Knowledge that Transforms

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.

THE possibility that there is a limit to the total tax burden which an economy can bear receives considerable public and professional attention from time to time, but few attempts have been made to examine this problem systematically. Presumably, this is a reflection of the fact that economists generally believe there is no single, immutable limit. However, Mr. Colin Clark has developed the bold generalization that there is a critical limit to taxation which is approximately the same for all nontotalitarian countries in time of peace. Although Mr. Clark first presented his thesis over six years ago in an article in the Economic Journal, it did not gain widespread public attention in the United States until late I950 when he summarized his views in a brief popular article published in Harper's.' Mr. Clark recently reaffirmed his views in a letter to the Joint Committee on the Economic Report.2 It is, therefore, timely to examine Mr. Clark's thesis and the statistical evidence which he presents to support it. Mr. Clark's thesis is that inflationary forces come into play when the tax burden (including federal, state, and local taxes) exceeds 25 per cent of the national income.3 This figure was derived from an analysis of data covering several countries for various periods. The limit is acknowledged to be approximate and should certainly be written 24-26 if not 23-27. 4 Beyond 27 per cent, there is a high degree of probability that inflation will materialize. The process may take as much as two or three years to work itself out. In his I945 article, Mr. Clark explained the limit primarily on the basis of the political argument that there is a transfer of allegiances by influential elements of the com munity toward inflation when taxation reaches the 25 per cent level. Since certain items of government expenditures, such as interest on the national debt and Civil Service salaries, are fixed in money terms, government expenditures are likely, during an inflation, to rise less than the general price level and national income Thus, the real burden of government expenditures may be reduced by inflation. As Mr. Clark puts it:

N international trade theory the concept of the elasticity of demand for a country's exports has had a long life. It is frequently advanced as one of the chief determinants of the effects of a currency revaluation, and recently has been the subject of some empirical studies. The justification of the first part of the present study, apart from its special interest for the country it deals with, Australia, lies in the fact that it attempts a more precise definition of the concept in measurable form than it has usually received, and that this definition leads to the study of the demand for exports one commodity at a time, instead of the demand for exports as a whole.' In the second part of the paper, similar methods are used to define and measure the elasticity of export demand with respect to income of the export market. The theoretical expressions obtained are applied to three principal Australian export commodities, using prewar data, to estimate in effect how their proceeds would have responded to a given change in the exchange rate, or in the income of the export market.

BY comparison with the voluminous literature on the theories of the firm and consumer, the amount of space devoted to the theory of the union is small indeed. This is not accidental; it results from the fact that the behavior of firms and consumers can be easily interpreted as maximizing while that of a union cannot. In recent years, however, the theory of the union has received increased attention. For example, John T. Dunlop in his now famous volume of essays, Wage Determiinationi Under Trade Unions,' has attempted to apply the maximization principle to labor union behavior, arguing that a union typically, although not universally, attempts to maximize the money income of its membership. The thesis that unions are maximizers has served as a spur to the enunciation of at least one antithesis: Ross's theory that union behavior is determined by considerations.' Ross's view of union behavior is not entirely new, but he has given the most lucid statement of this position of which I am aware. However, his arguments have not convinced Dunlop; in the preface to the new edition of Wage Determination he argues that the importance of the political determinants of wage rates has been exaggerated by Ross and others, and that political factors (although occasionally inmportant) are, on the whole, a relatively minor factor in wage determination.3 The issue is thus joined and a rather large-scale controversy is in the making;4 the present paper is offered as a contribution to this debate. Before embarking upon the discussion proper it nmight be well to define some of the crucial concepts used. When I speak of the political aspect of union behavior, or the political determinants of such behavior, I refer to those aspects of the behavior of individuals acting in behalf of a union ' which are best understood if it is assumed that they are motivated by a concern with the interests of the union qua organization,6 rather than with the interests of its members considered as individuals. It is not alleged that the interests of a unioil organization and those of its members are always or usually in conflict; indeed, the frequent confluence of these objectives has been a source of considerable theoretical difficulty. The individuals who act on behalf of a union -hereafter called union leaders -are alleged by Ross to be best understood as seeking primarily the well-being of the union organization rather than the welfare of its members. The well-being of the union organization, as I see it,7 involves the attitudes and behavior of three groups of people toward the union organization: (i) the members of the union,8 (2) the employers of the union members, and (3) the community at large, especially as its attitude is manifested in the behavior of the government toward the union. It is not seriously denied

TN their critical analysis of the evidence advanced by Colin Clark for his conclusion that taxation exceeding approximately 25 per cent of national income is inflationary, Messrs. Pechman and Mayer have successfully accomplished a much needed task. The concept of the 25 per cent limit was presented in both the Economic Journal and Harper's in an unqualified manner. It is little wonder that it has been incorporated into popular discussion on tax and budget policy as a new dogma. As is so often true, the assertion of an oversimplified proposition obscures the need for discriminating judgments in the formulation of alternative policies. The purpose of this note is to suggest some of the limitations and distinctions which should be recognized in applying the idea that taxation may be inflationary in policy determination. Three general propositions are stated below; on them there may be fairly general agreement. These are followed by brief comments on the current situation in the United States; on these there will inevitably be considerable disagreement. The latter opinions are expressed in a terse form, without full elaboration or listing of assumptions, to illustrate the extensive coverage, though not the thoroughness, of the analysis appropriate in the formulation of policy.