ATT EMPTS by economists and statisticians to deal with the problem of the best method for mathematical formulation of the laws of economic behavior from statistical data go back at least as far as Ragnar earlier contributions.' According to Jacob Marschak, however, Frisch did not take full account of the random disturbances (shocks) in the economic relations, nor of the simultaneous character of these relations. 2 In addition to this, Frisch's hypotheses on random disturbances (errors) in variables were not specified in probability terms. 3 These shortcomings have been corrected, over the years, by Koopmans,4 Wald,' Mann,' and Haavelmo.7 Out of this body of contributions has grown the Cowles Commission's simultaneous-equation approach as a method for mathematical formulation of the laws of economic behavior from statistical data, and in I947 two papers were published making a practical application of this method to the marginal propensity to consume ' and to the demand for food.' simultaneous-equation approach draws attention, among other things, to what might be called the inconsistency bias inherent in the single-equation, least-squares method of estimating the parameters (constants) of a functional relationship between two (or more) variables-where the so-called independent variable (or variables) is not completely independent of the dependent variable.10 In this particular respect, the principal purpose of these articles has been to demonstrate that the reduced-form, simultaneous-equation method of estimating parameters is superior superior in the sense that it leads to estimates for the parameters of these functional relationships which are consistent with the estimates for the parameters of the other relationships embraced by the entire system of equations encompassed by the model. Apparently the inconsistency bias of the single-equation, least-squares method can lead to results widely divergent from those of the reduced-form, simultaneous-equation method. rLna possible significance of this to economicmodel building-whether for purposes of 1 Correlation and Scatter in Variables, Nordi7 Journal, Vol. I, I929, Pitfalls in the Construction of Demand and Supply Curves, Veroffentlichungen der Frankfurter Gesellschaft fur Konjunkturforschuing, Neue Folge, Heft 5, Leipzig, I933; and others. For a more complete list see Inference in Dynamic Economic Models, ed. Tjalling C. Koopmans (New York, I950), pp. 423-28. 2 Inference in Dynamic Economic Models, p. 4 of the Introduction by Marschak. 3Idem. 'Tjalling C. Koopmans, Linear Regression Analysis of Time Series (Haarlem, 1937). 5 Abraham Wald, The Fitting of Straight Lines If Both Variables Are Subject to Error, Annals of Mathematical Statistics, September, I940. 'H. B. Mann and A. Wald, On the Treatment of Linear Stochastic Difference Equations, Econometrica, ii (July-October 1943). 7Trygve Haavelmo, The Implications of a System of Simultaneous Equations, Econometrica, iI (January I943); The Probability Approach in Econometrics, Econometrica, Supplement, 12 (July I944). 'Trvgve Haavelmo, Methods of Measuring the Marginal Propensity to Consume, Journal of the American Association, XLII (March 1947). ' M. A. Girshick and Trygve Haavelmo, Statistical Analysis of the Demand for Food: Examples of Simultaneouls Estimation of Structural Equations, Economofetrica, I5 (April 1947). 10 From the statistician's viewpoint this is terribly imprecise phraseology, but it is not easy to phrase precisely without falling into the very terminology and modes of expression this paper seeks to avoid. Essentially -and this is much of the essence of this paperwhat is meant by the so-called independent variable not being completely independent of the dependent variable is that the dependent variable is neither functionally nor stochastically independent of the independent variable. Chart i, for example, illustrates the assumed stochastic behavior of consumption as a function of income: consumption is functionally dependent upon income, but stochastically independent of it in the sense that its random fluctuations about the functional relationship do not affect income. Chart iI, on the other hand, is illustrative of both functional and stochastic dependence: consumption is functionally dependent upon income, but stochastic dependence also exists in the sense that random fluctuations about the functional relationship do affect income. It is the fact that stochastic independence between consumption and income cannot logically be assumed, where both are assumed to be jointly determined by a third variable (as is the case in the model here under discussion), that leads to a biased estimate of the functional relationship between consumption and income using the single-equation, least-squares method.