Fitting systems of two or more simultaneous equations
Introduction. In 1943, Haavelmo introduced a drastically different method of statistical analysis for estimating relationships among economic time series.1 Although this method was designed to handle problems in the field of economics, similar problems may well exist in other disciplines such as biology and physiology.
A complete description of the computations involved in handling fairly large sets of simultaneous equations is beyond the scope of this book. Friedman and Foote2 have published a handbook which is recommended to those who are interested in applying this approach to any but the simplest cases. Here we will simply examine the logic and mathematics on which the method is based, as illustrated by a two-equation model.
In earlier chapters we discussed two possible interpretations of regression equations. The relation between protein content of wheat and the percentage of vitreous kernels was presented as purely descriptive or empirical --it did not express a "causal mechanism" by means of which an increase in the percentage of vitreous kernels would inevitably (except for random errors) lead to an increase in the protein content. In the auto-stopping example, however, we found strong logical grounds for expecting the speed of a car to affect the distance to stop, and for the relationship to follow a second-degree parabola. Although changes in automobile design____________________
-----, "The probability approach in econometrics", Econometrica, Vol. 12, Supplement, 118 pp. July, 1944.