneous Equation Techniques

Excerpts from the paper Introduction: In my opinion, much needless confusion exists in the minds of economists and statisticians when they think about least squares versus simultaneous equation techniques. Some analysts believe that the method of least squares now is completely outmoded; others feel that simultaneous equation methods are so complex and computationally expensive that they should be avoided whenever possible. Each of these viewpoints is wrong. Simultaneous equation techniques are a useful addition to our kit of tools for use in problems that deal with regression analysis. When they are needed, they should be used, just as a hack saw is used to cut metal, whereas various woodsaws can be used to cut wood. In systems of equations, one, several, or perhaps all frequently can be fitted by least squares. Moreover, least squares equations are useful now. Just as they always have been, in showing normal or average relationships that exist between sets of variables. Many problems that relate to regression analysis, such as choice of variables, location of data, choice of functional forms, and the testing and interpretation of results, are almost identical regardless of whether the equations are to be fitted by least squares or by simultaneous equation techniques. Because of the confusion that exists, I propose to start with some extremely elementary concepts with which I am sure you are all familiar. We shall then proceed step by step in such a way as to show precisely when and why simultaneous equation techniques are needed. In later sections, I shall discuss some computational aspects of regression analysis and some considerations relating to the degree of complexity that may be desirable in formulating a system of economic relationships.