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The Theory Of Investment Programming: A Suggested Econometric Model
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The Theory Of Investment Programming: A Suggested Econometric Model
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THE THEORY OF INVESTMENT PROGRAMMING: A SUGGESTED ECONOMETRIC MODEL by Ahmed Kooros A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Economics) August 1960 UNIVERSITY O F SO U T H E R N CALIFORNIA G RADUATE SC H O O L UNIVERSITY PARK LOS A N G E L E S 7, CALIFOR N IA T h is dissertation, w ritten by Ahmed. Koorpe ..................... under the direction of h Dissertation C o m m ittee, an d a p p r o v e d by all its m em b ers, has been presented to and accep ted by the G raduate School, in partial fulfillm ent of requirements fo r the degree of D O C T O R O F P H I L O S O P H Y Dean Date .August 1?60 DISSERTATION COMMITTEE ACKNOWLEDGMENT An attempt to explore the uncoverable territory of investment programming with a few ramshackle chapters may well be considered a superficial venture. If these chap ters made such a high pretension in their office, there would, I think, be no answer to the charge. Preoccupied with notions encumbering the roots of capital programming, I have omitted many areas of investment decision which many professional economists may advise to be more deserving of study and including in my jurisdiction; the selection of problems has not, however, been a random one; it was a matter of generality and coherence that led me to ignore them. In this process of groping, I have incurred a debt to Mr. S. Porter, Director of the Computer Laboratory at the University of Southern California, who helped me with data processing, and to Mr. Vito Natrella and Arthur Gianelos of the Securities and Exchange Commission in Washington D.C., who furnished me with information on investment purchases of the selected firms covered in the sample. X am grateful to Professors Arthur L. Grey, John E. Elliott, and E. V. Pullias whose interest and ii criticism were the most vehement incentive for me in this journey. To Professors Arthur L. Grey and John E. Elliott whose creative criticism has banished a number of con fusions which might otherwise have remained, my debt is unexpressable. There are parts of this dissertation which could not be materialized, had they not criticized, re organized, and rebuilt my thoughts. To me, their contribu tions have been, indeed, invaluable. Neither of them should, however, be blamed for any error which has remained. TABLE OF CONTENTS CHAPTER PAGE I. INTRODUCTION .................................. 1 On the problems of investment programming ............................... 1 The perspective of traditional and modem theories of investment ................... 8 Epistemology and economic theory .......... 15 II. A MATHEMATICAL MODEL OF THE THEORY OF INVESTMENT................................. 19 Introduction and notations ................. 19 2.1 Introduction..................... 19 2.2 Power and exponential functions . . . 22 2.3 Notations....................... 23 Keynes' Theory of Investment .............. 23 2.4 Interest rate and the demand for m o n e y ......................... . 23 2.5 Interest rate and investment programming..................... 27 2.6 Interest rate, investment programming, and the source of finance........ 29 2.7 Interest rate and maximizing total profit..................... 32 2.8 Summary............................ 36 iv V CHAPTER PAGE The mathematical explanation of a multivariate theory of investment ........ 38 2.9 Matrix and its variates............ 38 2.10 The m o d e l ........................... 41 2.11 Investment and its regression with six variates................... 44 III. SAMPLE, METHODS OF PROCEDURE, AND VARIATES . . 49 Sample..................................... 49 Sample coverage........................... 52 Statistical methods and procedures ........ 59 Correlation and regression .............. 59 Time-series and cross-section analysis . . 62 Selection of related variates ............ 64 Variates of the matrix..................... 69 IV. STATISTICAL FINDINGS......................... 82 Determinants of investment................. 82 Investment, sales, and profits.......... 82 Investment and profit variables.......... 86 Investment, depreciation expense, and other financial variables ............... 88 Investment, changes in sales, and capacity variables............................... 100 The impact of external financing on investment decisions ................... 116 vi CHAPTER PAGE Investment and depreciation reserve .... 118 V. PROFIT M O D E L ................................. 121 Introduction ................................. 121 Investment, profits, and w a g e s............ 121 A model of profit determination............ 124 VI. CONCLUDING NOTES ............................... 129 BIBLIOGRAPHY......................................... 136 APPENDIX............................................. 148 vii LIST OF TABLES TABLE PAGE I. Investment Covered in Three Samples for 1956 ................................... 54 II. Indices of Investment, Profit, and Sales for 1956, 1957, 1958 ....................... 83 III. Annual Averages of Partial Correlations Between Investment, Profit, and Sales for 1956, 1957, 1958 .......... 84 IV. Partial Correlation Between Profit and Investment, 1956, 1957, 1958 .............. 87 V. Relative Importance of Profit to Depreciation Expense for Financing Investment Outlays . . 89 VI. Sources of Corporate Funds, 1946-1959 .... 91 VII. Sources of Corporate Funds by Industry, Year Ended June 30, Averaged Annually 1947-1957, and 1957-1959 ................... 93 VIII. Partial Correlations Between Investment and Depreciation Expense, 1956, 1957, 1958 . . . 99 IX. Partial Correlations Between Investment and Capacity, 1956, 1957, 1958 ................ 102 X. Percentage Deviation of Actual From Planned Investment of Manufacturing Firms According to Size Classification, 1955 .............. 104 viii TABLE PAGE XI. Index of Actual and Anticipated Plant and Equipment Expenditures of All Industries for 1955-1960 108 XII. Distribution of Manufacturing Firms According to Reasons for Changes from Investment Anticipation by Asset Size, 1955 ............ 110 XIII. Comparison of Sales '■nd Investment Expenditures of Manufacturing Industries . . 114 XIV. Average Partial and Simple Correlation Between Investment and Age Variable .... 115 CHAPTER I INTRODUCTION I. ON THE PROBLEMS OF INVESTMENT PROGRAMMING Under a private enterprise economy, every decision by an entrepreneur with regard to production, in one sense of the word, is an act of investment. But when one speaks of acts of investment as income-generating and capacity- creating process, one speaks of investment in fixed capital, of construction of plant and equipment. In the theory of profit-expectation this interpretation is of major importance by reason of the durability of the results. On the balance of this consideration investment is to be defined as addition to the existing stock of capital. Thus, if investment is the dependent variable, the question to be posed is: What should be the independent variable or variables? According to Ricardian economics a falling or rising rate of profit was the factor which set the pace. On the other hand, recent theories of investment have, by and large, assumed that investment is elastic to the rate of interest rather than the rate of profit. The practical implication of this emphasis, presumably, 1 has been that the investment can be influenced by an appropriate monetary policy which as investment proceeds permits the rate of interest to fall Pari Passu. This stress on the importance of the rate of inter est has raised a whole intellectual controversy. Numerous studies have been done which show that investment is interest-elastic; on the other hand, there are studies which have made investment a single monotonic function of the accelerator. Great importance has been attached, over the last quarter-century, to the aggregate level of invest ment as the determinant of the level of total output. Importance also has been attached to investment decisions as one of the elements in determining the valuation of that output (the degree of price stability). Finally, more recently an almost "classical” concern over the level of investment as determining economic capacity has moved into the forefront of economic concern. The great importance, in several different contexts, attaching to investment decisions has led to comparatively little study and incon clusive results concerning actual determinants of invest ment itself. This dissertation, thus, has drawn much inspiration from prior works on the subject of investment decision. The basic purpose and intention of this dissertation is to examine the factors that determine decisions concerning investment. 3 To approach the problem of Investment decisions and to put forward its determinants, a mathematical model is designed whose implications are tested statistically. The mathematical model, the content of the second chapter, attempts to contain the essential features of investment decision. The model has two parts. The first part en deavors to explain the necessary and sufficient conditions under which investment becomes a continuous function of the rate of interest, and also the position where investment is at its "optimum" level. The second part of the second chapter undertakes to suggest a general theory of invest ment which is in the field of matrix analysis of higher calculus. Here, in passing a remark is in order. It does not appear to be a disenchanting rule in a subject like eco nomics which is wedded with quantifiable, complex, and practical issues, to stand on solid ground, even if this is procured with the help of some logical elegance and impres sive precision of mathematical intuition and abstraction. Mention should be made, however, that in the course of abstract formulation the exclusion of certain variates (which are present in any actual situation and contain the common property), from exploration makes the primitive no more than an imperfect approximation to reality. Only can the set of implications of mathematical models, whose correctness or otherwise are determined by experience, by cognatlve knowledge of how actual situations behave, yield valid results. Contrariwise, there Is the spurious danger of hypostatlzlng one’s notions and abstractions; all too frequently, the conclusions which may ensue this procedure have little to offer. Being mindful of these limitations, the mathematical model can claim to have embraced all possible determining factors of investment programming. Statistical findings of the fourth chapter are used to test the foundation of the argument put forward in the second part of the second chap ter. The statistical model designed in the third chapter and also in Chapter IV is in the field of multivariate analysis and contains a matrix of (n) observations for (p) years. It is, briefly, a cross-section rather than time series analysis. The sample constitutes the content of the Appendix. The sample has 538 manufacturing firms of dif ferent sizes. The sources of information for these firms were the reports that they had submitted to the Securities and Exchange Commission and The Moody’s Industrial Manual. The reports that firms submit annually is called Form 10K 1There are, of course, different ways to measure the "size" of a firm. Here, the size-criterion is measured by gross fixed assets. For different ways of measuring the size of firm, see B. C. Churchill, "Size of Business Firms," Survey of Current Business. XXXIX (September, 1959), 14-20. 5 which contains among other items a supplement with a sepa rate reporting on capital investment purchasing of the previous year. All needed values were extracted from the Form 10K and The Moody's Industrial Manual. The size of the sample was enlarged by multiplying the original one by three for the years 1956, 1957, 1958. Then, in the final analysis, the matrix had 1,614 observations of homogeneous clusters with equal error variances. The selection of specified years was for their crucial importance: boom of 1956, recession of 1957, and recovery of 1958 could, theoretically, have shown different tendencies in invest ment programming. The third chapter of this dissertation is an attempt to explain the independent variables of capital budgeting, and the problems and limitations of exploring such a prob lem. The fourth chapter describes the degree of influence of each variable on capital programming. Briefly, sta tistical findings of Chapter IV have shown the sensitivity of investment to six independent variables out of a total of twenty-two selected for study on a priori basis. The regression of the six was found and determined through conventional Least Square (LS) method. The Least- Information-Single-Equation (LISE) method was used occa sionally when the degrees of freedom were less than 30. These six independent variables are: (1) depreci ation reserve considered as age-variable; (2) depreciation expense; (3) net profit or net income to surplus, which together with depreciation expense are known as liquidity variable; (4) net sales variable which is an approximate measure of output; (5) changes in sales; and finally (6) capacity variable for which only a relative value was calculated. Since the economy in 1956 was at its full employment approximately it was assumed that the economy was at full capacity approximately too. Then, the ratio of gross fixed assets to sales could, by and large, measure capacity needed. Capacity variable for each year was esti mated by multiplying that year's net sales by 1956 capacity ratio. Finally, for the sake of homogeneity, all these variates and investment were deflated at gross fixed assets. In this statistical inquiry, regression is to be meant a causal relationship between dependent and independ ent variables, while correlation does not denote anything of that matter. It is obvious from the findings that the accelerator was operative in that period. On the other hand, investment was not dependent on the rate of interest. It was found out that the relationship between investment and interest rate was related to the size of the firms. Already Professors Grey and Brockie have concluded that their survey "disclosed that, on balance, the small firm shows more concern with the rate of interest than the 7 o large [one].' By and large, it appears that Investment behavior has undergone a change; that Is, In practice other considerations, besides profit-maximization, have heavily and vehemently preoccupied managers of the firms. Chap ter IV is to show the pattern of investment behavior to these new considerations. All in all, it is hoped that this reexamination of the theory of investment is a contribution to economic analysis. As a contribution this dissertation, at its inception, seeks to play no revolutionary role. As a systematizer of the theory, it hopes to make the knowledge on the pattern of investment behavior cohesive and con sistent. The governing variates of investment are the con crete forms which practice assumes in a given situation of demand and technique. Included among the investment vari ates are other factors besides profit. This explanation economics has taken for granted and did not penetrate, was almost ready to explain and include among its variates, but did not achieve the explanation. Today, there has been an increasing tendency toward this recognition, or at least to retain them as substantial elements of investment pro gramming. ^A. L. Grey and M. D. Brockie, "The Rate of Inter est, Marginal Efficiency of Capital, and Investment Pro- ? ramming— A Rejoinder,” The Economic Journal. LXIX (June, 959), 340. 8 II. THE PERSPECTIVE OF THE TRADITIONAL AND MODERN THEORIES OF INVESTMENT As one might be led to expect, it is not astonishing that classical economists should have stirred their age and made an influence which was dynamic both to conventional notions and conditioned practices. The history of economic analysis has viewed the arrival of the classical economics as revolutionary because it explicitly gave birth to the concept of economic change and growth, which was the crux of the contemporary problems. Then, it is in the theory of growth and economic change that the direct evidence of abstract concepts of classical theory and classical con tribution is to be found. With classical theory, what is instructive is that their theory, which implicitly bears the stamp of the mathematical method, has been and con tinues to be the foundation for further exploration in the field of economic change and growth. It is, no doubt, a pretentious claim to herald the attachment of modem theories of growth to classical fountainhead. Equally, it would hardly be incorrect to say that modem theory of growth contains no gene from classical parents. As to the form and configuration of the classical reasoning, it was ruled by the premises of the Euclidean Geometry, a system of convergent series of functional relations In whose kernel resided the theory of value. In analyzing and studying society, classical economists were convinced that certain conditions had been necessary for economic change. The purpose that the classical theory of growth was intended to imply was that saving and capital accumulation is the most needed and dynamic factor. And to Adam Smith one fundamental condition for accumulation was that "the lowest ordinary rate of profit must always be something more than what is sufficient to compensate the occasional losses to which every employment of stock is a » exposed." And this profit must form an "insurance fund" intended for reproduction and expansion of the division of labor. Therefore, the scope of Smith's inquiry was the anatomy of commodity which comprises profit in its creation as the result of the process of production. In this pro cess money was considered as simply a medium of exchange. Having been actuated by the same issue, Ricardo commenced his inquiry with the determination of the magni tude of the value of commodity by labor time. The greater or smaller the labor time used to produce a commodity, the greater or smaller the value of it. Thus, he sponsored the Law of Markets and held the erroneous theory of money. ^Adam Smith, An Inquiry Into the Nature and Causes of the Wealth of Nations (New York: The Modem Library. 1937), p. 96. ^Karl Marx, Capital, A Critique of Political Economy (Chicago: Charles H. Kerr, 1902), II, 420. 10 The aim that Ricardo Intended to imply is fully represented in the following statement: Demand is only limited by production. No man pro duces, but with a view to consume or sell, and he never sells, but with an intention to purchase some other commodity, which may be useful to him, or which may contribute to future production. By production, then, he necessarily becomes either the consumer of his own goods, or the purchaser and consumer of the goods of some other person. . . . Productions are always bought by productions, or by services; money is only the medium by which the exchange is effected.* Thus, inevitably, Ricardo*s theory Petitio principi assumed a rising rate of profit as a dynamic factor. Hence, there appeared to him no reason why additional capital, invested in additional supplies of productive resources, should not continue to extract at least the same rate of profit as before. Notwithstanding, he visualized that a falling rate of profit, as capital accumulation proceeds, can only be explained by rising price of the workers' subsistence, which raises the price of labor power, and tends to lower the rate of profit. And this latter cycle is caused, he said, by the operation of the law of diminishing returns. In a letter to Malthus he wrote, I contend that there are no causes which will for any length of time make capital less in demand, however abundant it may become, but a comparatively high price David Ricardo, On the Principles of Political Economy and Taxation. Vol. I of The Works and Correspond ence or David Ricardo, ed. by P. Sraffa and M. H. Doob (Cambridge: Harvard University Press, 1951-1955), pp. 290-91. 11 of food and labor— that profits do not necessarily fall with the Increase of the quantity of capital, because the demand for capital Is Infinite, and Is governed by the same law as population Itself. They are both checked by the rise In the price of food and the consequent rise In the value of labor. If there were no such rise, what could prevent population and capital from Increasing without limit?” When Malthus said that rapid capital accumulation must lead to over-production, Ricardo suggested that in the specific circumstances described by Malthus (lowered profit and insufficient demand), ’ ’the specific want would be for population."7 It was this topic of saving and the tendency for the rate of profit to fall which provided the ground for tSte- a-tSte Malthus disagreement. Malthus declared that, Parsimony, or the conversion of revenue into capital, may take place without any diminution of con sumption if the revenue first increases. . . . [But] no nation can possibly grow rich by the accumulation; because such accumulation being greatly beyond what is wanted, in order to supply the effective demand for produce, a part of it would very soon lose both its use and its value, and cease to possess the character of wealth.8 This statement was impinged upon the assumption that mar ginal propensity is to exceed average propensity to save. 6The Works and Correspondence of David Ricardo, VI, 301. 7Ibid.. II, 169. Q Thomas R. Malthus, Principles of Political Economy (2nd ed.; London: W. Pickering, l83{>), pp. 326-27. 12 So Malthus' contention was that profit might fall not from a rise in wages, but from a fall in the prices of the com modities due to the emergence of a deflationary gap— a gap between the demand for saving and the supply of savings-- and this was likely to occur if saving proceeds at a rapid rate. With the triumph of the Ricardian tradition in Victorian England this doctrine of Malthus for long fell into obscurity, save as illustration of the cardinal fal lacy that luxury created employment and that it was better to spend than to save. The argument of Malthus has, in recent years, had revival; much of this has been due to the advocacy of John M. Keynes who expounded the theory in a novel manner. ^ In the classical theory, the crux of the problem was the validity of the Law of Markets. This debate touched upon the most important considerations affecting economic expansion. The classical economists turned to inquire the relevance of the independent variables which influenced ^John M. Keynes, "The Commemorations of T. R. Malthus; Three Allocutions,” The Economic Journal, XLV (June, 1935), 230-34. Eulogizing Malthus, Keynes said: "I claim for Malthus a profound economic intuition and an unusual combination of keeping an open mind to the shifting picture of experience and of constantly applying to its interpretation the principles of formal thought. I believe a century hence, here, in his Alma Mater, we shall com memorate him with undiminished regard" (p. 234). 13 economic change. To the majority of economists of the late eighteenth and early nineteenth centuries, saving was con sidered as the cause of the increase of wealth. In a letter to Malthus, Ricardo wrote, I deny that the wants of the consumers generally are diminished by parsimony--they are transferred with the power to consume to another set of consumers. . . . By increase of capital from revenue is meant an in crease of consumption by productive labourers instead of by unproductive.10 In a famous passage Adam Smith had said, "What is annually saved is as regularly consumed as what is annually spent, and nearly in the same time too; but it is consumed by a different set of people. Keynes had pronounced that many of these classical propositions rest on the assumption of full employment as a necessary condition, and hence can have no application to conditions of changing output or departures from full 1 9 employment equilibrium. ^ It seems clear that the classi cal economists assumed an infinitely elastic supply of all resources, the grand precept of full employment, held to be essential established capital accumulation or saving as an independent variable for economic change. While the mold ^Ricardo, op . cit., II, 164, 174. ^Smith, op. cit., p. 320. John M. Keynes, The General Theory of Employment, Interest, and Money (New York: Harcourt, 1936), pp. 3, 191. 14 In which the Keynes theory was cast was such as to focus attention upon investment, the theory implied the corollary that the road to full employment lay in investment. Investment was regarded as to greater fluctuations than any other variable; the variations of investment eventuates events in the business cycle; and in the course of prog ress, the vagaries of investment are regarded as being responsible for "the chronic stagnation" of a mature economy. Keynes said: The theory can be summed up by saying that given the psychology of the public, the level of output and employment as a whole depends on the amount of invest ment. 1 put it in this way, not because this is the only factor on which aggregate output depends, but because it is usual in a complex system to regard as the Causa Causans that factor which is most prone to sudden and wide fluctuations. More comprehensively, aggregate output depends on the propensity to hoard, on the policy of the monetary authority as it affects the quantity of money, on the state of confidence concern ing the prospective yield of capital-assets, or the propensity to spend and on the social factors which influence the level of the money-wage. But of these several factors it is those which determine the rate of investment which are most unreliable, since it is they which are influenced by our views of the future about which we know so little. Inadequacy of knowledge concerning those several "un reliable factors" which determine the rate of investment, under a private enterprise system, has always been evident. John M. Keynes, "The General Theory," The New Economics: Kevnes Influence on Theory and Public Policy. Seymour Harris, ed. (New York: Alfred A. Knopf, 1950), pp. 191-92. 15 Prior to a pioneering work in 1956,^ the independent variables of an investment planning were very imperfectly understood. Recently a writer complained, "Although we know fairly well what economic variables are apt to be of potential significance with respect to the investment decision of an individual firm, we are unable to evaluate their relative influence.it seems clear that this general dissatisfaction has been due to the lack of a generalized description of how things actually behave in the real world; any endeavor which may help clear the subject may not be altogether otiose. III. EPISTEMOLOGY AND ECONOMIC THEORY A model or theory is usually constructed for a specific problem. By problem is not to be meant a specific political question, related to public policy, but an ex ploration of some structural relationship such as: What will be the level of investment I, when the relevant variables X^, X2, X3 . . . Xn, are in such and such form? ^John Meyer and Edwin Ruh, "Acceleration and Related Theories of Investment: An Empirical Inquiry," The Review of Economics and Statistics. XXXVII (August, 1955), 2l7-3o. And The Investment Decision. An Empirical Study (Cambridge: Harvard University Press, 1959), p. "£84. ^F. E. Norton, "The Accelerator and the Overinvest ment and Underconsumption Models," The Economic Journal. LXVI (March, 1956), 65. 16 In formulating a theory for explaining such problem, there are a few roads along which one can proceed. In the first place, a theory may be based, as is done in this disserta tion, on the intuitive procedure of combining the proper ties common to a heterogeneous problem and building a model by abstraction and deduction. Sometimes, this method of progressive refinement of deduction has led to confusing sophisms; on the other hand, very often the results are enlightening because the theory arrived at accordingly bears fruitful implications which are deduced from them. This author adheres to this methodological position. With all its limitations, this method is not only valid but is an essential element in any generalization. In a sphere where generalization can take a quantitative form, the convincing ground of the method can usually yield useful and workable implications. As usual, the propositions which are products of this mode of abstraction have a general meaning. And this is the question of in ternal adequacy of a theory and the uses to which a theory should be put. The question of internal adequacy of a general theory means the conditions which it must fulfill if it is to be capable of sustaining corollaries of a certain type of generality. A general theory is expected to be capable of sustaining a certain type, but not every type, of 17 forecast, and achieving the highest degree of generality that is consistent with the complexity of the phenomena which one seeks to explore. The more general the problem in hand, the greater the number of surrounding forces which one is justified in assuming to be unimportant and con stant. ^ This is not to say that a general theory is to be reduced to a taxonomy. But such generalizations may for long remain applicable only to a limited type of situation and encompassing all important forces and be capable of sustaining forecasts of that more general type which relates simultaneously to the major events in the system as a whole. Precision is a most desirable, even an essen tial, ingredient of the process of thought. In conclusion, it is held that economic theory rests on postulates which are in fact elementary generalizations about any and every economic activity, and its corollaries represent ”inevitable implications,"^ which hold valid ^F. Machlup in his "The Problem of Verification in Economics," The Southern Economic Journal. XXII (July, 1955), 2-3, takes the position that a general theory is an analytical equipment which is used for investigating "par ticular" problems. See also, W. J. Baumol, Business Behavior. Value and Growth (New York: Macmillan Co., 1959), p. 3. Baumol feels that "a useful model will usually be appropriate only in particular circumstances and, even then, only for the analysis of particular problems. . . . For example, mathematical programming has been extremely successful in supplying tools which can be employed in the analysis of many concrete problems." ■^L. Robbins, Essay on the Nature and Significance of Economic Science (2nd ed.; London: Macmillan Co., 1935), pp. 80, lb5. 18 for any and every type of economic activity. So a model is set, in the light of a specific concrete problem, to explain the structural relationships; then, from this model a set of implications is deduced. The only way to test the validity of a behaviorial model, as defined above, is by comparing its implications and predictions with 1 o empirical evidence. ° The method used by this writer in the following pages is a procedure which sets a theory whose implications are tested empirically. It is a process of progressive elimination and refinement. For instance in Chapter III a large number of variables were taken into account, then gradually they were eliminated until there remained six critical variables which are called investment variables. This is related to the question of internal consistency of a theory which is enmeshed with the degree of abstraction which is appropriate for a theory. This is a practical question, depending on the nature and the character of the problem to which the theory is intended to relate. Friedman, Essays in Positive Economics (Chicago: University of Chicago Press, 1953), pp.8-9, 40 CHAPTER II A MATHEMATICAL MODEL OF THE THEORY OF INVESTMENT I. INTRODUCTION AND NOTATIONS 2.1 Introduction Investment decision is enshrined with a number of complex problems. These problems are of two kinds. They are those quantitative factors which might be called economic ones, such as interest rate, profit (its magnitude and rate), liquidity constraints, sales expectations, capacity utilization, and others. On the other hand, there are qualitative factors such as uncertainty,^ technology, population, etc. The former set of variables have been traditionally named static factors, while the latter ones have been conventionally called dynamic factors.^ ^Recently Professors Franco Modigliani and Martin H. Miller in their "The Cost of Capital Corporation Finance and the Theory of Investment," The American Economic Review. XLVIII (June, 1958), 261-97, have ventured to sug gest that by introducing a normal probability distribution to the model, the element of uncertainty is resolved. Let the Science of Statistics and the history of economic analysis judge the validity of this assertion. 2Roy Harrod, Essays in Dynamic Economics (London: Macmillan Co., 1956), pp. 11-16. 19 A mathematical model of investment which means a set of relations among a set of variables, can be con** strueted in different ways so far as its variables are concerned. One not uncommon and innocuous way is to divide its variables into exogenous and endogenous ones. The exogenous variables are usually called "non-economic" ones, whose values are determined outside the model. Like a parameter, an exogenous variable is capable to take on any set of values. On the other hand, the endogenous variables are interdependent whose values are determined by the model. An exogenous variable is not measurable while an O endogenous variable is quantitative. Since the exogenous variables are not quantitative and are incapable of measur ing, then, the precise degree of their influence and reper cussion in a condition can not be tested, and thereby verified or disproved; therefore any statement pertaining to the working of these variables is an unsupported con jecture and mere assertion. It seems clear, from the nature of its subject- matter and the type and the nature of statement which it is required to make, a consistent, mathematical model must be quantitative in form. In other words, the implications -i E. F. Beach, Economic Models: An Exposition (New York: John Wiley and Sons, 1957), pp. 29-30. 21 of a hypothesis constructed for a set of structural rela tionships are to be translatable into actual dimensions, but it is not always observed by those who construct prin ciples on purely formal bases, or those who unduly criti cize model-builders. The purpose of this chapter is to put forward a testable thesis. The first part of this chapter deals with Keynes' theory of investment, which appears to this writer to be the only consistent and cohesive theory which sought to explain the determining variables of investment. The crux of the matter is a precise interpretation of invest ment variables— factors which determine the behavior of investment. In pure economics, assuming the truth of "maximum-value-criterion" and perfect certainty concerning future stream of income, economists have postulated a condition which regulates investment decision. This con dition has been explained in terms of interest rates. Accordingly, investment is regarded as a quantity the size of which is determined by the interest rate. Given the assumptions on which it is based, this explanation appears to this writer to be satisfactory enough. Submitted to empirical verification, however, it is seriously incomplete since ’ ’profit, or maximum-value-criterion” has been ques tioned. Present day economic theory has, by and large, adduced no explanation for the emergence of other 22 independent variables besides interest rate for explaining investment planning. The second part of this chapter is an attempt to put forward an explanation for the important forces behind the demand for durable assets; it is claimed to be a "general" model in this sense of the word used in this dissertation. The essence of the hypothesis is based upon the emergence of other goals which have occupied a prominent position in capital planning. 2.2 Power and Exponential Functions It is desirable to make a distinction between power and exponential functions. A function with a constant index and a variable base is called a power function, which is a function of the base; i.e., Y = Xa is a power function where Y = f (X). On the other hand, a function with a variable index and a fixed base is called an exponential function, which is a function of index; i.e., Y = ex is an exponential function vrtiere Y = f (x). In brief, the value of the exponential depends entirely on the index of the function. Later on it will be seen that the application of the exponential function to the theory of investment is of crucial importance. 23 2.3 Notations These notations are used in the following discus sion: i - interest rate per time period, t - a number of time periods. C - a present sum of money, or the present value of the cost of an investment. Y - a sum of money (t) interest periods from the present date that is equivalent to C with interest (i). I - Investment in the sense defined in the first chapter. q - interest payments per time period, e - natural base which is equal to 2.71828. P - total profit, r - rate of profit. II. KEYNES1 THEORY OF INVESTMENT 2.4 Interest Rate and the Demand for Money If (C) is invested at interest rate (i), the inter est for the first year is iC and the total amount at the end of the first year is Y = C + iC = C (1 + i)1 (4.1) and at the end of the second year 24 Y (t) = C (1 + i) t = 1, 2 (4.2) and finally at the end of the t£k year it would be: Y (t) = C (1 + i)c t = 1, 2, 3, . . . n. (4.3) If interest is paid (q) times a year, then: Y (t) = C (1 + i)tq q (4.4) or, Y (t) = C {(1 + i) it (4.5) if q I = m then, Y (t) = C J( 1 + m it on the other hand: (4.6) Lim (1 + l)m = e m (4.7) then, Y (t) = Ce it (4.8) or, c = T «=> 25 (4.9) or C (t) = Y (t) e "it; (4.10) Since Y and e are fixed, then C = f (i) where di dC (4.11) C is called the discounted value, the present value, or the capital value of $Y available t years from now. C is dis counted with i at t; the higher is the rate of interest, the smaller the discounted value. The equation (4.10) explains the relationship between the expected receipt and its discounted value. That is, if a man would expect $Y at the end of (t) periods, and the interest rate is (i), (constant), then the amount to be loaned out (C) is found from the equation (4.10). It was in this sense that Keynes defined the rate of interest: Nothing more than the inverse proportion between a sum of money and what can be obtained for parting with control over the money in exchange for a debt for a stated period of time. . . . The rate of interest . . . is the "price” which equilibrates the desire to hold wealth in the form of cash with the available quantity of cash;--which implies that if the rate of interest were lower, i.e., if the reward for parting with cash were diminished, the aggregate amount of cash which the public would wish to hold would exceed the available supply, and that if the rate of interest 26 were raised, there would be a surplus of cash which no one would be willing to hold.' Assuming perfect certainty, in this way, an income "stream" of an investment can be calculated. If a man would expect to earn Y in the first year, and Y , . . . , 1 + i (1 + i)2 Y for the second and (t) years, he has to (i + D 1 invest: C (t) = Y + --------+ ___y _ , _. Y (1 + i) (1 + i) (i + i)3 (1 + i)t (4.11) or, C (t) = J Ye‘ifc. dt . (t = 1, 2, 3, . . . , n.) or, (4.12) C (t) = Y dt . (4.13) C (t) = Y 1 e-it (4.14) C (t) = Y ( - 1 e"it:) - Y ( - _1_). (4.15) i i C (t) = _Y_ ( 1 - e"it). (t - 1, 2, 3, . . . , n.) (4.16) Interest ^John M. Keynes, The General Theory of Employment, t, and Money (New York: Hare our t, W'J6), p. 167. 27 It is conceivable that with different interest rates, the capital value will be different. 2.5 Interest Rate and Investment Programming In (2.4) the importance of the rate of interest, as far as borrowing and loaning are concerned, was explained and emphasized. It is through the interest rate that a sum of money is allocated for borrowing and loaning, if the expected stream of income is worth taking. This stress gives practical reason for considering the time value of money in the economy. If an entrepreneur wishes to maximize his present value, according to "maximum-value - criterion," he has to arrange his resources to achieve that goal. If $X is obtained the first year, and $Z next year, and the relation between X and Z is given by: F (X, Z) = 0, and Z = f (X), then: Y = X + Z 1 + i (5.1) or Y = X f (X) 1 + i (5.2) And this would be at its maximum value when: 0 and d.X 28 or 0 (5.3) or (5.4) or i (5.5) Then the necessary condition for "maxiraum-value-criterion" is Keynes* marginal efficiency of capital. Keynes said: The marginal efficiency of capital as being equal to that rate of discount which would make the present value of the series of annuities given by the returns expected from the capital-asset during its life just equal to its supply price. . . . Now it is obvious that the actual rate of current investment will be pushed to the point where there is no longer any class of capital-asset of which the marginal efficiency exceeds the current rate of interest. In other words, the rate of investment will be pushed to the point on the investment demand-schedule where the marginal efficiency of capital in general is equal to the rate of interest.5 Then, is the marginal efficiency of capital if $Y is borrowed to purchase a new or used piece of physical capitalo is that (i) is to be equal to This expression The sufficient condition 5lbid., pp. 135-37. 29 the schedule of the marginal efficiency of capital is con cave from below. 2.6 Interest Rate. Investment Programming, and the Source of Finance Now, it is suggested that if, and only if, the "maxiraum-value-criterion,"--that is, ’ ’with a given tech nical knowledge”— is the objective, then the interest rate is the determining variate; and as Keynes said, it is the element that "set the pace."*’ In the field of borrowing and loaning, interest exists as a business fact; if a man borrows money he has to pay interest for it; and equally if a man has a sum of money, he feels that he can, at least, get the going interest rate for it. Thus, when there is a choice to be made between alternatives— whether to loan out or to purchase new or used capital goods— which involve different money receipts and disbursements at different times, it is necessary and sufficient to consider interest. Although businessmen sometimes reason differently about the situation in which money is actually borrowed to finance the purchase of new and used capital goods, and the situation in which money is available without borrowing, fi "The General Theory," The New Economics. Keynes* Influence on Theory and Public Policy. Seymour E. Harris, ed. (New York: Alfred A. Knopf, 1950), p. 190. 30 it should not be implied that there is a slight difference in the importance of the interest rate. In the latter case, it is the opportunity cost that is taken into con sideration by the businessman either intentionally or unintentionally. The interest rate is the determining variate as long as the businessman's goal is "maximum- value-criterion." The reason that business capital plan ning is not any more a single exponential function of the rate of interest is that businessmen are very much pre occupied with other goals such as "market position," "managerial control," and others, besides their "maximum- value-criterion." It is only under such condition that interest-sensitivity loses its determining position. Grey and Brockie's survey has disclosed that, . . . 59 per cent of the respondent firms indicated that they do not consider the market rate of interest in calculating the estimated returns from a proposed investment in plant or equipment to be financed with internally supplied funds. . . . Information also was obtained on the circumstances under which the respond ents would consider new types of investment. Two companies, including one which has a large business in government contracts and, therefore, favors diver sification at a low rate of return as insurance against the vicissitudes of its main operation, indicated they would not expect a new product to earn as high a return as an established product. Other firms, however, wanted returns of 50 and 100 per cent greater on a new product, and some companies were objectively not interested in a new product in any circumstances. One company reported that it would not be interested in a new product "unless we had sufficient facilities for the manufacture of our present products to protect 31 our industry position." Perhaps, this reservation is in the minds of many executives. Statistical procedures of the third and the fourth chapters undertake to explore and re-examine the existence of other variates. It is the purpose of these chapters to elucidate all of the economic considerations relevant to the making of investment decision. In concluding this section, it is interesting to Q note, however, that both Keynes and Fisher borrowed their concepts of the marginal efficiency of capital and the rate return over cost respectively from the field of borrowing and loaning, and applied them to the investment program ming. ^ M. D. Brockie and A. L. Grey, "Marginal Effici ency of Capital and Investment Programming," The Economic Journal, IXVI (December, 1956), 667. Q Irving Fisher, The Theory of Interest (New York: Kelley and Millman, 1954), pp. 151-55. ^J. m. Keynes erroneously alleged that his "mar ginal efficiency of capital" is the same as Fisher*s "rate return over cost," and they are used for the same purpose (Keynes, op. cit.♦ p. 141). Unfortunately this assertion is not correct. The error, however, is innocuous. Keynes* "marginal efficiency of capital" is the rate of discount which equates the present worth of the receipts stream of one investment outlay to the present worth of the expense stream of the same investment outlay, while Fisher's "rate of return over cost" ranks alternative investment outlays. Then, it is the opportunity cost considered by Fisher's formula which makes the difference. If there is only one investment project (A) at time period (t), let ®A (t) stand for investment expenditures and stands 32 2.7 The Interest Rate and Maximizing Total Profit According to Brockie and Grey, "the consensus of opinion among economists would appear to indicate that it is the difference between the present value of the cost and This is the "maximum-value-criterion" which makes invest ment a continuous exponential function of the rate of for expected receipts of the project (A) at time period (t), and Sa (t) for the difference between the Ea (t) and is Keynes' "marginal efficiency of capital." J. M. Keynes, op. cit., p. 141. On the other hand, if there are, at least, two investment projects, (A) and (B), and let eA (t)’ eB (t)> rA (t)> rB (t)» SA (t)> SB (t), stand respectively for expenditures, receipts, and the difference between expenditures and receipts of the alternative investment options, then. is Fisher's "rate of return over cost." Fisher's "rate of return over cost" as the formula suggests, includes oppor tunity cost involved in alternative investment options. I. Fisher, op . cit.. p. 151. On this matter, see 0. Lange, "A Note on Innovations," The Review of Economics and Statistics. XXV (February, 1943), 19-25. Also, A. A. Alchian, "The Rate of Interest, Fisher's Rate of Return over Costs and Keynes* Internal Rate of Return," The Ameri can Economic Review, XLV (December, 1955), 938-43. ^Brockie and Grey, op. cit.. p. 671. revenue streams (i.e., total profit) that is maximized."^ rA (t) then: (F.l) 0 (F.2) o 33 interest. Let us assume that the present value of an income stream is: \ / m V + v + - ^ - + • • • + — t V ( > = (T^ ( 1 + 1 > ( 1 + ,' > or v(t) = 4 ( j ) (7.2) Since (7.1) is a geometric progression with a common factor 1 and initiative factor V , then: T"+"T ^ (1 + i) V (*) = (t - 1, 2, 3, .... n) (7.3) Let us assume, also, that the present value of the cost is: C (t) = F (i), where C = (i) a iu dC /q di \ In a practical business situation total profit (P), as commonly understood may be expressed as: P (t) = V (t) - C (t). (7.4) The necessary condition for maximum value of total profit is: ff = 0 (7.5) and the sufficient condition for maximum value of total profit is: 34 .2 . 4£<° < 7 - 6 > or, for necessary condition, § 4 v w - i c w = o a-7> 4E_ a |Y_ (7.8) since, (-r) = 0 ( 7 - 9 ) then, ( t -) = ° (7ao) and, T ~ 3 t ( 1_* ) = T ie (7*n) or, ip -if = Y ^ -/(*,) = 0 (7-12) or, - it v e ' s/(i) ( 7 , 1 3 ) 35 and finally, e ~ = ill! (7.14) Y This last equation is the stability condition^ for maxi mizing "the difference between the present value of the cost and revenue streams (i.e., total profit)"; and the stability condition is, again, an exponential function of the rate of interest. If: - llZl (7.15) Y then, I = f (i) (7.16) If this equation has finite and continuous derivatives, 1 o then according to Taylor’s Theorem, ^ investment is maxim at i = r, if f (r + i) - f (r) ^ 0 The stability condition is that which is given as a limitation on the form of any functional relationship; that is, only under that condition will the system be determinate. ^ d. W. Bushaw and R. W. Clower, Introduction to Mathematical Economics (Homewood: Richard D. Irwin, 1957), pp. 251-33. R. G. Allen, Mathematical Analysis for Economists (London: Macmillan Co., 1956), Chap. XVII. Also, L. Brand, Advanced Calculus (New York: John Wiley, 1955), pp. 131, 474, 478. 36 Then '2- - K f (r+i) _f (r) = { (r)i + {“ (r) i- -+ . ■ • + fn(r) -L 7 M Lj -+ Rn (r«) • (7.17) Where (7.18) 1 1 This is Lagrange Remainder Theorem. J Assuming (o), and (n) are positive, there will be a convergent series if: and derivatives are finite and continuous: I = f (i) is maximum. 2.8 Summary Investment planning always constitutes an important source of difficulty for businessmen. The source of this Henceforward, if f’ (i) = 0 (7.19) and fn (r) <^0 ^Bushaw and Clower, op. cit.. p. 251. Also, Brand, op. cit., pp. 130, 330. 37 difficulty is the determination of the variates which determine investment programming. According to Keynes' theory of investment, assuming the truth of "maximum-value - criterion" and perfect certainty concerning future stream of income, investment is geared to the rate of interest; that is, investment is regarded as a quantity the size of which is determined by the rate of interest. Theoreti cally, given the assumption, the explanation is consistent. In other words, if one starts with "maximum-value- criterion" one will finally wind up with the rate of inter est as the single determinant of investment. But as it stands and bears statistical test the theory is incomplete. It is evident that "maximum-value-criterion" objective has lost its universal application. Today, businessmen pursue a good many objectives in attaining their wealth. It is difficult to believe that firms are not willing to invest on the "most favorable terms" that are available to them. Any positive rate of return on investment is precisely that "most favorable terms." Then, there remains this question: Why, even though the profit is not maximized according to empirical investigations, should investment be carried out beyond the point where the marginal efficiency of capital is more or less than the going rate of interest, or who fails to invest when the ex ante rate of return is or Apparently, he 38 positive, although the marginal efficiency of capital is less than the rate of interest, is offering the others the opportunity to get ahead of him. Then the businessman's decision to invest is intertwined with a number of objec tives. The introduction of other objectives has, indeed, made investment programming complex--the dependence of investment decision on a number of factors. Present day economic theory has adduced no explanation for the emergence of other independent variables besides the rate of interest for interpreting investment planning. Sensing this lacuna in their arguments, economists, particularly since 1950's, have sought to develop an ex planation of investment programming statistically. Yet, statistical findings have lacked a theoretical ground. The next part of this chapter endeavors to offer a theoretical explanation for the present practice of in vestment programming, and gives the stability condition necessary and sufficient for the system. The essence of this theory is based on the emergence of other goals which have occupied a prominent position in capital planning. III. THE MATHEMATICAL EXPLANATION OF A MULTIVARIATE THEORY OF INVESTMENT 2.9 Matrix and Its Variates It is a familiar fact in the history of any branch of scientific knowledge that inquiry has started with 39 description and classification of events within a somewhat vague and undemarcated field. On the basis of such classi fication, analysis is able, at a later stage, to construct certain limited generalizations. But such generalizations may, for a long time, remain applicable only to a limited type of situation or to a limited part of the field, and be incapable of sustaining forecasts of that more general type which relate simultaneously to the major events within the system and enable one to determine the configuration of the system as a whole. To achieve the latter, generaliza tions must reach a certain degree of comprehensiveness and refinement. Such a milestone in the path of knowledge seems to have been provided by the concept of a ’ ’ model” of relationships, which is simply an algebraic equation or set of equations expressing a certain precise kind of relation logically expected between or among two or more variables of a system discarding those factors which seem untenable and otiose. If such a model is to support the hypothesis and determine the value of statistics by examining the observed data, then it must fulfill certain "stability conditions" if it is to be capable of sustaining corol laries of a certain type of generality. Then, for in stance, the adequacy of a model of investment means the conditions which it must fulfill if it is to determine the mechanism of investment programming as a whole. So, one may refer to a model, the relationship between or among its parameters, and the forecasts which can be built upon them. Ex definitio, if a model is to sustain forecasts pertaining to the real world, it must do so via its form and content. And the significance of its parameters is not that they are necessarily changing, changeable, or capable of demonstrating certain way of change, but that they are some quantity which in any par ticular case can be known independently of the controlled variable, in the system. In fact, they ought to be postulated independently of the controlled factor.^ The independent parameters of a matrix are some quantities brought in from outside the system of events of which the set of equations refers; and in an important sense it is on these outside factors that the dependent variable is made to depend. When they are known, the "shape" and "position" of the dependent variable— in this instance, investment--can be fully calculated, for the reason that the unknowns or independent variables are all ultimately expressed in terms of their relation to it; and a dependent variable is a function of all independent ^Professor Ragnar Frisch has pointed out that when economic theory is expressed in a dynamic, and not in a static, form, dealing with movements, certain of these parameters will have the character of "given function of time." "On the Notion of Equilibrium and Disequilibrium," The Review of Economic Studies, III (February, 1936), 100. 41 parameters. The Independent variables, hence, are deter- mining factors. The third part of this chapter introduced an analytical problem which, in statistics, is called multi variate analysis. This study is a matrix composed of approximately 2,500 observations and seven variate dimen sions, which were established on the basis of the general 1 c theoretical and practical information of the system. This theoretical and practical information has served as logical foundation needed for mathematical equations, in corporated in the following section of this chapter, which express functional relationships. 2.10 The Model The following explicit and partial monotonic H. B. Chenery, "Application of Investment Criteria," The Quarterly Journal of Economics. LXVII (August, 1953), 76-96.Alfred E. Kahn, "Investment Criteria in Development Programmes," The Quarterly Journal of Economics. LXV (February, 1951), 38-61.John R. Meyer and Edwin Kuh, "Acceleration and Related Theories of Investment: An Empirical Inquiry," The Review of Economics and Statistics, XXXVII (August, 1955), 217-30, and by the same authors,The Investment Decision: An Empirical Study (Cambridge: Harvard University Press, 1959), Appendix B. Michael Gort, "The Planning of Investment: A Study of Capital Budgeting in the Electric Power Industry/' The Journal of Business of the University of Chicago. XXIV (April, 1951), 85. Walter Heller, "The Anatomy of Invest ment Decisions," The Harvard Business Review. XXIX (March, 1951), 95-103. Ruth Mack. The Flow of Business Funds and Consumer Purchasing Power (New York: Columbia University Press, 194l), pp. 1-16, 306-23. Joel Dean, Capital Budget ing (New York: Columbia University Press, 1951), pp. 37-43. continuous function is assumed,"^ 42 ^ (*1> *V *3' *4' *5; *6)' d = 1, 2,3, • • • 6 ( 10. 1) where (I) is standing for investment, and independent variable, and X^, X2, . . . X^ are independent variables. The differential of the dependent variable (I) is, then, defined in terms of the six independent differentials by the formula: d 1 = a x, + d x2 a d x 3 ^ + j % |i + a xs % + a x6. ( 10. 2) Mention ought to be made that dXp . . . , dXy are no more than an arbitrary increment in the seven inde pendent variables of investment programming. The complete differential equation (2.2) gives the variations of the fundamental and general equation of investment planning, 16 The elements of the functional are the parameters of the model which are arrived at statistically, and are called hereafter independent variables of investment model. They are: depreciation reserve, depreciation expense, net profit, net total sales, changes in sales, and finally capacity variables. For full explanation of these varia bles, see Chapter III. Actually, the matter of the number of variables is of indeference to the general matrix put forward in this part, because it may take an infinite number of variables. But the six variables mentioned here have shown the highest significance relative to a large number of variables statistically. as independent variates Xp X£, . . . Xy vary in any way, independently. If (Xp X£, X3, X^, X5, Xg, X7) are values making 1 = 0 and if dXp dX£, dX^, dX^, dXp dXg, dXy are vari ations from these values making 1 = 0; then dl = 0; Thus, (10.3) Where 44 So far (I) as a multi-value function of X-^, X2> X3, X^, X^, and X6. If (10.4) Then, dl=fx dx +fvdx2 + fxdx 3-hfx dX +f dX ff dX6=0 1 2 3 * 5 5 6 (10.5) or, ( 10. 6) and by the inverse Euler's Theorem: n = t ( i \ , <io-7> The equation (9.8) implies all six independent variates have equal values and equal influences on dependent variable. Since the statistical test of the fourth chapter does not allow the validity of assuming values for X^, X£, X3, X^, X^, and Xg which make 1 = 0 then, dl can not be zero. 2.11 Investment and Its Regression with Six Variates The six independent variates (X^, , X5) have different regressions wit investment variable; then, 45 their influences on investment are different. The combin ation of these values make investment maximum at: - Xl=a2 ' X3=a^ / - *5 = , a -5 ' if, ^(ai+Xl , a2+X 2, • • ' If it is assumed that the function of x« ) has continuous partial derivatives up to any desired order at the point (a-p a£, a%, . . . , a^), then Taylor's Theorem gives for any integral of (n) ^ (ai+*i / ’ ' '' a 6^ x6 )- ,a 2," = d1 + T\ + T » ^ + ‘ * ' ^ ^ +\ ( x i ' V ' * 6 ) ( 11. 2) where Rjj (Xp X£, X3, . . . , Xg) is the Lagrange's Theorem of Remainder, and is equal to: , w + t _* dl at the point (di+exl, + ®*i, a3+ e*3r « * • , af c + exg \ , where © > o 46 now I = f (Xp X£, X3, X^, X5, Xg) is maximum at a^ = Xp a2 = x2' a3 = x3> a4 = x4> a5 = x5> a6 = x 6 w^ien dl = 0 for all values and variations of the six variates from these values. Or: ^ 1 r d X l f x + ^ *2 + ^ *3 1 I + * ' ‘ d *6 T*6 a a x 1 2^%1 5 3X5 j?u # 3 ) It is the necessary condition for having an extreme value of investment and it simply implies that the partial derivatives of I must vanish at the extreme value, i.e. ■^T 3 1 31 31 3 X — 3 1 — q ax2~ 5 X " * *6 (U-4) Now, the sufficient condition for having a maximum value is when: dl ^ 0 on the other hand, ^ = d ) + d xid + ‘' + d x lClx2 ( | ^ ’ ) + d x 2 ( - ^ ) + - - v d X 1d>i( ^ ) + d xi d x3 (3^3X3)+ ■ '■/ d X3 c t Xj ( ^) + d Xjd X6 ( t <•V * * (jj£_y ■ ■ ■ ,j *< + d*idx=(srk.)+ dxs )+ d x 5d* < ( ^ ) + )J > --vdX5<*X6(^— ^> 5 ) i 6 (11.5) 47 All the partial derivatives being evaluated at the point ( °S ,*1 ■*. - * < , )• sufficient condition, it * , , 5 * ^ was said, for maximum value of (I) is obtained if the quadratic form is negative; i.e., all its principal minors including the discriminant of the form are alternatively negative and positive; that is, when d2I is negative definite if: il 3X ;< 0 • • • f dud 32J 1 2 il i l ax sx, i j- ax2 3 l il a 9 T ax2 3X ax* 3V * J ii it 3X 3X; * il 3X^X3 3 X^ < ° 32I 2 31 S2I 31 3l S2J 3 X* 5X, 3X(3Xj ax^Xi, 3X( <?X^. 3Xt ?X6 il 2 31 3ZI s2l 32I 32J S>X^X2 3>X2 2X23X3 3X2 3X^ ax^x^, 2. si 3T s2i S2I 32J 32J 3X,3X^ 5V x3 3x^3 x^ 3 X^ 3 X5 ax^ax^ 2 3 I a 3 I a2i al 31 2 31 3x,3XA 3 Xj J k X4 axA3X5 ^V*6 i . SI ax,^ 3>I 3X23X5 si ax^sx^- i l 3x^X5 si 5,<5 32X 3X5 3X^ V 3 T il 2t * 31 a2r a r 32I 3X3^X6 ^x 2 <° 48 Suppose that f^, f2, £3, f^, £5, and fg are all positive and that the inequalities are all satisfied for all combinations of the seven variates within a relevant range, as is found by statistical data of the fourth chap ter, then, for any set of variates and the demand for investment equilibrium is possible and the position deter mined is stable. The above inequalities are the stability condition for the demand for investment; these conditions are given as limitations on the form of the investment programming. For the investment programming satisfying the stability condition, the variates are uniquely determined and stable. If there is only one variate, the interest rate, it can be shown easily, that the stability condition implies that the schedule of the marginal efficiency of capital is sloped downward and concave to the origin at all points, at least within a certain range. CHAPTER III SAMPLE, METHODS OF PROCEDURE, AND VARIATES I. SAMPLE The sample used here contains (n) observations for (p) variables which constitute a matrix of (np) elements. A matrix with these characteristics is in the field, statistically speaking, of multivariate analysis. The matrix is composed of over 700 firms in the manufacturing section for three years— 1956, 1957, and 1958. Observa tions were undertaken for seven variates which were extracted by the author from copies of completed Form 10-K of the Securities and Exchange Commission and The Moody’s Industrial Manual. The basic analytical problem of the sample was heterogeneity of elements in the Securities and Exchange Commissions sample, which is supposed to be representative of the universe of all firms. And the sample of this dissertation is drawn from the Securities and Exchange Commission's sample. Then, Securities and Exchange Commission's sample is the universe used for the sample of this dissertation. Theoretically, a sample, such as the one used here, must be drawn from its universe 49 50 according to definite rules. Then the question is: How should a sample be drawn? One consideration is that it should not be biased. Then, a sample which is a selected portion of some universe drawn to provide information about the universe as a whole, ought to be according to sample design. For this study two designs of experiments could be taken-"random sample and stratified sample. Choosing the best design from a number of alternatives clearly calls for specifications beyond the requirement that the sample be unbiased. One, or perhaps the most important, criterion for making a choice is to take into account the nature and feature of the universe from which that panorama is to be drawn.^ ■*-To take a sample of a universe and to analyze it in a definite way is equivalent to declaring this sample to be an "isolated system," in the sense that it is connected with the rest of the population only through certain definable links, so that if one knows what is happening at these links at any moment, one can calculate what will happen to the rest of the population. As Whitehead had said, it means "that there are truths respecting this system which require references only to the remainder of things by way of a uniform systematic scheme of relation ships. Thus the conception of an isolated system is not the conception of substantial independence from the remainder of things, but of freedom from casual contingent dependence upon detailed items within the rest of the uni verse." Science and the Modern World (New York: The Macmillan Co., 1925), pp. 58-59. O ^Jerzy Nayman, "On the Two Different Aspects of the Representative Method: The Method of Stratified Sampling and the Method of Purposive Selection," The Journal of the Royal Statistical Society. XCVII (December, 1934), 558- 625. F. F. Stephan, "History of the Uses of Modem 51 For the problem in hand, two possible sampling designs, random and stratified, are appropriate. Random sampling design assumes homogeneity of the universe, on the other hand stratified sample design is used when the uni verse is heterogeneous. With stratified sample design, . . . the basic idea is that it may be possible to divide a heterogeneous population into sub-populations, each of which is internally homogeneous. This is sug gested by the name strata, with its implication of a division into layers.3 Because of the nature of the problem of investment decision and its heterogeneity characteristics, stratified sampling design was chosen. In most cases this hetero geneity was not so large, so the task of making each stratus homogeneous was not very burdensome. Analytically, the larger the variability and heterogeneity of the Sampling Procedures,” The Journal of the American Statisti cal Association. XLIII(March, 1948), 12-39. F. F. Stephan, "Practical Problems of Sampling Procedure," The American Sociological Review. I (August, 1936), 569-80. ^W. G. Cochran, Sampling Techniques (New York: John Wiley, 1953), p. 65. See also, A. T. Craig, "On the Mathe matics of the Representative Method of Sampling," The Annals of Mathematical Statistics, X (March, 1939), 26-34; M. G. Hagood and G. H. Bernert, “Component Indexes as a Basis for Stratification in Sampling," The Journal of the American Statistical Association. XL (September, 1945^ 330-41: G. W. Snedecor. Statistical Methods (4th ed.; Ames: Iowa State College Press, 1948), Chap. V; F. F. Stephan, "Stratification in Representative Sampling," The Journal of Marketing, VI (July, 1941), 38-46; J. S. Stock and L.— R. Frankel, "The Allocation of Samplings Among Several Strata," The Annals of Mathematical Statistics. X (March, 1939), 288-93. 52 universe, the more precise and more limited the boundaries of the stratum.^ So even from the viewpoint of precision alone, the stratified sample should have been used in this inquiry. Sample Coverage The Appendix contains the list of the industry and firm coverage of the sample. It was originally the SEC sample which was reduced to the present one by this author. There are a number of exclusions from the SEC sample for different purposes. The only justifiable purpose was homo geneity which was a desirable goal for recording the results. While it is conceivable that biases may have crept into the reduced SEC sample, it is the author's opinion that the extent of biases is negligible. The exclusions made were the following: First, if there were any merger, or substantial acquisitions of government property, abrupt changes in productive equip ment, firms were excluded. Also, when income and loss ^C. Eisenhart, "The Assumptions Underlying the Analysis of Variance," Biometrica, XXXIV (January, 1947), 1-21; R. A. Fisher, Statistical Methods for Research Workers (13th ed.; New York: Hafner Publishing Co., 1958), CKapST”7-8; J. 0. Irwin, "Mathematical Theorems Involved in the Analysis of Variance," The Journal of the Royal Statistical Society, XCIV (September, 1931), 285-300; Walter A. Hendricks, The Mathematical Theory of Sampling (New Brunswick, New Jersey: The Scarecrow Press, 1956), pp. 153-86. 53 statement, and balance sheet only covered a few months of activity rather than the whole year, the firms were rejected. Further, "young” firms were excluded because it was noticed that their investment decision was not follow” ing a regular trend: these were a series of exclusions due to special experiences of certain firms. There were also a number of exclusions for accounting peculiarities. That is, one reason for excluding some firms was that they did not report gross as well as net accounts such as depreci ation which was often lumped in with some expense account. Also net sales created some problems with firms which rent their equipments. The firms which reported an believable depreciation expense were excluded, as were those firms which failed to report either their gross or net accounts. Finally, the selected sample was thought to be reasonably extensive. Of course, it contains some biases, including biases of the original Securities and Exchange Commission sample. But these biases will not introduce any flaw, and should not be considered as any shortcoming of the sample, not because the sample is extensive, but be*: cause firms of all different sizes are normally distributed in the sample and the volume of investment undertaken by firms is a good proportion of total investment and a very high ratio to the SEC investment sample in the manufactur ing sector, as is explained in Table I for manufacturing TABLE I INVESTMENT COVERED IN THREE SAMPLES FOR 1956 ($ Millions) Industry Investment this sample** Investment total* Investment this sample as % of total Investment SEC sample as % of total Pulp and Paper 504 801 63 63 Chemicals 1,206 1,455 83 70 Petroleum 2,863 3,135 91 93 Rubber 194 201 97 87 Basic Iron and Steel 1,097 1,268 87 85 Electrical Machinery 556 603 92 92 Other Machinery 434 1,078 40 62 Motor Vehicles and Supplies 1,214 1,689 72 86 Textiles 274 465 59 34 *The Survey of Current Business, "1958 Investment Programs of Business," July, 1958, p. 8, and Statistical Abstract of the U.S., 1959, p. 497. **The figures are extracted from the sample. Ui • p * 55 industries for 1956. The sample covers firms and industries in the manu facturing sector. The original sample arranged by the Securities and Exchange Commission contains nine indus tries. For 1956, 1957, and 1958, the reported industries included in the Securities and Exchange Commission sample were the following: pulp and paper, chemicals, petroleum, rubber, basic iron and steel, fabricated metal products, electrical machinery, other machinery, motor vehicles and supplies, and textiles. This author was confronted with a number of problems when he wanted to use the Securities and Exchange Commis sion's industry classification: (1) Conventionally an industry embraces firms which are engaged in producing one kind of product. But in SEC's sample there were found many firms with multi-products which were to be placed in one or the other kind of in dustry. In this case, firms with multi-products were included in the industry that held the largest percentage of the firm's product. (2) The second problem, which was rather cardinal, was within-industry heterogeneity in the capital intensity of the SEC's sample. Here, a brief digression is in order. First, the author thought that homogeneity is desirable for the predictive conclusions of the statistical model. 56 Second, the writer supposed that capital intensity could be the best factor on which to homogenize the industry classification. Capital intensity, this author takes to define as capital:output ratio. Capital is measured by gross fixed assets, and output by total net sales, their best approximate magnitudes. Thus, capital intensity is defined in this dissertation, as gross fixed assets:total net sales ratio. Here, a word of warning is essential in passing. This ratio is not the same as what has been tradi tionally taken to mean the ratio of capital to labor as a measure of capital intensity. The relation between the two ratios depends on the change in labor-productivity resulting from any change in technique. With a "given technical knowledge," one can conclude (on the basis of "diminishing returns" to the use of more capital with a given quantity of labor) that the two ratios will tend to move in the same direction. Otherwise, if labor- productivity rises in greater proportion than the capital- labor ratio, the capital-output ratio would, of course, fall when capital-labor ratio rises. Taking this differ ence of definition into consideration, in comparing different lines of investment, there is no reason at all for associating a difference in the one ratio with a like 57 difference in the other. To repeat the second problem in brevity, for in dustry reclassification a within-industry homogeneity in terms of capital intensity, was thought, by the author, to be desirable. If capital intensity, as is defined here, is measured by the ratio of sales to gross fixed assets, a homogeneous industry classification means that there is statistically insignificant difference in the central tendency of capital intensity, while retaining similar product-groupings. This means that if we have an arbitrary industry classification, and array each industry according to the capital intensity of its component firms, there should not be any significant difference between the means of capital intensity of industries. An F-test of the capital intensity of the industry classification exposed a significant difference. This is the reason that an attempt was made to reclassify SEC's classification. Different classification was tried by the writer; finally an F-test of the following classification showed an For examples of the fallacy involved in confusing the two ratios, see citations given by A. E. Kahn, "Invest ment Criteria in Development Programs," Quarterly Journal of Economics. IXV (February, 1951), 39-40; see also further comments on the same point by W. Calenson and H. Leiben- stein, "Investment Criteria, Productivity, and Economic Development," Quarterly Journal of Economics, LXIX (August, 1955), 346-51. 58 insignificant difference in the central tendency of capital intensity. It is of great surprise that this reclassifica tion tried and used here in this dissertation is similar to the one employed by Professors Kuh and Meyer in the fi study of investment decision. They are the following: (1) pulp, paper, and allied products, including fifty-seven firms, (2) light chemicals, with six sub-groups and including forty-nine firms, (3) heavy chemicals, with six sub-groups and including fifty-three firms, (4) petroleum, including thirty-eight firms, (5) rubber, with three sub-groups including eighteen firms, (6) basic iron and steel, with six sub-groups in cluding fifty-six firms, (7) fabricated metal products, with twenty-one sub-groups including eighty-five firms, (8) other machinery, with nine sub-groups including 102 firms, (9) light chemical goods and machinery, with five sub-groups including thirty-five firms, (10) automotive, with seven sub-groups including seventy firms, (11) con sumer durables, with six sub-groups including forty firms, (12) machine tools, including thirty-four firms, (13) heavy electrical machinery, including twenty-nine firms, ^"Acceleration and Related Theories of Invest ment; An Empirical Inquiry," The Review of Economics and Statistics. XXXVII (August, 1955). 219-20: see also. The Investment Decision: An Empirical Study (Cambridge: Harvard University Press, 1959), pp. 48-52. 59 (14) basic textiles including thirty firms, (15) other textiles, with two sub-groups including twenty-one firms, and finally there is television and radio which was not included in this sample because of the paucity of its degrees of freedom. II. STATISTICAL METHODS AND PROCEDURES The eight variate-dimensions analysis for 717 firms for 1956, 1957, and 1958 could be approached in various ways. This matrix contains fifteen industries with years depth, so there are forty-five sub-matrices of data to analyze. Then there are forty-five correlation-matrices all of the order of eight. The matrix and its sub-matrices could be analyzed in different ways. It was decided by this author that regression and correlation models are the best choices. Correlation and Regression It is true, and indeed expectable, that when any statistical measure is determined from a sample selected from a given population, the true value of that measure in the population might be different from the value shown by the sample. The applicability of sampling concepts to correlation is different enormously according to the nature of the universe from which the sample is selected and the manner in which sample values of the independent variables are obtained. That is, the correlation analysis requires strictly random samples from normally distributed uni verses. This is tantamount to saying that the joint fre quency distribution of the two or more variables in the sample will be representative of the corresponding distri bution in the universe under study; further, the distribu tion of each variable will tend to follow the normal frequency curve, and that the standard deviation of the dependent variable (in this case, investment-decision), for all values of the set of the independent variables will be the same within normal sampling fluctuations.^ On the other hand, the interpretation of regression coefficients is much less dependent upon the shape of the underlying universe or the manner in which sample values of the independent variables are chosen. Also, the null hypo thesis has been that there is a causal relationship between investment and seven other independent variables. So, according to regression model, the values of the independ ent variables are selected in advance by this investigator, ^As noted by M. G. Kendall in The Advanced Theory of Statistics (London: Charles Griffin, 1943), I, 346, very little is known about the sampling distribution of the cor relation coefficient except in the case of normal uni verses. Hence, the interpretation of the correlation coefficient is uncertain unless both conditions of a cor relation model are met, namely that the sample values of the independent variables be drawn randomly and that the underlying universe be normal. 61 as is typical in controlled experiments, with no require ment that the distribution of the independent variables in the sample will be representative of those in the uni verse- -if there, indeed, exists a "natural" underlying universe at all. In this regression model, measures of relationship have only a very limited meaning; that is, either to accept, or to reject the null hypothesis. This is the reason that usually, regression models imply causal rela tionships, if it is the purpose of accepted null hypo thesis.® With respect to these two considerations, regression model was used, and whenever a coefficient is recorded, its standard error is mentioned under that regression co efficient in parentheses.^ The regression equations were all solved with the conventional least square method. Since the method of least square solution requires infinite or large degrees of freedom, whenever the exploration was handicapped by the fewness of observations, like in the case of heavy electrical machinery and other textiles, ®M. G. Kendall, "Regression, Structure, and Functional Relationship," Part I, Biometrica. XXXVIII (June, 1951), 1-25. ^Ezekiel Mordecai and Karl A. Fox, Methods of Cor relation and Regression Analysis: Linear and Curvilinear (3rd ed.; New York: John Wiley, 1959), p. 24. 62 the method of least-information-single-equation maximum likelihood, known as (LISE), was employed. The analysis of the results of data for these two industries indicates that least square (LS), where the number of observation is less than thirty, generally gives more variations than the (LISE) maximum likelihood; that is, the sample estimate of the variance of an (LISE) statistic is reliable on the average and that the t-distribution may be used in constructing confidence intervals with (LISE) estimates of the parameters and the sampling variance of the estimates.^ Time-Series and Cross-Section Analysis By and large, in time-series analysis there might be less "identification problem"--variation explanation--than in cross-section analysis. Theoretically, the identifica tion difficulty is least when there is insignificant auto correlation in the variates of the model; i.e., minimiza tion of unincluded variation has been tried all the way T. C. Koopman and W. C. Hood, eds., "The Estima tion of Simultaneous Linear Economic Relationships," Chap. VI in Studies in Econometric Methods. Cowles Com mission Monograph 14 (New York: John Wiley, 1953), pp. 160-77; and H. Chemoff and D. Nathan, "The Computation of Maximum Likelihood Estimates of Linear Structural Equations," Chap. X in ibid.. pp. 240-46. See also, L. R. Klein, A Textbook of Econometrics (Evanston: Row Peterson, 1953), pp. 122-33, 169-84. 63 through this cross section analysis. There is another advantage of using cross-section rather than true-series in not using an extensive amount of information. A time-series analysis which could offer precise, reliable, and accurate information should embrace an immensely large number of observations. The task for investment analysis would be increasingly unbearable and painful, had it been based on time-series testing. On the other hand, with a cross-section procedure which immedi ately reaches a probability test, one can formulate a con clusion reliable and conclusive. It has been observed with other statistical cross-section procedures that the proba bility of positive regression between explained and unexplained variations has been greatly reduced.^ This way a cross-section regression analysis with the aid of conventional least square (LS) or (LISE) was employed to study the pattern of investment behavior of manufacturing industries in the United States for 1956, 1957, and 1958. The results and their interpretations will constitute the content of the next chapter. ^James S. Duesenberry and Helen Kistin, "The Role of Demand in the Economic Structure," in W. Leontief, ed., Studies in the Structure of the American Economy (New York: Oxford University tress, 1953), pp. 451-82. They employed cross-section method of statistical analysis first. This cross-sectional data were in the form of family budget studies stratified by income for different cities. See also, Robert A. Bandeen, "Automobile Consumption, 1940- 1950," Econometrica, XXV (April, 1957), 239-48. 64 Selection of Related Variates Variate-selection, without fear of much dispute, is one of the most important problems which occasionally handicaps statistical testing. Of course one can construct an equational system about economic conditions, and make them congenial and coherent, merely by inventing the neces sary independent variables which are required to determine the whole— whether they are in fact so or not. This is an easy game. The smaller the degree of generality that one's questions require, the easier it often is to find a set of independent variables which may fit the case. That is, the more particular, and less general, the problem at hand, the greater the number of surrounding conditions which one is justified in assuming to be constant. The problem of determining the result then becomes relatively simple pro vided one can know enough of the surrounding conditions. But once one's question assumes greater generality, one will be in a harder condition to partial out certain factors. Precautions should be an investigator in select ing parameters required for a model. This requirement deserves explicit mention if only for the reason that it so frequently passes unnoticed. So far as the problem of variable-selection for the matrix of investment-programming is concerned, it seems clear, from the nature of its sub ject matter and the type of statement which it is required 65 to make, that an investment theory must be quantitative in form. If this is so, it is necessary that the independent variables which figure in the exponential system should be capable of expression quantitatively in the real world. That is to say, independent variables should be factually apprehended and known. This quantitative aspect of investment-progranining merits advantages as far as sta tistical testing is concerned. Guided by this assumption, all the independent variables were divided by this author into quantitative and qualitative categories. All qualitative variables such as "market position" and "managerial control," were excluded from the sample, because they were not capable of being tested statistically. At the outset, there were about twenty-five quantitative variables which were collected from Moody's Industrial Manual and Form 10-K which is sub mitted to the Securities and Exchange Commission by regis tered firms with that commission. Various combinations of variables could be taken. First, the number of variables was reduced to interpretable dimensions. Clearly any decision on variable-selection, even any understanding what factors ought to be involved, requires an answer to the question: What conditions must a cluster of investment- variables fulfill? Further, what relevance, at all, has a cluster of variables to the investment decision? It is 66 remarked that "at the conceptual level, variable choice is largely a matter of establishing homogeneous clusters within which selection may be made on such grounds as con- 12 venience, accounting properties, and availability." Then, it was decided that the total twenty-five variables were divided into clusters, and representative candidates were taken. This was done with two test-industries: tex tiles and machine tools. For these two industries, chosen on the basis of the size of their assets, extent of the degrees of freedom, products, cyclical experiences, simple correlation and later on Ezekiel graphic approximation 11 method were tried between investment and suggested inde pendent variables, then those independent variables which had shown the highest correlation with investment were chosen. Thus, all variables which demonstrated a high degree of certainty and regression with investment were collected. These variables are: (1) new investment, (2) used invest ment, (3) total assets, (4) gross fixed assets, (5) depreci ation reserve, (6) current assets, (7) inventories, (8) current liabilities, (9) total net sales, (10) depreci ation expense, (11) net profits, and finally (12) dividends. 12John Meyer and Edwin Kuh, The Investment Decision: An Empirical Study (Cambridge: Harvard University Press, 1959), p. 39. ^Mordecai and Fox, op. cit., pp. 204-48, 254-78. All these selected variables have reflected linear correla tion with investment, with the exception of depreciation reserve which had a curvilinear form whose character will be fully examined in Chapter IV. All these values were lagged and then were compared with unlagged ones; on the whole unlagged ones were more stable and reliable than lagged ones, then the unlagged values were taken. The other decision which was made and was important was the deflation of all values by a certain size. This decision had to be made for homogenizing the sample; that is, the sample originally constituted firms with different sizes, and raw materials could have been biased in favor of large-size firms. Then there was the possibility of a skewed distribution and thereby violation of the assumption of homoscedasticity— homogeneity of dispersion around a central tendency— of error terms. It was thought that gross fixed assets could serve as the best deflator value, and the rationale of it is that the ratio makes values homogeneous and approximate to normality, ^ and less to the Theory of Statistics (13th ed.; London: Charles Griffin and Co., 1947), ppT 227-40, suggest a good method of checking distribution-normality in a correlation table. They suggest that the equation of a normally-distributed correlation, where is the standard of X^, and that of X2 and the correlation between X^ and X2, is: G. Kendall and G. U. Yule, in An Introduction y _ * 1 \ l i-r^ where 68 heteroscedastic error variance.^ Having completed all these introductory processes, finally the following values remain for cross-section analysis: (1) unlagged new invest ment deflated by gross fixed assets, (2) unlagged used investment deflated by gross fixed assets, (3) inventories plus current liabilities subtracted from current assets, net quick liquidity, deflated by gross fixed assets, (4) lagged depreciation reserve deflated at gross fixed assets, (5) lagged depreciation expense deflated by gross If the two variates are to be normally correlated the standard deviations of parallel arrays ought to be equal and the regressions are to be linear too. Conversely, if the standard deviations are equal, a linear function of variates, each of which is normally distributed, is also normally distributed. In this special case, a test of normality of distribution was undertaken; that is, deflated values were correlated with deflated investment, and then proper standard deviations were calculated too; it was noticed that each pair of standard deviations was almost equal which assumed normal correlation. ■^F. N. David and J. Neyman, "Extension of the Markoff Theorem of Least Sauare," Statistical Research Memoirs, ed. Karl Pearson (London: Department of Statistics, University of London, University College, 1938), II, 105-116. On the other hand, there is the possibility of bias or so-called "spurious index cor relation,” which implies finding some correlation between two ratios while there is not actually any correlation between two values which were deflated. In this study, such a possibility is not conceivable. John R. Meyer and Edwin Kuh, "Correlation and Regression Estimates When the Data are Ratios," Econometrica, XXIII (October, 1955), 400-16. 69 fixed assets, (6) unlagged and deflated sales, (7) unlagged and deflated net profit, (8) the product of current sales times the ratio of 1956 peak gross fixed assets to 1956 sales, and (9) unlagged ratio of dividend declarations to net profits. III. VARIATES OF THE MATRIX The above-mentioned values were sorted and combined, and then formed the variates of the investment-model. They are the following: (1) Investment variable gross investment which in cludes new and used investment deflated by unlagged gross fixed assets. As was explained before, registered firms are required to submit an annual report of their financial activities of the previous year to the Securities and Exchange Commission. Including among other items, are listings for new and used investment purchases separately. The values used for this sample came from the "Schedule V, 10-K Report, Additions to Property, Plant and Equipment, Plant and Equipment Expenditures," for the period of 1956, 1957, and 1958 for the fifteen industries in manufacturing sector. Of course, the Securities and Exchange Commis sion^ classification of manufacturing industries is dif ferent from the classification used in this inquiry; this is done to homogenize capital-intensities of different 70 industries. According to the "Plant and Equipment Expendi tures" sheet of the Form 10-K, an investment good, capital expenditure, is that piece of capital equipment which is added to the property account. It does not make any dif ference whether the piece of capital equipment is used or new; as long as it is purchased and added to property account, it is called investment by the Securities and Exchange Commission. This principle of chargeability to property account is the definition of investment accepted and used in this inquiry, and it is the same as the con ventional or businessmen's definition of investment. This gross investment is the dependent variable of the model. (2) Sales. The figures for this variable came from the Form 10-K of the Securities and Exchange Commission for the year 1956, 1957, and 1958 for all fifteen reclassified manufacturing industries. In the economist's parlance, total revenue, gross sales, is equal to total output times price per unit of output. Thus, total sales are, more or 1 f i less, a good approximate measure of output, and ■^Output, when this information is taken from the Census of Manufacturers and Statistics of Income, is defined as the sum of sales, gross receipts £rom other operations, and the change in physical inventories valued in current prices. Danial Creamer, Capital and Output Trends in Manufacturing Industries. 1880-1948. Occasional Papers 41 (New York: National Bureau of Economic Research. 1954), p. 24. Strictly speaking, the change in physical inventories valued at current prices is estimated by the National Income Division of the Department of Commerce on 71 approximately represent the level of capacity utilization and expectations. The limitations of a cross-section analysis is that it assumes that marginal cost and prices are constant, and that the price-level affects all indus tries equally and uniformly. To have two feet planted firmly on the ground, mention should be made that the price-constancy assumption of the cross-section analysis is not very sound. _ _ _ At any given moment of time, and over any concrete "short period," price might diverge from "equilibrium" price. The "short period" price is seen to be in part dependent upon expectations in two ways: on the expecta tions as to the future which has prompted the original investment in the fixed plant and so determined its present amount, and on the contemporary expectations of entre preneurs as to the course of prices in the immediate future which determines how intensively the existing plant is utilized to produce current output. Then is it not pos sible that the events of the short-period expectations help to shape the very factors on which final equilibrium depends? It is true, if the firm is one among many, it is the basis of data derived from Statistics of Income. This item can be estimated only for total manufacturingand for the major industry groups. In none of the three years, 1956-1958, did this item amount to as much as 3 per cent of output. Sales constituted more than 95 per cent of output. 72 natural for it to assume that their action and hence the future price will be unaffected by its own action. Con sequently, the entrepreneur will base his present decision as to output and sales on a consideration of the prices ruling at the moment modified by a more or less blind guess as to the course of future prices. Outside the oligopoly area, firms can have only a negligible influence on the total market situation and the expectations of any single individual price are, therefore, irrelevant to the final outcome. If this is so, nothing can introduce uncertainty for the individual as to the future course of prices arising from uncertainty as to the action of his rivals. Granted this, a constant-price assumption is congenial with market phenomena. But in the real world, of course, things do not work instantaneously, so constant price assumption may not be congruent with the permanent shape of events. Clearly, an expectation, which is a common pheno menon to a whole market, or to a substantial group of buyers and sellers, can influence the price of the moment or of the immediate future. Every fluctuation in the market bears witness to this fact. Moreover, where deci sions bear fruit a long time ahead (as with lengthy pro duction periods) or are embodied in very durable objects, as occurs especially in decisions relating to capital 73 accumulation and investment, such expectations may exercise an influence on the situation far into the future, extend ing over years or even decades. Then a cross-section analysis is confronted with price-difficulty which may arise. This is, indeed, a short-coming, nevertheless sales and output in a cross-section analysis is the most superior alternative for measuring capacity utilization, especially if industries are so reclassified that their products are more or less homogeneous. The reclassification suggested below is ventured for removing this difficulty. To be sufficient anchorage for a determinate theory of investment, even formally viewed, it is necessary that sales and output should be conceived as an expression of some fairly permanent and consistent aspect of capacity utilization. (3) Depreciation expense variable. In the United States depreciation expense allowed for one period has usually been a great part of the gross investment of that period, and those who were actuated by employment-function of investment, like Keynes and others, once were worried about the magnitude of this fraction.^ At the micro- ^J. M. Keynes, The General Theory of Employment, Interest and Money (New York: Harcourt, 1936), pp. 98-106. Keynes said that in the U.S., for example, by 1929, the rapid capital expansion of the previous five years had led cumulatively to the setting up of sinking funds and depreciation allowances, in respect of plant which did not need replacement, on so huge a scale that an enormous 74 economic level, depreciation expense is a good approximate measure of capital intensity and capital durability of a firm; by and large, it is a good source for firm liquidity 1 8 and reinvestment. volume of entirely new investment was required merely to absorb these financial provisions and it became almost hopeless to find still more new investment on a sufficient scale to provide for such new saving as a wealthy com munity in full employment would be disposed to set aside. This factor alone was probably sufficient to cause a slump. And, furthermore, since financial prudence* of this kind continued to be exercised through the slump by those great corporations which were still in a position to afford it, it offered a serious obstacle to early recovery." Ibid., p. 100. See also, Alvin H. Hansen, Fiscal Policy and Business Cycles (New York: W. W. Norton & Co., 1941), pp. 384-88. 5nd also, United States Temporary National Economics Committee, Investigation of Concentration of Economic Power, Final Report and Recommendations of the Temporary National Economic Committee Transmitted to the Congress of the United States, Seventy-fifth Congress (Washington, D.C.: IT. S. Government Printing Office, 1941). Also, Hearings Before the Temporary National Economic Committee, Seventy-fifth Congress (Washington, D.C.:U.S. Government Printing Office, 1939-1941), Part 9. Also, Final Report of the Executive Secretary to the Temporary National Economic Comnittee, Monograph15-37 (Washington, D.C.: U.S. Government Printing Office, 1941). For the influence of depreciation expense to the theory of economic growth, see E. D. Domar, "Depreciation, Replacement, and Growth," The Economic Journal, LXIII (March, 1953), 1-32, in which he pronounces the other aspect of depreciation expense "needed just to keep the capital stock intact" when there is a shortage of savings. Ibid., p. 1. Mack once remarked that "depreciation accruals seem to be sufficient to finance not only replacement of plant, but most of the improvement in process, changing customer demand and increase in output required by the average company in established industries." Ruth P. Mack, The Flow of Business Funds and Consumer Purchasing Power (New York: Columbia University Press, 1941), p. 3o3. 75 Today, practically all larger size firms rely on their depreciation funds as some of their internal sources for capital-expenditures. To save repetition, the word depreciation expense means allowances to depreciation reserve for depletion, amortization of fixed assets, and loss on retirement of fixed assets charged to costs. The relatively stable nature of the depreciation expense— that temperamental business cost— means that it is independent of all endogenous factors except capacity utilization. All determinants of depreciation expense are endogenous and, according to Ruth P. Mack, are as follows: (1) The types of assets required for business oper ation, (2; the depreciation rates acceptable to the Bureau of Internal Revenue, (3) the history of the acquisition of plant and equipment in the company and attitudes towards current acquisitions, (4) consider ations of expediency in the statement of current in come, (5) judgments concerning the incidence of obsolescence, (6) maintenance policy, and finally (7) judgments concerning the incidence of physical wear and tear.*9 The size of depreciation expense is related to the psy chology of "financial prudence" of American entrepreneur. The data on depreciation expense, for the covered sample, have been obtained from information submitted to the Securities and Exchange Commission on Form 10-K by cor porations whose securities are sold on listed exchanges. ^Ibid., pp. 235-36. 76 The statistical procedure and manipulation of these data is grounded in the accounting technique known as the source and application of funds work sheet. This tech nique isolates sources and applications of funds between two balance sheet dates for each account. These fund move ments represent true money flows, rather than interaccount changes in valuation. From the work sheet, two primary analyses can be made. The first one is called the Retained Income Analysis, which is concerned with business-operating costs. One of the component parts of retained income cost is the current allowance for depreciation of plant and equipment; the expenditure related to the depreciation accrual is current expense on plant and equipment. Depreciation expense was earlier suggested as an independ ent variable for investment.^ Taking this into account, then if one wishes to have the available information for the firms included in the sample throw light on the way in which investment is related to depreciation expense, one should not confine oneself to aggregate figures which, in a sample like this, are bound to be biased in favor of the largest firms. This is tantamount to implying that one is forced 2QIbid., p. 260. 77 to use a ratio or an index number, deflated or inflated, for comparison of data for different firms and for differ ent years. Like investment and sales, the volume of depreciation expenses for different firms was deflated by gross fixed assets; for the sake of homoscedasticity of error variance and homogeneity of firms involved. (4) Net profit. Net profit is the difference between gross operating profit and profit disbursements. Whenever gross profits exceed profit disbursements there will be a net retention or source of fund. So far in this chapter, attempts have been made to explain the money magnitudes of fund flows to and from industrial enterprises in a given unit of time--the internal sources of funds for investment expenditures. So far, the total liquidity-flow has been partitioned into two sections relating to grouped decisions of businessmen and therefore having a rational entity when conceived in terms of the dynamics of change. The profit figure used in the statistical analysis is for the most part the one given as "profit from oper ations" on corporate profit and loss statements. In the few cases where depreciation expense has been shifted from the non-operating to the operating group, profits from operations have to be reduced by the amount of depreciation charge. After all profit disbursement, firms arrive at their net profit. Figures for net profit were extracted 78 from Form 10-K of the Securities and Exchange Commission and are all deflated by the size of gross fixed asset to reduce error variance, and alleviate the difficulty of bias against firms with smaller assets and investment. Net profits, now, are one of the most important sources of internal funds which give liquidity to a firm. Once, as it was indicated earlier, it was thought by classical economists that profit is the single independent variable of investment. That notion no longer holds true, once other important liquidity factors are taken into consider ation. (5) Depreciation reserve or age variable. Three variates--sales, net profits, and depreciation expense-- mentioned above are all flow-variables, but depreciation reserve is a stock-variable. It measures the relative age of capital assets. Depreciation expense is the credit off setting depreciation provisions, less retirement. It is the total depreciation suffered by an asset or asset group, based on customary or fairly determined rates or estimates of useful life.^ The values for this variable were extracted from the same source as previous ones. These obtained values were deflated by this author by the gross n 1 ^ Eric L. Kohler, A Dictionary for Accountants (2nd ed.; Englewood Cliffs, New Jersey: Prentice Hall, 1957), pp. 417, 419. 79 fixed assets to measure the relative age of equipment, and also to homogenize the values in the sample. (6) Capacity variable. The difficulty of measuring capacity is well known. It is, however, understood that at full utilization, capacity is at its maximum. Having assumed so, one can at any time measure relative needed- capacity or capacity. For all the firms covered in the sample, capacity was at its full employment during 1956- 1957. Then to measure capacity needed for any given year, total expected sales for that year should be by total sales of the peak years 1956-1957 and the quotient should be multiplied by the full capital capacity of 1956-1957. If the full capital capacity of 1956-1957 is shown by Kp, the volume of sales for that year by Sp, and the expected sales for any given year by Se, then the relative capacity needed for the given year is -=£- K . Here capital equipment is sp ? 22 measured by gross fixed assets. This way needed capital capacity is measured by comparing it with full employment level of capacity. The data on all these figures for all firms covered by the stratified sample are obtained from the same source as previous variables, and they were ultimately deflated by gross fixed assets of the given year to satisfy the ^Meyer and Kuh, op. cit., p. 67. homoscedesticity error variance assumption. This variable like the previous one is a stock. (7) Output-variation variable. As it was said before volume of sales can be a good measure of output; likewise changes in sales can also estimate output- variation. Since profit depends on output, then changes in output measure changes in profit, ceteris paribus. The source of this variable was Form 10-K of the Securities and Exchange Commission, and the data, like the rest of varia bles, are deflated by gross fixed assets for satisfying the same condition which was essential for all variables. In conclusion, the multivariate model of investment is composed of eight variables as follows: (1) investment (I), which is the combination of new and used capital purchases, as the dependent variable, (2) sales (S) as an independent variable, measuring output approximately and (4) net profit (P), as an independent variable for investment, and measuring with depreciation expense, liquidity flow and its relation with investment variable is defined by ^Z-N o » (5) depreciation reserve (A), o BP / age variable which represents liquidity-stock; it is an independent variable measuring the relative age of the by and (3) depreciation reserve (D) as an inde pendent variable, measuring liquidity-flow by 81 plant, and it is related to investment by \ n , BA / (6) capacity-variable (K) as an independent variable measuring fixed capital for investment-model, which embodies liquidity stock and its relationship to invest ment is explained by \ Q , (7) output-variation (0), 3K ' which is measured by changes in sales, and taken as an independent variable, and its relationship to investment variable is described by the side-relation: F (I, P, 0) = 0 where JLZ. N o and S q , then BP / 30 / indirectly through profit-changes JL~-\ o • If (t) stands BO / for time-period and (j) for a given firm, the system of variate-analysis can be summarized as: ( ^ t f ' / \ j > K t > ) r = 1,2, « * • , n n = oo j = 1. 2, « “ * , n roo CHAPTER IV STATISTICAL FINDINGS I. DETERMINANTS OF INVESTMENT Investment, Sales, and Profits The statistical findings of Tables II and III reveal that whenever investment is increased, sales and profits are increased too. And, conversely, with a fall in invest ment, output and profits were reduced. The data of Table II, which are indices of investments, profits, and sales for 1956, 1957, and 1958, show a systematic trend between investment, profit, and sales covered in this sample of manufacturing industries. The trend of profit- flows is very much closer to investment than sales trend to investment. Finally, the result for all industries in the manufacturing sector is a systematic trend for all invest ment, profit, and sale. Average-value-data for Table II reveal that in 1957, actual investment, profit, and sales rose, and in 1958, because of recessionary trend, invest ment, sales, and profits all shrank. The same results are exactly inferred from looking closely at the data of Table III which are annual averages of partial correlations between investment, profit, and sales for 1956, 1957, 82 TABLE II INDICES OF INVESTMENT, PROFIT, AND SALES FOR 1956, 1957, 1958* (Previous Year = 100) Industry Investment Profit Sales 1956 1957 1958 1956 1957 1958 1956 ■ 'j ; 9 57" 1958 Pump and Paper 100 98 93 100 88 85 100 102 101 Chemicals 100 119 80 100 103 90 100 112 99 Petroleum 100 93 84 100 102 80 100 110 96 Rubber 100 111 72 100 100 92 100 103 97 Basic Iron and Steel 100 138 70 100 105 73 100 106 80 Electrical Machinery 100 119 78 100 125 98 100 114 95 Other Machinery Motor Vehicles and 100 143 75 100 79 83 100 106 94 Supplies 100 63 64 100 99 79 100 106 83 Textiles 100 91 76 100 96 51 100 103 95 Average 100 108 76 100 101 81 100 107 93 *The figures are extracted from the sample. 00 U) 84 TABLE III ANNUAL AVERAGES OF PARTIAL CORRELATIONS BETWEEN INVESTMENT, PROFIT, AND SALES FOR 1956, 1957, 1958* Year Profits Sales 1956 .054 .074 1957 .318 .321 1958 .379 .365 Correlations are based on the data of sample. 85 and 1958. In arriving at these partial correlation coefficients, there was no statistical problem because the numbers of the degree of freedom were large enough to make the test and results reliable. Given exogenous variables, an investment decision is dependent upon two sets of variables: on the one hand, is the demand side which accounts for profit and sales expectations, which were explained in the previous section. On the supply side, it is limited by the availability and cost of funds to finance an investment project. Recently there has occurred a systematic trend in business financing in recession, expansion, and normalcy. Usually in postwar period a cyclical peak has been preceded by an exceptionally high rate of investment which exerted heavy demand pressures on the supply of available funds. These demands, coupled with credit restraint policies, have brought borrowing costs to new postwar highs. In a downturn, there has been a sharp cutback in fixed capital programs while corporate financing require ments have been lowered. New external borrowing was cur tailed, and there has been a heavy reliance on internal sources. Expansion of long-term debt has slightly con tinued. In downswing, since corporate profits underwent a substantial decline, depreciation expenses were the most important sources of corporate financing. The constructing 86 trends in costs of equity and debt financing have brought dividend yields into approximate equality with interest rate costs in the most recent period. Investment and Profit Variables Now, there is the problem of dependence of one variable upon the other which remains for discussion. Table IV is a partial correlation between profits and in vestment for 1956, 1957, and 1958 of manufacturing indus tries, with profits lagged one year. As the table reveals, in 1956, when economy was at its peak, investment financing had a slight correlation with profit; i.e., businessmen were not depending heavily on their profits as the source of financing their projects. On the other hand, in 1958, when business was suffering from the recessionary effects of late 1957, and money became scarce, businessmen relied heavily on their internal sources. This pattern is not only apparent in individual industries, but in over-all manufacturing section as is represented by average cor relation. There is a slight deviation from the general pattern in the case of heavy chemicals and consumer durables where the correlation is not very significant, because of the saturation of demand of these two industries. Perhaps the pattern of the profit variable, and its importance in relation to investment, can be found better by contrasting 87 TABLE IV PARTIAL CORRELATION BETWEEN PROFIT AND INVESTMENT 1956, 1957, 1958* Industry Sample Size 1956 1957 1958 Pulp and Paper 37 .020 .685 .502 Light Chemicals 37 .037 .132 .015 Heavy Chemicals 42 .196 .435 .038 Petroleum 31 .196 .436 .654 Rubber 16 .213 .907 .754 Basic Iron and Steel 53 .066 .412 .324 Fabricated Metal Products 63 .321 .415 .312 Other Machinery 78 .093 .158 .381 Light Electric Machinery 27 .101 .261 .172 Heavy Electric Machinery 19 .092 .151 .230 Vehicles and Supplies 47 .002 .080 .251 Consumers Durables 21 .045 .624 .821 Machine Tools 29 .023 .142 .521 Basic Textiles 23 .042 .143 .532 Other Textiles 15 .212 .214 .616 Average** 36 .116 .347 .388 *The correlations are based on the data of this sample. **The average correlations were computed according to Fisher’s Z-distribution. See R. A. Fisher, Statistical Methods for Research Workers (13th ed.; New York: Hafner Publishing Co., 1956), p. 2lO. See also, G. W. Snedecor, Statistical Methods (Ames: The Iowa State College Press, 1946), pp. 151-55. 88 it with depreciation expense in financing investment out lays. Table V shows the relative importance of profit and depreciation expense in financing investment outlays for all firms. The table shows clearly that from 1946 to 1951, profit had a greater influence than depreciation expense in investment programming. But from 1952 to 1959, depreci ation expenses exerted greater influence than profit on investment decisions. Theoretically, they should have almost equal influence on investment decision, because both are the most significant parts of flow-variables. However, there are some institutional explanations which may remove the obstacle. From 1952, there have been two statutory provisions which have provided for setting aside a larger amount for depreciation expense, which can be plowed back to investment. These two are Internal Revenue Code of 1950 and 1954. On the other hand, profits were more important than depreciation from 1946 to 1951, basically because of the larger amount of profit accrued to busi nesses after the War. These are the plausible reasons why profit and depreciation have shown slight differences in their degree of impact on investment. Investment, Depreciation Expense, and Other Financial Variables Mention was made before that one factor which in fluences investment decision is the source of funds for 89 TABLE V RELATIVE IMPORTANCE OF PROFIT TO DEPRECIATION EXPENSE FOR FINANCING INVESTMENT OUTLAYS* Year Profit Depreciation expense 1946 100 58 1947 100 46 1948 100 49 1949 100 91 1950 100 60 1951 100 90 1952 100 141 1953 100 149 1954 100 214 1955 100 144 1956 100 165 1957 100 208 1958 100 327 1959 100 176 *Figures for 1946-1952 are extracted from H. I. Liebling, "Financing Business in Recession and Expansion," Survey of Current Business, XXXVIII (October, 1958), 18; and figures for 1953-1959 from B. Kenadjian and G. F. Derrickson, "Business Financing in 1959," Survey of Current Business, XXXIX (October, 1959), 12. 90 financing investment projects. As Table VI shows, since 1946 corporations have relied primarily on their own internal sources. About 64.1 per cent of total investment outlays of all corporations have been financed by their own internal funds--depreciation expenses and retained earn ings. In prosperous years, retained earnings, and in downswing depreciation expenses contributed more to invest ment financing. By and large, the corporate earnings have constituted 28.7 per cent of total sources of business finance in 1946-1959, and depreciation expenses 35.3 per cent; low from 1946-1950, and high from 1950-1959. Financing business investment through depreciation expenses and retained earnings is the most typical pro cedure in the American economy today. This has been the conservative policy adopted by businesses in the last few years. This policy has been especially dominant in manu facturing industries. About 81 per cent of investment funds in manufacturing industries were financed by combined depreciation expenses and profits from 1946 to 1959, as the data of Tables VI and VII indicate. Conversely, still the liberal policy of public utilities is to rely on external funds. They financed 56.7 per cent of their investment outlays through external funds composed of long-terms and short-terms debts including bonded debt, bank loans, mort gage, trade payables, and Federal tax liabilities. TABLE VI SOURCES OF CORPORATE FUNDS, 1946-1959* ($ billions) 1946 1947 1948 1949 1950 1951 1952 Sources--total 21.9 32.4 29.1 15.5 44.2 39.6 30.8 Internal sources— total 11.4 16.6 18.8 14.9 20.8 19.0 17.8 Retained earnings 7.2 11.4 12.6 7.8 13.0 10.0 7.4 Depreciation expenses 4.2 5.2 6.2 7.1 7.8 9.0 10.4 External long-term sources— total 4.2 6.3 7.2 4.3 4.2 7.8 9.4 Stocks 1.3 1.4 1.2 1.6 1.7 2.7 3.0 Bonds 1.1 3.0 4.7 3.3 2.0 3.6 4.9 Other debts 1.8 1.9 1.3 -.6 .5 1.5 1.5 External short-term sources— total 6.3 9.5 3.1 -3.7 19.2 12.8 3.6 Bank loans 2.1 1.4 .5 -1.7 2.1 3.9 1.6 Trade payments 3.7 4.5 1.3 -.3 8.8 2.7 2.7 Fed. income tax liabilities -1.6 2.1 .9 -2.2 7.3 3.3 -3.1 Other 2.1 1.5 .4 .5 1.0 1.9 2.4 TABLE VI (continued) SOURCES OF CORPORATE FUNDS, 1946-1959* ($ billions) 1953 1954 1955 1956 1957 1958 1959 1st quarter Sources--total 30.4 22.2 50.3 47.9 39.5 30.2 26.2 Internal sources— total 19.7 19.8 26.6 27.8 27.7 25.6 16.0 Retained earnings 7.9 6.3 10.9 10.5 9.0 6.0 5.8 Depreciation expenses 11.8 13.5 15.7 17.3 18.7 19.6 10.2 External long-term sources--total 7.6 6.4 8.6 11.1 11.9 10.8 4.7 Stocks 2.3 2.1 2.7 3.2 3.5 3.5 2.1 Bonds 4.8 3.8 4.2 4.7 7.0 6.0 1.9 Other debts .5 .5 1.7 3.2 1.4 1.3 .7 External short-term sources--total 3.1 -4.0 15.1 9.0 -.1 -6.2 5.5 Bank loans -.1 -1.1 3.7 2.2 .3 -2.4 1.1 Trade payments .4 -.2 5.5 5.5 -.7 -1.4 2.0 Fed. income tax liabilities .6 -3.1 3.8 -1.7 -1.9 -2.5 .5 Other 2.2 .4 2.1 3.0 2.2 .1 1.9 *Figures for 1946-1952 are extracted from H. I. Liebling, "Financing Business in Recession and Expansion," Survey of Current Business, XXXVIII (October, 1958), 18; and figures for 1953-1959 from B. Kenadjiah and G. F. Derrickson, "Business Financing in 1959," Survey of Current Business. XXXIX (October, 1959), 12. VO K> 93 TABLE VII SOURCES OF CORPORATE FUNDS BY INDUSTRY, YEAR ENDED JUNE 30, AVERAGED ANNUALLY 1947-1957, AND 1957-1959 ($ Billion) ___________Manufacturing___________ Average 1947-57* 1957** 1958** 1959** Total Sources 17.0 25.4 11.4 26.1 Retained profit 6.3 7.7 4.5 7.2 Depreciation 5.7 9.1 9.5 9.6 Long-term debt# 2.3 4.5 3.1 2.4 Short-term debt## 1.7 4.1 -5.7 6.9 94 TABLE VII (continued) SOURCES OF CORPORATE FUNDS BY INDUSTRY, YEAR ENDED JUNE 30, AVERAGED ANNUALLY 1947-1957, AND 1957-1959 ($ Billion) Rails Average 1947-57* 1957** 1958** 1959** Total Sources 1.0 1.4 0.5 1.0 Retained profit .4 .7 .3 - Depreciation .5 .6 .6 .8 Long-term debt# .1 - -.1 -.2 Short-term debt## .1 -.3 .4 95 TABLE VII (continued) SOURCES OF CORPORATE FUNDS BY INDUSTRY, YEAR ENDED JUNE 30, AVERAGED ANNUALLY 1947-1957, AND 1957-1959 ($ Billion) Transportation Average 1947-57* 1957** 1958** 1959*' Total Sources 1.1 1.5 1.6 2.0 Retained profit .1 .1 - - Depreciation .7 1.0 1.2 1.2 Long-term debt# .2 .2 .5 . 6 Short-term debt## .1 .2 -.1 .2 96 TABLE VII (continued) SOURCES OF CORPORATE FUNDS BY INDUSTRY, YEAR ENDED JUNE 30, AVERAGED ANNUALLY 1947-1957, AND 1957-1959 ($ Billion) Public Utilities Average 1947-57* 1957** 1958** 1959*: Total Sources 5.5 8.5 8.6 8.0 Retained profit .2 .3 .1 . 6 Depreciation 1.6 2.6 2.9 3.2 Long-term debt# 1.9 4.9 5.3 3.7 Short-term debt## .3 .7 .3 .5 97 TABLE VII (continued) SOURCES OF CORPORATE FUNDS BY INDUSTRY, YEAR ENDED JUNE 30, AVERAGED ANNUALLY 1947-1957, AND 1957-1959 ($ Billion) Commercials Average 1947-57* 1957** 1958** 1959** Total Sources 4.1 3.8 1.4 5.3 Retained profit 1.5 1.6 .8 1.5 Depreciation 1.3 1.9 2.0 2.1 Long-term debt# .2 - - -.1 Short-term debt## .9 .3 -1.4 1.8 *H. I. Liebling, "Financing Business in Recession and Expansion," Survey of Current Business. XXXVIII (October, 1958), 14. **B. Kenadjian and G. F. Derrickson, "Business Financing in 1959," Survey of Current Business, XXXIX (October, 1959), 15. #Includes bonded debt, long-term bank loans, mortgage. ##Includes short-term bank loans, trade payments, Fed. income tax liabilities. 98 The capital market supplied 23.4 per cent of funds for investment outlays of all corporations, and the money market 14.2 per cent of total funds in 1946-1959. The tendency among businessmen is to plow back more of their own funds than to borrow in the long- and short-term markets. Although the average percentage of external funds for the period 1946-1959 is still high, it is due to higher percentages in the early years. That is, the relative importance of external funds was more in the period between 1946-1949, than in the later years. Contrariwise, the importance of internal funds, especially depreciation funds, has been the opposite. Depreciation charges have risen to the forefront among available corporate funds in the postwar period, constituting the most important source of financing over the past eight years. This growing im portance is illustrated in the increase of its share from one-fourth of total financing requirements in 1950, to merely one-half in 1957, and since 1952, it even exceeded the retained earning in importance. This "financial prudence" was more evident in the manufacturing section than in any other industry. Table VIII shows a strong correlation between investment and depreciation expenses. This strong correlation is partly due to the fact that there has been a step-up in average depreciation rates, partly associated with 99 TABLE VIII PARTIAL CORRELATIONS BETWEEN INVESTMENT AND DEPRECIATION EXPENSE, 1956, 1957, 1958* Industry Sample Size 1956 1957 1958 Pulp and Paper 37 .052 .101 .231 Light Chemicals 37 .083 .582 .475 Heavy Chemicals 42 -.022 .489 .212 Petroleum 31 -.185 .173 .316 Rubber 18 -.093 .883 .787 Basic Iron and Steel 53 .033 -.002 -.113 Fabricated Metal Products 63 .269 .389 .155 Other Machinery 78 .159 .136 .364 Light Electric Machinery 27 -.058 .237 .729 Heavy Electric Machinery 19 -.010 .182 .005 Vehicles and Supplies 47 .232 .294 .343 Consumers Durables 21 .355 .311 .143 Machine Tools 29 .423 .319 .518 Basic Textiles 23 .463 .482 .819 Other Textiles 15 .112 .397 .011 Average** .164 .319 .330 *The correlations are based on the data of this sample. **The average correlations were computed according to Fisher’s Z-distribution. R. A. Fisher, Statistical Methods for Research Workers (13th ed.; New York: Hafner Publishing Co., 1956), p. 210. See also, G. W. Snedecor, Statistical Methods (4th ed.; Ames: The Iowa State College Press, 1946), pp. 151-55. 100 statutory changes and partly the results of the greater proportion of equipment relative to plant facilities in the capital base. Under the 1954 Revenue Code, the permitted alternatives to straight-line depreciation have resulted in the write-off of about two-thirds of the purchase costs of an asset during the first half of its useful life. Moreover, the Internal Revenue Act of 1950, which permitted five years1 amortization of defense-related facilities, increased depreciation charges of assets qualifying under provision. By and large, the potential impact of the depreciation of 1954 Revenue Code method is currently far greater than of the 1950 program and is of rising import ance. In concluding this section, it is safe to say that the basic fact underlying the importance of internal funds for investment programming is the gradual reversion to "financial prudence" and the rapid capital accumulation undertaken to extend existing productive facilities as well as to introduce new methods of production. Investment, Changes in Sales, and Capacity Variables The accelerator hypothesis, viz., that a change in sales will result in a larger percentage change in net investment, impinges upon a few necessary assumptions. To be more accurate, the accelerator hypothesis should be formulated as follows. Given (1) financial considerations, (2) capacity utilization, and (3) the size of the firm, 101 a change in sales will bring about a larger change in net investment. By financial consideration is meant the importance of the sources of financing investment projects. It was explained before that firms are becoming more reliable on their own internal sources than capital and money market. In this regard, retained earning and depreciation expenses showed a high regression with invest ment. In the matrix model of investment of this sample a relative measure of capacity was introduced, and it was estimated by the gross-fixed-assets and net sales ratios of 1956, in relation to specific year. This writer took 1956 ratio because the economy was at full employment then, and it could be taken that the capacity was, then, fully utilized. It is true that an increase in sales will not result in net addition to the stock of gross fixed assets unless capacity is fully utilized. To this extent, hence, capacity variate reflects investment needed, given changes in sales and financial considerations. Thus, a partial correlation between investment and capacity variable would delineate the importance of capacity on investment pro gramming, because a partial correlation would partial out all other factors except the one under investigation. The data of Table IX show partial correlation between invest ment and capacity variables for 1956, 1957, and 1958. 102 TABLE IX PARTIAL CORRELATIONS BETWEEN INVESTMENT AND CAPACITY, 1956, 1957, 1958* Industry Sample Size 1956 1957 1958 Pulp and Paper 37 .397 .082 .101 Light Chemicals 37 .723 .396 .218 Heavy Chemicals 42 .584 .412 .533 Petroleum 31 .075 .232 .002 Rubber 18 .812 -.115 -.423 Basic Iron and Steel 53 .484 .483 .001 Fabricated Metal Products 63 .594 -.121 .178 Other Machinery 78 .423 .302 .072 Light Electric Machinery 27 .563 .278 .009 Heavy Electric Machinery 19 .712 .283 .001 Vehicles and Supplies 47 .211 .061 -.123 Consumers Durables 21 .302 .003 -.026 Machine Tools 29 .424 .218 .958 Basic Textiles 23 .672 .573 .211 Other Textiles 15 .723 -.054 -.034 Average** . 494 .223 .183 *The correlations are based on the data of this sample. **The average correlations were computed according to Fisher's Z-distribution. R. A. Fisher, Statistical Methods for Research Workers (13th ed.; New York: Hafner Publishing Co., 1958), p. 210. See also, G. W. Snedecor, Statistical Methods (4th ed.; Ames: The Iowa State College Press, 1946), pp. 151-55. 103 The data reveal the fact that in 1956, when capacity was fully utilized, there was a very strong correlation between these two variables, but in 1957 and 1958 when the economy was in a recession capacity variate did not play a major role, and often it was not operative at all. In three cases (rubber, metal products, and consumer durables), the capacity partial correlation was even negative. The reason that can be adduced is that the demand for the products of these industries fell sharply in the latter part of 1957 and 1958. By and large, the average correlation between capacity and investment was very strong in 1956 (.494), changed drastically to .223 in 1957, and went to .183 in 1958. The trend is exactly what it was expected to be. As to the importance of the size of the firms, an examination of all manufacturing industries' data, shown in Table X, indicated that generally speaking, the larger the firm as measured by its gross fixed assets, the greater the ability to project capital outlays within relatively close limits. Or the size of the firm has a greater impact upon investment decisions. The data of Table X reveal that the larger the anticipated expenditure relative to gross fixed assets, the more accurate are the predictions and anticipa tions. This phenomenon explains the better predictive performance of large firms, since such firms are engaged in relatively large scale programs more frequently than 104 TABLE X PERCENTAGE DEVIATION OF ACTUAL FROM PLANNED INVESTMENT OF MANUFACTURING FIRMS ACCORDING TO SIZE CLASSIFICATION, 1955* Per cent deviation of actual from planned investment Under $10 million Expenditure, 7 o of total of this class Firm, 7 o of total of this class -100 to -60 9 5 -59.9 to -20 16 15 -19.9 to 19.9 34 21 20 to 59.9 20 16 60 and over 21 43 Total 100 100 Actual less than planned 40 30 Actual more than planned 60 70 105 TABLE X (continued) PERCENTAGE DEVIATION OF ACTUAL FROM PLANNED INVESTMENT OF MANUFACTURING FIRMS ACCORDING TO SIZE CLASSIFICATION, 1955* From $10 to $50 million Per cent deviation of actual from planned investment Expenditure, % of total of this class Firm, % of total of this class -100 to -60 1 2 -59.9 to -20 22 19 -19.9 to 19.9 45 32 20 to 59.9 20 21 60 and over 12 26 Total 100 100 Actual less than planned 48 38 Actual more than planned 52 62 106 TABLE X (continued) PERCENTAGE DEVIATION OF ACTUAL FROM PLANNED INVESTMENT OF MANUFACTURING FIRMS ACCORDING TO SIZE CLASSIFICATION, 1955* $50 million and over Per cent deviation of actual from planned investment Expenditure, 7o of total of this class % of Firm, of total this class -100 to -60 - 1 -59.9 to -20 16 21 -19.9 to 19.9 69 47 20 to 59.9 13 20 60 and over 2 11 Total 100 100 Actual less than planned 51 49 Actual more than planned 49 51 *M. F. Foss and Vito Natrella, "Investment Plans and Realization," Survey of Current Business, XXXVII (June, 1957), 17-19. 107 small firms. The large companies are more conservative in their investment programming, perhaps because they do not want to make a mistake whose legacy may persist for long in their actions. But the influence of scale of program is strong enough in investment decisions to make small and medium size firms with relatively large programs generally more accurate in their projections than large firms engaged in small programs. Table XI distributes firms into their respective industries and compares industries' actual and anticipated investment expenditures. In six years under investigations, the maximum deviation for over-all indus tries has not been more than 6 per cent. Another factor which helped achieve this tendency has been the magnitude of the anticipated capital expendi ture relative to the size of the firms. This is evident especially with manufacturing firms which are considered very conservative. If this systematic trend is reliable, then future predictions might appear feasible. Let us seek to explore the reasons for deviations of investment anticipations from actual investment outlays. Table XII is a good guide. The table is divided into "firms spending more than anticipated" and "firms spending less than anticipated," and they are classified for "small" (under ten million dollars gross assets), "medium" (between TABLE XI INDEX OF ACTUAL AND ANTICIPATED PLANT AND EQUIPMENT EXPENDITURES OF ALL INDUSTRIES FOR 1955-1960 (Actual Expenditures in Previous Year = 100) Years Manufac turing Mining Rail road Transporta tion, other than rails Public Utilities Commercial and others All Indus tries 1955* Actual 104 98 108 106 102 115 107 Anticipated Per cent actual 97 92 89 99 104 107 101 of anticipated 107 107 121 107 98 107 106 1956* Actual 132 129 136 109 111 116 122 Anticipated Per cent actual 131 119 142 111 116 112 122 of anticipated 100 108 96 98 96 104 100 1957 Actual** 107 100 113 103 127 88 105 Anticipated# Per cent actual 110 98 119 106 125 88 106 of anticipated** 97 102 95 97 102 100 99 1958 Actual** 72 76 54 85 98 133 83 Anticipated# Per cent actual 83 85 62 82 103 123 87 of anticipated** 87 89 87 104 95 108 95 o 00 TABLE XI (continued) INDEX OF ACTUAL AND ANTICIPATED PLANT AND EQUIPMENT EXPENDITURES OF ALL INDUSTRIES FOR 1955-1960 (Actual Expenditures in Previous Year = 100) Years Manufac turing Mining Rail road Transporta tion, other than rails Public Utilities Commercial and others All Indus tries 1959 Actual** 107 99 100 127 101 99 104 Anticipated** 114 98 100 154 102 90 108 Per cent actual of anticipated# 94 100 100 83 100 100 96 1960## Anticipated as per of actual 195/ cent 95 81 73 121 98 112 100 Anticipated as per of actual 1958 cent 132 107 135 143 100 119 121 Anticipated as per of actual 1959 cent 125 102 110 106 107 107 114 *M. F. Foss and Vito Natrella, "Ten Years’ Experience with Business Investment Anticipation," Survey of Current Business, XXXVII (January, 1957), 17. **M. F. Foss, "Business Anticipations of 1959, Investment and Sales," Survey of Current Business. XXXIX (March, 1959), 13, 17, 11. ^Estimated figures. ##M. F. Foss, "Business Expanding Investment in 1960-“Expects Higher Sales," Survey of Current Business, XL (March, 1960), 13. 109 TABLE XII DISTRIBUTION OF MANUFACTURING FIRMS ACCORDING TO REASONS FOR CHANGES FROM INVESTMENT ANTICIPATION BY ASSET SIZE, 1955* Firms spending more Firms spending less than anticipated than anticipated Under Over Under Over $10 $10-$50 $50 $10 $10-$50 $50 million million million million million million No. % No. % No. I No. % No. 1 No. % Section I Changes from expectations in: Net profit 46 18 14 15 3 13 29 31 9 20 1 3 Sales 133 51 40 43 9 40 19 20 3 7 1 3 Construction progress & equipment deliveries 23 9 16 17 3 13 35 37 29 66 26 84 Capital goods prices 14 5 13 14 1 4 3 3 1 2 0 0 Working capital require ments 3 1 0 0 0 0 5 5 2 5 0 0 Competitive conditions 21 8 2 2 1 4 0 0 0 0 1 3 Other economic conditions 21 8 8 9 6 26 4 4 0 0 2 7 Total Section I 261 100 93 100 23 100 95 100 44 100 31 100 TABLE XII (continued) DISTRIBUTION OF MANUFACTURING FIRMS ACCORDING TO REASONS FOR CHANGES FROM INVESTMENT ANTICIPATION BY ASSET SIZE, 1955* Firms spending more than anticipated Under Over Firms spending less than anticipated $10 million No! T $10-$50 million no; T $50 million No! I Under $10 million No. % $10-$50 million W. % Over $50 million No. % Section II Other explanatory factors: Equipment breakdowns 24 18 4 Management changes 16 10 1 Mergers 5 3 12 Incomplete anticipations 31 19 15 Accounting errors Routine over & under 13 8 5 estimates 36 23 13 All others 31 19 15 Total Section II 160 100 65 TOTAL SECTIONS I & II 421 - 158 6 0 0 2 4 0 0 0 0 2 0 0 2 4 1 5 0 0 18 1 4 3 7 0 0 0 0 23 6 22 0 0 2 11 1 20 8 5 18 7 16 1 6 1 20 20 3 11 19 42 5 28 1 20 23 12 45 12 27 9 50 2 40 100 27 100 45 100 18 100 5 100 - 50 - 140 - 62 - 36 - *M. F. Foss and Vito Natrella, "Investment Plans and Realizations," Survey of Current Business, XXXVII (June, 1957), 15. 112 ten and fifty million dollars gross fixed assets), and "large" firms (with gross fixed assets of over fifty million dollars). On the other hand, reasons are divided into Section I, i.e., "economic reasons," and Section II, i.e., "non-economic reasons." Section I contains net profits, sales, construction progress, capital goods prices, working capital requirements, competitive condi tions, and other economic conditions. Section II comprises equipment breakdown, management changes, mergers, incom plete anticipations, accounting errors, routine-error, and others. For both sets of firms, those spending less and spending more than anticipated, smaller firms registered more deviations from the anticipated than larger ones; most of deviations are ascribed by changes in sales for smaller firms than large ones. Out of 377 firms whose actual capital outlays exceeded their anticipated ones due to "economic reasons" in 1955, 261 were small firms, ninety- three medium-sized, and twenty-three large-sized firms of the same universe. And out of 170 firms whose actual outlays lagged behind anticipations, ninety-five were small-sized, forty-four were medium-sized, and thirty-one large-sized firms. Taking "economic" and "non-economic" reasons all into consideration, the same trend is evident. Now, to repeat again what has been found to be 113 typical in the postwar period, viz., that generally speak ing the larger the firm (as measured by its gross fixed assets), the greater its ability to project capital outlays within relatively close limits, and the larger the antici pated expenditures relative to gross fixed assets, the more accurate are the anticipations, and the magnitude of anticipated capital expenditures relative to the size of the firms. It was said, and is no longer an unsupported con jecture, that change in sales is one of the factors which has repercussions on investment decisions. This is the backbone of the accelerator hypothesis which was operative from 1956 to 1959, assuming financial considerations, capacity variable, and the size of the firm. Table XIII is a comparison of actual and anticipated investment and changes in sales of manufacturing indus tries. As is revealed by the data reflected in Table XIV, the percentage changes in sales and investment expendi tures for 1957, 1958, and 1959 were very closely related. Perhaps the slight change was due to other factors as explained in Table XII, page 110. It is expected, if the accelerator hypothesis is reliable, that actual investment in 1960 will be 17 per cent up from 1959. But actual investment in 1960 will be expected to fall eight points from the anticipated 1960 investment outlays, because 114 TABLE XIII COMPARISON OF SALES AND INVESTMENT EXPENDITURES OF MANUFACTURING INDUSTRIES (Actual Expenditure in Previous Year = 100) Year Investment Sales 1957 Actual 107* 102** Anticipated 111* 108** % actual of anticipated 97* 95** 1958 Actual 72* 96** Anticipated 83* 108** % actual of anticipated 87* 89** 1959 Actual 107* 109** Anticipated 114* 114** % actual of anticipated 94* 95** 1960 Actual 124## 102## Anticipated 132# 108# 7 8 actual of anticipated 94## 94## ^Estimated on the basis of data of Table XI. **Estimated from the figures of M. F. Foss, "Business Expanding Investment in 1960— Expects Higher Sales," Survey of Current Business, XL (March, 1960), 17. #Ibid., p. 13. ##Expected figures for 1960. TABLE XIV AVERAGE PARTIAL AND SIMPLE CORRELATION BETWEEN INVESTMENT AND AGE VARIABLE* Industry Pulp and Paper Light Chemicals Heavy Chemicals Petroleum Rubber Heavy Steel Metal Products Other Machinery Light Electrical Machinery Heavy Electrical Machinery Vehicles and Supplies Consumer Durables Machine Tools Basic Textiles Other Textiles ______Annual data________ Three year Three year average average simple partial correlation correlation -.182 -.238 -.213 -.189 -.172 -.016 -.184 -.097 -.263 -.201 -.014 -.022 -.234 -.095 -.203 -.037 -.218 -.128 -.319 -.388 -.138 -.030 -.187 -.252 -.108 -.253 -.059 -.227 -.285 -.228 Averaged data_____ Simple Partial correlation correlation -.084 -.121 -.568 -.565 -.033 -.058 -.274 -.387 -.574 -.023 -.087 -.211 -.094 -.075 -.078 -.089 -.073 -.297 -.089 -.044 -.575 -.686 -.119 -.027 -.287 -.251 -.068 -.138 -.158 -.094 *The correlations are based on the data of this sample. 116 the actual sales will be expected to fall six points from the anticipated sales of 1960. The Impact of External Financing on Investment Decisions The most outstanding aspect of the postwar cyclical patterns of financing is the heavy dependence on internal funds and a tremendous drop in demand for external sources. But, while the bulk of corporate long-term financing is supplied from internal sources, business firms typically need some outside capital to supplement their requirement for capital budgeting. The cessation of debt expansion which featured all three recessions was reflected in a liquidation of short-term liabilities which offset some further increases in long-term debt. It might be said that external equity financing in 1949 and 1954 was well main tained, although the volume of such financing was much lower in those years than in the latter 1950's when net sales of equities moved downward with general business activity. There are two reasons for submerging this new trend. First, in that earliest postwar cycles, the Federal Reserve System's policies had served to limit increases in interest rates during the upswing, and there was no fall off in rates in the subsequent downturn comparable to later ex periences. In all 1949, 1954, and 1957 cycles, the high points in the upward pressures in interest rates had been, 117 roughly speaking, coincident with the cycle peak, and borrowing costs coursed down as demand for funds fell off and the monetary authorities acted to ease supply condi tions. At the peak of 1957 cycle, interest rates were substantially higher than at either of 1949 and 1954 cyclical highs, and the subsequent decline was larger both in absolute and relative terms. Reflecting the more abrupt nature of the decline in economic activity, the reduction in borrowing costs developed faster than in either reces sions. Long-term interest rates also tended downward once the cyclical peak of 1957 was past. The second, and most phenomenal, feature of the recent financial panorama has been the bouyancy of cor porate security prices. Common stock values moved moder ately lower in the second half of 1957, but since the start of 1958, prices moved strongly forward and in September of 1958, and finally in December of 1959, were at all-time highs. Corporate long-term bond yields, as measured by Moody's series, are currently close to 5 per cent, one-half of a percentage point higher than 1958, and one point above the recession low. The cost of short-term borrowing has risen even more sharply in the recent business upturn. While present financial conditions are relatively favorable to equity financing, it is clear from Table VI, page 91, that the bulk of outside financing by corporate 118 business is raised by borrowing, with internal funds providing the principal source of equity capital. Thus, the rise in interest costs superimposed on the growing debt level has substantially raised fixed interest charges both absolutely and in relation to funds available for paying such cost-profits before taxes and interest payments. The considerable change in the interest burden from the early postwar situation appears less striking when viewed against the historical background of the twenties. Compared with the nearly 30 per cent of all corporate income absorbed by interest payments in the late 1920's, the current 13 per cent ratio appears to provide consider able "elbow room" in financial planning. However, this new development has not, thus far, resulted in any major shift in financing in favor of new external funds. While this may possibly reflect lagging response to market trends, it may be noted that from the point of view of corporate management, debt financing might still be preferred in as much as interest on debt is deductible for profit tax purposes whereas such taxes are levied on income before dividend payments. Investment and Depreciation Reserve If depreciation reserve can be regarded as a measure of the age of capital equipment, Table XIV, page 115, shows a negative correlation between age variable and investment. 119 This implies that the older the capital equipment, the less the investment outlays. This is opposite to "echo-effect" theory of investment which purports to assert that the older the equipment, the larger the investment. On the other hand, a negative correlation between investment and age variable implies that a low rate of investment is undertaken by a firm which has old capital equipments; and those firms which invest at higher rate are having relatively newer equipments. These two aspects of investment and age variable are evident according to Table XIV, page 115. There are, of course, some reservations which should be made. "Echo-effect" is concerned with the age. of capital stock and investment for replacement purposes. Since replacement by itself is an alluding name, and usually firms do not report it separately, gross invest ment was taken by this author as a measure of replacement. Of course a comprehensive rejection of "echo-effect" must await a definite time series analysis which correlates replacement values with depreciation reserve. Now, as a first approximation gross investment and depreciation reserve can be a good test of "echo-effect." One more point to be made in concluding this sec tion is the following. A negative correlation between the age variable and investment implies that the older 120 the equipment, the lower the rate of investment. And according to the statistical findings, advanced in the first part of this chapter, low investment accounts for low output and low profit. Thus, the stability condition is a positive and rising rate of investment, if higher output and profit are the objectives. CHAPTER V PROFIT MODEL I. INTRODUCTION This chapter offers an analysis of the relationship between the volume of investment and its expected profit. It is basically a ramification of Chapter II which set forth the general theory of investment programming. It is evident that investment decision is intertwined with profit expectation, through sales-maximization objective. That profit is, inter alia, a positive function of the volume of investment, so that a rise in the rate of investment will encourage entrepreneur to invest, thereby inducing a fur ther rise in the rate of investment. This analysis is a part and, perhaps, a prolegomenon to the theory of invest ment programming. II. INVESTMENT, PROFITS, AND WAGES Perhaps no term has been the subject of more debate and controversy in Economics than profit. David Ricardo, that fountainhead of Economics, more than others, was first and foremost concerned with the movement of profits, wages, and rents--the three great revenues of society. The theory 121 122 of profit which he purported to expound was the outstanding corollary of his theory of value. It is summed up in the statement, "when wages rise, profits fall." The truth which the statement was intended to imply is more likely and fully represented in another statement of Ricardo that, "profits depend on high or low wages, and on nothing else."'*’ In other words, profit is uniquely determined by the ratio of the value of labor-power to the value of com modities in general, and these two quantities can move independently of each other. It implied that the rate of profit could be increased neither by an increase in the quantity of money nor by an increase of consumption as Maithus was asserting. According to Ricardo, then, profit was an inverse function of wages. In this sense, profit was regarded as a residual quantity, the size of which was determined by these other given factors--the value of the product and the value of labor-power. The nature of profit, the why and wherefore of its existence as a category of income at all, •^Ricardo used "high wages" as synonymous with a high "proportion of the whole produce necessary to support the labourer." The Works and Correspondence of David Ricardo, ed. by P. Sraffa and M. H. Dobb (Cambridge: Harvard Univer- sity Press, 1952), pp. 134-35. James Mill said that if profit be used "to denote the ratio of values [i.e., the rate of profit] it may be shown that profits in that sense depend wholly upon wages." Elements of Political Economy (3rd ed.; London: Baldwin and Cradock and Joy, 1821), pp. 58-59. 123 remained a secret; and until this secret was revealed, not only were important practical questions not answered, but there could be no certainty that the terms of the relations which were said to determine profit (namely, wages and the value of the product), could properly be treated as inde pendent . Again, the successors of Ricardo sought to explain and to develop an explanation of profit along two lines-- on the one hand, by inventing a new category of "real cost" and, on the other hand, in terms of "productivity" of capital. It is evident that neither "real cost" nor O "productivity" theory could explain profit. The explanation of profit is an important under taking. Classical theory had adduced no explanation for the emergence of profit and its acquisition by "profit- recipients." That this is no superfluous inquiry can be seen from the importance of the type of question which ^Since the successors of Ricardo, either evaded the issue or provided inadequate solutions, they provoked Marx’s condemnation and scorn. He regarded the "cost of production" theory of J. S. Mill as a superficial evasion of the issue. The "cost of production" theory of value solved nothing, because it left the determination of the "cost of production" unexplained. With regard to J. S. Mill’s attitude, Edwin Cannan remarked: "Senior is at least entitled to the credit of having seen that profits had not been satisfactorily explained. ... J. S. Mill, on the other hand, seems to have been totally unaware that any thing was lacking." History of Theories of Production and Distribution (London: P. S. King^ 1954), p. 168. 124 depends on it: for instance, what would be the effect if profit were taxed or otherwise appropriated, or if invest ment depends on profit, and investment is income-generating and capacity-expanding? On the balance of these consider ations an attempt is made to explain the origin and source of profit, and to show on what factor it depends. III. A MODEL OF PROFIT DETERMINATION Let the following notations be assumed: 0r = net sales, an approximate measure of output, of firm (r). Pr = net income to surplus, profit, of the same firm. Wr = wages and salaries of firm (r). I = investment S = saving Sp = "profit”— recipients* propensity to save. sw = "wage-earners*" propensity to save. For the whole economy, we can write: r=J 0p = Oj ■+ 01 - V * * * , + ° r \ ' r = La, — , " (4 • ! ) r=n and 125 n-\ Pr = P ) + r i + • • '' r = l 2 ,---s (40) and T-i \ Wr = Wj -v W 2 -V ' ", - r = i, 3,-' • n (4-3-J r=n by definition: r=l r=i v=i ) P r = } O r (4.4 J r=n r=n r=n or , r=i r=i r=l r = X _ ° r - J 2 T r ( 4 '5 ) r_ r , r= n r= n Again, by definition: 1 = s 126 Then, S = S p - t - (4-6) Where Sp and are standing for profit--recipients' saving and wage-eamers1 saving respectively. Since % = sp F and S ^ JW W Then for the whole economy r= 1 r = . i r-=i sr = ^ r i„w (i *^) r=n r=n r = n Integrating and simplifying equations (4.5) and (4.7), then, V-i r=l r - l r - i r r-n r=n r=r? Or, 127 r=l y-=i r= 1 r = y ~ 7 A i r ^ h * j ~ o r ■ (*■»> r=n i~=o Integrate equations (4.6) and (4.9), then, r=' r=1 r=1 y ~ T r =■ \ or (4.1°) r=n r^i r_ n 1 Divide equation (4.10) by Cy then, r-1 r i — t r = 1 \ / p. V=h r- h r- 1 r= i ) °r > 0r r=n i>_ - b , w / + 3w (4- 11 ^ Reduce and simplify equation (4.11), then, O 1 ( — ) ■ \ ^P-s w) Ju / o SP - s (4. 12) V The equation (4.12) tells us: (1) profit is a single function of investment, that is, the more the investment, the more output and consequently the more profit; (2) profit is a "functional share" and wages are "residual payments," the incidence of taxation falls on wages, rather than on profits— that is exactly the inverse of Ricardo’s model; (3) the stability condition is that the profit-- recipients' propensity to save--should exceed that of the wage-eamers, otherwise the system is indeterminant; (4) the factor which influences the businessmen’s decision to invest is profit expectation and profit anticipation, or if they want to increase their profit they should increase and augment their investment, given demand for their products; and finally (5) profit does not depend on wages as Ricardo argued, nor can it be sought in surplus-value as Marx dreamed, but it originates in investment. CHAPTER VI CONCLUDING NOTES The conclusions arrived at in the previous chapters may be summarized as follows: 1. Some of the factors which make for growth in the American economy lie deep in American institutional structure--the characteristics of corporate enterprise and corporate financing, business objectives, and the competi tive process. Today, the American manager is preoccupied, basically, with the volume of sales, and, perhaps, market share. He will take vigorous and immediate actions, if there is a decline in his sales. This is a practical fact, and, indeed, a business thermometer. By all means, manage ment is not content to play a passive role in the growth process; that is, it is not prepared to wait for fortuitous events to impose growth upon it. Managers comprehend their position in the markets and they realize that a fall in sales will force them out. Then, the obvious goals of management are maximization of sales and maintaining a relative position in the market, in the short run. Now, if granted that the summation of the changes in individual firms’ sales will result in changes in aggregate output, 129 130 which is not an unsupported conjecture, the institutional ized structure and psychology of American business enter prise provides a powerful and sustained force making for the growth and expansion of the economy. Theoretically, given demand, in any event, some increase in investment can always be expected to be followed, concomitantly, with rising sales, output, and finally profits. That is, according to profit model set forth in Chapter V, profit is a single function of investment; or, the more the invest ment, the more output, and consequently the more profit, given the demand. The desire to increase their incomes and to accumulate wealth should, in the short run, lead manage ments to keep their investment demand as high as they can manage. 2. According to Keynes* theory of investment, the rate of interest is, logically, the only force which governs the decision to invest. The obvious assumption, "maximum-value-criterion,M of this assertion is that the firm tries to maximize its profit as though it were in isolation. The consequences of such an assumption are not particularly satisfying, because it leaves unexplained some frequently noted features of the behavior of a firm in capital budgeting. Due to these goals of American enter prise changes in the rate of interest have, often, very little effect on the motive to invest; and investment 131 demand may well continue high as long as it yields any positive returns, however small. Psychologically speaking, managements who pursue maximum-sales-objective, who want "to catch up" with others, undertake increases in invest ment by the invidious aspects of accumulation. He who fails to invest when the rate of return is positive is offering to others the opportunity to catch up, or to get ahead of him. In this occasion, he cannot afford to wait to equalize the marginal efficiency of capital with the rate of interest. On the balance of these institutional considerations, this writer is suggesting that the decision to invest is geared to business behavior and business objectives in American economy, rather than to the rate of interest; that the fluctuations in the rate of interest, compared to other institutional forces, has very little effect on investment programming. 3. In the second chapter a mathematical model was presented to explain the investment behavior. It is a matrix which has the generality aspect and, as a mathe matical tool, can include an infinite number of variates which might be capable of explaining investment behavior. On reading this chapter one must be struck by the largely impressionistic basis of its straightforward conclusions. But one cannot easily dismiss the suspicion that such a matrix is born in a situation with given exogenous 132 variableso Perhaps the matrix can justify its own cause. 4. The problem in hand is a precise interpretation of investment behavior. Empirical evidences have led this writer to believe that the American economy, because of its psychological features, has provided strong pressures which drive continuously for increased investment and conse quently output and profits. The empirical findings of Chapter IV have put forth the hypothesis that investment in the short run is influenced by the following factors: (1) sales, (2) changes in sale, (3) profit, (4) depreci ation expense, (5) age of the equipment, as measured by the size of depreciation reserve, and finally (6) the extent of capacity utilization. To be more precise, given demand, there are the sales' financial and technological consider ations that determine investment decision. 5. Manufacturing firms usually attach great import ance to the volume of their sales. This fact is empiri cally striking. Sales promotion for a firm is a means for furthering its other goals, namely operational efficiency, and finally profit realization. The first consideration is that investment planning and anticipation depends on sales expectations. Empirically it was found out that the larger firms, measured by the size of their gross fixed assets, show smaller deviations between their anticipated and actual investment; and the smaller the firm the larger 133 the deviations between the anticipated and actual invest ment outlays. This efficiency and accuracy of the predic tive performance of larger firms is a new and outstanding phenomenon of American economy of today; in the theory of profit expectations, this new feature is of great import ance. If this is the case, then the task of predicting future events seems rather easier and feasible. On the basis of this feature, this author has ventured to predict the expected actual investment for 1960. 6. The second factor impinges upon financial con siderations. Now, another institutional characteristic of the contemporary American economy is a reversion of busi nessmen to a "financial prudence" of the past. Businessmen would rather rely on their own internal funds than to borrow from outside by going to capital and money markets, or to expand their capital capacity on equity. The major sources of internal resources are retained earnings and depreciation expenses. The importance of retained earnings and depreciation expenses has been practically the same in the last decade. There is one implication here that impinged upon welfare theory. In the situations where profits and depreciation expenses are to be used for investment allocation, a higher corporate profit taxes, and a lower depreciation rate would theoretically affect incentives and the allocation of resources. As far as 134 profits are concerned, if the businessman accepts the tax imposition, he will shift it, like other overheads, to the consumers. In 1950 and 1954, depreciation rates were increased which have granted, in the form of tax conces sions, more generous depreciation allowances which have stimulated investment. 7. The last point is related to capacity variable and the age of capital equipment. Capacity is a relative term and a measure of economic growth. Evidently, there is a strong tendency among manufacturing industries to main tain a fairly constant level of capacity utilization. This is, indeed, an historical accident. Given capacity- utilization ratio, and also output-investment ratio, a rise in demand would result in a potential increase in invest ment. Thus, every enlargement of the output-capacity of capital goods is, therefore, creating the possibility of a rapid rise in some future date. Statistically, it is evident that whenever capacity is fully utilized, it has impacts on investment. On the other hand, the older the capital equipment, the lower the rate of investment. Conversely, the newer the equipment, the larger the rate of investment. 8. The unifying theme of this dissertation is its preoccupation with the strategy rather than the tactics of investment programming. 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New York: National Bureau of Economic Research, Inc., 1951. Natrella, V., and M. F. Foss. "Ten Years’ Experience with Business Investment Anticipations," Survey of Current Business, XXXVII (January, 1957), 16-24. ______ . "Business Anticipations of Capital Expenditures and Sales, 1957," Survey of Current Business, XXXVII (March, 1957), 5-10. _______. "Investment Plans and Realization," Survey of Current Business, XXXVII (June, 1957), 12-18. Office of Business Economics. "Nineteen Hundred Fifty- Eight Investment Programs of Business," Survey of Current Business, XXXVIII (July, 1958), 6-8. 141 U.S. Temporary National Economic Committee. Investigation of Concentration of Economic Power. Final Report and Recommendations of the Temporary National Economic Committee to the Congress of the U.S~ Seventy-fifth Congress. Washington, D.C.: U.S. Government Printing Office, 1941. C. PERIODICALS Alchian, A. A. MThe Rate of Interest, Fisher's Rate of Return Over Costs and Keynes' Internal Rate of Return," The American Economic Review, XLV (December, 1955), 936-43. Andrews, Philip. "A Further Inquiry into the Effects of Rates of Interest," Oxford Economic Papers. Ill (February, 1940), 33-73. Arrow, K. J. "Alternative Approaches to the Theory of Choice in Risk-Taking Situations," Econometrica, XIX (October, 1951), 404-437. Bain, J. S. "The Relation of Economic Life of Equipment to Reinvestment Cycles," The Review of Economics and Statistics, XXI (May, 1939), 79-88. _______. "Economics of Scale, Concentration and Entry," The American Economic Review, XXXIX (March, 1949), 448-64. Bandeen, R. A. "Automobile Consumption 1940-1950," Econometrica, XXV (April, 1957), 239-48. Brems, H. "A Discontinuous Cost Function," The American Economic Review, XLII (September, 1952), 377-86. Brown, J. W., and others. "A Study of Index Correlations," The Journal of the Royal Statistical Society, LXXVII (September, 1914), 317-46. Calenson, W., and H. Leibenstein. "Investment Criteria, Productivity, and Economic Development," Quarterly Journal of Economics. LXIX (August, 1955), 343-70. Chenery, H. "Overcapacity and the Acceleration Principle," Econometrica, XX (January, 1952), 1-28. 142 Chenery, H. "Application of Investment Criteria," The Quarterly Journal of Economics, LXVII (August, 1953), 76-96. Chemoff, H. "Rational Selection of Decision Function," Econometrica, XXII (October, 1954), 422-43. Cochran, W. G. "The Chi-Square Test of Goodness of Fit," The Annals of Mathematical Statistics, XXIII (September, 1952), 315-45. Craig, A. T. "On the Mathematics of the Representative Method of Sampling," The Annals of Mathematical Statistics, X (March, 1939), 26-34. Domar, E. D. "Depreciation, Replacement, and Growth," The Economic Journal, LXIII (March, 1953), 1-32. Ebersole, J. F. "The Influence of Interest Rates upon Entrepreneurial Decisions in Business--A Case Study," Harvard Business Review, XVII (September, 1938), 35-39. Eisenhart, C. "The Assumptions Underlying the Analysis of Variance,” Biometrica, XXXIV (January, 1947), 1-21. Frisch, R. "The Interrelation Between Capital Production and Consumer-Taking," The Journal of Political Economy, XXXIX (October, 1931), 646-54. "On the Notion of Equilibrium and Disequi- librium," The Review of Economic Studies, III (February, 1936), 100-105. Gort, M. "The Planning of Investment: A Study of Capital Budgeting in the Electric Power Industry," The Journal - - of the Business of the University of Chicago, XXIV (April and July, 1951), 79-95, 181-202. Greenberg, B. G., and A. E. Sarham. "Matrix Inversion, Its Interest and Application in Analysis of Data," The Journal of the American Statistical Association, LIV (December, 1959), 755-65. Grey, A. L. "The Marginal Efficiency of Capital and Investment Programming," The Economic Journal, LXVI (December, 1956), 662-75. _______, and H. D. Brockie. "The Rate of Interest, Marginal Efficiency of Capital and Investment Program- ming--A Rejoinder," The Economic Journal, LXIX (June, 1959), 333-43. 143 Haavelmo, T. "The Probability Approach in Econometrics," Econometrica (Supplement), XII (July, 1944), 1-117. Hagood, M., and E. H. Bemert. "Component Indexes as a Basis for Stratification in Sampling," The Journal of the American Statistical Association, XL (September, 1940), 330-41. Heller, W. "The Anatomy of Investment Decision," Harvard Business Review, XXIX (March, 1951), 95-103. Henderson, H. D. "The Significance of the Rate of Interest," Oxford Economic Papers (October, 1938), pp. 1-13. Irwin, J. 0. "Mathematical Theorems Involved in the Analysis of Variance," The Journal of the Royal Statistical Society, XCIV (September, 1931), 285-300. Kahn, A. E. "Investment Criteria in Development Programmes," The Quarterly Journal of Economics, LXV (February, 1951), 38-61. Kaldor, N. "Mr. Hicks on the Trade Cycle," The Economic Journal, LXI (December, 1951), 833-47. Kalicki, M. "The Principle of Increasing Risk," Economica (New Series), IV (November, 1937), 440-47. "A Theory of Profits," The Economic Journal. LII (June-September, 1942), 258-66. _______. "A New Approach to the Problem of Business Cycles," The Review of Economic Studies. XVI (1949- 1950), 57-154^ Katona, G., and J. N. Morgan. "The Quantitative Study of Factors Determining Business Decisions," The Quarterly Journal of Economics. LXVI (February, 1952), 67-90. Kendall, M. G. "Regression, Structure, and Functional Relationship," Part I, Biometrica, XXXVIII (June, 1951), 11-25. Keynes, J. M. "The Commemorations of T. R. Malthus; Three Allocutions," The Economic Journal, XLV (June, 1935), 230-34. 144 Kisselgoff, A. "Investment in Plant and Equipment in Private Electrical Utilities in the United States," Econometrica. XIX (January, 1951), 58-59. Koopmans, T. C. "Statistical Estimation of Simultaneous Economic Relations," The Journal of the American Statistical Association. XL (December. 1945), 5^8-66. _______. "Identification Problems in Econometric Model Construction," Econometrica, XVII (April, 1949), 125- 44. Lange, 0. "A Note on Innovation," The Review of Economics and Statistics. XXV (February, 1943), 19-25^ Lintner, J. "Distribution of Incomes of Corporations Among Dividends, Retained Earnings and Taxes," The American Economic Review, XLVII (May, 1956), 97-113. Machlup, F. "The Problem of Verification in Economics," The Southern Economic Journal, XXII (July, 1955), Marschak, J. "Money and the Theory of Assets," Econometrica, LXIII (October, 1938), 311-25. _______. "On Combining Market and Budget Data in Demand Studies: A Suggestion," Econometrica, VII (October. 1939), 332-35. Meade, J., and W. S. A. Philip, "Summary of Replies to Questions on Effects of Interest Rates," Oxford Economic Papers (October, 1938), pp. 14-31. Metzler, L. A. "Wealth, Saving, and the Rate of Interest," The Journal of Political Economy, LIX (April, 1951), 93-116. Meyer, J. R., and E. Kuh. "Acceleration and Related Theories of Investment: An Empirical Inquiry," The Review of Economics and Statistics, XXXVII (August, 1955), 217-30. _______. "Correlation and Regression Estimates when the Data Are Ratios," Econometrica, XXIII (October, 1955), 400-416. Modigliani, Franco, and M. H. Miller. "The Cost of Capital, Corporation Finance and the Theory of Invest ment," The American Economic Review, XLVII (June. 1958), 261-97.---------------------- 145 Neyman, J. "On the Two Different Aspects of the Repre sentative Method: The Method of Stratified Sampling and the Method of Purposive Selection," The Journal of the Royal Statistical Society, XCVII (December, 1934), 558-625. Norton, F. E. "The Accelerator and the Over-Investment and Under-Consumption Models," The Economic Journal, LXVI (March, 1956), 49-65. Orcutt, Guy H., and D. Cochrane. "Application of Least Squares Regression to Relationships Containing Auto- Correlated Error Terms," The Journal of the American Statistical Association, XLIV (September, 1949), 32-61. Poarson, Karl. "On a Form of Spurious Correlation Which May Arise When Indices Are Used in the Measurement of Organs," The Proceedings of the Royal Statistical Society o£ London, LX (1897), 489~96. Preinreich, Gabriel A. D. "Annual Survey of Economic Theory: The Theory of Depreciation," Econometrica, VI (July, 1938), 219-41. _______. "The Practice of Depreciation," Econometrica, VII (July, 1939), 235-65. Robinson, Joan. "The Production Function," The Economic Journal, LXV (March, 1955), 67-71. Stephan, F. F. "History of the Uses of Modem Sampling Procedures," The Journal of the American Statistical Association, XLIII (March, 1943), 12-39. _______. "Practical Problems of Sampling Procedure," The American Sociological Review, I (August, 1934), 569-80. _______. "Stratification in Representative Sampling," The Journal of Marketing, VI (July, 1941), 38-46. Stock, J. S., and L. R. Frankel. "The Allocation of Samplings Among Several Strata," The Annals of Mathe matical Statistics, X (March, 1939), 288-93. Stuart, A. "The Efficiencies of Tests of Randomness Against Normal Regression," The Journal of the American Statistical Association, LI (June, 1956), 285-87. 146 Triang, S. C. "Accelerator, Theory of the Firm, and the Business Cycle," The Quarterly Journal of Economics, LXV (August, 1951), 325-41. Weekstein, R. S. "On the Use of the Theory of Probability in Economics," The Review of Economic Studies, XX (1952-1953), Yntema, D. B. "Measures of the Inequality in the Personal Distribution of Wealth and Income," The Journal of the American Statistical Association, XXVIII (December, 1933), 423-33. D. ESSAYS AND ARTICLES IN COLLECTIONS Bridge, L. "The Financing of Investment by New Firms," Conference on Research in Business Finance. New York; National Bureau of Economic Research, 1952. Pp. 65-86. Chemoff, H., and D. Nathan. "The Computation of Maximum Likelihood Estimates of Linear Structural Equations," Studies in Econometric Method. Cowles Commission Monograph 14, W. C. Hood and T. C. Koopmans, editors. New York: John Wiley, 1953. Pp. 240-46. David, F. N., and J. Neyman. "Extension of the Mark-off Theorem of Least Square," Statistical Research Memoirs, II. Ed., Karl Pearson. London: Department of Statistics, University of London, University College, 1938. Pp. 105-116. Dean, J. "Department Store Cost Functions," in Studies in Mathematical Economics and Econometrics. Ed., 0. Lange, F. Muntyre, and T. 0. Yntema. Chicago: University of Chicago Press, 1942. Pp. 222-54. Duesenberry, J. S., and H. Kistin. "The Role of Demand in the Economic Structure," Studies in the Structure of the American Economy. Ed. by W. Leontief. New York: Oxford University Press, 1953. Pp. 451-82. Hart, A. G. "Risk, Uncertainty, and the Unprofitability of Compounding Probabilities," in Studies in Mathe matical Economics and Econometrics. Ed., 0. Lange, F. Muntyre, and T. 0. Yntema. Chicago: University of Chicago Press, 1942. Pp. 110-18. 147 Keynes, J. M. "The General Theory," The New Economics: Keynes* Influence on Theory and Public Policy. S. Harris, ed. New York: Alfred A. Knopf, 1950. Pp. 181-93. Koopmans, T. C., and W. C. Hood. "The Estimation of Simultaneous Linear Economic Relationships," Studies in Econometric Method. Cowles Commission Monograph 14, W. Co Hood and T. C. Koopmans, editors. New York: John Wiley, 1953. Pp. 166-70. Tintner, G. "A Contribution to the Nonstatic Theory of Production," in Studies in Mathematical Economics and Econometrics. Ed., 0. Lange and others. Chicago: University of Chicago Press, 1942. Pp. 92-109. APPENDIX APPENDIX Pulp, Paper, and Allied Products American Box Board Co. American Seal-Kap Corp. American Writing Paper Co. of Del. Central Fibre Products Co. Champion Paper & Fiber Co. Chesapeake Corp. of Va. Consolidated Paper Co. Consolidated Water, Power, & Paper Co. Container Corp. of America Crown Zellerbach Corp. Crystal Tissue Co. Eddy Paper Co., Ltd. Federal Paper Board Co., Inc. Fort Wayne Corrugated Paper Co. Glatfelter Co., P.H. Hanmermill Paper Co. Hudson Pulp & Paper Corp. International Paper Co. Keyes Fibre Co. Kimberly-Clark Corp. Mead Corp. Nashua Corp. Nekoosa-Edward Paper Co. 150 Puget Sound Pulp & Timber Co. Rayonier Inc. St. Regis Paper Co. Sealright-Oswego Falls Corp. Sonoco Products Co. Southland Paper Mills, Inc. Standard Packaging Corp. Stone Container Corp. Sutherland Paper Co. Union Bag-Camp Paper Corp. United Board & Carton Corp. United Wallpaper, Inc. Warren Co. (S.D.) West Va. Pulp & Paper Co. II. Light Chemicals Abbott Laboratories Allied Laboratories, Inc. American Home Products Corp. American Marietta Co. Archer-Daniels-Midland Co. Avon Products, Inc. Babbitt Inc. (B.T.) Bristol-Myers Co. Central Soya Co., Inc. Chemway Corp. Chickasha Cotton Oil Co. Colgate-Palmolive-Peet Co. Cook Paint & Varnish Co. Coty, Inc. Curtis Industries, Inc. (Helene) Devoe & Raynolds Co., Inc. Drackett Co. (The) Ferro Corp. General Pacific Corp. Glidden Co. Grand Rapids Varnish Co. Lehn & Fink Products Corp. Merck & Co., Inc. Norwich Pharmacal Co. Parke, Davis & Co. Patterson-Sargent Co. Plough Inc. Procter & Gamble Co. Purex Corp., Ltd. Reliance Varnish Co. Rexall Drug & Chemical Co. Robinson Inc. (Helena) Spencer Kellogg & Sons, Inc. Sterling Drugs, Inc. Universal American Corp. 152 Valspar Corp. Vick Chemical Co. III. Heavy Chemicals Air Reduction Co., Inc. Allied Chemical Corp. American Agricultural Chemical Co. American Cyanamid Co. American Potash & Chemical Corp. American Viscose Corp. Atlas Powder Co. California Ink Co., Inc. Catalina Corp. of America Celanese Corp. of America Chemetron Corp. Columbian Carbon Co, Commercial Solvents Corp. Dow Chemical Co. duPont de Nemours 6c Co., (E.I.) Eagle-Picher Co. General Dynamics Corp. Harshaw Chemical Co. Hercules Powder Co. Hooker Chemical Corp. Industrial Rayon Corp. Interchemical Corp. Koppers Co., Inc. Lithium Corp. of America Monsanto Chemical Co. National Distillers and Chemical Corp. National Vulcanized Fibre Co. Nalco Chemical Co. Nopco Chemical Co. Olin-Mathieson Chemical Corp. Park Chemical Co. Parker Rust Proof Co. Pennsalt Chemical Corp. Pfizer & Co., Inc. (Chas.) Potash Co. of America Publicker Industries, Inc. Sun Chemical Corp. Stauffer Chemical Co. Union Carbide Corp. United Carbon Co. Victor Chemical Works Wallace & Tieman Inc. Petroleum American Petrofina Inc. Anderson-Prichard Oil Corp. Ashland Oil & Refining Co. Atlantic Refining Co. (The) Colorado Oil & Gas Corp. Continental Oil Co. Cosden Petroleum Corp. Frontier Refining Co. Gulf Oil Corp. Mohawk Petroleum Corp. Kerr-McGee Oil Industries Inc. Ohio Oil Co. (The) Phillips Petroleum Co. Pure Oil Co. Quaker State Oil Refining Corp. Richfield Oil Corp. Shamrock Oil & Gas Corp. Shell Oil Co. Sinclair Oil Corp. Skelly Oil Co. Socony-Mobil Oil Co. Standard Oil Co. of California Standard Oil Co. (Indiana) Standard Oil Co. (N.J.) Standard Oil Co. (Ohio) Sun Oil Co. Sunray Mid-continent Oil Co. Texaco, Inc. Tide-Water Oil Co. 155 Union Oil Co. of California Wilcox Oil Co. V. Rubber Armstrong Rubber Co. Baldwin Rubber Co. Dayton Rubber Co. Firestone Tire & Rubber Co. General Tire & Rubber Co. Goodrich (B.F.) Co. (The) Goodyear Tire & Rubber Co. Hewitt Robins, Inc. Kleinert Rubber Co. (I.B.) Mansfield Tire & Rubber Co. Midwest Rubber Reclaiming Co. Lee Rubber & Tire Corp. O'Sullivan Rubber Corp. Plymouth Rubber Co. Seiberling Rubber Co. United States Rubber Co. VI. Basic Iron and Steel Acme Steel Co. Alan Wood Steel Co. Alleghany Ludlum Steel Corp. American Brake Shoe Co. Armco Steel Corp. Bethlehem Steel Corp. Bliss & Laughlin, Inc. Byers Co. (A.M.) Carpenter Steel Co. Central Foundry Co. Colorado Fuel & Iron Corp. Continental Steel Corp. Copperweld Steel Co. Crucible Steel Co. of America Detroit Gray Iron Foundry Co. Detroit Steel Corp. Duraloy Co. Eastern Stainless Steel Corp. General Steel Castings Corp. Granite City Steel Co. Indiana Steel Products Co. Inland Steel Co. Interlake Iron Corp. Jessop Steel Co. Jones & Laughlin Steel Corp. Keystone Steel 6c Wire Co. Lukens Steel Co. Molydenum Corp. of America Moore Drop Forging Co. National Maaeable 6c Steel Castings Co. 157 National Steel Corp. Phoenix Steel Corp. (Del.) Pittsburgh Coke & Chemical Co. Pittsburgh Forgings Co. Pittsburgh Metallurgical Co., Inc. Pittsburgh Steel Co. Pittsburgh Steel Foundry Corp. Poor and Co. Republic Steel Corp. Shahmoon Industries Inc. Sharon Steel Corp. Standard Forgings Corp. Transue & Williams Steel Forging Corp. United States Pipe and Foundry Co. United States Steel Corp. Universal-Cyclops Steel Corp. Vanadium-Alloys Steel Co. Vanadium Corp. of America Vulcan Materials Co. Washington Steel Corp. Wheeling Steel Corp. Woodward Iron Co. Youngstown Sheet & Tube Co. 158 VII. Fabricated Metal Products Aero Supply Mfg. Co. Akron Brass Mfg. Co., Inc. American Can Co. American Chain and Cable Co. American Metal Products Co. American Radiator & Standard Sanitary Corp. American Screw Co. Anaconda Wire & Cable Co. Associated Spring Corp. Atlas Tack Corp. Belmont Iron Works Birdsboro Steel Foundry & Machinery Co. Black, Sivalls & Bryson, Inc. Buffalo-Eclipse Corp. Consolidated Electronics Industries Corp. Continental Can Co., Inc. Continental Copper & Steel Industries Inc. Crane Co. Ekco Products Co. Elastic Stop Nut Corp. of America Federal Mogul-Bower-Bearing Inc. Fenestra Inc. General Bronze Corp. General Cable Corp. Hall Lamp Co. (C.M.) Holland Furnace Co. Hoover Ball & Bearing Co. Hupp Corp. Hurd Lock & Mfg. Co. Iron Fireman Mfg. Co. Kawneer Co. Lakey Foundry Corp. Lamson and Sessions Co. McKinney Mfg. Co. MacWhyte Co. Metals Disintegrating Co., Inc. Mt. Clemens Metal Products Co. Nachman Corp. National Can Corp. National Presto Industries, Inc. National-Standard Co. National Tank Co. National - U.S. Radiator Corp. Parkersburg-Aetna Corp. Peninsular Metal Products Corp. Reading Tube Corp. Rheem Mfg. Co. Rome Cable Corp. Russell Co. (The F.C.) Ruud Mfg. Co. 160 Screw 6c Bolt Corp. of America Serrik Corp. Signode Steel Strapping Co. Smith Corp. (A.O.) Soss Mfg. Co. Standard Products Co. Standard Tube Co. Timken Roller Bearing Co. Trane Co. United-Carr Fastener Corp. United Industrial Corp. Van Dorn Iron Works Co. Yale 6c Towne Mfg. Co. Young Spring 6c Wire Corp. (L.A.) VIII. Other Machinery Acme Precision Products Inc. Air Products Inc. Allis-Chalmer Mfg. Co. American Laundry Machinery Co. American Machine 6e Foundry Co. American Machine 6c Metals, Inc. Aro Equipment Corp. Athey Products Corp. Balerank, Inc. Binks Mfg. Co. Bourjois Inc. Bowser, Inc. Briggs & Stratton Corp. Bucyrus-Erie Co. Buffalo Forge Co. Case Co. (J.I.) Caterpillar Tractor Co. Chain Belt Co. Cherry-Burrell Corp. Chicago Pneumatic Tool Co. Chicago Rivet & Machine Co. Continental Gin Co. Continental Motors Corp. Copper Bessemer Corp. Cummins Engine Co., Inc. Daystorm Inc. Deere & Co. Dodge Mfg. Co. Dorr Oliver Inc. Dresser Industries Inc. Fairbanks, Morse & Co. Food Machinery & Chemical Corp. Foster Wheeler Coirp. Gar Wood Industries Inc. Gardner-Denver Co. Gellman Mfg. Co. Hercules Motors Corp. Hamishfeger Corp. Harris-Interrype Corp. Hein-Wemer Corp. Hobart Mfg. Co. Hoe & Co. R. Ingersoll-Rand Co. International Harvester Co. Jaeger Machine Co. Joy Mfg. Co. Lamson Corp. of Del. Lanston Industries Inc. Le Toumeau Inc. (R.G.) Link-BeIt Co. Locke Steel Chain Co. Lunkenheimer Co. Lynch Corp. Mathews Conveyor Co. Merganthaler Linotype Co. Meyer Blanke Co. Myers & Bo. vjo., The F. E. National Rubber Machinery Co. Oliver Corp. Otis Elevator Co. Outboard Marine Corp. Randall Co. Reece Folding Machine Co. Reed Roller Bit Co. Sterling Aluminum Products Inc. Stewart-Warner Corp. Super Mold Corp. of California Thor Power Tool Co. Torrington Co. Towmotor Corp. United States Hoffman Mach. Co. Universal Winding Co. Victor Equipment Co. Walworth Co. Waukesha Motors Co. Westinghouse Air Brake Co. Worthington Corp. Yates-American Machine Co. Light Electrical and Machinery Addressograph-Multigraph Corp. Aerovox Corp. American Bosch-Arma Corp. Burroughs Corp. Clarostat Mfg. Co. Comell-Dubillier Electric Corp. Electric Auto-Lite Co. Electric Storage Battery Co. The General Instrument Corp. General Railway Signal Co. Globe Union Inc. Gould-National Batteries Inc. International Business Machine Corp. International Resistance Co. Ironrite Inc. Muter Co. National Cash Register Co. National Union Electric Corp. Oak Mfg. Co. Pi tney - Bowe s Inc. Potter Co. Royal McBee Corp. Sperry Rand Corp. Sprague Electric Co. Sunbeam Corp. Tung-Sol Electric Inc. Underwood Corp. Automotive Aerojet General Corp. American Motors Corp. Arvin Industries Inc. Borg-Wamer Corp. Budd Co. The Chrysler Corp. Clark Equipment Co. Clevite Corp. DTM Corp. Dana Corp. Detroit Aluminum & Brass Corp. Detroit Harvester Co. Diveo-Wayne Corp. Eaton Mfg. Co. Fedders Corp. Fruehauf Trailer Co. Gabriel Co. General Motors Corp. Hercules Gabon Products Inc. Houdaille Industries Inc. Kaiser Industries Corp. Kilsey-Hayes Co. King-Seeley Corp. McCord Corp. McQuay-Norris Mfg. Co. Mack Trucks Inc. Marmon-Herrington Co. Gulf 6c Western Corp. Midland-Ross Corp. Modine Mfg. Co. Monroe Auto Equipment Co. Motor Products Corp. Motor Wheel Corp. Muskegon Piston Ring Co. Perfect Circle Corp. Pierce Industries Inc. Ross Gear & Tool Co., Inc. Ryerson & Haynes Inc. Schwitzer Corp. Seagrave Corp. Sheller Mfg. Corp. Studebaker-Packard Corp. Thompson Ramo Wooldridge Inc. Twin Coach Co. Universal Control Inc. Weatherhead Co. White Motor Co. Consumer Durables Allied Paper Corp. American Air Filter Co., Inc. American Stores Co. Bell 6c Gosset Co. Carrier Corp. 167 Coleman Co. Inc. Cribben & Sexton Co. Easy Washing-Machine Corp. Hoover Co. Hussman Refrigerator Co. Gilbert Co. The A.C. Gillette Safety Razor Co. Knapp-Monarch Co. Maytag Co. The Roper (George D.) Corp. Silex Co. Tappan Co. Utility Appliances Corp. Welbilt Corp. Whirlpool Corp. White Sewing Machine Corp. XII. Machine Tools Allied Products Corp. Avildson Tools & Machines, Inc. Black and Decker Mfg. Co. Brown & Sharpe Mfg. Co. Bullard Co. Bliss Co. (E.W.) Cincinnati Milling Machine Co. Cross Co. 168 Ex-Call-0 Corp. Giddings & Lewis Machine Tools Co. Gishot Machine Co. Hanson-Van Winkle-Munning Co. Rearing & Trecker Corp. Koehring Co. McKay Machine Co. Mesta Machine Co. Micromatic Hone Corp. Monarch Machine Tool Co. National Acme Co. New Britain Machine Co. Simonds Saw & Steel Co. South Bend Lathe Works Starrett Co. The L.S. Sundstrand Machine Tool Co. Udylite Corp. Union Twist Drill Co. United Engineering & Foundry Co. Van Norman Industries Inc. Warner & Swasey Co. XIII. Heavy Electrical Machinery Allis Co., The Louis Century Electric Co. Clark Controller Co. 169 Cutler-Hammer Inc. Duro-Test Corp. Gamewell Co. General Electric Co. Emerson Electric Mfg. Co. Howell Electric Motors Co. Hubell Inc. Harvey Jack & Heintz Inc. Kerite Co. Leece-Neville Co. Northeast Capital Corp. Ohio Brass Co. Penn-Controls Inc. Reliance Electric & Engineering Co. Speer Carbon Co. Square D Co. Wagner Electric Corp. Westinghouse Electric Corp. XIV. Basic Textiles Bates Mfg. Co. Beaunit Mills, Inc. Belding Heminway Co. Inc. Blumental & Co. Inc. Sidney Burlington Industries Inc. Cannon Mills Co. Century Industries Co. 170 Collins 6c Aikman Corp. Cone Mills Corp. Dan River Mills Inc. Duplan Corp. The Kendall Co. Lowestein & Sons, Inc. M. Mount Vernon Mills Inc. Powdrell 6c Alexander, Inc. Riegel Textile Corp. Pacific Mills Reeves Bro. Inc. Stevens 6e Co., Inc. J.P. Strook 6c Co., Inc. S. Textron Inc. United Merchants 6c Mfg. Inc. Winsor Industries Inc. Wyandotte Worsted Co. XV. Other Textiles Adams-Millis Corp. Armstrong Cork Co. Bigelow-Sanford Carpet Co. Chadboum-Gothan Inc. Congoleum-Naim Inc. Davenport Hosiery Mills, Inc. Firth Carpet Co. Kayser-Roth Corp. Lees & Sons Co. James Mojud Co. Inc. Phoenix Hosiery Co. Real Silk Hosiery Mills Inc. Sandura Co. Van Raalte Co. Inc. Wayne Knitting Mills, Inc.
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Kooros, Ahmed
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The Theory Of Investment Programming: A Suggested Econometric Model
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