Knowledge that Transforms

DR. JAMES TOBIN, in his interesting analLI ysis of the shape of the liquidity preference function and the effectiveness of alternative monetary-fiscal policies,' refers to my discussion of the same problems.2 I would like to develop more fully some statements contained in my earlier discussion and to comment on Dr. Tobin's views and findings. In a passage in which he criticizes my views on interest, Dr. Tobin argues in effect that, for logical reasons, it is necessary to assume that the liquidity preference function becomes infinitely elastic at sufficiently low rates of interest (or, in any event, before the rate becomes negative). For, at the zero rate there surely exists an unqualified preference for cash as against claims;3 and if we take into account the institutional costs of credit operations, then this floor is set not at the zero rate but at some very low positive rate. An economist who maintains that, in the range of changes in interest rates, the demand for idle balances may possess little elasticity to interest, should add that the liquidity function must become perfectly elastic at the institutional floor-level (i.e., above the zero rate, at a level determined by institutional costs) . I am in agreement with Dr. Tobin. In my book in which I suggested that liquidity functions may be rather inelastic in the range of changes in interest rates I made at least one explicit statement which is the precise equivalent of the foregoing (italicized) proposition (pp. I86-87). I should have made an explicit statement also in another passage, and I will do so in the forthcoming second edition of the book (on pp. I70-7I). However, throughout my analysis, I assumed the validity of this proposition. My statements concerning the small elasticity of liquidity functions are explicitly limited to the usual range of changes in interest rates. The diagrams in my book are drawn merely for positive interest rates, and I believe that it is made clear that the lower limit is not really meant to be the zero rate proper but some very low rate including the institutional costs in question. Negative rates are not included because it is maintained that negative rates are qualitatively different phenomena in that they express subsidies.4 No private individual or institution can be made to hold securities at negative rates, if money can be held free of cost.5 Acceptance of the italicized proposition in the preceding paragraph does not imply abandonment of views expressed in my book. But Dr. Tobin is right in insisting that the implications of this proposition should be made clear. The main point in this connection is that as long as the liquidity function is inelastic above the floor-level in question, the conclusion with respect to policy is that which was presented in my book.6 The conclusion with respect to pol-

IN ALMOST any science, quantitative problems arise for which approximation methods provide the most expedient solution. Refined methods often do not justify the labor they entail, either because the problem in hand does not require great precision, or because errors in the basic data limit the precision attainable. In exterior ballistics, for example, the gravitational attraction of the moon, which affects the motion of a projectile, is not taken into account in the calculation of firing tables because the effects of this attraction are small in comparison with the random errors resulting from unavoidable variations in the most carefully standardized ammunition and the most skillfully manufactured gun barrels. Some time ago in this REVIEW an approximation method for estimating the size distribution of incomes was discussed.' For most years little information is available on the distribution of incomes, but for I935-36 the National Resources Committee has compiled excellent data. Could the N.R.C. distribution be used as the basis for estimating the distribution for other years? If the aggregate income for some other year, say I946, can be determined (or predicted for some future year), and if the inequality of the distribution can be assumed to remain unchanged, the distribution for this other year can be estimated quite readily. This assumption of the same degree of inequality naturally suggests the Lorenz curve as a tool of analysis; however, the real key to the problem is the cumulative frequency curve. In a later article, graphical interpolation with the cumulative frequency curve was proposed as the most direct approach.2 It had the advantage of being simple, easy, and quick. Its accuracy, though not great, appeared adequate. Great precision was almost impossible, regardless of method, because the basic data and the underlying assumptions were approximations themselves. Moreover, most of the problems involving income distributions such as estimates of consumer expenditures or tax receipts do not require great precision. As an example, a problem originally proposed by Ames was discussed: to estimate an income distribution having the same inequality as the N.R.C. distribution, but an average income of $2000 instead of the $I502 for the N.R.C. distribution. cumulative frequency curve was drawn for families (including single persons) from the N.R.C. data -and also the corresponding curve for incomes received and the required distributions of both families and incomes received were read directly from these curves.3 In this example, the curves were drawn on semi-logarithmic paper, and the class intervals chosen were those of the N.R.C. distribution; however, it was stated that many other graphical devices would suffice, and it should have been obvious that any other set of class intervals could have been chosen. Furthermore, the fundamentals of the method are perfectly adaptable to numerical interpolation. In commenting upon this example, Eugene Clark and Leo Fishman might have criticized the arbitrary assumption of an unchanging inequality of income, or pointed out some of the fundamental weaknesses of the underlying data that make precise calculations difficult.4 Instead, they made a major issue out of a very minor point: namely, that the average income in any class interval depends upon the slope of the distribution curve, and that a change in the slope will inevitably affect the average income. 1 Edward Ames, A Method for Estimating the Size Distribution of a Given Aggregate Income, this REVIEW, XXIV (I942), Pp. I84-89. 2David Durand, A Simple Method for Estimating the Size Distribution of a Given Aggregate Income, this REVIEW, XXV ( 943), Pp. 227-30. 3 Ibid., Table I. 4 Eugene Clark and Leo Fishman, Appraisal of Methods for Estimating the Size Distribution of a Given Aggregate Income, this REVIEW, XXIX (I947), PP. 43-46.

S IN CE the end of the war, most of the widely publicized forecasts of the level and direction of change in national income (or gross national product) have been derived from models built around the consumption function. As these estimates resulted in a series of incorrect predictions, the literature has been filled with reconsiderations designed to show that the mistakes resulted from an incomplete statistical treatment of models which were in themselves essentially correct. This paper does not examine the validity of Keynesian-type models for longer analysis, but it does suggest that certain variables which have been suppressed in constructing simplified models cannot be ignored in short economic forecasting. 2 A common cause of difficulty in econometric forecasts has been the assumption that a consumption function, derived from data extending over a period of time, can be applied to successive short cases. Whether or not such a function may be correct for analysis, it will probably yield erroneous results when used to predict changes in income and consumption over two, three, or four quarterly periods in the future -because the consumption-income relation appears to shift from one short period to another. Since the needs in both business and governmental planning are primarily for short forecasts, quarter by quarter, an approximation of the varying, short schedule of consumption-income relationships would seem to be needed. The only concession by most writers and forecasters has been to make provision for a regular upward shift in the consumption function in small annual increments. Others, notably Modigliani, have gone further to distinguish conceptually between a varying short relation and the long run function customarily used.' Having made this logical distinction, even Modigliani has, however, ruled aside most of the short influences upon the relation, in the interest of statistical manageability. He has identified short movements with a cyclical pattern, measured by the percentage variation of disposable income (real, per capita,) from its previous highest level. Cyclical uniformity is thus implied by his assumption that the savings ratio will always be the same whenever disposable income is a given percentage below previous highest income. Differences attributable to the direction of cyclical income change are ignored. Nor is there allowance for the possibility that some significant short changes might not be uniquely related to a repetitive cyclical pattern. While the aggregative techniques used in forecasting have, implicitly or explicitly, disregarded short influences on the consumption-income relation, consumer budget studies have been focusing increased attention upon such influences. Changes in income distribution, by income-size groups and among occupational groups; the associated effect of changes in tax rates; recent changes in price levels and in relative prices; the distribution and aggregate volume of liquid assets; and the state of consumer expectations all these, and other influences, have been highlighted by the ' While this paper has gained considerably from the personal comments of many colleagues at the Federal Reserve Bank of New York, and those of other economists both within and outside the Federal Reserve System, the writer alone is responsible for the views expressed. The writer is especially grateful to Professor John H. Williams and Dr. P. A. Baran for major criticisms of earlier drafts. 2 It must be recognized from the outset that most of the emphasis upon the consumption function in economic literature, apart from actual forecasting, has been directed toward problems not discussed in this paper. 3 Franco Modigliani, Fluctuations in the Savings Ratio: A Problem in Economic Forecasting, a paper to be published by the National Bureau of Economic Research in a volume of Studies on Research in Income and Wealth. Both Modigliani and James S. Duesenberry have constructed equations which yield reasonably accurate forecasts of the current rate of savings.

ESPITE the time that has elapsed since the appearance of Professor Schultz's Agriculture in an Unstable Economy,1 and the critical comment that it has already evoked,2 there seem to be good reasons for re-examining that work now. The book is probably the most widely read study of the basic economic problems relating to American agriculture that has appeared since the war. It can be fairly confidently forecast that the continuing improvement of European agriculture will be accompanied by a renewed consideration of agricultural problems and that Schultz's book will be significant in the formulation of policies directed toward their solution la It seems justifiable, therefore, to review once more, and in a different way, certain aspects of Schultz's work. Early in the book Schultz makes the useful and clarifying distinction between long and short run agricultural problems. In his words: