Knowledge that Transforms

PROFESSOR THEIL [5] recently gave the derivation of the best linear (B. L.) index number formulae for price and quantity. In an application of the formulae to Dutch import and export data, Kloek and DeWit [3] found that there is some slight, though persistent, bias to the effect that the index vectors yield larger current values than the individual data do. As this feature is related conceptually to the factor reversal test, they considered it desirable to devise a method which would control this bias on the average and worked out what may be called the best linear average unbiased (B. L. A. U.) index number. The aim of the present note is to indicate what relationship the B. L. and the B. L. A. U. indexes bear to the factorial indexes, that is, to those obtained through the factorial approach [1, 2, 4]. We conclude that the factorial indexes2 appear to compare well with the B. L. A. U. indexes. Incidentally, it is also pointed out that it might be possible to obtain a closer algebraic approximation to the B. L. index number formulae.

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This paper presents first a general theory of a capitalistic optimum and a model illustrating its essential features, and, secondly, the empirical justification of this model, and its principal applications. Under very general conditions it is possible to show that we cannot expect, from an indefinite increase of available real capital, an indefinite increase of real national income consumed per inhabitant, and that there is an optimum amount of capital for which the real income per inhabitant is maximum. The conditions under which this maximum is attained are given. The general model, which is presented, and, in particular, its exponential variety, appear quite remarkably confirmed by all presently available empirical data, with respect to both the hypotheses and the results. A very simple expression of consumed real income is given in terms of the rate of interest i and the rate of growth Q.

of the postwar U. S. economy in the Tinbergen-Klein [32, 15, and 16] tradition,2 and to apply the model to an analysis of certain types of monetary and fiscal policy. The model is crude and exploratory,3 and the analysis is in aggregate terms. Needless to say, the U. S. economy cannot be adequately described by such a simple model, and the findings are necessarily highly tentative. The model and the simulations presented here are the initial result of a limited attempt to gain some knowledge about certain aspects of the economy in quantitative terms and to throw some light on the problems involved. The lag in effect in monetary and fiscal policy (Baumol [3], Culbertson [7 and 8], and Friedman [12]) is a case in point. Such a problem cannot be settled by theoretical analysis. An indication of the answer to the question can only be obtained through a quantitative study, however crude the approach and the indication may be. The model is constructed on fifty quarterly observations from the third quarter of 1947 to the fourth quarter of 1959. The structural equations are presented in Appendix A, with the variables and the sources of data listed in Appendix B. Sections 1-3 describe the model. The investment and consumption functions are presented in Section 1. A sub-model on inventory and price movements is formulated in Section 2. Functions for monetary and certain other variables are presented in Section 3. Extrapolations for the magnitudes of the major components of gnp are computed for 1960 and the first quarter of 1961 from the respective individual equations in Sections 1 1 The author wishes to express appreciation to the Ford Foundation whose faculty research fellowship made this research possible, to the Social Science Research Center of Cornell University for grants to support the initial computations, and to his colleagues at the Cornell Computing Center for their untiring cooperation. He is indebted to Marc Nerlove and A. S. Goldberger for discussion at various stages of the preparation