BESAGGREGATED ANALYSIS OF THE SHWTENG 0F THE CQRPORATEQN iNCOME TAX Thesis for the Degree 01 Ph. D. MICHlGAN STATE UNIVERSITY ARTHUR ASCHER BAYER 1968 LIBRARY Michigan State University This is to certify that the thesis entitled DISAGGREGATED ANALYSIS OF THE SHIFTING OF THE CORPORATION INCOME TAX presented by Arthur Ascher Bayer has been accepted towards fulfillment of the requirements for Ph.D. degree in Economics far [a - A? 3401/41 V Major professor .‘7 Date /////L7i/éi 0-169 -7... mm ABSTRACT DISAGGREGATED ANALYSIS OF THE SHIFTING OF THE CORPORATION INCOME TAX By Arthur Ascher Bayer Since 1934, the corporation income tax has accounted for 12.6 to 38.1 percent of the federal receipts from the public. In 1965, this source of federal receipts amounted to 21.3 percent of the total; exceeded only by the individual income tax. Despite its predominance, no other tax has raised as much controversy over who actually assumes the burden. Is it the stockholder, the consumer, or the wage earner? The answer is germane to any analysis of our entire tax structure. This study attempts to measure the degree of shifting that is accomplished by seventeen, two—digit (SIC) industries in the manufacturing sector of our economy during the period 19H7-1963. Using time series regression analysis for each industry, the before—tax rate of return on gross assets is regressed on several explanatory variables, one of which is the tax liability as a percent of gross assets. The regres- sion equation is based upon the behavioral assumption that the firm attempts to take compensatory action to recoup as much of the tax burden as possibly by either shifting the burden forward in higher price or backwards in lower payments to labor. According to the specification of the model, the Arthur Ascher Bayer measure of shifting becomes the regression coefficient of the tax variable. As part of the analysis, various theories of the firm are examined by comparing their shifting predictions with the empirical results. The traditional models of pure competi— tion and monopoly, the Baumol sales-maximizing model, and the Williamson expense preference model all predict a limit of 100 percent shifting in the long-run. Only the Krzyzaniak and Musgrave model, with its "signal" theory of business behavior, can predict more than 100 percent shifting. The empirical results indicate that nine of the seventeen industries shift no significant amount of the tax burden; eight show shifting measures significantly greater than zero; and one of the eight (Tobacco Manufactures) shows a shifting measure significantly greater than 100 percent. The measures of shifting are then correlated by industry, using rank correlation, with concentration ratios, changes in total assets, and percentage changes in average weekly earnings of production workers in each industry. The most significant inference is that wages advanced less in those industries which shift moreof the tax, implying the possibility that the burden is shifted backwards upon the wage earner. The findings of this study cannot adequately substan- tiate any discrimination among the various models. Although the Krzyzaniak and Musgrave model is the only model which Arthur Ascher Bayer can support the results of the Tobacco Manufactures indus— try, one industry out of seventeen is comparatively weak evidence upon which to base such a crucial judgement. Further study is needed to test the applicability of the various theories of the firm to the shifting problem, and if possible, on a more disaggregated basis once the data are available. DISAGGREGATED ANALYSIS OF THE SHIFTING OF THE CORPORATION INCOME TAX By Arthur Ascher Bayer A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Economics 1968 ACKNOWLEDGEMENTS I acknowledge with gratitude the encouragement, advice, and criticism that my dissertation committee has given me. To Professor John R. Moroney, Chairman, whose early interest encouraged me to undertake the project and whose professional guidance and challenging direction has been invaluable. Professor Moroney's insistence for clarity and completeness led to significant improvements in detail and perspective. To PrOfessors Peter J. Lloyd and Bruce T. Allen, my appreciation for their comments on specific points which needed explanation. I should also like to express my appreciation to Professor Thomas G. Moore for his critical views on the methodology which sharpened my own thinking and eventually led to an improved model. In addition, I should like to thank my colleague, Professor Gene Laber, with whom I exchanged views during the last stages of this research and whose computer . programming assistance facilitated the final calculations. Finally, I should like to acknowledge the unfailing moral support that I received from my wife, Judith. Her positive attitude about everything connected With the pursuit of this advanced degree enabled me to complete the thesis and thus reach our common objective. ii TABLE OF CONTENTS Chapter I. INTRODUCTION . . . . Background Definition of the Shifting Concept THE ANALYSIS OF SHIFTING UNDER VARIOUS II. THEORETICAL CONDITIONS . . . . . Traditional Theoretical Models Questionable Assumptions of Traditional Theory Profit Maximization Qualifications Alternative Hypotheses Conclusion III. POSSIBLE INDICATORS OF SHIFTING AND RECENT EMPIRICAL STUDIES. Possible Indicators of Shifting Recent Empirical Results IV. THE COMPLETE REGRESSION MODEL. The Functional Relationship of Key Variables Description of Key Variables Non—Tax Influences on the Rate of Return Basic Model V. AN EVALUATION OF EMPIRICAL RESULTS Conclusions BIBLIOGRAPHY APPENDICES A. Adjustment Procedure for Income Data B. Industry Classification Used by Frank de Leeuw iii Page 03H 11 22 25 28 H1 45 57 68 69 72 77 82 89 105 109 115 115 122 Table 3a. 3b. A1. LIST OF TABLES History of Federal Corporation Income Tax Rates . . . . . . . Recent Empirical Results Regression Results for Shifting Industries Regression Results for Non—Shifting Industries . . . . . . . . Shifting Measures and Concentration Ratios. Industry Percentage Change in Total Assets Shifting Measures and Percentage Change in Average Weekly Earnings Adjustment Ratios iv Page 58 90 93 100 103 104 118 CHAPTER I INTRODUCTION Background The corporation income tax was enacted in 1909 under the protective guise of an excise on the privilege of doing business as a corporation. To this day, it is a proportional income tax levied on the accounting profits of all legally defined, non-exempt corporations. Exemptions, partial or whole, are granted to some qualifying, non—profit corpora- tions; e.g., charitable, educational, religious, and literary organizations.l Since 1939, it has accounted for 12.6 to 38.1 percent of the federal receipts from the public. In 1965, this source of federal receipts amounted to 21.3 percent of the total; exceeded only by the individual income tax, which contributed 90.8 percent. DeSpite its predominance, no other tax has provoked as much controversy and disagreement about who actually assumes the burden. Opposite conclusions have been reached by many economists who have studied the tax and its Some believe that it is borne by the corpora- operation. tions, and, hence by the stockholders. Others conclude that it is paid by the consumer through higher prices, 1Section 7701 (a) (3) of the Internal Revenue Code of 1954. l 2 while still others argue that the burden is shifted back upon the workers in the form of lower wages. Lastly, there is a group who believes that the burden of the tax is borne jointly by the three groups—~stockholders, consumers, and wage earners. This study attempts to measure the degree of shifting that is accomplished by various industries in the manufacturing sector of our economy during the period 1947—1963. The seventeen years of the analysis encompassed three corporation income tax rate changes as presented in Table 1. Thus, it was possible to select a test period which was relatively short and yet provided acceptable_tax rate variability, especially since effective tax rates are used in the regression model. TABLE 1 HISTORYOF FEDERAL CORPORATION INCOME TAX RATES Year Exemptions, Brackets, or Type of Tax Rate 1946 First $25,000 21-25 $25,000 to $50,000 53 over $50,000 38 23 42 1950 Normal Tax Surtax (over $25,000 surtax exemptions) 19 1951 Normal Tax 28 3/4 50 3/4 Surtax (over $25,000 surtax exemptions) 22 1952 Normal Tax 30 Surtax (over $25,000 surtax exemptions) 22 52 Source: Joseph A. Pechman, Federal Tax Policy (Washington: The Brookings Institute, 1966), p. 245. 3 Instead of the entire manufacturing sector as a unit, seventeen industries are studied.2 The numerous differences between the characteristics of each industry indicate the advantages to be gained from a more disaggre- gated approach. Unfortunately, only a few of these distinguishing characteristics can be quantified, and an effort will be made to determine their relative influence upon the observed performance in each industry. Definition of the Shifting Concept The uncertainty about the burden of the corporation income tax has been complicated by the ambiguity of the terms used in the analysis. In the classical system, where planned savings and investment are equal and full- employment is maintained automatically, the concepts of impact, shifting, and the incidence of the income tax are clearly delineated. The impact is the initial imposition of the tax on some person or business entity; shifting is the transfer of this obligation to others by whom it is actually assumed; and the incidence is the settlement of the burden on the ultimate taxpayer, or the result of shifting. A fourth definition, effects of pressure, encompasses all secondary consequences of the impact, shifting, or incidence of a tax. Thus, shifting refers only to the process; incidence denotes the result, and 2Seventeen of the possible twenty major industries which are classified by the Standard Industrial Classifica— tion are used in this study. 4 effects are a residual, including both changes in output and income distribution which are not considered a part of the direct money burden. In a system where variations in aggregate demand may originate from changes in the desire to spend available funds, and where such variations may give rise to changes in the level of employment as well as in prices, the tradi- tional distinction between direct incidence and indirect effects involves an arbitrary separation between various elements of the total change. Shifting the impact of the tax through higher prices or lower payments to factors of production may initiate a chain of subsequent adjustments which make the concept of locating the ultimate burden of little significance. The changes must all be considered as interdependent parts of the adjustment, proceeding in one and the same system of_general equilibrium. The indirect effects of price and/or output variations must be included in the concept of shifting. Consequently, the most useful concept of shifting should be concerned with the result instead of the adjustment process. This more inclusive definition eliminates the troublesome task of differentiating between direct and indirect effects of a change. The important consideration becomes whether there is a difference between impact incidence and effective incidence, with the . . 3 degree of shifting measured by the amount of the inequality. 3Musgrave's distinction between effective and impact 5 In the case of the corporation income tax, shifting describes the results of particular actions taken by the corporation in response to an increase in the income tax. The motive is to pass forward to its customers or backward upon its employees as much of the impact incidence as possible. In the short-run, when capacity is constant, forward shifting is accomplished by price increases. Backward shifting is imposed by the downward pressure on wages and/or on the payments to owners of other productive factors (including equity owners). incidences will be used in this study. See Ridhard A. Musgrave. The Theory of Public Finance (New York: McGraw-Hill Book Company, 1959), p. 230. Professor Musgrave defines effective incidence as "the actual change in dietribution that results as a given tax is imposed or tax substitution is made," and impaCt incidence as "the change that would result if the income position of a new taxpayer were reduced.by the amount of tax remission, while the positions of all others remained unchanged." CHAPTER II THE ANALYSIS OF SHIFTING UNDER VARIOUS THEORETICAL CONDITIONS Traditional economic theory has maintained that in the short-run it is not possible for firms under pure compe- tition or monopoly to adjust price and output so as to shift the corporation income tax. The precision of this theory is rigorous and appealing. However, whether the traditional theoretical models of pure competition and monopoly are applicable to the examination of tax incidence remains an Open question. It is imperative that any modification of the traditional theory of the firm, which is based on the behavioral assumption of profit—maximization, be stated precisely. Specifically, any such modification should be judged on the basis of its predictive power by comparison with the traditional model. A model is a tool, and as such, it must provide a mechanism for making inferences about reality based upon incomplete data and observations which show only correlations and not the structural relationships that are sought. Because reality is obviously too complex to be fully characterized in any workable model, we must rely upon abstractions and 6 over-simplifications. One might perhaps accept a model as useful if it satisfies the requisites stated by William J. Baumol. A useful model describes an imaginary world which is sufficiently complex and similar to reality to permit us to make some legitimate inferences about the behavior of the economy, but which is at the same time sufficiently simple for us to understand and manipulate with the tools at our disposal. The degree of usefulness is influenced by the selec- tion of the elements which are omitted from the model. The social scientist differs from the natural scientist in that the latter usually bases an experiment on controlled environ— mental conditions. The variables that are omitted by the economist correspond to the environmental conditions that may in principle be held constant by the natural scientist. The exclusion of certain variables from an economic model may seriously limit its general validity, and the model‘s usefulness may therefore be restricted to specific problems. As stated by Baumol, The facts of the problem on hand and the questions which are being asked must decide what we can afford to leave out and what we must put in to avoid being misled. Thus, a model can only be designed around and judged in light of a specific problem. Inherent in the selection of relevant variables is the important task of Specifying the assumptions. Erroneous or irrelevant assumptions can mislead the analysis, and can contribute towards the generation of unreliable conclusions. 1 William J. Baumol, Business Behavior, Value and Growth (New York: The Macmillan Company, 1959), p. 2. 2 Ibid, p. 2. 8 Whatever the favored methodological position, guidelines must be chosen for determining the appropriate assumptions. One position is that theoretical results from an economic model should be generally valid. Unfortunately, a theoreti— cal model which purports to be generally valid must neces— sarily suffer the consequences of over—simplification and abstraction. To produce a theory which is applicable to a variety of circumstances requires certain abstractions and reliance can be placed only on those characteristics which are common to all circumstances. Generalizations can be costly, and even though it must be admitted that results that are applicable everywhere would be valuable, the benefits must be related to the costs. In some cases, the economist is interested in problems that are influenced by variables not generally present in all sit— uations. These unique variables are consequently omitted from the general model, and reliable inferences are not obtained. An alternative methodological position is taken by those who desire greater realism in economic models. When realism becomes an end in itself, the complexity of the anal— ysis challenges even the most sophisticated mathematical systems. The benefits are again offset by the costs associ- ated with the loss of insight into the workings of the models. It is unfortunate that the adherents to the above positions are predisposed in their over~concern about either the general usefulness of the theory or the realism of the assumptions. In contrast, Milton Friedman has stimulated considerable thought in the area of hypothesis evaluation.3 He stated that it is wrong to concentrate all attention on the realism of the assumptions when evaluating an economic hypothesis. The relevant question to ask about 'assumptions' is not whether they are descriptively 'realistic,’ for they never are, but whether they are sufficiently good approximations for the purpose in hand. By rejecting the practice of assessing the quality of the assumptions, Friedman was partially obligated to propose a better method of evaluating an economic model. He did this by arguing that empiricists should not stagnate in the discussion of assumptions but should examine the predictive powers of the hypotheses. Friedman claimed that Theory is to be judged by its predictive power for all classes of phenomena which it is intended to 'explain.’ Only factual evidence can show whether it is 'right' or 'wrong' or, better, tentatively 'accepted' as valid or rejected...the only relevant test of validit of a hypothesis is comparison of its predictions with experience. The hypothesis is rejected if its predictions are contradicted ('frequently' or more often thap predictions from an alternative hypothesis). The methodological position taken in this study can best be described as a compilation of the arguments by Baumol and Friedman. Since the analysis of the corporation income tax incidence is a specific problem, as suggested 3Milton Friedman, Essays on Positive Economics (Chicago: The University of Chicago Press, 1966). ”Ibid, p. 15. 51bid, pp. 8—9. 10 by Baumol, the specific variables and relationships deserve individual consideration within the general theoretical model of the firm. The assumptions associated with the traditional model should be adhered to until it can be shown that the prediction generated by the model differs from the empirical observation. Thus if the empirical results differ from the model and show that short-run shifting of the corporation income tax did occur, then the usefulness of the traditional model deserves questioning. However, the consequential rejection of the traditional theory should be tempered and carefully considered. The implication of Friedman's essay is that assumptions should be judged on the basis of their prediction ability. The severity of his methodological approach can be tempered to accommodate Baumol's argument that "one of the most convenient instruments for judging the apprOpriateness of our necessarily imperfectly realistic models is the examination of the plausibility of their assumptions."6 The synthesis involves the evaluation of the prediction ability of traditional theory when related to a particular problem, namely the corporate income tax incidence. Depending upon the degree of similarity between the predicted results and the empirical findings, the theory should be either accepted or partially or wholly rejected. When rejection is warranted, all elements of the theoretical model should be carefully analyzed. This means —_ 6Baumol, op. cit., p. 6. 11 that both included and excluded variables, assumptions, and the structural relationships should be examined under the restricting guidelines of the particular problem. If changes can be made to the components of the model while maintaining the basic economic concepts, then the altered economic tool is not a new theory but the same one adjusted in light of the specific problem.7 The proposed steps in following this methodological approach are first, to develOp the short and long run traditional arguments about the feasibility of shifting the corporation income tax under conditions of pure compe- tition and monopoly. The next step is to alter the traditional model according to specific behavioral assump— tions and determine what degree of shifting, if any, is predicted by these alternative models. Finally, the empirical results should lead to both a solution of the shifting questions and an apprOpriate test of the altered theory compared to the traditional theory of the firm. Traditional Theoretical Models Certain distinctions are normally made when discussing the theory of the firm. The distinctions are based upon the length of time under consideration and market 7I believe it is a matter of semantics whether the adjusted model constitutes a new approach or remains the same under slightly different assumptions. The position taken in this paper is that the traditional theory remains useful and that most recent theories are nothing more or less than "variations on a theme"; the "variations" being different behavioral assumptions. ‘ 12 structure. Time plays an important part in differentia- ting between the short and the long run. The short run is generally considered that time period when the production process is constrained by the fixity of capital equipment. Output can be altered, but only within the limitsgoverned by the quantity of fixed capital. The long run denotes the period when capital equipment can be changed and output becomes more flexible. The market structure in which the firm Operates governs the degree of operational constraints and the assumed conduct of the firm. For reasons of comparative simplicity, this discussion will be limited to the analysis of shifting under conditions of pure competition and monopoly in the short and long run. One important behavioral assumption of the traditional model is that the entrepreneur attempts to maximize profit. Thus all conduct and decisions are based on the goal of obtaining the greatest profit under the given market conditions and production possibilities, both in the short and the long run. A. Pure Competition An entrepreneur Operating under conditions of pure competition produces a homogeneous product along with many other sellers; sells his product in a market serving many buyers who possess perfect knowledge about price, quality, and market Opportunities; buys his inputs in competitive markets (and therefore must Operate to satisfy a competitive 13 capital market). Short-run In the short-run, the entrepreneur attempts to maximize profits, given the inputs (xi), the market price of inputs (ri), and the selling price of his product (p). The total revenue (R) is given by the number of units sold (q) multiplied by the fixed unit price. The profit (fl) is the difference between the total revenue and the total cost (C): N = pq - C (l) where q = f(xl, x2), and x1, x2 are inputs. The total cost equation is: C = rlxl + rzx2 + r3x2 (2) where: x1 = labor x2 = capital r1 = cost of labor r2 = user cost or operating cost of capital r3 = sunken cost Of capital Combining the cost function with the production function, the profit equation (1) can be rewritten: 0 : pf(Xl, x2) - rlxl - r2x2- r3x2 (3) where prOfit is a function of inputs x1 and x2. When (3) is maximized with respect to the two input variables, the first- Order condition for profit maximization is that each input be utilized up to a point where the value of its marginal product equals its price. The second-order condition is 14 that the marginal products Of both inputs be decreasing.8 The same type of analysis can be done with cost functions. In this case the entrepreneur must equate the marginal cost with the market price of the product as the first—order condition for prOfit-maximization. The second-order condition is that marginal cost must be increasing at the profit—maximizing output.g Thus, for the competitive firm, profit-maximization is at the particular output where marginal cost equals the price of the product, and the marginal revenue product of each input equals its cost. Since the product is homogeneous and there are many sellers, each competitive entrepreneur will be selling his output at the prevailing market price. However, in the short-run, equilibrium for each firm will not necessarily be at an output where price equals average total cost. Time does not permit the equilibrating entry and exit of firms, and above-normal profits and/or losses may persist within an industry. The traditional argument against the probability of short—run shifting of the income tax necessitates a clear understanding of the difference between costs which are direct returns to variable factors and costs which are returns to fixed factors and are therefore price determined. 8See James M. Henderson and Richard E. Quandt, Microeconomic Theory (New York: McGraw-Hill Book Company, 1958), Chapter 3. 9151a, pp. 55-57. 15 In the short-run, capital stock is fixed, and the return to this fixed investment is determined by the price of the product. The excess of total revenue minus total variable cost is the return to the fixed capital or quasi-rent. This quasi—rent is subject to the income tax in the short-run. Quasi-rent differentials indicate the presence of more or less efficient firms in the industry. Only in the long—run, when it is possible to alter the stock of capital, must the entrepreneur consider the necessary return sufficient to attract and maintain capital. In the long—run this necessary return becomes a cost and shows up as the difference between total costs and total variable costs. Instead of labeling this differential, which is no longer price determined, quasi-rent, the entre— preneur considers this return the normal profit. Profit above normal profit in the long-run is economic rent or economic profit. It is important to emphasize that all profits are taxed, whether quasi-rents, normal profits, or economic rents. In the short—run, since the income tax does not affect marginal revenue or marginal cost, the profit maximizing output will not change as a result Of the tax. The burden of the tax falls fully upon the return to capital. However, the conclusion that a corporate income tax will not be shifted in the short-run is dependent upon the presumption that taxable profits are a return to a fixed 16 amount of invested capital. Profits are considered to be net of all variable costs; i.e., total revenue minus total costs. Since output and prices remain the same, the tax—reduced rate of return on invested capital cannot be increased. The neglected consideration is that not all invested capital, whether equity or debt, is fixed in the short—run. Working capital; i.e., work in process, inventory, and cash on hand, is relatively flexible and can be adjusted as the needs arise. Thus, the return on this more liquid form of capital can be deemed a variable cost included in profits. The capacitytb increase the rate of return on total invested capital in the short—run becomes a function of the ratio of working capital to total capital; the higher the ratio, the easier it becomes to increase the after—tax rate of return by reducing the amount of working capital. Long-run As a result of the reduction in the normal profit due to the income tax, in the long—run, some capital will leave the taxed industry. Since the prOportional corpora— tion income tax does not apply to all sectors Of the economy, capital can find alternative investment opportunities. The mobility of capital will eventually equate the yield on all comparable types (risk classes) Of investments. This decrease in the stock or in the growth rate of capital will have an effect upon the total output. Output will be reduced, 17 and the resultant market price will be higher in the long— run due to the effect of the income tax. The conclusion is that the tax will be shifted in the long-run, but not in the short—run by the competitive firm. Due to the competi— tive forces of the industry, no firm is capable, in the long-run, of shifting forward more than 100 percent of the tax burden.10 B. Monoply The market conditions Of the monopolist are differ— ent from those experienced by the competitive firm. The product is differentiated; he is the only seller in a market serving many buyers; and he has the capacity of setting the market price. Even so, traditional theory predicts no shifting of the income tax in the short—run by a profit—maximizing monopolist. Short-run The production decisions are essentially the same for the monopolist as they are for the competitive firm.ll Since the monopolist can determine the price, he chooses a price and output which will maximize the difference between total revenue (R) and total cost (C). 10For the immediate purposes of this chapter, 100 percent shifting is defined as the end result of compensa— tory action taken by the firm to recover the entire burden imposed by the tax. 11It is assumed that the monOpolist purchases his input factors in competitive markets, and his individual demand has negligible effect upon the input costs. 18 Given the demand function for the monOpolist, p = p(q) and the average total cost function c = c(q), total revenue equals R(q) pq pq. (u) and total cost equals C(q) = cq c(q)q, 12 (5) where C(q) does not include the return to capital in the short-run. As with the competitive firm, the return to capi- tal is price determined in the short-run. First and second—order conditions are assumed to be satisfied in the allocation of inputs. Profit equals the difference between total revenue and total cost: 0 = R(q) - C(q) (6) To maximize profit set the derivative of (6) with respect to q equal to zero: d0 = R'(q) — C'(q) = 0 3? R'(q) = C'(q) (7) or marginal revenue equals marginal cost. An income tax requires that the monopolist pay a certain prOportion of the difference between total revenue and total cost. Thus, (6) can be restated: 0* R(q) - C(q) - t[R(q) — Cfiqfl (1 — t)[R(q) — C(q)] (8) The tax t is Where t equals the tax rate and 0 < t < 1. ¥ 12See Musgrave, pp. cit., p. 278, n. l. 19 levied on total profits and 0* is after-tax profits. Maxi— mizing (8) by setting the derivative with respect to q equal to zero gives: 91 = (1 — t)[R'(q) — C'(q)] = 0 (9) dq Since 0 < t < l, R'(q) - C'(q) = 0 and R'(q) = C'(q) (10) The output position implied by equation (10) is the same as that implied by equation (7). Therefore, the imposi- tion of an income tax upon a monOpolist will have no effect on output and price in the short—run.13 The only way that a monOpolist can reduce the profits tax is by reducing before—tax profits (and this would entail a reduction of after-tax profits as well). Thus as long as the tax rate is less than 100 percent, it is advantageous for the monOpolist to continue to equate marginal revenue with marginal cost and produce at the same output and price as before the tax change. Long-run The traditional view holds that in the before—tax equilibrium, the monOpolist employs capital at that rate such that the marginal revenue product is equal to the cost of capital. Then when a tax is imposed, to the extent that 13Henderson and Quandt, pp, cit., Chapter 6. 20 the new after—tax marginal revenue product is less than the cost of capital, output and prices will be adjusted so as to regain the equilibrium. The reduction of out- put is the direct result of the decrease in the capital employed in the industry. As with the competitive firm, shifting is limited to 100 percent Of the tax. More than 100 percent shift- ing implies that the monOpOly firm was not maximizing profits before the tax change. The first-order condition for Optimum allocation Of inputs for the profit—maximizer is MPPL : MPPK 01> "SIE.’ or, that the marginal rate Of technical substitution equals the ratio of input prices (where r equals the cost of capital and w equals the wage rate). The price of capital (r) can be regarded either as the apprOpriate return which must be paid to investors in a competitive capital market or the marginal profit rate necessary to attract and retain capital. The profit—maximizing firm will employ units of a variable input up to a point where the marginal revenue product equals the input price (marginal revenue product is equal to marginal product multiplied by marginal revenue). MRPk = r (12) Assuming diminishing marginal productivity of capital, when the quantity of capital is decreased, due to 21 the substitution and output effects, output will be lowered. Under conditions of monopoly pricing, the market price of the product will increase. When the income tax is increased, after—tax profits are decreased, and the marginal revenue product of capital now is lessihan the cost of capital. Thus, (11) and (12) no longer hold. By decreasing the amount of capital, MPPK and MRPK will be increased up to a point where (11) and (12) are again in equilibrium. Reduction of the use of capital beyond the new point Of equilibrium in hOpes of shifting more of the tax burden to the consumer in the form of higher prices would result in the subOptimum utilization of capital. At any point below the Optimum amount, the marginal revenue product of capital would be above the market price, and the firm could increase profit by using more capital and increasing output. The long-run adjustment process, which results in the forward shifting of the income tax by the monOpolist or the competitive firm, is not without limitation. In order for 100 percent shifting to occur alternative investment Opportunities must be available for the capital which is leaving the taxed industries. To the extent that this invested capital must settle for a return less than was provided before the tax, the market equilibrium in the capital market will force less than 100 percent shifting. The presumption that the exodus of capital in the long-run will equate the marginal revenue product to the unchanged 22 market rate of interest depends upon the existence of investment Opportunities that offer net rates of return which are coincidentally higher after the tax than before or that offer_gross rates of return which were previously higher than the shifting industries before the tax change. The former explanation is unlikely, and the latter is negated by the assumption of equilibrium in the capital market. Consequently, in the long—run, shifting will be somewhat less than 100 percent by both competitive and monOpolistic firms. Questionable Assumptions Of Traditional Theory The arguments that are usually reiterated by econo- mists discussing the incidence of the corporation income tax are based on the assumptions indigenous to the models of pure competition or monopoly. When some of these assumptions are relaxed, what remains is not a new theory of the firm, but the basic relationships performing within a different framework. The new framework is constructed of assumptions concerning market structure and entrepre- neurial behavior that are closely related to the specific problem of tax incidence. Consider first a modification Of market structure. Many authorities feel that the industrial market structure in the United States does not conform to the descriptive characteristics of either pure competition or monopoly. The extent or absence of competition in any particular 23 industry can in principle be measured relative to other industries on a scale bounded by these two extremes. In the manufacturing sector of the United States many econo— mists feel that industries can be described as OligOpOlies of varying degree. Two important assumptions of the competitive model are consequently altered. The first is that of homogeneous products. Product differentiation is a generally accepted requisite for successful distribution, and substantial resources are Spent in creating physically or psycholo- gically distinguishing features. The second altered assump- tion, consequent upon the alteration of the first, is that the firm faces a demand schedule that is less than perfectly elastic. Thus the firm has pricing discretion within the limits of its demand curve. Besides the product and market structure qualifi— cations, many students of incidence have questioned other premises of traditional theory. The following discussion is not a list of universally accepted qualifications, but simply a recognition of some of the problems encountered by the analyst. In the short-run, prOfit—maximizing behavior Of the monOpolist may well be subordinated to long—run objec- tives. Maximum immediate gains may be foregone in order to insure market control, good-will, and/or consumer accep— tance that will facilitate long-run profit targets. Sub- ject to the monopolist's discretionary pricing policies, 24 profits and prices can be kept below the current (or short-run)profit—maximization level, which will make price increases more feasible in the short-run to recoup tax payments. However, this compensatory pricing behavior would be tempered by long—run profit considerations. Market policy and pricing may be influenced by the considerations of government antitrust action, public reaction to its conception of excess profits, or the effect upon wage negotiations. Consequently, market Opportunities may not be fully eXploited, leaving room for future tax—motivated price increases which will not necessarily lead to retaliatory action because they can be readily defended against accusations by government, labor, and the public. Under conditions Of OligOpOly, the market price is even less clearly defined. Assuming that the pricing mechanism borders on the limits of "conscious parallelism," or is, at least, characterized by conditions of mutual interest, the prevailing price will fluctuate between the 14 monopoly and competitive normative levels. The market structure and the possible presence of a dominant firm may 1”Cf. Edward H. Chamberlin, The Theory of Monopo- listic Competition (8th ed; Cambridge, Massachusetts: HarvardIUniversity Press, 1962), pp. 47-48. "When a move by one seller evidently forces the other to make a counter move, he is very stupidly refusing to look further than his nose if he proceeds on the assumption that it will not... For one competitor to take into account the alterations of policy which he forces upon the other is simply for him to consider the indirect consequences of his own acts." 25 lead to an administered price, which tends to be above the competitive equilibrium. What this means for shifting of the corporation income tax is dependent upon whether the tax affects normal profits or only reduces economic profits. Profit Maximization Qualifications The assumption of profit maximizing conduct as essential to the theory of the firm is not immune to qualification. The suspicion that other goals motivate the entrepreneur and influence his behavior has been suggested by both past and present economists; the latter critics have been able to add creditability to their criticism by being more specific. Where Alfred Marshall had to rely upon an intuitive description when he stated that "everyone who is worth anything carries his higher nature with him into business; and, there as elsewhere, he is influenced by his personal affections, by his conceptions of duty and his reverence for high ideals. And it is true that the best energies...are stimulated by a noble emulation more than by a love of wealth for its own sake."15 Contemporary economistswho have modified the assumption of profit maxi— mization have rigorously develOped theoretical models to SUpport their contentions.l6 * 15Alfred Marshall, Principles of Economics (8th ed; London: Macmillan and Company, Ltd., 19617, p. 14. 16For an excellent coverage of the more recent revisions to the theory of the firm see: Oliver E. Williamson, The Economics of Discretionary Behavior: Managerial Objec- Eiyes in the Theorypof the Firm (Englewood Cliffs, New Jersey: 26 The modern corporation is characterized by the divestiture of management responsibilities from the owner- ship Of the assets. The develOpment and perpetuation of a unique group of salaried managers may have created a schism between the short-run objectives of the share—holders and those of the managers. The more diversified the ownership and the less control the owners have over the Operations of the company, the greater may be the disagreement. Conversely, the more intimately the ownership participates in the Opera— tion of the corporation, the more dominant will short—run 'goals become, and these objectives will serve as_guide1ines for action. The distinguishing difference between the stockholder and the manager is that the stockholder is best defined as a prOfit—maximizer; whereas the manager is also motivated by additional considerations. The stockholder is more interested in maximization of the present value of the firm's assets which will possibly increase the yield on his investment or lead to the market appreciation of his stock. Reduction in the present yield will only be accepted if it is attributed to the reinvestment of profits in order to insure continued growth and profitability in the future. The intentional limitation of the profits for the more subtle reasons associ- ated with increasing market power and successfully Prentice-Hall, Inc., 1964), Chapters 2 and 3. For the purposes of this study it suffices just to highlight the pertinent arguments and to suggest how they weaken the norma- tive assumption of profit maximization. 27 merchandising the product in the long—run is not accepted as a substitute for present earnings. This inherent reluctance on the part of the stock- holder to be motivated by the same stimuli as the manager is quite rational. The position Of stockholder is ancil— lary to the investor's behavior in society. The return on his investment provides the means by which he can satisfy his materialistic desires, while the accomplishment of his more subjective goals is relegated to Opportunities outside the corporation. Consequently, it is only logical that the stockholder would favor any action taken by the firm which will enhance the maximization of the present value of his investment. His pursuit of other social and economic goals is not connected with maximizing income. The manager, as an individual, may be motivated by the same personal desires as the stockholder. However, his behavior in the organization is influenced by the fact that alternative means of satisfying his "social" needs are limited to the constrictions of the corporation environment. If we accept the premise that the ”social" and "economic" man can function in the corporation matrix of alternatives, then we must alter the theory of the firm in compliance with this modification. Profit maximization as a determinant of managerial behavior becomes one of several weighted con- siderations which govern performance, and positive economic analysis must include in the subset of behavioral assumptions 28 some recognition of the diversity of goals.17 If profit-maximization is not the dominant impetus behind business conduct, is there some other motivational force which can be generally assumed? The behavioral approach to the theory of the firm attempts to answer many questions about business conduct by substituting various alternative goals in place of profit-maximization without discarding the fundamental concepts associated with Optimum allocation of inputs given an output constraint. The behavioralist studies the determination of output on the basis of goals in addition to short-run prOfit-maximization. .Alternative Hypotheses C118 Several behavioral models have been prOpose as variants of a prOfit—maximization model. William J. Baumol 17Proponents of Organization Theory have made noble attempts at solving the problems associated with measuring discretionary behavior of managers. For example, Williamson, pp. pi:., concludes that there are four managerial motives: salary, security, dominance, and professional excellence. He develops the notion Of expense preference as a means of making the connection between motives and economic activity, and examines the significance of these non—pecuniary Objec- tives and their influence on behavior. EXpense preference is a method of quantifying management's attitude toward all classes of expenses, and is a way Of modifying conventional economic theory which assumes that managers are neutral toward costs. 18For additional models see W. W. COOper, "Theory of the Firm: Some Suggestions for Revision," The American Economic Review, XXXIX (December 1949), pp. 1204-1222; J. Margolis, "The Analysis of the Firm: Rationalism, Con- ventionalism, and Behaviorism," The Journal of Business, XXXI (July 1958), pp. 187-199; and Richard M. Cyert and James G. March, A Behavioral Theory of the Firm (Englewood Cliffs, New Jersey: Prentice—Hall, Inc., 1963). 29 suggests an explanation of firm behavior based upon the assumption that firms attempt to maximize total revenue rather than profits. The goal of maximum sales or revenue is limited by the firm's concern for a minimum level of 19 However, once this level is achieved, sales 20 profits. maximization becomes of major importance. Oliver E. Williamson develOped a managerial 21 of business behavior which focuses on the discretion model egocentric responses of corporate managers. Because of the previously discussed gap between the material rewards and the psychological needs of the hired executive, there is a 'tendency for nonessential management perquisites to increase beyond the level required for effective Operation of the firm. These nonessential perquisites are termed "management slack", and are part of the firm’s cost function. In response to demand and/or tax changes, manage- ment will adjust the discretionary level of management slack while maintaining profits sufficiently high enough to retain effective control of the firm. A third alternative model was proposed by Krzyzaniak 22 and Musgrave. They acknowledged the businessman's approach 19As stated by Baumol, "the firm's usual rate of return on investment played an explicit and very fundamental role in these deliberations." pp. cit., p. 49. 20Baumol, pp. cit., Chapter 6. In this chapter, Baumol gives some justifications of this hypothesis. 21Oliver Williamson, pp. cit. 22Marian Krzyzaniak and Richard A. Musgrave, 30 to the corporation income tax, and based a behavioral function upon the anticipated reSponse to a tax change. The businessman is assumed to regard the income tax as a cost when determining prices. Accordingly, a change in the tax rate leads to adjustments in price, wage, or output so as to compensate for the increased cost. Krzyzaniak and Musgrave realized that this price policy is not consistent with the usual concepts of profit maximization, but found that their statistical results were compatible with the stated model. Finally, a pOpular variant of the traditional model is that the firm practices markup pricing. The procedure calls for increasing average total cost by a predetermined percentage to arrive at the selling price. The calculation of the markup percentage depends upon the desired profits and required taxes related to a particular forecasted level of sales. The markup hypothesis and its relevance to shifting of the corporation income tax has been tested by Robert J. Gordon.23 He found that the degree Of shifting was very slight over the test period 1925—62. A full discussion of his model and results is presented in Chapter III. Baumol's model of sales maximization with a profit ‘Y_ The Shifting of the Corporation Income Tax (Baltimore: The John HOpkins Press, 1963). 23Robert J. Gordon, "The Incidence of the Corpora— tion Income Tax in U. S. Manufacturing, 1925-62," American Eponomic Review, LVII (September 1967), p. 731. 31 constraint is an adaptation of traditional theory with a few modifications designed to fit certain assumptions. One major modification is that Baumol's production function separates the inputs into two basic categories, resources and expenditures on advertising and service competition. The function can be written: X = f(xl...xm, Xm+l"°xn)’ (13) where m n 2 lei: C and X ijj: A i=1 j=m+l xi = 1,2, . m xj = m+l, m+2,...n The costs of production are given by C, and the other inputs are grouped together under the general classification of advertising A. Each component Of total cost can be changed independently of the other, and each type of eXpenditure is reflected in the product price, P. However, emphasis is given to the restriction that total revenue, which is quantity multiplied by price, be greater than total cost by a predetermined amount. It is assumed that sales can be increased by additional expenditures on advertising, where sales maximi- zation refers to the maximization of total dollars and not to physical volume. However, this relationship must be restricted to dR < 1 (14) 32 i.e., total revenue can be increased by spending money on advertising and other related service eXpenditures, but an extra dollar spent on advertising will increase costs more rapidly than total revenue.2” With a profit constraint, maximized revenue becomes (R - c — A) 3 K1 (15) where K1 is the absolute level of minimum profits. The profit constraint can also be designated as a minimum return on investment: (R - c - A) a K (16) I + k c + k A C a where K2 equals the net rate of return and investment is con- sidered to be a linear function of the two types of costs, A and C. In (16), total investment is an amount I, which is the amount of capital stock that is not a function of C and A, plus a certain prOportion of total expenditures on C and A. Baumol assumes that there is a relationship between costs and the amount of required investment over and above the amount of I. It is noteworthy to recognize the similarity between 2”See Kalman J. Cohen and Richard M. Cyert, Theory of the Firm (Englewood Cliffs, New Jersey: Prentice-Hall, Inc., 1965), pp. 378-379. Cohen and Cyert present a mathe— matical proof that the necessary conditions for revenue maximization are: dR < l , where S = A dS and dR < dC dX dX 33 Baumol's profit constraint and the more common "target-rate- "25 Of—return. Both are discretionary profit minimums deemed necessary to attract and maintain capital investment. Both result in firm behavior different from that predicted by the assumption of profit—maximization. At the Optimum price—output combination of the profit maximizer, MR = MC. Since MC is always positive, MR must be positive at the Optimum output. It follows that R can be increased by increasing the quantity sold even though profits decrease. The relationship between advertising and total revenue implies that total revenue can be continually increased to its maximum by additional eXpenditures on advertising until the profit constraint is met. However, MR K, (17) However, at the pre-tax sales—maximization output, the after- tax profit is now below the constraint. According to (14) and dR/dX > 0, advertising and output will be decreased until the constraint is again reached. As with the long—run purely competitive and monopoly models, the Baumol behavior model cannot predict more than 100 percent shifting. Although Baumol is not explicit about changing the profit constraint, compensatory action by management which is solely aimed at maintaining a constant after-tax rate of return on investment is self-limiting, the limit being the tax increase. Without the specification of additional reasons for changing the profit constraint (which would complicate the isolation of the tax effect), maximum shifting of the income tax is limited to 100 percent of the tax. Using (17) as the statement of the businessman's behavior, the tax liability is considered as a cost: T = t(R - C - A): (18) where t = tax rate. Restating (17) as (1 - t)(R - C - A) > K (19) K ’ 2 where K equals aggregate capital stock, the gross rate of 35 return with the profit constraint becomes K R ' C ‘ A > 2 (20) K ’ (I—4 t) If 100 percent shifting is defined as Y - Y' : T t t (21) ga ,E: K where Y equals before-tax rate of return, and priming denotes the value before the tax change, then _ l : _ _ Ygat Yg,t t(R C A) (22) ' K Defining ' K and t - _ _ v Yg,t - (R C A) (2”) K then R - C - A -(R — C — A)’ = t(R - C - A) (25) K K K Solving for the rate of return after the tax change in terms Of the rate of return before the tax change gives: R - C — A = (R - C — A)'/ l-t (26) K K OI‘ l-t (27) 36 The Baumol model predicts a maximum increase of the profit constraint, or the rate of return, which is limited to 100 percent of the tax rate change in the long—run. There is no justification for more than 100 percent shifting of the corporation income tax in the long—run. The Williamson model introduces four concepts of profits: maximum profits, 0*. which are obtained by the traditional prOfit-maximizing firm; actual profits, HA, which differ from maximum profits by an amount of management slack absorbed in staff expenditures; reported profits, ER, which differ from actual profits by an amount expended on management slack absorbed in costs; and minimum profits, to, which are the lowest amount acceptable for effective manage— ment control and agrees closely with Baumol's profit con- straint.26 Thus: : 3': _ MS (28) WA 0 and w = 0* — MS - M (29) R and TrR > 7TO/l—t (30) where t is the tax rate. 26The notation used in this discussion of the tgga shift is taken from Cohen and Cyert, pp, c1t., pp. 356- . 37 If M > 0, then HA > E 'n' . R and FR < 1. A H Let _B,= 6, where 0 < O s 1. n A According to the discretionary model, pp < 0; i.e., as the tax rate is increased, manage- 8t ment reports more of the perquisites as operating costs, and the ratio of reported profits to actual profits decreases. In this model, the rate of return before the tax can be stated as r' = _:R (31) K .n-l where __B.= 6', with 0 < O'Sl. n A After levying a tax, t, the net rate of return becomes r : (l—t)1TR _ (l-t)61rA (32) n _______, ________ K K Where 0 =60’, R ' A According to the definition of 100 percent shifting Of the corporation income tax, the firm will attempt to equate r and r' so that I1 (33) Kt 38 or l :3. 1 3 (31+) K (l—t) K' With 6 < 6', (34) implies OH 1 80" ___A=_____{\_ (35) K l-t K' or I 15:1...115 (36> K 1-t 6 K' Therefore 1! :ZTA=__:_ 6' K 1-t K' (37) and 1A>ilé K l—t K' since 6/6' < 1. Thus 100 percent shifting in terms of reported rate of return implies more than 100 percent shifting in terms of actual rate of return. The only way that more than 100 per- cent shifting, based upon reported rate of return, would occur is if the management decided to reduce the amount of perqui- sites included in costs. A plausible explanation for this conduct is not included in the discretionary model since management's compensatory actions are presumed to be primarily 39 motivated by the desire to keep the reported net rate of return unchanged. Any reduction Of perquisites which result in the lessening of actual rate of return and an increase of the reported rate Of return cannot be justified by the Williamson discretionary model. Therefore, in the long—run, 100 percent shifting is the limit and can be theoretically substantiated with this model. The Krzyzaniak and Musgrave model is based upon the functional relationship between the before—tax rate of return and the tax liability such as: Y — Y' - all (39) . K where Y t is the before-tax rate of return, T is the tax 9: liability, and K is the capital stock. Priming denotes the value in the absence of the tax. The behavioral assumption of (39) implies that the firm attempts to adjust its before- tax rate of return so as to recoup a given fraction, a, Of the negative rate of return. In the case of 100 percent shifting, a = 1. However, Krzyzaniak and Musgrave state the possibility Of a > 1. They substantiate this assertion with two hypotheses. The first is that the tax increase may be taken as a "signal" by cer- tain OligOpolists for price increases which may include adjustments for other factors besides the tax factor. The second is that firms may be over anxious to recoup the tax burden, and they overshoot the mark. Consequently, with the no possibility that a > 1, it follows that the firm may be able to shift more than 100 percent of the tax increase. Throughout the preceding discussion, the corporation income tax has been considered as a general tax on profits. If this were the case, then any inferences about the possi— bility of shifting would raise serious questions about the _general equilibrium effects. In fact, if all profits were taxed at the same proportional rate, successful shifting by any particular firm, industry, or sector would be doubtful. However, the corporation income tax is not a general tax. It does not affect the unincorporated sector of the economy; nor does it apply to tax—exempt investment returns. There- fore, depending upon the time period, the mobility of capital, and the availability of alternative investment Opportunities, shifting by incorporated firms of a particular industry, or by an incorporated sector of the economy as a whole is possible. Krzyzaniak and Musgrave (by assuming the constancy of the capital stock over the twenty year period) relied primarily upon price changes to eXplain their shifting infer- ences. The traditional models of competition and monopoly and the behavioral models of Baumol and Williamson allow time for the necessary adjustments in prices and/or capital (be it interindustry movement or to the unincorporated sector) for shifting to occur. The conditions which govern how readily the unincor- porated form of business can be substituted for the 41 incorporated form, and how easily capital can be shifted to the unincorporated sector are very important. Successful shifting of the corporation income tax will be greatly influenced by whether these conditions encourage or retard capital movement.27 Conclusion The implications of this analysis of the traditional models, the Baumol model, the Williamson model, and the Krzyzaniak and Musgrave model are that shifting of the corporation income tax in the long—run is a distinct possi- bility and can be accomplished within the basic framework of any/or all of the models. In the case of the Baumol hypothesis, the prediction Of 100 percent shifting is more definite because of the primary objective of sales maximi- zation. The discretionary model, presented by Williamson, predicts up to 100 percent shifting but is less definite in its conclusions. The traditional models of the competitive firm and the monopolist predict up to 100 percent shifting, but the final results are tempered by alternative Opportuni— ties and external influences of the capital market. The Krzyaniak and Musgrave model predicts income tax shifting which may exceed 100 percent. 27cf. Krzyaniak and Musgrave, pp. pi£., pp. 4-7, M. A. Adelman, "The Corporate Income Tax in the Long—Run," qurnal of Political Economy, LXV (April, 1957) pp. 151-157; and Arnold Harberger, "The Incidence of the Corporation Income Tax," Journal of Political Economy, LXX (June 1962), pp. 215-240. 42 When the assumption is made that business behavior is motivated by the desire to recoup the tax liability by some compensatory action, more than 100 percent shifting can be theoretically justified by only one of the models, the Krzyaniak and Musgrave model. The task of this study is to investigate whether the tax is shifted in the long—run by analyzing statistics in the manufacturing sector of the United States. From the results, it is hOped that some inferences can be made pertaining to the applicability of either the traditional model or the variants proposed by Baumol, Williamson, and Krzyaniak and Musgrave to the shifting problem. CHAPTER III POSSIBLE INDICATORS OF SHIFTING AND RECENT EMPIRICAL STUDIES The degree of confusion and disagreement over the incidence of the corporation income tax has in no way been lessened.by the ability and ingenuity of the many students of the subject. Although over the past ten years there has been a gradual change aWay from the more generalized theoret- ical approach, recent empirical studies have seemingly uncovered as many questions as they have answered. Formerly the discussion concerned the relative influence of the many factors affecting the inability of the corporation to shift the tax in the short—run with little effort directed towards quantifying their importance.1 More recently the contro- versy has centered on the prOper method of isolating the effect of the income tax and assessing its position in the assemblage of profit determinants. The complexities of the problem and the interdependence of the influencing factors have induced students to apply econometric methods to the analysis. 1An excellent review Of the arguments and conclusions of the early major studies has been written by B. U. Ratchford and P. B. Han, "The Burden of the Corporation Income Tax," National Tax Journal, X (December, 1957), pp. 310-24. 43 04 Unfortunately the process of building and testing econometric models is not devoid of personal bias. The specification Of the model and the determination of the explanatory variables require subjective judgement. Accord- ingly, a wide variety of alternative tax incidence models has been proposed. It is perhaps not surprising that in view of the range of models used, the empirical findings have often been contradictory. One particular point of contention is over the most appropriate indicator of shifting of the corporation income tax. For the purposes of this study, ”shifting" relates to the recovery of the burden imposed upon the taxpayer by the corporation income tax. The "burden" refers to the differ- ence between the firm's profit position with the tax and what it would have been without the tax. The difference is measured by means of various "indicators" such as gross or net rate of return on invested capital, absolute profits, or capital income share. The assumption is made that when the non-tax factors are accounted for in the model, then the indicator will measure the degree Of shifting. Therefore it becomes imperative to study the various indicators, and to select the best available statistic. The choice involves careful evaluation of the advantages and limitations of each prOposal within the guidelines defined by both feasibility and significance. Three possible indica— tors are: a) absolute level of profits, b) income share, and c) rate of return. In the first section, each indicator will 45 be discussed with pertinent studies mentioned as examples. In order that this study might be evaluated in per- spective, other empirical results will be presented for comparison in the last section of the chapter. Possible Indicators of Shifting A. Absolute Level of Profits The comparison of the necessary assumptions asso- ciated with each indicator is instructive and helps to narrow the selection. First is the change in the absolute level of profits, eXpressed either in net or gross terms. The premise is that all non—tax influences on the level of absolute profits are absent on balance; i.e., negative and positive effects offset one another. Thus any change in the indicator represents the effect of the income tax. If before—tax profits increase over a period when the tax rates have ad- vanced, then it follows that the burden has been shifted either forward upon the consumer or backward upon the payment to input factors. Conversely, if the before—tax income remains constant after the tax rate increase, then the tax is assumed to have been absorbed by the capital owners. The reliability of this indicator is negated by the untenable assumption that non-tax factors are absent throughout the period, and that changes in capital stock have no effect upon the absolute level of profits. This latter influence could be partially neutralized by restricting the analysis to the short-run when capital stock is assumed tO remain constant; 46 however, the conclusions would still be dependent upon the more restrictive ceteris paribus conditions implied by the 2 test specifications. B. Profit Share The income share approach has been utilized by 3 Depending upon several economists over the past few years. the specification of the model, the degree of shifting is indicated directly by the change in the capital income 4 or indirectly from a fitted production function.5 As share commonly defined, the capital income share is the ratio Of profits to Gross National Product. In the case where the analysis is restricted to the manufacturing sector, the capital income share equals the ratio of profits to income originating in the manufacturing sector; specifically, profits 6 to value added in the sector. The assertion is made that an 2Consequently, the use of this indicator as a measure of shifting has been restricted to statements about its inad- equacies, cf., Marian Krzyzaniak and Richard A. Musgrave, pp. pi£., pp. 13—14. I 3See M. A. Adelman, "The Corporation Income Tax in the Long Run," Journal of Political Economy, LXV (April, 1957), pp. 152; Challis Hall, Jr., "Direct Shifting of the Corpora- tion Income Tax in Manufacturing," American Economic Review, LIV (May, 1964), p. 258; Arnold C. Harberger, "The IncidenEe of the Corporation Tax," Journal of Political Economy, LXX (June, 1962), p. 215; and Robert J. Gordon, pp. pi£., p. 731. ”Adelman, pp. cit. 5Hall, pp. cit. 6The precise definition of profits varies from one economist~ to the other. It can be specified as before or after tax; it can include depreciation, interest on debt, and/ or inventory valuation adjustments; and when aggregated, it 47 increased before-tax capital income share can be attributed to the ability of the corporation to shift the burden in the short-run by raising prices. The limitations of this type of analysis can be illustrated by examining two previous studies.7 The first was completed by M. A. Adelman. On the basis of his hypoth- esis that the best indicator of no shifting would be con- stancy of corporation profits before taxes as a fraction of all income originating in corporate enterprises, he concluded that "there is no evidence here that any perceptible part of the increase in the tax burden was shifted either forward to consumers in higher prices or backward to employees in lower wages."8 Profits included both interest on debt capital and inventory valuation adjustments in order to com- pensate for possible changes in the debt-equity ratio and inventory profits arising from price level fluctuations. The weakness Of this type Of indicator stems from its inclusiveness and the presumption that non-tax factors have a neutral effect upon the income share of capital. Stability in the ratio could arise from the offsetting effect Of a change in the input mix, which could compensate for the can either include or exclude loss corporation. The selec- tion depends Upon the model specification and the degree Of inclusiveness judged best to describe the influence of the corporation income tax. 7Adelman, pp, cit., and Hall, pp. cit. 8Adelman, pp. cit., pp. 152—53. 48 higher pre—tax return attributed to shifting.9 A more sophisticated approach was taken by Challis Hall10 in his recent study of the income tax incidence. He questioned whether there had been Short-run shifting of the tax during the period of 1919-1959, and he made the qualified conclusion that "profits taxation had not been shifted in the Short—run."ll The method consisted Of deriving a produc— tion function, corrected for technical change, under three different shifting assumptions, and then examining the inter- nal consistency of these relationships as estimators of output and property income. The degree of consistency would imply the reliability of the shifting assumption included in the production function Specification. In the derivation of the production relationship from time series, certain adjustments were made to compen- sate for the influence Of technology. The first step was to calculate a residual measure of the change in output per 9See Arnold Zellner, "Rejoiner," Journal of Politi- cal Economy, LXVI (October, 1958), p. 448. Also, John R. Moroney, TrThe Share of Corporate Income, 1922—61," The Quarterly Review of Economics and Business, IV (Winfg? 1964), p. 72. In this article, Moroney discusses the problems of aggregation and their effects upon the consistency or changes in distributive shares. Accordingly, Adelman' s constancy of aggregated shares could be eXplained by offsetting shifts in subsector shares. The partial solution to the problem would be a disaggregated study of corporate taxes within individual industries. Nevertheless, the substantial problem Of changes in factor proportions and technological progress as poten- tial determinants of relative shares remains in this sort of analysis. 10Hall, pp, cit. llHall, pp. cit., p. 271, 49 man-hour due to technical progress. The procedure was a modified application Of the method formulated by 12 Robert M. Solow. Solow's estimating equation was IW' Wk (1) A K 3-2L 9 where A was the technical change index, q was the output per man-hour, K was the capital per man-hour, and wk was the share of capital. The dots indicated time derivatives. Hall adjusted the share of capital according'b the three separate shifting assumptions. Each time the inferred capital Share varied according to the underlying shifting Specification. The inferred Share which was based upon a "no-shift" hypothesis was the largest, and was comparable to Solow's w . The one calculated on the basis of a "full wage shift" was the lowest. With each measure of the inferred capital share, Hall determined the approximate relative increase in output per man-hour due to technical change. The formulation was 2:51-35}: (2) q k where s equaled the inferred marginal product of capital times capital per unit of output (the inferred capital share). The index of technical change fluctuated inversely 12Robert M. Solow, "Technical Change and the Aggre— ,gate Production Function," Review of Economics and Statis— ticsz Vol. XXXIX (August, 1957), pp. 312—20. 50 with the value of s, which was a function Of a particular shifting hypothesis. Annual output was deflated by the apprOpriate index of technical change. The alternative tax-shifting assump— tions were evaluated by comparing the closeness Of fit Of deflated output per man-hour with capital per man-hour. In order to do this, the production relationship derived from the Cobb-Douglas function, (3) IT'IK 9 L was fitted by least-squares to the logarithms of the vari- ables for all years in the 1919-59 period. Here, 0 = Q/A, where A was given by the value of z, and b was capital's contribution to output. The variance in deflated hourly output was best explained with the "no—shift" hypothesis. Therefore, Hall concluded that the traditional assumption of no—shifting deserved credence. Two restrictive assumptions were pertinent to the Hall analysis. First, there was the asserted assumption that technical change was Hicks neutral throughout the test period. Technological progress is defined as any change in the production function which allows the same output to be produced with less inputs or enables the same level of in- puts to produce a greater output. Hicks defined technologi- cal change as neutral if the marginal rate of substitution of labor for capital remained unchanged at the original 51 capital—labor ratio. Hall defended his assumption by relying upon the empirical work Of Professor Robert M. Solow, who showed that technological change for the whole non—farm econ- omy was neutral and could be isolated for the examined period Of 1909—1949.13 However, this conclusion is far from unani- mous. There is some evidence that technological change in the 1” Other evidence implies United States has been labor—using. that technical change has been labor—saving over roughly the same period, 1899-1960.15 Whether technical change was neu— tral or non—neutral over the period is still an unanswered question. Aggregated production functions have been esti- mated by many scholars but no single one has been unanimously accepted. The second assumption was implied by the use of the Cobb-Douglas production function as the test relationship. l3Solow, pp. pip. l”See Murray Brown and John S. de Cani, "Technical Changes in the United States, 1950-1960," Productivity Measure- ment Review, May, 1962, pp. 26-39; and C. E. Ferguson, "Sub— stitution, Technical Progress, and Returns to Scale," American Eponomic Review, Papers and Proceedings, LV (1965), pp. 296-305. 15P. David and T. van de Klundert, "Biased Efficien- cy Growth and Capital-Labor Substitution in the U.S., l899~ 1966," American Economic Review, LV (June 1965), pp. 357-94. They found technological progress to be labor—saving in the non-farm, private, domestic economy during 1899-1960, and the elasticity of technical substitution was 0 < O < 1. In a more recent study, John R. Moroney found that over the period 1942—1957 six industries out of the thirteen tested were characterized by labor-saving technical progress. One indus— try manifested a capital—saving bias, and the rest displayed neutral technological progress; "Technological Progress, Factor ProportiOns, and the Relative Share of Capital in American Manufacturing, 1942—1957," Western Economic Journal (forthcoming, 1968). 52 Since (3) is equivalent to 0 = Kb Ll'b (4) it follows from (4) that there will be constancy Of relative Shares. A necessary and sufficient condition for constancy of relative shares with no technical progress or Hicks neutral technical change is unitary elasticity Of substitu— tion. This restrictive assumption influences the interpre- tation of the results. If the elasticity Of substitution is equal to one, then any change in the profit/wage ratio is precisely offset by the same percentage change in the capital/labor ratio, leaving relative shares the same. Therefore, it becomes easier to interpret the constancy of the gross capital share/labor share ratio during a period of tax increase as indicative Of the inability of the corpora- tion to shift the income tax. If, however, the elasticity of substitution is less than one, then a decrease in the prOfit/wage ratio due to a relative increase in the wage rates would result in a less— than—proportionate increase in the capital/labor ratio, altering the relative shares in favor of labor. Empirical evidence has shown that this is what has happened in the manufacturing sector of the United States over the postwar period.16 16See J. W. Kendrick and Ryuzu Sato, "Factor Prices, Productivity, and Growth," American Economic Review, LIII (December, 1963), pp. 974—1003; I. B. Kravis, "Relative Income Shares in Fact and Theory," American Economic Review, 53 When the assumptions of neutral technological change and unitary elasticity of substitution are relaxed, Hall's results may be interpreted differently. He found that in the shift cases the consistency between deflated hourly out— put and hourly capital broke down into two subperiods, 1919-41 and 1942—59. Deflated hourly output was lower for equivalent combinations of capital and labor in the latter period. With technical change classified as labor-using and the elasticity of substitution less than unity, the relative drOp in the deflated hourly output could be explained with the Shift model. In fact, Hall admits that the hypothesis that the profits tax was shifted is consistent with techno- logical change which lowers the marginal productivity of capital relative to that of labor, or is labor-using in the Hicksian definition. These two studies by Adelman and Hall serve to point out the difficulties inherent in any shifting analysis based upon a capital share approach. The problem Of isolating the effect of the income tax from non-tax influences is only intensified by the questionable measures Of technical change and elasticity of substitution. The relative inadequacies of the income share approach encourage the develOpment of a XLIX (December, 1959), p. 917; and Robert M. Solow, "The Constancy of Relative Shares," American Economic Review, XLVIII (September, 1958), p. 618. Kendrick and Sato esti— mated the elasticity of substitution to be approximately 0.6; Kravis estimated an "historical" elasticity of substi— tution of 0.64; and Solow implied an elasticity of substitu- tion of 2/3 in his study on the constancy of relative shares. 54 better, less restrictive indicator. C. The Rate of Return The rate of return on invested capital is another possible indicator of shifting which has been used by various economists.l7 Traditionally, theorists used the rate of re— turn as the cornerstone in their discussion of short and long— run shifting possibilities. Under the assumption of profit maximization, short-run shifting by the firm was judged an improbability because price increases could only result in lower profits from reduced sales. The imposition of an income tax has no effect upon marginal revenue or marginal costs except in the case where marginal cost is affected by the reduction in working capital. Consequently, the burden of the tax would fall upon the capital owners in the short— run. This resultant reduction in the rate of return on in— vested capital in the Short—run would presumably affect future investment. With a competitive capital market and investment a function of the rate of return, capital would flow from one industry to another or to non-corporate invest- ments until the return became equalized.l8 The relative l7See Krzyzaniak and Musgrave, pp. pi:.,; Gordon, pp, pip}; Robert W. KilpatriCk,"The Short-Run Forward Shift- ing of the Corporation Income Tax," Yale Economic Essays, Vol. 5 (Fall, 1965), pp. 355-420; and John G. Cragg, Arnold C. Harberger, and Peter Miezkowski, "Empirical Evi- dence on the Incidence of the Corporation Income Tax," %pprnal of Political Economy, LXXV (December, 1967), pp. -821. . 18Equalization of rates of return includes compensa- tion for risk differentials. 55 decrease in the stock of capital in the taxed industry would reduce output and indirectly shift the tax through the higher equilibrium prices. In this way, it was theoretically possible (and indeed, inevitable under competitive conditions) for the firm to Shift the income tax in the long—run. The indigenous assumptions of the traditional theory of the firm have been questioned. The first question con— cerns the hypothesis of profit maximization in the short—run; and the second concerns the importance Of the rate of return as an explanatory variable in the investment function.19 If the short—run rate of return is not dependent upon profit maximizing behavior, then the explanation of the annual changes in the rate become less restricted. Discretionary conduct by management, motivated by many other goals in addi- tion to maximizing profits, becomes an important determinant of the rate of return. When the corporation income tax is changed, compensatory action may be taken to shift the burden of the tax. By isolating the effects of the non—tax factors, the residual changes in the rate of return become the basis of a tax shifting measure. 19See Bert G. Hickman, Investment Demand and U.S. Economic Growth, (Washington, D.C.: The Brookings Insti: tute, 1965); and R. E. Hall and D. W. Jorgenson, "Tax Policy and Investment Behavior," American Economic Review, LVII (June, 1967), pp. 391-414. Both of these studies indicate that net or gross investment in capital stock is more respon— sive to increases in the flow of internal funds and/or the utilization of existing capacity than to any change in the rate of return on capital. Granting the fact that these empirical results and others have not removed all doubt, their findings may raise doubts concerning the traditional neo-classical theory. 56 Throughout the analysis Of shifting it is important to keep in mind that the process Of shifting can involve many direct and indirect changes which result in the burden of the tax being borne by someone other than the taXpayer. In a _general equilibrium system it is difficult to isolate the chain of events. Consequently, reliance must be placed upon a broad description of shifting which is concerned with the result rather than the process of adjustment. The result is measured by the difference between the legislative intent and the actual incidence of the tax. A possible indicator of the successful accomplish- ment of shifting is the relationship between income tax rate changes and the resultant rate of return on invested capital. The rate of return is a final measure of the shifting process because it quantifies the cumulative effect of output, price, and factor—proportion changes. Therefore, the answer to the questionable incidence of the corporation income tax relies upon the capacity to isolate the explanatory variables, in addition to the income tax, which influence the rate of return. D. Conclusion The reliability of any regression analysis using the rate of return as the regressand depends upon the quality of the regressors. The quality, in turn, depends upon the available data and the ability to disaggregate variables which may affect one another. The possible weaknesses Of 57 the rate of return as a dependent variable do not destroy its usefulness, but simply warn the analyst to interpret with caution. Nevertheless, the influence of the corporate income tax on the rate of return seems clearly to be the most appropriate technique for making inferences about shifting of the tax. Consequently, the remainder of this thesis is concerned with the specification and estimation of econometric models in U.S. two—digit manufacturing industries in which the rate of return is utilized as the dependent variable. Recent Empirical Results Since 1957 there have been several attempts by noted economists to isolate the incidence Of the corporation in- come tax and to determine whether it has been shifted in the short-run and in the long-run. The difficulty of isolating the many factors which influence business profits is com— pounded by the perplexing problem of selecting an appropri— ate analytical technique. The most recent empirical studies are summarized in the following table. Although tabular representation is limited in depth, a chronological description of the studies does provide a basis for comparison. 58 .MIA cab ca Pcoosom omHnom mm: GOOSSQ xmp mo onmnm m.Hm#fidmO .mmapaoapmmam may mo mosam> mabflmsmflm com: pommm . Xmfi. 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The prOperties and limita— tions will be discussed below. Description Of Key Variables A. Gross Rate of Return Gross rate of return is defined as the ratio of before—tax profit to the gross stock of capital. The pre- cise specifications of these two measures have an important bearing upon the model and the interpretation Of the results. Profits Before—tax profits are profits from the Operation of the business plus interest paid on debt. To be consistent with the definition of the gross capital stock, annual allowance for depreciation, depletion, and amortization are included in profits. By defining profits in this manner, the following problems are avoided: a. The shifting hypothesis is based upon the premise that the firm can be instrumental in maintaining a certain rate of return from its own Operations. This rate of return is defined as the ratio of annual net profits to the stock Of capital, and it serves as a guideline for business decisions. The differential between a target rate of return and the rate of return generated under profit—maximizing 73 behavior is dependent upon the relative importance of the social and economic objectives discussed in Chapter II. In order to maintain a net target rate of return on capital during periods of increasing tax rates, the firm must take compensatory action to increase its before—tax rate of return. It is the effect of this discretionary action by the firm, predicated upon shifting the burden of the income tax, that is of interest. Consequently, gross profits are restricted to those attributed to the operation of the firm and do not include dividends and interest received from outside investments. b. The point is sometimes made that due to the allowable deduction of interest payments from taxable income, changes in the statutory tax rates influence the capital structures of corporations. Increasing income tax rates may influence the marginal investment decisions of corpora- tions. Debt financing becomes more attractive because of the deductability of the interest payments from taxable income. Over an extended period, this may alter the capital structure in favor of a greater proportion of debt-financed assets. A shifting analysis which is based upon the exam- ination of the rate of return on equity capital may be indirectly biased by the tax-induced change in the capital structure. An increased debt-equity ratio may result in a changed rate Of return on equity capital and a nO-shift inference, when, actually, a fraction of the income tax was shifted. The potential tax effect upon capital structures 74 can be accounted for by considering the total return to capi- tal as profits before—tax plus interest on debt. Capital Stock The measure Of capital stock is gross Of deprecia- tion, depletion, and amortization. To specify it in any other way would fail to account for the effectcf various de- preciation and amortization methods. If assets are measured on a net basis, there would be some difference between the rates of return of the Older and new companies. Also, if assets are stated net of depreciation, we lose sight Of the productivity of the fully depreciated capital stock, and the calculated rate of return overstates the true rate of return on utilized capital. In order to be consistent with our concepts of profits originating in the enterprise, the capital stock for any firm is measured net of investments in other enterprises. Thus, the rate of return is a measure of the productivity of assets under the direct control of the firm's management. B. The Tax Variable In equation (1) above, the tax variable enters the formulation as an absolute measurement of the negative rate of return on capital. Two questions concerning the inclusive- ness of the tax variable had to be answered. The first was whether or not to include the "no—income" corporations in the analysis and have their assets added to those of the "income" corporations. The Obvious effect of the latter 75 procedure is to lower the negative rate of return of the industry while leaving the tax liability the same. The second question was whether or not to include the excess profits tax in the tax liability, which amounted to 17% in 1951 and 18% in 1952—53. Again, the effect would have been to increase the tax variable for these three years and wOu1d have limited the comparability of 1951-53 with the other years. The answer to the first question was based upon an attempt to maintain all factors which are not included in the regressbn as constant as possible. Because there is a change in the composition of the grOUp of nO—income corpora— tions from one year to the next, there would be a change in certain aggregated characteristics of the industry which are not considered in the regression. By including all corporations, the possibility of exogenous factors, which are associated with the no-income group, influencing the shifting inference, is reduced. Exclusion of the loss com— panies would introduce a degree of non-homogeneity because the group of companies examined would change over time. Also, it would be impossible to isolate completely the effect of the no-income years for any corporation because of loss- carryovers in profitable periods. Offsetting past losses against current profits reduces the actual tax liability below the statutory rate. Therefore, all corporations are included in the analysis. 76 The second problem was substantially reduced by the business behavior underlying the specification of equation (1). According to this formulation, the firm attempts to take corrective action to compensate for the increased income tax liability. The response by the firm to the tax burden is based upon forecasted sales and a known tax rate applicable to all profits. Since the excess profits tax is levied upon a residual income, over and above a specified base,6 it remains more of an unknown liability. Hence, the excess profits tax cannot be estimated or compensated for pg pppp. The benefit Of any action taken in order to main- tain a stable after-tax rate Of return is limited by the specifications of the excess profits tax. Profits over a specified base are reduced by the tax. In the past, the base has been determined by the average taxable income of highly profitable years. The effect of limiting income above an already high level would tend to reduce the evi- dence of shifting rather than over—emphasize the successful shifting of the tax burden. Therefore, the tax variable which best describes the functional relationship of (l) is the tax rate exclusive of the liability attributed to the excess profits tax. 6The excess profits tax is levied upon the residual of taxable income minus profits credit. The excess profits credit is based upon prior taxable income. For example, the excess profits credit used during the Korean Conflict, 1951-53, was based upon the average taxable income of 1946-49. Federal Excess Profits Tax (New York: Prentice- Hall, 1954). 77 Non—Tax Influences on the Rate of Return A. Percentage of CapacitypUtilization Although an increase in demand in the short—run is likely to result in an increase in the rate of return, the extent of the influence is limited by the degree of capacity utilized during the period. Above a certain rate of output, it is well—documented that marginal costs increase with increased output. The marginal cost curve determines the short-run supply curve of the purely competitive firm. If the rate of increase accel- erates as the quantity produced increases, (or the second derivative of the total cost curve is positive) then it follows that the supply curve becomes more inelastic as out- put is expanded. The increasing degree of inelasticity of the supply curve is indicative of the difficulties inherent in eXpanding output above near-capacity rates. And although marginal cost is not the supply schedule of the firm under imperfect competition, in most imperfectly competitive indus- tries it seems likely that marginal and average costs rise as output eXpandS beyond a certain level. Consequently, a given change in demand could increase profits and the rate of return more when the firm is Operating close to capacity than when idle machinery is available. Some of the increase in the before—tax rate of return can be attrib- uted to the inelasticity of supply rather than exclusively to the ability Of the firm to shift the tax burden. The prede— termined variable denoting the percentage of capacity 78 utilization Should be positively related to the rate of return, other things equal. 7 criticized the Krzyzaniak and Richard E. Slitor Musgrave study for not including some variable in the model that indicated the degree of pressure upon the economic system during the period of tax-shifting analysis. He states that "(as) a consequence, the burden of explaining earnings is thrust upon the corporate tax variable, itself collinear with 'economic pressure' levels which are important deter- minants of corporate profits."8 To compensate for this deficiency, he both supplemented and replaced the other variables in the Krzyzaniak and Musgrave model and re-esti- mated the shifting parameter. As one might suppose, there was a decrease in the shifting measure. Slitor used a "pressure" variable calculated by Knowles, which was a ratio of actual to potential'GNP.9 I have utilized, however, an industrial index calculated by Frank de Leeuw, published in the Federal Reserve Bulletin,10 7Richard E. Slitor, "Corporate Tax Incidence: Eco— nomic Adjustments to Differentials Under a Two-Tier Tax Structure," Effects of Corporation Income Tax, ed. Marian Krzyzaniak (Detroit: Wayne University Press, 1966). BSlitor, Ibid., p. 157. 9James W. Knowles (with assistance of Charles B. War- den, Jr.) The Potential Economic Growth Of the United States, Jan. 30, 1960 (Washifigton: U.S. Prifiting Office, 1960). 10Frank de Leeuw (with assistance of Frank E. Hopkins and Michael D. Sherman), "A Revised Index of Manufacturing Capacity," Federal Reserve Bulletin, Vol. 52, (November 1966), pp. 1605-1615. The construction of the capacity estimates was 79 because Slitor restricted his investigation to the total manufacturing sector, in which an aggregated capacity measure was applicable. De Leeuw's estimates were divided into three ’groups called Total Manufacturing, Primary Processing Indus- tries, and Advanced Processing Industries. They could be applied more readily in the disaggregated approach of this study. The de Leeuw estimates for the primary industries and the advanced processing industries were applied to the seventeen industries of this study according to the cate- 11 gorization given in his article. Consistent with Slitor's results, I found a positive correlation between the rate Of return and the "pressure" variable for most industries.12 based upon three series: a perpetual inventory utilization measure of gross capital stock, a McGraw—Hill index of capacity, and a Federal Reserve index of production divided by a McGraw—Hill rate-Of-Operations measure. The mathemat— ical representation of the relationship is given by the following equations: _ t (1) Xl/X2 - alblut (2) x = a btv l/X3 2 2 t where X = Federal Reserve index Of industrial production dividedlby McGraw-Hill estimates of end—Of—year rate Of Operations; X2 = McGraw—Hill capacity index; X3 = capital stock series; a. = the antilogarithm of the regression inter- cept for the imlequation (i = 1,2); b- = the antilogarithm Of the time trend regression coefficient of the ith equation (i = 1,2); u , v = random disturbances in the appropriate equations; and t = time in years (1954 = l). The final capacity measure was estimated by multiplying the "calculated" valuesin (l) by X and the "calculated" values in (2) by X and averaging thege two estimates. 3 11See Appendix B for the listing of the industries by classification. 12cf., L. R. Klein and R. S. Preston, "Some New 80 B. Employment Index In their recent examination of the incidence of the corporation income tax, Cragg, Harberger, and Mieszkowski13 recalculated the Krzyzaniak and Musgrave model for the manu— facturing sector. They stated that the deficiencies of the model resulted in the coefficient of the tax variable (the shifting parameter) accounting for influences upon the rate of return not directly related to the income tax. To correct these deficiencies, they introduced two additional variables: the employment rate and a dummy variable for the mobilization and war years 1949, 1954, and 1958. Instead of the manufacturing sector employment rate, an industry index of aggregate average weekly man-hours is used in this study.1u This measure of employment is more sensitive to exogenous forces because it accounts for the fluctuations in production man—hours which occur before and after any change in employment takes place. As expected, there was a positive simple correlation between the rate of Results in the Measurement of Capacity Utilization," American Economic Review, LVII (March 1967), pp. 34—58. This study‘ produced capacity utilization estimates that compare closely with those calculated by de Leeuw. Both series display similar turning points, however, the Klein-Preston series _give slightly higher percentage utilization of capacity estimates for the years 1947-1965. 13John G. Cragg, Arnold C. Harberger, and Peter Mieszkowski, pp. cit., Vol. 75. lL'Emplpyment and Earnings Statistics for the United States 1909-1962, Bulletin No. 1312—1, U.S. Department of Labor; Data for 1963 from Earnings and Employment, Vol. 10, 1964. 81 return and the employment index in most of the industries (11 out of 17). C. Dummy Variable ‘It is not unusual for the effects of a wartime economy to alter an otherwise stable relationship. In the case where tax incidence is measured on the basis of an estimated relationship between the rate of return and selected independent variables, the extraordinary demand for war materials can bias the shifting inferences. The dummy variable is a way of accounting for the high profits and high tax rates during periods Of mobilization which do not necessarily imply direct shifting of the tax burden. The functional relation between the dependent vari— able and the tax variable can be redefined as T l _ Yg - Yg : a1 + b t 1 (wartime) (3) Kt—l Y Y' Tt-l ( ' ) ~ g _ g =. a2 + b ____ peacetime (4) ’ Kt-l where al > a2. These relations could be fitted to wartime data (3) and peacetime data (4). However, since we are making the assumption that the shifting parameter is constant throughout the testing period, (3) and (4) may be combined into one relation with the use of a dummy variable.15 15For a more complete eXplanation of dummy variables and the problems encountered, see J. Johnston, Econometric 82 Pooling wartime and peacetime observations, one may estimate Ysat ‘ Yé.t = R1 + 52x + b3 Eili (5) t-l where the dummy variable is 0 in each peacetime year 1 in each wartime year The Korean War had a substantial effect upon the level of induStrial production and associated profits during the early fifties. By using the dummy variable and giving it a value of one for the four observations 1950-1953, and zero for the other Observations, the possibility of wartime Shifts in the intercept of the rate of return function may be accounted for. Basic Model The following notation and definitions are used in the statement of the model. Pt = annual before—tax profit; including interest paid on debt K = capital stock at the end Of the year; gross of depreciation, depletion, and amortization Methods (New York: McGraw—Hill Book Company, Inc., 1963), pp?"§21;222. 83 Yt = before-tax rate of return = 33 Kt T = tax liability = ZPt Z = statutory tax rate Lt = general tax variable = 33:1 Kt-l Ct = measure of capacity utilization Et = employment index; aggregate weekly man-hours for each two— digit industry; 1958 = 100 X = dummy variable; equals one (1) for 1950-1953; equals zero (0) for the other years U = stochastic disturbance A. Regression Equation and Estimating Method The general approach of this study is to apply time series analysis to fit a function where the rate of return for each industry is the dependent variable, and the negative rate of return is one of several predetermined variables. On the basis of the regression coefficients of the tax variable, the difference between the observed rates of return and what the rates of return would have been without the tax can be estimated. Assuming that changes in the rates of return can be eXplained by the tax variables and other predetermined 84 variables, we can determine the relative influence of the tax variables by fitting industry data to the following regression equation. Y =a+aL+ C-l- + + pg,t 0 1 t a2 t a3Xt a4Et Ut (6) Since T ZP Lt = Kt-l : Kg,t-l = Z¥g,t-1 t—l t—l equation (6) is autoregressive, and the regression coeffi- cients have limitations depending upon the statistical prOperties of the data. First, assuming that the disturbance terms are inde- pendent, least squares applied to Y = a + a Y + U (7) will give an estimate of a2, designated 32, so that 32 < a2.16 However, the negative bias creates no great problem because this study is primarily concerned with whether there has been any degree of shifting. The way the model is specified, a negative bias means that inferences drawn from the estimates may indicate less shifting than would be inferred from unbi- ased estimates. However, autocorrelation in the disturbance may greatly affect the estimation of the coefficients when this E. Malinvaud, 15 . cit. . 214—215- Johnston, pp 9 PP ’ Rand McNally 8 Statistical Methods of Econometrics (Chicago: Company, 1966), p. 456. 85 regression is calculated by least squares.17 The simulta- neous presence of autocorrelated disturbances and lagged variables produces a substantial positive bias.18 Unfor- tunately, it is not possible in this study to make a reliable assessment of autocorrelation in disturbances. The commonly used Durbin-Watson Statistic is biased towards two (2), and there is always the presumption against finding evidence of . . . . l pOSitive serial correlation. 9 20 the introduction of As discussed by Malinvaud, exogenous variables has the effect of reducing the bias. It should be emphasized, however, that the possible presence of autocorrelation in disturbances, even with the mitigating effect of additional exogenous variables, yields regression coefficients that should be interpreted with caution. B. The Measurement of Shifting The specified model (7) permits one to estimate the tax variable coefficient for each industry. It remains to translate these coefficients into a measure of the degree of shifting. With the gross rate of return used as the indicator, l7Johnston, pp. cit., p. 216; Malinvaud, pp. cit., p. 462. l8Johnston,_1_b_:_i_p. lgMarc Nerlove and Kenneth F. Wallis, "Use of the . . . . . . " Econo— Durbin-Watson Statistic in InapprOpriate Situations, metrica, Vol. 34 (January, 1966), p. 235; Malinvaud, pp. c1t., p. 462. 20Malinvaud, pp. cit., p. 463. 86 the conditions of zero and 100 percent shifting may be defined as Zero shiftin Y = Y' g gat ,gat T 100 Percent shifting Y - Y' : t-l gfit g,t These two formulations suggest a measure of shifting which can be written Y Y' Ft : igat ' Eat (8) T t—l K t-l The significance of Ft is that it is the ratio of the increase in the gross rate of return after the tax has been raised to the amount of the new tax liability. Since the denominator of the ratio equals Tt—l, Ft is the proportion K t-l of the negative rate of return attributed to the income tax which has successfully been shifted by the firm. In order to arrive at the value Of Ft’ we must first estimate Y'g,t or what the rate of return would be in the absence of the income tax. This is accomplished by estimating the regression equation (7) with Lt = 0 and subtracting from the first estimation of (7). Because the other variables in the equation are independent of the tax, we arrive at _ ' : Yg,t Yg,t alLt (9) 87 If Ft is redefined as Y Y' Ft = gut - Bat (10) then (11) The coefficient of the tax variable in the regression equation (7) becomes the measure of shifting and is given directly by the value of the estimate. It is assumed to be constant over the time span of the analysis. C. Time Period Considered bypthe Study The years covered by this study were 1947-1963. The two foremost determinants Of the selection of the years were the absence of certain exogenous forces (e.g., the stringent wartime price controls of the early 1940's and depressed econo- mic conditions reminiscent Of the 1930's), and the availability of industrial concentration data for these years. Although the Korean War did occur during this period, the consequences were minor when compared to the effect upon the economy Of the Second World War. And in any case, the use of a dummy vari- able in the rate of return function permits a test of struc- tural shifts attributable to the Korean periOd. The peculiarities of the industrial data caused by the occasional changes in the Standard Industrial Classifica— tion necessitated many adjustments. The comparability of the adjusted data was increased by limiting the scope of the 88 test and restricting the examination to seventeen recent years.21 Even though over the seventeen years included in this study there have been some changes in the compositon of the two-digit industries, it was possible to adjust the reported statistics so as to achieve much_greater compara- bility than if the analysis had commenced in the 1920's. The adjustments are discussed in the Appendix A to this study. 21Even these few industries which have changed the least are considerably different today than they were in 1925. The procedure used by Gordon was to start with the original ten, two-digit industries listed for the 1920's and combine all the subsequent changes into these ten inclusive classifications. Unless he used a very complicated weighting system, I fail to understand how his aggregated data describe the changing importance of products within a broad category and how these changes might have altered the possibility of shifting the income tax. The value of any disaggregated approach to the shifting problem is limited by the conglom- erate nature of any industry data. The less the study relies upon combined data the more meaningful will be the final results. CHAPTER V AN EVALUATION OF EMPIRICAL RESULTS Initially, equation (6) of the preceding chapter was used to estimate the shifting coefficients for the seven- t’ Bt’ and Xt and their standard errors are presented in Tables 3a teen industries. The regression coefficients of Lt’ C and 3b. Since this study is primarily interested in the magnitude and significance of the coefficient of L the t3 equation was changed. The collinearity of Ct and Et caused the estimates of Lt to have relatively high standard errors when both were used as regressors. In most cases, C was t more highly correlated with Yt' When Et was drOpped from the estimating equation, the standard errors of Lt were 4generally reduced, and the regression coefficients were more reliable. The regression equation used for the analysis was (1) Y = a + a t 0 lLt + a Ct + a X + U 2 3 t t’ and the regression coefficients are also presented in Tables 3a and 3b. 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