Accounting Research Center, Booth School of Business, University of Chicago
An Empirical Evaluation of Accounting Income Numbers
Author(s): Ray Ball and Philip Brown
Source: Journal of Accounting Research, Vol. 6, No. 2 (Autumn, 1968), pp. 159-178
Published by: Blackwell Publishing on behalf of Accounting Research Center, Booth School of Business,
University of Chicago
Stable URL: http://www.jstor.org/stable/2490232
Accessed: 16/09/2010 06:07
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless
you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you
may use content in the JSTOR archive only for your personal, non-commercial use.
Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at
http://www.jstor.org/action/showPublisher?publisherCode=black.
Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed
page of such transmission.
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of
content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms
of scholarship. For more information about JSTOR, please contact support@jstor.org.
Accounting Research Center, Booth School of Business, University of Chicago and Blackwell Publishing are
collaborating with JSTOR to digitize, preserve and extend access to Journal of Accounting Research.
http://www.jstor.org
An Empirical Evaluation of Accounting
Income Numbers
RAY BALL* and PHILIP BROWNt
Accounting theorists have generally evaluated the usefulness of account-
ing practices by the extent of their agreement with a particular analytic
model. The model may consist of only a few assertions or it may be a
rigorously developed argument. In each case, the method of evaluation has
been to compare existing practices with the more preferable practices im-
plied by the model or with some standard which the model implies all
practices should possess. The shortcoming of this method is that it ignores
a significant source of knowledge of the world, namely, the extent to which
the predictions of the model conform to observed behavior.
It is not enough to defend an analytical inquiry on the basis that its
assumptions are empirically supportable, for how is one to know that a
theory embraces all of the relevant supportable assumptions? And how does
one explain the predictive powers of propositions which are based on un-
verifiable assumptions such as the maximization of utility functions?
Further, how is one to resolve differences between propositions which arise
from considering different aspects of the world?
The limitations of a completely analytical approach to usefulness are il-
lustrated by the argument that income numbers cannot be defined sub-
stantively, that they lack "meaning" and are therefore of doubtful utility.'
The argument stems in part from the patchwork development of account-
* University of Chicago. t University of Western Australia. The authors are
indebted to the participants in the Workshop in Accounting Research at the Univer-
sity of Chicago, Professor Myron Scholes, and Messrs. Owen Hewett and Ian Watts.
1 Versions of this particular argument appear in Canning (1929); Gilman (1939);
Paton and Littleton (1940); Vatter (1947), Ch. 2; Edwards and Bell (1961), Ch. 1;
Chambers (1964), pp. 267-68; Chambers (1966), pp. 4 and 102; Lim (1966), esp. pp. 645
and 649; Chambers (1967), pp. 745-55; Ijiri (1967), Ch. 6, esp. pp. 120-31; and Sterling
(1967), p. 65.
159
160 JOURNAL OF ACCOUNTING RESEARCH, AUTUMN, 1968
ing practices to meet new situations as they arise. Accountants have had to
deal with consolidations, leases, mergers, research and development, price-
level changes, and taxation charges, to name just a few problem areas.
Because accounting lacks an all-embracing theoretical framework, dissimi-
larities in practices have evolved. As a consequence, net income is an ag-
gregate of components which are not homogeneous. It is thus alleged to be
a "meaningless" figure, not unlike the difference between twenty-seven
tables and eight chairs. Under this view, net income can be defined only as
the result of the application of a set of procedures { X1, X2, ... } to a set of
events { Y1, Y2, -.. } with no other definitive substantive meaning at all.
Canning observes:
What is set out as a measure of net income can never be supposed to be a fact in
any sense at all except that it is the figure that results when the accountant has
finished applying the procedures which he adopts.2
The value of analytical attempts to develop measurements capable of
definitive interpretation is not at issue. What is at issue is the fact that an
analytical model does not itself assess the significance of departures from its
implied measurements. Hence it is dangerous to conclude, in the absence
of further empirical testing, tha~t a lack of substantive meaning implies a
lack of utility.
An empirical evaluation of accounting income numbers requires agree-
ment as to what real-world outcome constitutes an appropriate test of use-
fulness. Because net income is a number of particular interest to investors,
the outcome we use as a predictive criterion is the investment decision as it
is reflected in security prices.3 Both the content and the timing of existing
annual net income numbers will be evaluated since usefulness could be im-
paired by deficiencies in either.
An Empirical Test
Recent developments in capital theory provide justification for selecting
the behavior of security prices as an operational test of usefulness. An im-
pressive body of theory supports the proposition that capital markets are
both efficient and unbiased in that if information is useful in forming capital
asset prices, then the market will adjust asset prices to that information
quickly and without leaving any opportunity for further abnormal gain.4
If, as the evidence indicates, security prices do in fact adjust rapidly to new
information as it becomes available, then changes in security prices will re-
2 Canning (1929), p. 98.
8 Another approach pursued by Beaver (1968) is to use the investment decision,
as it is reflected in transactions volume, for a predictive criterion.
4 For example, Samuelson (1965) demonstrated that a market without bias in its
evaluation of information will give rise to randomly fluctuating time series of prices.
See also Cootner (ed.) (1964); Fama (1965); Fama and Blume (1966); Fama, et al.
(1967); and Jensen (1968).
EMPIRICAL EVALUATION OF ACCOUNTING INCOME NUMBERS 161
fleet the flow of information to the market.' An observed revision of stock
prices associated with the release of the income report would thus provide
evidence that the information reflected in income numbers is useful.
Our method of relating accounting income to stock prices builds on this
theory and evidence by focusing on the information which is unique to a
particular firm.6 Specifically, we construct two alternative models of what
the market expects income to be and then investigate the market's reac-
tions when its expectations prove false.
EXPECTED AND UNEXPECTED INCOME CHANGES
Historically, the incomes of firms have tended to move together. One
study found that about half of the variability in the level of an average
firm's earnings per share (EPS) could be associated with economy-wide
effects.7 In light of this evidence, at least part of the change in a firm's in-
come from one year to the next is to be expected. If, in prior years, the in-
come of a firm has been related to the incomes of other firms in a particular
way, then knowledge of that past relation, together with a knowledge of the
incomes of those other firms for the present year, yields a conditional ex-
pectation for the present income of the firm. Thus, apart from confirmation
effects, the amount of new information conveyed by the present income
number can be approximated by the difference between the actual change
in income and its conditional expectation.
But not all of this difference is necessarily new information. Some changes
in income result from financing and other policy decisions made by the firm.
We assume that, to a first approximation, such changes are reflected in the
average change in income through time.
Since the impacts of these two components of change-economy-wide
and policy effects-are felt simultaneously, the relationship must be esti-
mated jointly. The statistical specification we adopt is first to estimate, by
Ordinary Least Squares (OLS), the coefficients (aijt, a2pt) from the linear
regression of the change in firm j's income (AIlj,t) on the change in the
average income of all firms (other than firm j) in the market (AMj,tT)8
using data up to the end of the previous year (r = 1, 2, ... , t - 1):
ljt- = dljt + 42itAMj,t-r + U3,t-T r = 1, 2, ... , t - 1, (1)
5 One well documented characteristic of the security market is that useful sources
of information are acted upon and useless sources are ignored. This is hardly surpris-
ing since the market consists of a large number of competing actors who can gain from
acting upon better interpretations of the future than those of their rivals. See, for
example, Scholes (1967); and footnote 4 above. This evaluation of the security market
differs sharply from that of Chambers (1966, pp. 272-73).
6 More precisely, we focus on information not common to all firms, since some in-
dustry effects are not considered in this paper.
7Alternatively, 35 to 40 per cent could be associated with effects common to all
firms when income was defined as tax-adjusted Return on Capital Employed. [Source:
Ball and Brown (1967), Table 4.]
8 We call M a "market index" of income because it is constructed only from firms
traded on the New York Stock Exchange.
162 RAY BALL AND PHILIP BROWN
where the hats denote estimates. The expected income change for firm j in
year t is then given by the regression prediction using the change in the,
average income for the market in year t:
AIit = dlit + 42jtAMjt
The unexpected income change, or forecast error (pjt), is the actual income
change minus expected:
Uit =Ijt - At . (2)
It is this forecast error which we assume to be the new information con-
veyed by the present income number.
THE MARKET'S REACTION
It has also been demonstrated that stock prices, and therefore rates of
return from holding stocks, tend to move together. In one study,' it was
estimated that about 30 to 40 per cent of the variability in a stock's monthly
rate of return over the period March, 1944 through December, 1960 could
be associated with market-wide effects. Market-wide variations in stock
returns are triggered by the release of information which concerns all firms.
Since we are evaluating the income report as it relates to the individual
firm, its contents and timing should be assessed relative to changes in the
rate of return on the firm's stocks net of market-wide effects.
The impact of market-wide information on the monthly rate of return
from investing one dollar in the stock of firm j may be estimated by its
predicted value from the linear regression of the monthly price relatives of
firm i's common stock'0 on a market index of returns:"1
9 King (1966).
10 The monthly price relative of security j for month m is defined as dividends
(dim) + closing price (pjmpi), divided by opening price (pjm):
PRim = (pi,m+i + djm)/pim.
A monthly price relative is thus equal to the discrete monthly rate of return plus
unity; its natural logarithm is the monthly rate of return compounded continuously.
In this paper, we assume discrete compounding since the results are easier to inter-
pret in that form.
11 Fama, et al. (1967) conclude that "regressions of security on market returns over
time are a satisfactory method for abstracting from the effects of general market
conditions on the monthly rates of return on individual securities." In arriving at
their conclusion, they found that "scatter diagrams for the [returns on] individual
securities [vis-A-vis the market return] support very well the regression assumptions
of linearity, homoscedasticity, and serial independence." Fama, et al. studied the
natural logarithmic transforms of the price relatives, as did King (1966). However,
Blume (1968) worked with equation (3). We also performed tests on the alternative
specification:
In. (PRim) = b1i + b2In6 (L.) + vim (3a)
where Ine denotes the natural logarithmic function. The results correspond closely
with those reported below.
EMPIRICAL EVALUATION OF ACCOUNTING INCOME NUMBERS 163
[PRim - 11 = bij + b2j[Lm - I] + VjmX (3)
where PRjm is the monthly price relative for firm j and month m, L is the
link relative of Fisher's "Combination Investment Performance Index"
[Fisher (1966)], and vjm is the stock return residual for firm j in month m.
The value of [Lm - 1] is an estimate of the market's monthly rate of return.
The m-subscript in our sample assumes values for all months since January,
1946 for which data are available.
The residual from the OLS regression represented in equation (3) meas-
ures the extent to which the realized return differs from the expected return
conditional upon the estimated regression parameters (bj, b2J) and the
market index [Lm - 1]. Thus, since the market has been found to adjust
quickly and efficiently to new information, the residual must represent the
impact of new information, about firm j alone, on the return from holding
common stock in firm j.
SOME ECONOMETRIC ISSUES
One assumption of the OLS income regression model'2 is that Mi and ui
are uncorrelated. Correlation between them can take at least two forms,
namely the inclusion of firm j in the market index of income (Mj), and the
presence of industry effects. The first has been eliminated by construction
(denoted by the j-subscript on M), but no adjustment has been made for
the presence of industry effects. It has been estimated that industry effects
probably account for only about 10 per cent of the variability in the level
of a firm's income.'3 For this reason equation (1) has been adopted as the
appropriate specification in the belief that any bias in the estimates aljt and
a2jt will not be significant. However, as a check on the statistical efficiency
of the model, we also present results for an alternative, naive model which
predicts that income will be the same for this year as for last. Its forecast
error is simply the change in income since the previous year.
As is the case with the income regression model, the stock return model, as
presented, contains several obvious violations of the assumptions of the OLS
regression model. First, the market index of returns is correlated with the
residual because the market index contains the return on firm j, and be-
cause of industry effects. Neither violation is serious, because Fisher's index
is calculated over all stocks listed on the New York Stock Exchange (hence
the return on security j is only a small part of the index), and because in-
dustry effects account for at most 10 per cent of the variability in the rate
12 That is, an assumption necessary for OLS to be the minimum-variance, linear,
unbiased estimator.
13 The magnitude assigned to industry effects depends upon how broadly an indus-
try is defined, which in turn depends upon the particular empirical application being
considered. The estimate of 10 per cent is based on a two-digit classification scheme.
There is some evidence that industry eff ects might account for more than 10 per cent
when the association is estimated in first differences [Brealey (1968)].
164 RAY BALL AND PHILIP BROWN
of return on the average stock.'4 A second violation results from our predic-
tion that, for certain months around the report dates, the expected values
of the v/s are nonzero. Again, a~ny bias should have little effect on the re-
sults, inasmuch as there is a low, observed autocorrelation in the Vj's,'5 and
in no case was the stock return regression fitted over less than 100 observa-
tions.16
SUMMARY
We assume that in the unlikely absence of useful information about a
particular firm over a period, its rate of return over that period would re-
flect only the presence of market-wide information which pertains to all
firms. By abstracting from market effects [equation (3)] we identify the
effect of information pertaining to individual firms. Then, to determine if
part of this effect can be associated with information contained in the firm's.
accounting income number, we segregate the expected and unexpected
elements of income change. If the income forecast error is negative (that is,
if the actual change in income is less than its conditional expectation), we
define it as bad news and predict that if there is some association between
accounting income numbers and stock prices, then release of the income
number would result in the return on that firm's securities being less than
14 The estimate of 10 per cent is due to King (1966). Blume (1968) has recently
questioned the magnitude of industry effects, suggesting that they could be somewhat
less than 10 per cent. His contention is based on the observation that the significance
attached to industry effects depends on the assumptions made about the parameters
of the distributions underlying stock rates of return.
15 See Table 4, below.
16 Fama, et al. (1967) faced a similar situation. The expected values of the stock
return residuals were nonzero for some of the months in their study. Stock return
regressions were calculated separately for both exclusion and inclusion of the months
for which the stock return residuals were thought to be nonzero. They report that
both sets of results support the same conclusions.
An alternative to constraining the mean v; to be zero is to employ the Sharpe Capi-
tal Asset Pricing Model [Sharpe (1964)] to estimate (3b):
PRjm-RFm- 1 = b'i + b;j [Lm-RFm- 1] + vm (3b)
where RF is the risk-free ex ante rate of return for holding period m. Results from
estimating (3b) (using U.S. Government Bills to measure RF and defining the abnor-
mal return for firm j in month m now as b'1 + v'm) are essentially the same as the
results from (3).
Equation (3b) is still not entirely satisfactory, however, since the mean impact
of new information is estimated over the whole history of the stock, which covers at
least 100 months. If (3b) were fitted using monthly data, a vector of dummy variables
could be introduced to identify the fiscal year covered by the annual report, thus
permitting the mean residual to vary between fiscal years. The impact of unusual
information received in month m of year t would then be estimated by the sum of the
constant, the dummy for year t, and the calculated residual for month m and year t.
Unfortunately, the efficiency of estimating the stock return equation in this partic-
ular form has not been investigated satisfactorily, hence our report will be confined
to the results from estimating (3).
EMPIRICAL EVALUATION OF ACCOUNTING INCOME NUMBERS 165
TABLE 1
Deciles of the Distributions of Squared Coefficients of Correlation, Changes in Firm
and Market Income*
Decile
Variable
.1 .2 .3 .4 .5 .6 .7 .8 .9
(1) Net income .03 .07 .10 .1-5 .23 .30 .35 .43 .52
(2) EP S .02 .05 .11 .16 .23 .28 .35 .42 .52