Abacus Volume 17 Issue 1 1981 [Doi 10.1111%2Fj.1467-6281.1981.Tb00099.x] NORM ECKEL -- The Income Smoothing Hypothesis Revisited

ABACUS, Vol. 17, No. 1, 1981

NORM ECKEL

The Income Smoothing Hypothesis Revisited

Key words: Accounting procedures; Averaging; Income measurement. 1. INTRODUCTION

The purpose of this paper is to review earlier studies of income smoothing, and to offer an alternative conceptual framework for detecting or identifying income smoothing behaviour of firms. There has been a number of studies conducted in the area; however, the conceptual framework for most of these studies tended to be similar with differences limited to the sample of firms, the expectancy model ussd, the time-frame studied, or the soothing objects and smoothing variables considered. The present study proposes a conceptually different manner of viewing income smoothing behaviour.

The supposition that firm may intentionally smooth income was fist suggested by Hepworth [1953] and further elaborated upon by Gordon [1966]. The latter constructed a framework from which one could logically deduce the impetus for the act of income smoothing. There followed a number of empirical studies (Copeland and Licastro [1968], Copeland and Wojdak [19691, Cushing [1969], Simpson [1969], White [1970], Ronen and Sadan [1975], Barnea, Ronen and Sadan [1976]) all aimed at ascertaining whether or not firms intentionally smooth reported income.* The general findings of these and other such studies, suggest that fkms do behave as if they are smoothing income, although there was not complete unanimity.

2. TYPES OF INCOME SMOOTHING The identification of income smoothing behaviour poses no trivial task for the researcher. Income smoothing behaviour is diagrammatically presented in Figure 1. The necessity to distinguish between the potentially different types of smooth income streams has been recognized in previous studies of income smoothing behaviour. Dascher and Malcolm ([1970], pp. 253-4), Shank and Burnell ([1974], p. 136) and Horwiu ([1977], p. 27) all made similar distinctions.

A naturally smooth income stream simply implies that the income generating process inherently produces a smooth income stream. For example, one would expect the income generating process of public utilities to be such that income streams would be

I The conceptual framework employed by most researchers was similar to that proposed by Gordon ([1966],

* See Ronen, Sadan and Snow [1977] for an excellent review of the income smoothing literature.

NORM ECKEL is an Assistant Professor of Accounting and MIS, Bowling Green State University, Ohio.

p. 223). Hereafter it will be termed the Gordon methodology.

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I N C O M E S M O O T H I N G H Y P O T H E S I S

FIGURE 1

Smooth Income

1, Intentionally Being

Smoothed by Management

1

Smoothing

naturally smooth. But both real and artificial smoothing are the result of actions taken by management.

Real smoothing represents management actions undertaken to control underlying economic events. Horwitz ([1977], p. 27) asserts that real smoothing affects cash flows whereas artificial smoothing does not. Dascher and Malcolm ([1970], pp. 253-4) indicate that real smoothing represents actual transactions undertaken or not undertaken on the basis of its smoothing effect on income. For example, a lirm might select capital projects on the basis of the co-variance of their expected income series. This represents the control of actual economic events that directly affect future income, and is thus termed real smoothing.

Artificial smoothing represents accounting manipulations undertaken by management to smooth income. These manipulations do not represent underlying economic events or affect cash flows, but shift costs and/or revenues from one period to another. For example, a firm could increase or decrease reported income simply by changing its actuarial assumptions concerning pension costs.)

3. PREVIOUS IDENTIFICATION OF INCOME SMOOTHING BEHAVIOUR: THE GORDON METHODOLOGY

Copeland ([1968], p. 105) suggests three general methods for identifying income smoothing behaviour: (1) directly ascertain from management by interview, questionnaire, or observation; (2) contact second parties such as CPAs; or (3) examine

For other examples of artificial smoothing and its accounting manipulations, see Ronen ef a/. ([1977], pp. 17-19).

29

A B A C U S

ex post data. By far the great majority of researchers selected the last method. In fact, I know of no such studies that utilized the other methods.

Generally speaking, those researchers examining expost data have assumed the same conceptual framework; that is, if the variability of normalized earnings generated by a specified expectancy model is lessened by the inclusion of a potential smoothing variable utilized by the firm, then the firm has smoothed income.

The problems inherent in the use of the above conceptual framework are now examined. Firstly, these examinations require the specification of an expectancy model for normalized income which is indeed a difficult task. If the expectancy model does not adequately describe the process generating the income time series, the inferences made concerning the inclusion of a specific smoothing variable could be a function of random error. Some researchers used what is generally termed the naive prediction model (El = El-,), in which the preceding periods income becomes the predicted income for the next period. Other researchers used a linear time trend model, exponential smoothing model, Box-Jenkins Model or some other method of generating a normalized ir~corne.~ One common element of these expectation models is that in all of them, El (earnings at time t) is a function of time, a constant growth rate, or pre-specified parameters (exponential- smoothing, Box-Jenkins, etc). Imhoff [1977] was the fmt to suggest that normalized earnings could be a function of an independent variable rather than the above. The independent variable selected by Imhoff was sales, with the implicit assumption that sales revenues are not subject to smoothing, or are subject only to a minimal e ~ t e n t . ~

Secondly, and more importantly, the examination of one smoothing variable at a time on the normalized income stream could produce biased results. The smoothing effect of one potential smoothing variable on the normalized income stream could possibly be mitigated by the aggregate effect of several potential smoothing variables on the normalized income stream. In other words, it may be possible that managements selection of some variables tends to smooth income, whereas their selection of other variables tends to work in the opposite direction, thereby affording no conclusive evidence for the income smoothing hypothesis.

Finally, some studies examined the effect of a potential smoothing variable on the normalized income of one period only. Clearly, as indicated by Copeland ([1968], p. 107) and Imhoff ([1977], p. 86), any inferences concerning income smoothing behaviour made from a cross-sectional (one-period) study are tenuous at best. To be sure, when making inferences concerning income smoothing behaviour, one is implicitly alluding to a pattern of behaviour over time, not just in a single period. Therefore, empirical tests of income smoothing behaviour should be conducted on time series data.

4. IMHOFFS IDENTIFICATION OF INCOME SMOOTHING Imhoff [1977] offered a radically different framework for the identification of income smoothing behaviour. Rue ([1977], p. 101) indicates that Imhoffs concern that the results of previous studies of income smoothing behaviour might have reached

See Ronen er a/. ([1977], p. 21) for a discussion of expectation models. Imhoffs procedure will be further elaborated upon in Part 4 of this study.

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I N C O M E S M O O T H I N G H Y P O T H E S I S

inconclusive results because of the inclusion of natural smoothers in their samples led him to construct an alternative methodology for the identification of income smoothers.

Imhoff first regressed income and sales on time: Income = a + p (time) and Sales = a + p (time). He then defined variability as the size of R2 for each regression. For example, if the R2 of sales as a function of time is greater than the R2 of income as a function of time (R2(s = f (t) ) ) > (R2(I = f (t) ) ), then the sales time series is defined as less variable than the income time series. Additionally, Imhoff regressed income on sales (I = f ( s ) ) to determine the extent to which income is related to sales.

To determine whether or not a specific firm was exhibiting smoothing behaviour, Imhoff (p. 92) applied the following criteria:

(i) . . . we define smoothing to be a smooth income stream and a weak association between sales and income, or

(ii) a smooth income stream and a variable sales stream. He concludes from the data analyzed that there was not a single case of obvious smoothing. As before, with the discussion of the Gordon, the difficulties associated with the conceptual framework will be examined.

The first difficulty that one would encounter when attempting to use the Imhoff methodology would be to establish how smooth is a smooth income stream, how weak is a weak association between sales and income, and how variable is a variable sales stream. In other words, Imhoff did not state the cutoff points of his criteria; the present study attempts to remedy this deficiency.

A second difficulty of the Imhoff methodology is his reliance on the R2s of regressions 011 time as the measure of variability. For example, consider the following information:6

dollar( $)

- 1 - - 6 Income (R2 = .lo) (R*(I=f(s))) is small

0 time (t) Imhoff would conclude from the above information that the firm is a non-smoother because the variability of income is greater than the variability of sales, and the relationship between income and sales is small (per his definition that the larger the R2 the lower the variability). Let us examine a perhaps more realistic example of the same difficulty:

Although the reduction of income variability at the expense of displaying slower growth is somewhat unrealistic, it is nevertheless possible.

31

A B A C U S

dollar ($)

(ii) Income (R2 = .60) (R2(1=f(s))) is small

> time (1)

In this example, Imhoff would conclude that the firm is a smoother because the income stream is less variable than the sales stream (per his notion of variability). Alternative notions of variability could lead to opposite conclusions for both of these examples.

5 . PROPOSED CONCEPTUAL FRAMEWORK

The proposed conceptual framework attempts to overcome the perceived weaknesses of those used previously to detect income smoothing behaviour.

The primary difficulty with the Gordon methodology is its assumption that if a firms selection of a single accounting variable tends to smooth income (given a specific expectation model), then that firm is prima facie, an income smoother. The primary difficulty with the Imhoff methodology is his reliance on the R2s of income and sales regressed on time as the measure of variability.

The proposed conceptual framework suggests that an income smoothing firm is one that selects n number of accounting variables such that their joint effect is to minimize the variability of its reported income. For example, if (A) is the set of all possible accounting variables that could be utilized by the firm, and si represents one of many possible combinations of these variables, then the income smoothing firm will attempt to:

n Minimize: S,CA - C. (x,~-E(X) )* where x is the annual reported income, N-1 j=1 and j represents time in years.

Recalling Figure 1 of this study, where three types of income smoothers were identified, it should be made explicit that the type of income smoothing behaviour that this study is attempting to identify, is artificial smoothing.-Because natural smoothness is not the result of any overt actions on the part of management, and real smoothing represents an underlying economic reality, they are not relevant to this study. On the other hand, artificial smoothing represents intentional management actions undertaken

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I N C O M E S M O O T H I N G H Y P O T H E S I S

to smooth the reported income timeseries and thus distort the representation of economic reality. Moreover, the proposed conceptual framework of this paper is used to identify only successful income smoothing behaviour. As with the Gordon and Imhoff methodologies, the model utilized in this study cannot identify unsuccessful attempts by managers to smooth artifically the reported income time-series.

It appears to me that a major problem with Imhoffs conceptual structure is that he assumed that all three types of income smoothness (naturally smooth, real smoothed, artificially smoothed) must be mutually exclusive. The present study explicitly assumes them not to be mutually exclusive. Imhoff (p. 87) states that a firm with an extremely high degree of income variability might be classified as an income smoother. Of course, Imhoff considers this to be incorrect. However, this researcher considers that to be possible. For example, a company that is in the electric utility industry (naturally smooth) that does not practice either real or artificial smoothing may nevertheless have an income stream that is less variable than a company in the automobile industry that does practice artificial smoothing.

Therefore, it is not the degree of variability in the income time series (in any absolute sense) that the income smoothing hypothesis is addressing, but rather whether or not the reported income variability is a function of any overt actions undertaken on the part of management to explicitly reduce the variability of reported income and distort the representation of the economic reality of the firm.

First, some premises should be stated: 1. Income is a linear function of sales: Income = Sales - Variable Costs - Fixed

costs. 2. The ratio of variable costs in dollars to sales in dollars remains constant over time. 3. Fixed costs may remain constant or increase from period to period, but may not be

4. Gross sales can only be intentionally smoothed by real smoothing; that is, gross

The four research premises represent my a priori assumptions, and as such remain open to empirical validation. The premises are general in nature and are assumed to be reasonable representations of real world phenomena. It is not known how large deviations from the premises would need to be before the veracity of the research results could be questioned.

reduced.

sales cannot be artificially smoothed.

Given premises 1 to 4, the following conclusions may be stated:

If

and C 2 > 0

I = s - c,s- c,

and c2,1+1 3 c2, and

and

then CVAS 1. c v ~ ?

0 < C, < 1 Cl.t+l = C1,t = c,

The proof of this relationship is contained in Appendix B.

33

A B A C U S

where: I = income in dollars;*

S

c2 = fixed costs;

c, = variable cost ratio, ie, the ratio of variable costs to sales; CV,, = the coefficient of variation for the change in sales time series;

CV,, = the coefficient of variation for the change in income time series.

Given the previous analyses, one part of the testing procedure is to determine whether the specified variability measure of sales is greater than the same variability measure of income. If not, it would appear at first glance that the firm is artificially smoothing. In addition to the first test, it was considered necessary to add an 'industry filter'. For example, what if there were the unlikely situation that most of the firms in a particular industry had income time series that were less variable than their sales time series? It would indicate an unusual process underlying the relationship between sales and income, which would negate the assertion of premises 1 to 4.9 Therefore, dual tests were used.

Tests for Artijcial Smoothing

= sales revenues in dollars;

and

If cv,,, > cv,, 1 " and d, > 1 u smaller than {- P I CVAIi i CV,? I ]

then the firm is an artijcial smoother

where:

n i=l

(ii) d, = I CVAIi t CV,? I

To illustrate this procedure, a hypothetical example should prove beneficial. Assume that industry A consists of four different firms identified as numbers 1, 2, 3 and 4. Furthermore, assume the following:

Firm 1: CV,, = 2.024, CV,, = 6.322 Firm2: CV,, = 4.876, CV,, = 2.667 Firm3: CV,, = 5.775, CV,, = 2.389 Firm4: CV,, = 5.367, CV,, = 2.228

If income is a linear function of sales (as postulated), it must be assumed that [income (I) = reported income] in the absence of income smoothing behaviour. The empirical evidence of this paper wherein all but two of the fums' CV,, > CV,, suggests that the research premises may be well specified.

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I N C O M E S M O O T H I N G H Y P O T H E S I S

The first part of the dual testing procedure indicates that the CVAS > CV,, for any firm to be identified as an income smoother. Therefore, only firm 1 appears to be a likely candidate. The second part of the dual testing procedure then is to determine whether or not firm 1s ICV,, + CV,, 1 is significantly less than the industry average.]@ Given the above data, the mean ICV,, + CVAS I for the industry is 1.74 and the standard deviation of the ratios is .99; therefore, firm 1 would be identified as an income smoothing firm.

6 . THE EMPIRICAL STUDY

Given the purpose of the present research to offer an alternative conceptual framework and an alternative schema with which to identify income smoothers, it was deemed appropriate to test both the Gordon and the Imhoff methodologies with that of this study.

A study by Barnea et al. [1976] was selected as the base study with which to undertake this comparative analysis. Barnea et al. used the Gordon methodology on a sample of 62 firms over the years 1951-1970 to examine whether these firms artificially smoothed reported operating income by discretionary manipulation of extraordinary items. The present empirical examination will use the income smoothing tests of Imhoff, and the conceptual framework proposed here on the same sample of 62 firms and same twenty year time frame as the Barnea et al. study. The results of these three tests of income smoothing behaviour will be evaluated relative to each other.

Results and Conclusions Table 1 presents a summary of the analyses for the sixty-two companies that comprised the sample.

As previously discussed, Imhoff did not fully describe his methods of identifying income smoothing behaviour; therefore, I can only deduce that identification. The asterisks in Table 1 depict those firms that had a smoother income time series than sales time series. Therefore, using Imhoffs definition, only eight firms or 13 per cent of the sample firms exhibited income smoothing behaviour.

The methodology proposed in this paper resulted in the identiation of only two firms or approximately 3 per cent of the sample firms that appeared as ifthey were smoothing their income during the twenty year period. These two firms, numbers 31 and 34, were both in the chemical industry. Both firms had (1) CV,, > CV,,, and (2) the (CV,, + CVAS I for each firm was more than one standard deviation smaller than the industry average, the two elements necessary to identify the firms as income smoothers. Moreover, it is noteworthy that both of the firms were also identified as income smoothers by the Imhoff methodology. The Barnea et al. study (from which the sample firms were taken) indicated that between 50-94 per cent of the companies were exhibiting income smoothing behaviour, with the percentages varying as a function of the measurement of income.

I @ Although t:ie measure (using one standard deviation less than the industry average) was ad hoc in nature, it nonetheless appeared to me to be reasonable, given the purpose of the industry filter.

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A B A C U S

TABLE 1 SUMMARY TABLE OF STATISTICAL ANALYSIS

Company R:S=f(t) Rz:I=f(t) R:I=f(s) CVAS A, IcvAI+cvASl

1 P 2 P 3 P 4 P 5 P 6 P 7 P 8 P 9 * P

10 P 11 P 12 c 13 C 14 C I 5 C 16 C 17 C 18 C 19 C 20 c 21 c 22 c 23 C 24 * C 25 * C 26 C 27 C 28 C 29 C 30 C 31 t* C 32 C 33 c 34 t* c 35 c 36 C 37 c 38 C 39 A 40 A 41 A 42 A 43 A 44 * A 45 A 46 A 47 A 48 A 49 A 50 A 51 A 52 R 53 R 54 R

.869 ,979 .845 ,944 ,979 ,913 ,970 .978 ,889 ,931 .988 ,936 ,945 ,943 ,956 .893 ,808 ,883 .893 ,808 ,740 ,929 .924 ,035 ,861 ,791 ,950 ,778 .667 ,496 ,935 .971 ,917 .746 ,970 ,964 .917 ,980 ,899 ,795 ,846 .864 ,841 - ,967 ,869 ,849 ,926 .783 .890 ,898 ,863 ,967 ,891 ,490

.238 ,556 ,710 ,420 ,479 ,658 .765 .720 ,947 ,801 ,359 ,908 ,641 ,171 ,878 ,622 ,800 ,402 ,177 ,602 ,733 .852 ,164 ,044 ,863 ,734 ,915 .476 ,342 ,081 ,962 ,739 -.053 ,747 .512 ,823 ,870 ,515 ,027 ,145 ,307 .757 -.030 ,969 ,366 ,732 ,546 .061 SO5 .553 ,396 ,684 ,559 ,339

.I34 ,593 ,902 ,517 .395 ,693 ,768 .700 ,893 ,849 ,429 ,989 ,645 ,213 .886 .674 ,929 ,540 .ox ,615 ,913 .838 ,069 ,728 ,945 ,726 ,914 .013 .659 ,767 ,993 ,755 -.OW .832 ,566 ,800 ,808 ,374

-.015 .062 ,215 .878

-.058 ,979 ,676 .872 ,579

-.022 ,490 ,611 ,210 ,671 ,530 ,246

.709

.973 2.107 1.036 ,804 1.287 ,914 1.016 1.003 1.140 ,830 ,937 1.712 1.529 ,874 ,979 2.497 2.281 45.902 1.428 1.757 .725 1.249 9.508 1.369 1.237 1.054 1.483 3.662 3.324 .709 ,882 1.759 12.314 1.422 ,855 1.377 1.173 .866 1.238 1.01 3 .944

1.075 ,514 2.231 2.014 .879 1.737 .905 ,862 1.131 1.332 1.151 2.635

3.660 3.505 6.482 5.305 3.088 7.554 4.545 4.924 2.024 3.293 3.087 1.067 9.216 14.874 3.190 4.800 9.193

- 12.177 -350.227

1.618 3.306 4.909 6.133 11.965 2.804 4.078 1.924

23.791 6.785 ,690 9.163 18.050 5.931 2.727 3.969 3.440 9.794

-8.714 -4.74 21.120 2.579

,726 41.354 2.699 5.926 63.238 6.137 7.706

15.003

17.610

- 10.438

-170.95

-92.962

-7.159

~

5.163 3.602 3.076 5.120 3.841 5.869 4.973 4.846 2.018 2.888 3.720 1.139 5.383 9.728 3.650 4.900 3.681 5.338 7.629 1.133 1.882 6.772 4.910 1.258 2.048 3.297 1.825 7.038 6.497 2.041 ,974

10.389 10.261 .482 1.918 4.642 2.498 8.349 10.06 3.829 20.849 2.732

159.025 1.412 18.536 1.340 6.741

6.781 8.940 92.194 11.263 6.22 6.683

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TABLE 1 - continued SUMMARY TABLE OF STATISTICAL ANALYSIS

ampany R2:S=f(t) R:I=f(t) R2:I=f(s) CVAS CV,, lCVAl+CVA,

55 * R .747 .835 ,630 1.582 4.480 2.832 56 R .852 ,793 ,863 1.374 4.792 3.487 57 R ,874 - ,000 -.051 1.902 -8.259 4.343 58 * R ,866 ,887 .953 1.252 2.209 1.765 59 R ,630 ,190 ,400 8.356 22.561 2.700 60 R .876 ,640 ,620 1.464 32.064 2 1.902 61 R ,928 ,850 ,914 ,720 I .952 2.71 1 62 R .850 .099 .27Q 14.460 -46.585 3.22

Nores: P = pulp and paper industry, C = chemical industry; A = air transport industry, R = rubber industry;

Rz:S = f(t) = the adjusted Rz of gross sales regressed on time; R2:I = f(t) = the adjusted R2 of net income regressed on time; R2:I = f(s) = the adjusted R2 of net income regressed on gross sales;

CV,, = the coefficient of variation of the change in gross sales; CV,, = the coefficient of variation of the change in net income;

* = income smoothing behavior indicated by the lmhoff methodology; t = income smoothing behavior indicated by the proposed methodology; of this paper.

The extreme difference in findings between the Gordon methodology employed by Barnea et al. and the methodology used here are difficult to reconcile. Both methodologies are subject to potential difficulties that could result in questions concerning the veracity of their findings. The primary weaknesses of the Gordon methodology are the necessity of normalizing the income stream vis-a-vis some specified expectation model, and the examination of the income smoothing effect of one accounting variable at a time. The primary weakness of the methodology of this paper rests with the qualitative effects of the research premises. No account is taken of the quantitative effects of the premises. The methodology employed here does not enable us to identify firms which may have reduced the variance of its income series, but not to the extent that it is less than the variance of sales. That is, while it is shown that CV,, > CVAS no account is taken of the magnitude of this difference. The methodology employed here is unable to identify firms for which CV,, was significantly greater than

CVAS and which were still smoothing, but not to the extent that CV,, > CV,,. The possible distortion of findings that may result from the use of these two different income smoothing identification methods is at best, difficult to assess.

The empirical results reported in this paper suggest that sixty (97 per cent) of the sample firms were not successfully artificially smoothing their income time series. These results may be interpreted in a couple of ways: first, that the management of the sample firms were not overtly attempting to smooth their respective income time series; or second, they were unable to smooth their respective income time series. Some authors (Ball and Watts [1972), Gonedes [1972]) offer the proposition that if the income generating processes are of a certain type(s), then attempts at smoothing the income time series will prove fruitless and may as well not be undertaken.

Unlike the bulk of previous empirical findings indicating the presence of income smoothing behaviour, the findings of the present study suggest that firms are unable to

37

A B A C U S

reduce the variability of their income time series below the variability of their sales time series. For the income smoothing hypothesis this may indicate that the jury is still out.

APPENDIX A

ARTIFICIAL SMOOTHING BEHAVIOUR

The following objectives represent the rationale for using the coefficient of variation of the chunge in income and sales as opposed to the ordinary coefficient of variation.

1. If income is a linear function of sales, then the variability measure of sales should equal the variability measure of income.

2. Companies in the same industry experiencing the same macro-economic affects should have variability measures that are equal.

3. Number 2 should be true regardless of the absolute sales dollar size, or the form of the linear relationship.

For Example: Linear Relationship: I = S - .7S - 70

Macro-economic Firm 1 effect Sales

200 +20% 240 -15% 204 -10% 183.60 +30% 238.68 +20% 286.42

TI = 255.42 a,, = 31.52

CVs, = .I65

AFirm 1 Sales +40 -36 -20.4 +55.08 +47.74

AT, = 17.28 uAS, = 42.22

CVAS, = 2.44

Linear Relationship: I = S - .2S - 150

Firm 2 Sales 400 480 408 367.20 471.36 572.83

F2 = 450.89 uS2 = 74.63

CV,= .I65

AFirm 2 Sales +80 -72 -40.8

+110.16 +95.47

A q = 34.57 uAS, = 84.45

CVAS, = 2.44

-

Firm 1 Income -10

2 -8.80

-14.92 1.60

15.93 - I , = 2.365 uIt = 11.19

cv = -4.73 I 1 AFirm I Income

+I2 - 10.80 -6.12

+16.52 +14.33

A 6 = 5.19 ITAI, = 12.67

CVAI, = 2.44

-

Firm 2 Income

50 74 52.40 40.16 73.21

101.85 = 65.27

u , ~ = 22.39 CV,,= ,343

A Firm 2 Income

+24

+33.05 +28.64

-21.60 -12.24

A& = 10.37 uA12 = 25.33

C V A I , = 2.44

A Firm 1 Firm 1 Firm I A Firm 1 Sales Income Sales Income 200 10 240 42 +40 +32 204 13.20 - 36 -28.8 183.6 -3.12 -20.4 -16.32 238.6 40.88 +55.08 +44.00 286.42 79.14 47.74 +38.26

= 225.42 7 = 30.35 As; = 17.28 A q = 13.83 US, = 31.32 uI, = 29.85 UAS, = 42.22 aAI, = 33.78

CVs, = .I65 CV, = .98 CVASl = 2.44 CV,,, = 2.44 1

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By using CVAX = - Ax

one is able to meet all three of the objectives slated earlier.

APPENDIX B Define: (a) DS, = S,,, - S,;

(1) 1, = s, - C,,?, - c,,, 0) c,,t+I 2 CZ,, O

(b) DC2.t = c2,1+1 -c2,,; (c) DI, = I,,, - 1,; (dl De, = e,+, - el;

If

where:

(ii) Cl,,+l = C,,, = C, with0 < C, < 1 (iii) C,,, = a + kS, + e, with

Cov(DS,,De,) = 0 and E(eJ = 0 for all t

(iv) 1 - C, - k > 0 then CVAs SCV,, with CVAI = CV,, when el = 0

Case I: (2) C,,, = a + kS,; i.e., e, ~0

It follows from (1) and definitions a, b, c, d that;

(3) DI, = (1-C,) DS, - DC,,, (by subtraction)

(4) DI, = (l-Cl-k) DS, from (2) & (3)

( 5 ) E(D1,) = (I-C,-k) E(DS,) from (4)

(6) V(D1,) = (1-C,-k)2V(DSJ from (4)

then from ( 5 ) & (6);

since 1-C,-k > 0

:. CVAS = cv,, Case 11: (7) C,,, = a + kS, + el

(8) DC,,, = kDS, + De, from (7)

(9) DI, = (I-C,)DS, - LDS, - De, from (3) & (8)

(10) DI, = (1-Cl-k) DS, - DE, from (9)

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A B A C U S

from (10) it follows that:

(11) E(D1,) = (l-C,-k)E(DS,)

(12) V(D1,) = (I-C,-k)*V(DS,)+V(De,)

then from (11) & (12);

since 1-C,-k > 0 :. cv,, > CV,,

REFERENCES

Ball, R. J. and R. L. Watts, Some Time Series Properties of Accounting Income, Journal of Finance, June 1972. Barnea, A., J. Ronen and S. Sadan, Classificatory Smoothing of Income with Extraordinary Items, The Accounting Review, January 1976. Copeland, R., Income Smoothing, Empirical Research in Accounting: Selected Studies, 1968. Copeland, R. and R. Licastro, A Note on Income Smoothing, The Accounting Review, July 1968. Copeland, R. and J. Wojdak, Income Manipulation and the Purchase Pooling Choice, Journal of Accounting Research, Autumn 1969. Cushing, B. E., An Empirical Study of Changes in Accounting Policy, Journal of Accounting Research, Autumn 1969. Dascher, P. and R. Malcolm, A Note on Income Smoothing in the Chemical Industry, Journal ofAccounting Research, Autumn 1970. Gonedes, N., IncomeSmoothing Behavior Under Selected Stochastic Processes, Journal of Business, October 1972. Gordon, M. J., Discussion of the Effects of Alternative Accounting Rules for Nonsubsidiary Investments, Empirical Research in Accounting: Selected Studies. 1966. Hepworth, S . R., Periodic Income Smoothing, The Accounting Review, January 1953. Horwitz, B., Comment on Income Smoothing: A Review by J. Ronen, S. Sadan, and C. Snow, Accounting Journal, Spring 1977. Imhoff, E. A., Income Smoothing - A Case for Doubt, Accounting Journal, Spring 1977. Ronen, J. and S. Sadan, Do Corporations Use Their Discretion in Classifying Accounting Items to Smooth Reported Income, The Financial Analysts Journal, September-October 1975. Ronen, J., S. Sadan and C. Snow, Income Smoothing: A Review, Accounting Journal, ipring 1977. Rue, J. C., Critique of: Income Smoothing - A Case for Doubt, Accounting Journal, Spring 1977. Shank, J. K. and M. A. Burnell, Smooth Your Earnings Growth Rate, Harvard Business Review, January- February 1974. Simpson, R. H., An Empirical Examination of Possible Income Manipulation, The Accounring Review, October 1969. White, G., Discretionary Accounting Decisions and Income Normalization, Journal of Accounting Research, Autumn 1970.

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