Division of Research Graduate School of Business Administration The Universtiy of Michigan December 1977 The Effect of Measurement Error on Comparisons of Alternative Theories of Corporate Investment Behavior Working Paper No. 158 R.D. Nair The University of Michigan FOR DISCUSSION PURPOSES ONLY None of this material is to be quoted or reproduced without the express permission of the Division of Research.

The Effect of Measurement Error on Comparisons of Alternative Theories of Corporate Investment Behavior The quality of the data used in tests of economic hypotheses has long been of concern to economists. When theories regarding firm behavior have been tested a commonly used data source for the measurement of economic variables has beeA the published financial statements of corporations. These statements, however, are the end product of the application of various accounting techniques, which may introduce errors in measuring the variables of interest to the economist. General concern about the possible impact of accounting measurement procedures on the results of empirical tests conducted by economists has been expressed by Morgenstern, Jhbnston, Griliches, Kuznets (1971, 1972), Hall and Weiss, and McCracken among others. This paper reports a specific attempt to assess this impact; it deals with the effect of accounting methods on attempts to rank alternative theories of corporate investment behavior by their explanatory power. Tests of corporate investment behavior were selected for assessing the impact of accounting methods for three reasons. First, -attempts to distinguish between alternative theories of corporate investment are considered important, as can be seen in Eisner, page 138, and Okun, page 19. Second, the economics literature already contains well-documented attempts —by Jorgenson and Siebert (JS) and Elliott —to rank these theories.- The methodology used in these two studies could therefore be used to provide a structure for the present research. Moreover, the end result of those studies has been a ranking of investment theories and different rankings of theories on different accounting methods, if

-2 -obtained, would provide a vivid illustration of the possible impact of accounting methods on empirical tests of economic theories. Third, these studies have been concerned with firm behavior and have used accounting data from financial statements of firms. JS and Elliott both compared the explanatory power of four different theories of corporate investment, the Neoclassical, Accelerator, Expected Profits and Liquidity models, with respect to time series data for a sample of firms. The Elliott study was a methodological replication of the JS study using a larger sample (184 firms versus 15 firms) and resulted in contradictory conclusions about the relative performance of investment theories. This contradiction is taken up again later in the conclusions of this paper when a possible cause for it is pointed out. The possible impact of accounting methods on these tests of investment theories derives from the fact that the variables entering the models were measured from financial accounting data. For example, in the liquidity model, both studies measured the internal funds available for investment in a given firm by accounting net income less dividetnds paid plus accounting depreciation. The value of this measure will be affected by the various techniques used by accountants, such as alternative depreciation methods or inventory flow assumptions, as well as methods of accounting for subsidiaries or translation into dollars; of accounts denominated in foreign currencies. A different accounting technique would produce a different value for this measure of liquidity without any corresponding change in the underlying economic variable, the funds available for investment. Thus the empirical performance of the model would be influenced by the accounting methods used by the firm

-3 - to produce financial data. Similarly, the value of output in the Accelerator and Neoclassical models was measured by adding the change in inventory to sales revenue. This measure would be affected primarily by the inventory valuation assumptions which the accountant made. Likewise, the measurement of the cost of capital services in the Neoclassical model would be sensitive to the depreciation method followed by the firm. Only the Expected Profits model does not have an accounting variable entering directly into the measurement process, and changes in accounting methods would not be expected to affect the explanatory power of this model at all. Given the above reasons for expecting accounting methods to have an impact on the performance of models through the measurement of relevant variables; it was decided to select alternative methods of depreciation accounting and inventory valuation for assessment. These two categories were selected because 1) they are the most important areas in which accounting alternatives exist; 2) both affect three of the-four investment models discussed above; and 3) it is easier to derive estimates of numbers under alternative assumptions for these two methods. The two inventory valuation methods considered were first-in first-out (FIFO) and last-in first-out (LIFO). Three depreciation accounting methods were considered: straight line (SL), sum of years digits (SYD), and double declining balance (DDB). There were, therefore, six combinations of inventory and depreciation techniques to consider.

-4 - Research Procedure The research procedure, in summary, was as follows. The exact methodology used by JS was used to fit the four models to a set of data produced under one combination of accounting methods for a sample of firms. The rankings of models by standard error was noted, because this was how JS ranked the four investment theories. The accounting method was then changed to produce a different set of data on the independent variables for the same firms. The measurement of the depenaent variable, gross investment, which is not influenced by accounting methods, was left unchanged. The same models were then fitted to this set of data on the independent variables and the resulting rankings were noted. This was done for the six combinations of accounting methods with the dependent variable staying unchanged. The rankings of models for each firm were then compared across accounting methods to see whether each of the methods yielded the same rankings of models. Kendall's coefficient of concordance was used to provide a numerical measure of agreement between the rankings. If the rankings were not in complete agreement across the accounting methods, this would indicate that attempts to rank theories of corporate investment could be influenced by the accounting methods followed by the sample firms. A ranking of accounting methods across the four models was also done to test whether one combination of accounting methods would consistently provide the best fit for all models. If this did not happen, it would indicate that comparative tests of investment models could not be performed using data from any combination of accounting methods.

-5 -Before the results of the experiment are presented, certain facets of the research procedure will be explained in greater detail. To compare alternative investment theories JS employed the flexible accelerator in which: (1) Kt - Kt_ = (1-X) (Kt - Kt_l) when K and K are actual and desired levels of capital in period t. t t Assuming replacement to be a constant proportion, 6, of actual capital enables the changes in capital to be expressed as: (2) Kt - Kt_ It - 6K where I is the level of gross investment in period t. Expressions 1 and t 2 are combined to produce a flexible accelerator framework for analysis of gross investment: (3) It = (1-X) (Kt - Kt_) + 6KtJS show that expression 3 can be generalized to: co (4) u. (K* K* 9+ 6K <I = Ui (Kti - Ktil) tt U -- ti-l t-it-l i=o where the u are weights which are non-negative and sum to unity. JS i assume that the distributed lag influence of each K on I follows a generalized Pascal distribution, and they obtain the operational version of the model used to compare the statistical importance of alternative specifications of desired capital (K ): 2 2 1=- wi (Ii 6K + 1(5) It =X (K t-i t-i-) t-I 1~~~~~~~~~ —Os

-6 -JS fitted this distributed lag model to time series data for a sample of firms by ordinary least squares, using four different specifications of desired capital stock. As can be seen, up to three desired capital stock changes and up to two lagged net investment terms were admitted into the specification of this distributed by model. Changes in desired capital and lagged net investment were allowed to enter the distributed lag function so long as they lowered the residual variance around the regression. JS compared four alternative representation of K representing major branches of investment theory. Different investment theories have emphasized the primacy of different influences on K. The four that were considered were:, 1) The Neoclassical formulation, in which K is taken as proportional to the value of output in constant dollars (Pt Qt) deflated by the price of capital services (c ). The value of output was measured by sales plus the change in inventory, a measure which is susceptible to both the inventory and depreciation methods used by accountants. The price of capital services, ct, was measured as: c= t (1 - v w ) 6+ r -t -- t t t 1-v where qt is the investment goods price index; 6 is the rate of replacement obtained in the calculation of net capital stock; rt is the cost of capital measured as the ratio of accounting net income (adjusted for current cost depreciation) to the total market value of the firm's securities; v is the rate of taxation of corporate income and is measured from financial reports as the ratio of accounting income before

-7 -taxes less accounting income after taxes to accounting income before taxes. The variable wt is the ratio of depreciation taken for tax purposes to depreciation at current replacement cost. The values of all the above measures, except qt, can be influenced by the accounting methods followed by the firm without any change in the underlying economic reality. <2) The Accelerator model, in which desired capital is taken to be proportional to output., The measurement of this variable and the in-.fluence of accounting procedures on it has already been discussed in connection with the Neoclassical formulation. 3) The Liquidity model, in which desired capital is taken to be proportional to internal funds available for investment. This was measured by accounting net income after taxes plus accounting depreciation less dividends paid, in constant dollars. 4) The Expected Profits Theory of investment behavior, in which desired capital is proportional to the market value of the firm. This was measured as the market value of stocks outstanding plus the book value of debt, all in constant dollars. The statistical importance of each of the four different formulations of desired capital was evaluated by JS by its separate insertion into the distributed lag model given in (5). The best specification of the distributed lag model given fitted to time series data for a given firm for each specification of desired capital was found by-selecting thelag structure with the minimum residual variance. Once this had been done the alternative -theories of investment behavior were compared and ranked on afirm-by-firm basis by their explanatory power as measured by the size of the standard error.

-8 — As mentioned earlier, the present research used exactly the same statistical procedure to fit alternative investment models to the data and compare their performance. Care was also taken to utilize the same sources for data —such as price indexes used for deflating variables and financial data of firms —as JS used. These data sources are described in their paper and a statistical appendix to a longer version of the same paper available directly from the authors. All variables are denominated here in millions of dollars rather than in billions of dollars. Procedures with regard to measurement identical to those used by JS were also used here. What was changed were the accounting methods used to produce the numbers to which these measurement procedures were applied. For example, the liquidity variable was still measured as accounting net income after taxes plus depreciation less dividends paid. In this research the accounting methods with regard to inventory valuation and depreciation used by accountants to calculate net income and depreciation were changed. There were six combination of accountingmethods beingtested and they thus yielded six different measures of liquidity to be inserted into the distributed lag model above to see the effect of different accounting methods on the performance of the Liquidity model. The same was done for the measures of the independent variables in the other investment models, and thus the impact of accounting methods on the relative performance of thefour models in explaining the same dependent variable could be evaluated. In order to produce the six different sets of financial data for any firm it was necessary to use estimation procedures, because a firm

-9 -using a given set of accounting methods for inventory and depreciation, such as FIFO and SL, will not reveal financial data under some other set of accounting methods, such as LIFO and SYD. It is necessary, therefore, to estimate the financial data which would be produced under inventory and depreciation methods different from those currently used by a firm. The method used to estimate FIFO inventory values for firms which use LIFO and vice versa is an adaptation of the Dollar-Value LIFO technique. The technique itself is described in Hirsch. Its use for estimation of alternative inventory values in another context can be found in Derstine and Huefner. The method used to compute depreciation expense under alternative methods was to layer the existing dollar value of gross plant by capital expenditures each year to find the various years in which the existing balance in gross plant was acquired. This method assumes that retirements of plant come from earlier purchases and the existing balance comes from the most recent purchases. A similar estimation pro. cedure.can be found in short. Alternative depreciation procedures using asset age estimates adapted from the Asset Depreciation Range System can then be applied to the acquisition layers to determine alternative depreciation expense for a given year. These estimation methods contain a fair number of assumptions and the accuracy of the estimates produced was, therefore, assessed using data from a sample of firms. The validation procedures used is described by Nair along with a detailed description of the above estimation techniques (see Working Paper No. 157 of this series). It was found I

\ -10 --.. -4- 4- ^- Estimated less Actual that the average error in percentage terms (ie., 100 X s timate l Actual Actual for the FIFO to LIFO restatement technique for 20 observations was 1.34 percent. For the LIFO to FIFO restatement the average percentage error over 7 comparisons was -4.5 percent, whereas the average percentage error produced-by the depreciation estimation technique across 26 comparisons was 1.46 percent. To ensure that the final conclusions of the study would be robust it was decided not to rely completely on the accuracy of the estimation procedure but to perform the entire model fitting and ranking process three times: once with the estimates and then with the estimates plus 10 percent as well as minus 10 percent. This step, although adding considerably to the computational effort involved, should serve as an adequate test of the sensitivity of the conclusions drawn to any errors in the estimation process. Finding the best-distributed lag structure for one investment model according to the criterion of minimum residual variance for each firm under just one of the three sets of estimates for one of the six combinations of accounting methods in itself was to involve the examination of nearly thirty regression equations. Because, in addition to the estimation computations described above, seventy-two distributed lag structures had to be determined for each firm in the sample (6 combinations of accounting methods x 4 investment models x 3 sets of estimates), it was decided to limit the sample size in this study to ten firms. JS, in comparison,had a sample of fifteen firms. This

-11 -limitation does not constitute a departure from the JS methodology, however, since the models are being fitted on a firm-by-firm basis. The -criteria used in the selection of the ten firms were as follows: The sample represented a cross-section of the six combinations of accounting methods. Such a sample design prevents complete reliance on the accuracy of the restatement procedures, since for any given combination of accounting methods at least one firm in the sample actually followed those methods in its financial reporting. It was also decided to select the firms to represent a cross-section of industries with a bias towards the larger firms-in an industry for the same tworeasons cited in JS: the availability'of accurateandr consistent data for a time period going back to 1935 to layer gross plant for restatement purposes; and the importance of the investment activity of larger firms. The sample selected for this study is given in Table 1. As shown they are the largest firms- in their industries and-account for a-sizable percentage of investment expenditure in their industries. The firms common with the JS sample are: Anaconda, General Electric, General Motors and R.J. Reynolds. The period of analysis used in this study is 1961 to 1975. The length of this time period, 15 years, is the same as -that in the JS study, which considered the time period-1949-63. The -agreement among rankings of these investment models across accounting methods could of course be examined visually. However, in order to provide a numerical measure of the agreement between rankings Kendall's coeffiecient of concordance, W, was used. This coefficient takes on the value of 1 in the case of perfect agreement and 0O in the case

-12 - of no agreement between rankings. Tests of statistical significance of W can be conducted, although it should be noted that any value of W not equal to 1 would indicate that accounting methods have a distorting impact on attempts to rank investment models. The calcultaion of W has to be amended-if tied ranks are present. In ranking investment models across accounting methods no tied rankings were given. In ranking the six accounting methods across the four models, however, ties were unavoidable, especially with the Expected Profits and Accelerator models, and therefore necessary adjustments as suggested in Siegel were made. For a more detailed exploration of the agreement in rankings of methods, the Spearma1n Rank Correlation Coefficient was used to examine the rankings of the Neoclassical and Liquidity models. Empirical Results Tables 2-11 present the results of ranking the four investment models across data on six accounting- methods for the ten' firms inL the sample. The actual standard errors obtained for each model are shown across the top of the tables, while the rankings are given in the middle section of the tables. As can be seen, every firm except General Motors exhibits some disagreement in rankings between the different accounting methods. This would indicate that accounting methods do have an impact on tests of comparative performance of investment models. The value of W, the coefficient of concordance given in the lower section of each table, reflect this disagreement, ranging from 1.0 for General Motors to 0.6333 for Allis-Chalmers. The average coefficient of concordance across

-13 -the ten firms is 0.8108,where 1.0 would indicate-perfect agreement. However from a statistcal point of view we can reject the null hypothesis that the rankings disagree at the.01 level.of significance for all ten firms. The tentative conclusion to be drawn from these results, then, is that an economist conducting a comparative test of investment models on two firms identical with respecttto-every substantive:attribute -exceptC the accounting methods they follow to record their transactions may obtain different rankings of models. The difference in those rankings will not be statistically significant, but it should be noted that tests for statistical significance of differences in rankings have not been part of studies which have ranked investment models, such as those of JS and Elliott. As noted earlier the procedure used to estimate financial data under different accounting methods is susceptible to error. The sensitivity of Sthe results obtained was therefore tested using the estimates plus 10 percent as well as minus 10 percent. That is, the above procedure was repeated and the models were again ranked by standard error for these twoc additional sets of data across the six accounting methods for each firm. For the sake of economy of space, however, these rankings will not be presented. Instead, Table 12 sets forth only the coefficients of concordance calculated to quantify the agreement among rankings of models across the six methods using these two sets of data, and to aid comparison of —the results, repeats the coefficients of concordance using the original set of data (and reported in Tables 2 to 11) in its first column. The results using the estimates plus 10 percent are similar to

-14 - those using the unadjusted estimates. Nine out of the ten firms continue to show disagreement in rankings, with General Motors again being the only exception. The range of the disagreement as measured by the coefficient of concordance W is slightly greater, being from 0.5778 for Anaconda to 1.0 for General Motors. The average coefficient of concordance for the ten firms is now 0.8099. Again, from a statistical point of view the null hypothesis that the rankings disagree can be rejected at the.01 level of significance for all ten firms. When the original estimates minus 10 percent are used to develop the rankings, the number of firms showing complete agreement increases to four. Besides General Motors they are Standard Oil of California, Zenith, and Consolidated Foods. The range of the disagreement as measured by the coefficient of concordance is now from 0.6444 for Allis-Chalmers to 1.0 for the above four firms. The average coefficient of concordance for the ten firms is now 0.8964. However, the nulJlhypothesis that the- rankings disagree is rejected at the.01 level of signif-icance! for all ten firms. The results of this sensitivity analysis tend to bolster the conclusion reached above that differences in accounting methods may lead to unwarranted inferences about the relative merits of investment models. That conclusion seems fairly robust with respect to any error in the techniques used to estimate the data produced by different accounting methods. In the light of this conclusion it would be interesting to see if

-15 - the rankings of accounting methods across the four models are in agreement. A finding that one combination of methods, say FIFODDB, uniformly provided the best fit for all four models would indicate that comparative tests of those models could then be conducted on data developed by using that combination of methods. If, however, the accounting methods which yield the best fit differ from model to model it would imply that compara — tive tests should be conducted using other, possibly nonaccounting,> measures of the variables in the models. ' To investigate this issue, the same methodology used earlier to compare rankings of models across methods was used. Tables 13-22 present the rankings of six accounting methods for each of the four models on the basis of standard error. They were derived from the information given in Tables 2-11. Thus, for example, in the case of RCA (Table 13) the best fit for the Liquidity model was obtained by using FIFOSYD data, while for the Neoclassical model FIFODDB data yielded the best fit. As expected, the same inventory method yields the same results for the Accelerator model with the standard error changing only when we change inventory methods. With the Expected Profits model the explanatory power does not change at all and therefore all the methods tie for the same position. Once again, the coefficient of concordance, W, was calculated in each case with suitable adjustments made for the occurrence of ties. It should be remembered that 1 indicates perfect agreement while 0 indicates no agreement. In this case, it was found that the null hypothesis that the rankings are in disagreement could not be rejected at the.05 or.01 levels in nine- out of the ten cases.- The exception is

-16 -Allis-Chalmers. From this it can be concluded that there is no one set of accounting methods which can be applied uniformly across models for the purpose of comparative tests. Sensitivity analyses similar to the previous case using the standard error developed from the estimates -plus-and minus O -percent1 were also conducted. The rankings themselves are not being presented here for the sake of economy of space. Instead, the coefficients of concordance between the rankings in the two sensitivity runs are displayed. in Table 23 together with coefficients calculated using the unadjusted estimates. Thus Table 23 also summarizes Table 13-22 and serves as an easy reference for comparing the three sets of estimates. As can be seen, the coefficients seem to indicate a persisting disagreement-between the rankings of the six methods across models, which would indicate that greater effort should be devoted to developing other more accurate, possibly nonaccounting measures of variables. This point is elaborated upon later in the paper., To explore the issue in greater detail it was decided to examine the agreement between rankings of the six methods for only the Liquidity and Neoclassical models, the other two models having shown,-a high proportion of tied ranks. The appropriate statistic for measuring the agreement between two sets of rankings is the Spearman Rank Correlation'Co — efficient. This statistic was used to measure the agreement between the rankings of the six accounting methods for the Liquidity and Neoclassical models for the ten firms. The sensitivity analyses were again conducted

using the same range of 10 percent around the estimates. The results are presented together in Table 24, along with the critical values of r for the.05 and.01 levels of significance. As can be seen, none of the coefficients has the value of 1 (which would indicate perfect agreement). Nearly half of the coefficients (thirteen out of thirty) are negative, although not significantly so except in the case of Consolidated Foods and R.J. Reynolds in one of the sensitivity runs. The extreme case of Consolidated Foods indicates no agreement at all in the rankings. Significant degrees of agreement can be found in the sensitivity runs for RCA, Standard Oil of California, General Electric, and Zenith. The relationship between the rankings of models by accounting methods and the rankings of accounting methods by models can be seen by examining, for the sake of exposition, the relative performance of the Liquidity and Neoclassical models for a given firm. This can be done with reference to Monsanto with good effect, because for that firm these two models switch relative positions as we change accounting methods. The relevant Tables are 4 and 15. From Table 4 it can be seen that the Liquidity model does worse than the Neoclassical model when FIFOSL, LIFOSL, and LIFODDB are used. -Table 15 reveals that this could have been expected to happen because those three combinations of accounting methods provide the worst fit for the Liquidity model and the best fit for the Neoclassical model. The rankings of the two models are reversed when the two models are on FIFOSYD, FIFODDB, and LIFOSYD data, which provide a better fit for the Liquidity model and a worse fit for the Neoclassical model.

-18 -These results seem to indicate that comparative tests of the two models can not be conducted on any given combination of accounting methods, the method being used may provide the best fit for one model and the worst fit for another and thus may seriously bias any attempt at ranking models. Conclusions The findings of this study suggest that the accounting methods followed by firms have a distorting impact on inferences to be drawn from financial data of those firms. Depending upon the firm's accounting methods, different conclusions may be drawn as to which investment theory provides the best explanation of corporate investment behavior. It was also found that no one combination of accounting methods provides the best fit uniformly for all models. The implications of the first conclusion are that care should be exercised in comparing results obtained from two different samples of firms. This would be the case, for example, in comparing the results of the Elliott study with the JS study. If the samples were not comparable with _respect to accounting methods the results of this study would lead one to expect different rankings of-models. The second conclusion above points out another reason why the Elliott and JS studies disagreed on the relative performance of the Liquidity and Neoclassical models. As noted earlier, it was found,that the accounting methods providing the best fit for one of those two models were not the accounting methods providing the best fit for the other model. These findings imply comparative tests of models should be conducted using more accurate, possibly nonaccounting, measures of the variables of interest. For I example, in computing the value of output, actual production data for firms can be used instead of balance sheet inventory fiqures. Similarly,.1 — _ i,?

-19 -in determining the funds available for investment in a firm, more accurate measures of this variable can be constructed from the Statement of Changes in Financial Position presented in the financial reports. Comparison of alternative investment models using such data is essential and will improve assessment of the relative merits of various investment theories.

References Derstine, R. P., and Huefner, R. J. "LIFO-FIFO, Accounting Ratios and Market Risk." Journal of Accounting Research, Autumn 1974, pp. 216 -34. Eisner, R. "Capital Expenditures, Profits and The Acceleration Principle." In Models of Income Determination. Princeton: National Bureau of Economic Research, 1964. pp. 137-76. Elliott, J.W. "Theories of Corporate Investment Behavior Revisited." American Economic Review, March 1973, pp. 195-207. Griliches, Z. "Errors in Variables and Other Unobservables8.' Econometrica, November 1974, pp. 971-998. Hall, M. and Weiss, L. "Firm Size and Profitability." Review of Economics and Statistics, August 1967, pp. 319-31, Hirsch, A. J. "Dollar-Value and Retail LIFO: A Diagrammatic Approach." Accounting Review, October 1969, pp. 840-42. Johnston, J. "Statistical Cost Functions: A Re-Appraisal." Review of Economics and Statistics, November 1958, pp. 339-50. Jorgenson, D. W., and Siebert, C. D. "A Comparison of Alternative Theories of Corporate Investment Behavior." American Economic Review, September 1968, pp. 681-712. Kuznets, S. S. Data for Quantitative Economic Analysis:.. Problems of Supply and Demand. Stockholm: Federation of Swedish Industries, 1071. _ Quantitative economic research: trends and problems. General Series No. 96 Stockholm: National Bureau of Economic Research, 1972. McCracken, P. W. "1974's Economic Air pocket." Wall Street Journal April 25, 1975. Morgenstern, O. On the Accuracy of Economic Observations. Princeton: Princeton University Press, 1963. Nair, R. D. "Methods of Restating Inventory and Depreciation Numbers." Working Paper No. 157, Graduate School of Business Administration, The University of Michigan, 1977. Okun, A. M. The Political Economy of Prosperity..Washington, D.C.: Brookings Institution, 1970. -20 -

-21 -Short, D. G. "A Study of the Usefulness of Price-Level Adjusted Accounting Numbers in the Context of Risk Asessment. Unpublished Ph. D dissertation. The University of Michigan, 1977. Siegel, S. Non-parametric Statistics for the Behavioral. Sciences. York, Pa.: Maple Press, 1956.

Table 1 FIRMS IN THE SAMPLE BY INDUSTRY Firm Capital Capital Expenditures as Firm Expenditures by Industry Industry Expenditures by Percentage of InFirm in 1975* Number Name Industry in 1975' dustry Expenditur Consolidated Foods 52.961 2000 Food. 612.884 8.64% Anaconda 163.063 3331 Primary Smelting 532.563 30.6% General Electric 448.200 3600 Electric 1,316.616 34% General Motors 1,200.889 3711 Motor Vehicles 2,068.225 58% Allis-Chalmers - 40.070 3522 Machinery- 425.698 9.4% Agricultural Monsanto 544.200 2801 Chemicals 5,082.795 10.7% Standard Oil of California 1,158.796 2913 Oil 11,408.080 10.2% R.C.A. 680.899 3600 Electric 1,316.616 51% R.J. Reynolds 190.419 2111 Tobacco 548.825 34.7% Zenith 21.281 3651 Radio-TV only firm listed in industry Manufacturing_ Firm Accounting we Methods FIFOSL LIFOSL LIFOSYD FIFODDB FIFOSL FIFOSYD LIFODDB FIFOSL LIFOSYD FIFODDB * In millions of 1975 dollars. Source: Compustat Tapes I No No

Table 2 RCA: STANDARD ERROR, MODEL RANKINGS, AND COEFFICIENT OF CONCORDANCE Accounting Method LIFOSYD FIFOSYD LIFODDB FIFODDB FIFOSL LIFOSL Model: Liquidity Accelerator Expected Profits Neoclassical Rankings: Liquidity Accelerator Expected Profits Neoclassical 36.030 36.611 36.812 29.813 35.989 36.727 36.812 29.742 36.046 36.611 36.812 29.296 2 3 4 36.014 36.727 36.812 29.171 2 3 4 1 38.476 36.727 36.812 33.287 4 2 3 1 37.676 36.611 36.812 33.381 I w I 2 3 2 3 4 2 3 1 4 4 1 1 Agreement: Coefficient of Concordance, W = 0.7333. I,,

Table 3 STANDARD ERROR. MODEL RANKINGS. AND COEFFICIENT OF GENERAL MOTORS: CONCORDANCE Accounting Method_ LIFOSYD FIFOSYD LIFODDB FIFODDB FIFOSL LIFOSL Model:,. Liquidity 289.23 289.37 288.70 288.74 289.03 288.88 Accelerator 283.88 283.88 284.08 283.22 283.89 283.89 Expected Profits 245.52 245.52 245.52 244.01 245.53 245.53 Neoclassical 269.06 258.04 274.20 263.10 268.57 277.56 Rankings: Liquidity 4 4 4 4 4 4 Accelerator 3 3 3 3 3 3 Expected Profits 1 1 1 1 1 Neoclassical 2 2 2 2 2 2 Agreement: Coeffiecient of Concordance, W = 1.000. I

I. i ill t,1 i i I I 1 - I l.I Table 4 ERROR, MODEL RANKINGS, NONSANTO: STANDARD AND COEFFICIENT OF CONCORDANCE Accounting Method LIFOSYD FIFOSYD LIFODDB FIFODDB FIFOSL- L' J -XC Model':, Liquidity 48.536 48.226 49.448 49043 49.788 50.117 Accelerator 41.324 41.181 41.324 41.181 41.181 41.324 Expected Profits 54.062 54.062 54.061 54.061 54.062 54.062 Neoclassical 56.463 55.732 48.376 53.745 47.532 50.865 Rankings: Liquidity 2 2 3 2 3 3 Accelerator 1 1 1 1 Expected Profits 3 3 4 4 4 4 Neoclassical 4 4 2 3 2 2 Agreement: Coefficient of Concordance, W 0.7444. 0n I

Table 5 STANDARD OIL OF CALIFORNIA: STANDARD ERROR, MODEL RANKINGS AND COEFFICIENT OF 'CONCORDANCE.Accounting Method.. IFOSYD FIFOSYD LIFODDB FIFODDB FIFOSL LIFOSL Model: Liquidity 63.456 65.071 64.563 65.933 64.506 63.563 Accelerator 58.974 59.269 58.976 59.270 59.270 58.976 Expected Profits 60.932 60.932 6932 60.932 60.932 60.932 Neoclassical 59.820 63.149 61.082 62.632 63.102 60.983 Rankings: Liquidity 4 4 4 4 4 4 Accelerator 1 1 1 1 1 1 Expected Profits 3 2 2 2 2 2 Neoclassical 2 3 3 3 3 3 Agreement: Coefficient of Concordance, W = 0.9444. I I

Table 6 ANACONDA: STANDARD ERROR, MODEL RANKINGS, AND COEFFIECIENT OF CONCORDANCE Accounting Method LIFOSYD FIFOSYD LIFODDB FIFODDB FIFOSL LIFOSL Model: Liquidity $35.881 36.411 35.835 36.403 36.386 35.468 Accelerator 35.689 36.027 35.673 36.011 36.026 35.688 Expected Profits 32.990 32.990 32.975 32.975 32.990 32.990 Neoclassical 36.125 33.845 36.850 36.469 36.854 34.900 Rankings: Liquidity 3 4 3 3 3 3 Accelerator 2 3 2 2 2 4 Expected Profits 1 1 1 11 Neoclassical 4 2 4 4 4 2 Agreement: Coefficient of Concordance, W = 0.6778! I I

Table 7 STANDARD ERROR, MODEL RANKINGS. GENERAL ELECTRIC: AND COEFFICIENT OF CONCORDANCE.._... ____Accounting Method LIFOSYD... FFIFOSYD LIFODDB FIFODDB FIFOSL LIFOSL Model: Liquidity Accelerator Expected. Profits Neoclassical 87.748 68.161 70.957 62.084 81.890 68.298 70.957 59.879 93.387 68.161 70.957. - 71.499 87.408 68.298 70.957 67.445 85.551 68.298 70.957 59.379 91.788 68.161 70.957 66.563 o Rankings: Liquidity Accelerator Expected Profits Neoclassical 4 2 3 1 4 4 2 3 1 1 2 3 4 2 3 1 4 2 3 1 4 2 3 1 Agreement: Coefficient of Concordance, W = 0.8333....... ~ ~... ~..

Table 8 R.J. REYNOLDS: STANDARD ERROR, MODEL RANKINGS, AND COEFFICIENT OF CONCORDANCE Accounting Method LIFOSYD FIFOSYD LIFODDB FIFODDB F-IFOSL LIFOSL Model: Liquidity 46.948 43.858 51.403 44.746 42.810 47.473 Accelerator 53.060 62.295 53.060 62.295 62.295 53.060 Expected Profits 58.960 58.960 58.960 58.960 58.960 58.960 Neoclassical 53.110 55.314 53.601 55.704 56.351 54.758 Rankings: Liquidity 1 1 1 1 1 1 Accelerator 2 4 2 4 4 2 Expected Profits 4 3 4 3 3 4 Neoclassical 3 2 3 2 2 3 Agreement: Coefficient of Concordance, W = 0.7000. f 3

Table 9 ZENITH: STANDARD ERROR, MODEL RANKINGS, AND COEFFICIENT OF CONCORDANCE Accounting Method LIFOSYD ' LIFODDB FIFODDB FIFOSL - LFOSL Model: Liquidity 4.7249 4.7731 4.6994 4.7569 4.7432 4.6901 Accelerator 4.5698 4.5977 4.5698 4.5977 4.5977 4.5698 Expected Profits 6.6606 6.6606 6.6606 6.6606 6.6606 6.6606 Neoclassical 6.6021 6.7132 6.6297 6.7300 6.7851.6.6524 Rankings: oL Liquidity 2 2 2 2 2 2 Accelerator 1 1 1 1 1 1 Expected Profits 4 3 4 3 3 4 Neoclassical 3 4 3 4 4 3 Agreement: Coefficient of Concordance, W = 0.9000.

Table 10 STANDARD ERROR, MODEL RANKINGS. AND COEFFICIENT OF CONCORDANCE CONSOLIDATED FOODS: Accounting Method LIFOSYD FIFOSYD LIFODDB FIFODDB FIFOSL LIFOSL Model: Liquidity Accelerator Expected Profits Neoclassical Rankings: Liquidity Accelerator Expected Profits Neoclassical 5.140 6.434 5.954 5.195 1 4 3 2 4.312 6.423 5.954 5.327 1 4 3 2 5.157 6.434 5.954 5.191 4.322 6.423 5.954 5.324 5.115 6.423 5.954 5.295 5.454 6.434 5.954 5.135 I H I 1 1 4 3 2 4 3 2 4 3 2 2 4 3 1 Agreement: Coefficient of Concordance, W = 0.9444.

Table 11 ALLIS-CHALMERS: STANDARD ERROR, MODEL RANKINGS, AND COEFFICIENT OF CONCORDANCE Accounting Method LIFOSYD FIFOSYD LIFODDB FIFODDB FIFOSL LIFOSL Model: Liquidity 5.242 5.331 5.243 5.332 5.323 5.185 Accelerator 5.297 5.304 5.297 5.304 5.527 5.297 Expected Profits 3.638 3.638 3.638 3.638 3.638 3.638 Neoclassical 5.016 5.283 5.182 5.415 5.475 5.312 Rankings Liquidity 3 4 3 3 2 2 Accelerator 4 3 4 2 4 3 Expected Profits 1 1 1 1 1 1 Neoclassical 2 2 2 4 3 4 Agreement: Coefficient of Concordance, W = 0.6333.

-33 - TABLE 12 COEFFICIENT OF CONCORDANCE.FOR RANKINGS OF INVESTMENT MODELS BY ACCOUNTING METHOD FOR THREE SETS OF DATA FOR THE TEN FIRMS Estimated Estimated Data Estimated Data Firm Data Minus 10 Percent Plus 10 Percent RCA 0.7333 0.7333 0.8111 General Motors 1.0000 1.000 1.0000 Monsanto 0.7444 0.7444 0.7000 Standard Oil of California 0.9444 1.0000 0.9444 Anaconda 0.6778 0.6778 0.5778 General Electric 0.8333 0.8333 0.8333 R. J. Reynolds 0.7000 0.7000 0.7444 Zenith 0.9000 1.000 0.9111 Consolidated Foods 0.9444 1.000 0.9000 A11is-Chalmers 0.6333 0.6444 0.6778

-34 - TABLE- 13 RCA: METHOD RANKINGS AND COEFFICIENT OF CONCORDANCE USING ESTIMATED DATA Model - - Expected Method Liquidity Neoclassical Accelerator Profits FIFOSL 6 5 5 3.5 FIFOSYD 1 3 5 3.5 FIFODDB 2 1 5 3.5 LIFOSL 5 6 2 3.5 LIFOSYD 3 4 2 3.5 LIFODDB 4 2 2 3.5 Agreement Coefficient of Concordance, W = 0.2758

-35 - TABLE 14 GENERAL MOTORS: METHOD RANKINGS AND COEFFICIENT OF CONCORDANCE USING ESTIMATED DATA Model Etxpec tea Method Liquidity Neoclassical Accelerator Profits F1FOSL 4 3 4 4 FIFOSYD 6 1 2 4 FIFODDB 2 2 1 1 LIFOSL 3 6 4 4 LIFOSYD 5 4 4 4 LIFODDB 5 6 4 Agreement Coefficient of Concordance, W = 0.3793

MONSANTO: METHOD TABLE 15 RANKINGS AND COEFFICIENT OF CONCORDANCE USING ESTIMATED DATA Model Expected Method Liquidity Neoclassical Accelerator Profits FIFOSL 5 1 2 3.5 FIFOSYD 1 5 2 3.5 FIFODDB 3 4 2 3.5 LIFOSL 6 3 5 3.5 LIFOSYD 2 6 5 3.5 LIFODDB 4 2 5 3.5 Agreement Coefficient of Concordance, W = 0.1727

-37 - TABLE 16 STANDARD OIL OF CALIFORNIA: METHOD RANKINGS AND COEFFICIENT OF CONCORDANCE USING ESTIMATED DATA Model Expected Method Liquidity Neoclassical Accelerator Profits FIFOSL 3 5 5 35 FIFOSYD 5 6 5 3.5 FIFODDB 6 4 5 3.5 LIFOSL 2 2 2 3.5 LIFOSYD 1 1 2 3.5 LIFODDB 4 3 2 3.5 Agreement Coefficient of Concordance, W = 0.6263

-38 -TABLE 17 ANACONDA: METHOD RANKINGS AND COEFFICIENT OF CONCORDANCE USING ESTIMATED DATA Model Expected [ethod Liquidity Neoclassical Accelerator Profits 1 M FIFOSL FI FOSYD FI FODDB LIFOSL LiFOSYD L I FODDB 4 6 5 1 3 2 6 1 4 2 3 5 5 6 4 2 3 1 3.5 5.5 1.5 3.5 5.5 1.5 Agreement Coefficient of Concordance, W = 0.3339

-39 - TABLE 18 GENERAL ELECTRIC: METHOD RANKINGS AND COEFFICIENT OF CONCORDANCE USING ESTIMATED DATA Model Expected Method Liquidity Neoclassical Accelerator Profits FIFOSL 2 1 5 3.5 FIFOSYD 1 2 5 3.5 FIFODDB 3 5 5 3.5 LIFOSL- 5 4 2 3.5 LIFOSYD 4 3 2 3.5 LIFODDB 6 6 2 3.5 Agreement Coefficient of Concordance, W = 0.1727 - - I - r~~~~~~~~~~~~~~

-40 - TABLE 19. R.J. REYNOLDS: METHOD RANKINGS AND COEFFICIENT OF CONCORDANCE USING ESTIMATED DATA - ----------------— HloB-l - -.... - -- Expected Method Liquidity Neoclassical Accelerator Profits FIFOSL 1 6 5 3.5 FIFOSYD 2 4 5 3.5 FIFODDB 3 5 5 3.5 LIFOSL 5 3 2 3.5 LIFOSYD 4 1 2 3.5 LIFODDB 6 2 2 3.5 Agreement Coefficient of Concordance, W = 0.1108 ~~~~~~~~~~~~~~~~~ —

-41 - TABLE 20 ZENITH: METHOD RANKINGS AND COEFFICIENT OF. USING ESTIMATED DATA Model thod Liquidity Neoclassical CONCORDANCE Me txpected Accelerator Profits FIFOSL 4 6 FIFOSYD 6 4 FI FODDB 5 5 LIFOSL 1 3 LIFOSYD 3 1 LI FODDB 2 2 Agreement Coefficient of Concordance, W = 0.6263 5 5 5 2 2 2 3.5 3.5 3.5 3.5 3.5 3.5 - - - -

-42 - TABLE 21 CONSOLIDATED FOODS: METHOD RANKINGS AND COEFFICIENT OF CONCORDANCE USING ESTIMATED DATA Model - Expected Method Liquidity Neoclassical Accelerator Profits FIFOSL 3 3 2 3.5 FIFOSYD 1 6 2 3.5 FIFODDB 2 5 2 3.5 LIFOSL 6 1 5 3.5 LIFOSYD 4 3 5 3.5 LIFODDB 5 2 5 3.5 Agreement Coefficient of Concordance, W = 0.0696

TABLE- 22 ALLIS-CHALMERS: METHOD RANKINGS AND COEFFICIENT OF CONCORDANCE USING ESTIMATED DATA Model Expected Profits Method Liquidity Neoclass ical Accelerator Fl FOSL FI FOSYD Fl FODDB 4 5 6 1 2 3 6 3 6 4.5 6 3 5 3 LIFOSL LIFOSYD 4 1 2 2 3 2 3 LI FODDB 2 3 Agreement Coefficient of Concordance, W = 0.6717

-TABLE 23 COEFFICIENT OF CONCORDANCE FOR RANKINGS OF ACCOUNTING METHODS FOR THE FOUR MODELS FOR THREE SETS OF DATA FOR THE TEN FIRMS Estimated Estimated Data Estimated Data Firm Data Minus 10 Percent Plus 10 Percent RCA 0.2758 0.5644 0.5644 General Motors 0.3793 0.3421 0.6659 Monsanto 0.1727 0.2552 0.1194 Standard Oil of California 0.6263 0.6000 0.6540 Anaconda 0.3339 0.4389 0.3396 General Electric 0.1727 0.2345 0.1727 R.J. Reynolds 0.1108 0.1108 0.0799 Zenith 0.6263 0.0714 0.1339 Consolidated Foods 0.0696 0.1933 0.0696 All is-Chalmers 0.6717 0.4629 0.6059.o

TABLE 24 SPEARMAN RANK CORRELATION COEFFICIENT OF RANKINGS OF ACCOUNTING METHODS FOR THE LIQUIDITY AND NEOCLASSICAL MODELS FOR THREE SETS OF DATA FOR THE TEN FIRMS Estimated Estimated Data Estimated Data Firm Data Minus 10 Percent Plus 10 Percent RCA 0.6571 '. 8857 0. 8857 General Motors -0.4857 -0.5508.0.2354 Monsanto -.07714 -0.5798 -0.7537 Standard Oil of California 0.7143 0.4857 0.9276 Anaconda -0.1429 0.0857 -0.2571 General Electric 0.7714 0.7714 0.9429 R.J. Reynolds -0.7714 -0.6000 -0.9429 Zenith 0.5429 0.8286 0.5429 Consolidated Foods -1.0000 -0.6571 -1.000 All is-Chalmers 0.4286 0.0286 0.2571 Critical values: at.05 level = 0.829 at.01 level = 0.943