Evidence on the Information Content of Accounting Numbers 1973

8/10/2019 Evidence on the Information Content of Accounting Numbers 1973

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Evidence on the Information Content of Accounting Numbers: Accounting-Based and Market-Based Estimates of Systematic RiskAuthor(s): Nicholas J. GonedesSource: The Journal of Financial and Quantitative Analysis, Vol. 8, No. 3 (Jun., 1973), pp. 407-443Published by: Cambridge University Press on behalf of the University of Washington School of BusinessAdministrationStable URL: http://www.jstor.org/stable/2329643 .Accessed: 10/12/2013 01:57

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JOURNAL OF FINANCIAL AND QUANTITATIVE ANALYSISJune 1973

EVIDENCE ON THE INFORMATION CONTENT OF ACCOUNTING NUMBERS:

ACCOUNTING-BASED AND MARKET-BASED

ESTIMATES OF SYSTEMATIC RISK

Nicholas J. Gonedes*

I. Preliminary Remarks

There exists a relatively large body of evidence that is consistent with

the proposition that the market for securities (in particular, the New York

Stock Exchange) is an efficient market in the sense that market prices reactinstantaneously and unbiasedly to new information and, therefore, market prices

fully reflect all publicly available information.1 To what extent do account-

ing numbers reflect the kinds of information reflected in market prices? One

might not, of course, expect accounting numbers to reflect all events reflected

in current market prices. For example, if an economically significant piece

of legislation is under discussion in, say, the United States Senate, then

the expected effects (if any) of this legislation may be impounded in current

market prices. One should not, however, expect these effects (if any) to bereflected in currently issued accounting numbers because of the nature of

accepted accounting procedures. Yet, in general, over a period of time, there

may be a systematic correspondence between some types of events reflected in

market prices and accounting numbers. That is, over time, there may be a

correlation between the information impounded in market prices and that im-

pounded in accounting numbers.

This issue seems to be important for those who use accounting numbers

(e.g., sales numbers, income numbers, etc.) in work that is supposed to have

*University of Chicago. I am indebted to the participants in the Work-shops in Accounting Research and Finance at the University of Chicago for theirhelpful comments and criticisms. In this regard, a special note of thanks isdue to Ray Ball, Philip Brown, E. F. Fama, Merton Miller, and Robert Officer.

This paper is an abridged version of Report No. 7115, issued (under thesame title) by the Center for Mathematical Studies in Business and Economics,University of Chicago, 1971. All test results excluded from this paper may befound in the original report, which can be obtained from the Center.

lAn extensive recent review of the available theory and evidence regard-ing efficient capital markets is provided in Fama t141. Some implications ofcapital market efficiency for external accounting are discussed in Gonedes (241.

407

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implications regarding market transactions' behavior. For example, if the

correlation between the information reflected in accounting numbers and the

information impounded in market prices is "low," then the valuation models

that use these numbers (primarily) may have little descriptive validity regard-

ing market behavior simply because these models would not capture much of the

information impounded in market prices (i.e., much of the information that

affects the behavior of market transactors, in the aggregate). From a dif-

ferent point of view, the same issue seems to be important for those who

produce accounting numbers. The accounting process may be viewed as a produc-

tion process. Presumably, the general objective of this process is: the

production of numbers that possess informational content. The extent to which

accounting numbers reflect information that is impounded in market prices

serves as a means of empirically evaluating the informational content of

accounting numbers. Observed market prices may be used as a standard for

evaluation in this case because of the observed efficiency of securities markets.

The purpose of this report is to provide some empirical evidence on the

information content of accounting numbers, a subject that has been receiving

increased attention during the past few years (see, for example, Ball and

Brown (1 and 2], Brown and Ball [10], Beaver (3, 4], Benston [5], and Gonedes

[21 and 22]). Attention is restricted to accounting income numbers. The main

question asked is: Do accounting income numbers convey information about the

risk of an asset? Estimates of systematic variability (or systematic risk)

are used to represent the risk-information impounded in market prices and that

reflected in accounting numbers. Evidence is presented on the correlation

between market-based and accounting-based estimates of systematic risk.

Estimates of systematic variability conditional upon market price data

were secured via the market (or single-factor) model. Analogous linear models

were applied to accounting income numbers. Details on the estimation models

and the data used for estimation are provided in Section II. Of course, if

these models suffer from important misspecifications, then the estimation

results may induce unwarranted inferences.. Thus, examining the adequacy of

each model is no less important than the main question of this report. Evidence

pertaining to this issue is presented in Section III. Particular attention was

paid to the stationarity of the market model's regression parameters; the

evidence reported here suggests nonstationarity at the level of individual

assets.

According to the results presented in Section IV, there is (in general)

a "statistically significant" relationship between market-based and accounting-

based estimates of systematic risk if the accounting-based estimates are

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conditional upon first differences in income numbers or scaled first differ-

ences. This inference suggests that accounting income numbers, if appropriately

transformed, do convey some information on the risks of assets. The trans-

formations (e.g., differencing) seemed to induce "better" specifications of

the estimation models.

Throughout this report, the phrase "information content of accountingincome numbers" is frequently used instead of the phrase "the information

about risk conveyed by accounting income numbers." But note that we are only

concerned with risk-information.

II. Test Design

A. Estimation Models

The market-based estimates of systematic risk were secured via the

,'market model"2 applied to the natural logarithms of price relatives (adjustedfor dividends):3

pnit it} +.~~ iIn { ~ ~ i i = ai + gi tn It cit

it_

E{. }= 0; E{- 2 a ; E{i ? iO,Vkkt;it Cit it ik

E{s t itI= 0 Vs # i; E{Zn {It} I } = 0;

where

= the price of the i firm's common stock at time t (adjusteditfor capital changes),

thD = the dividend payment on the i security at time t,

it

.I = the price relative of a representative market index at time t

(adjusted for dividends and capital changes),

ai,3. = parameters to be estimated.

In the above, a tilde denotes a random variable.

Observe that (1) assumes the interrelationships among securities are

fully determined by the securities' comovements with the market index, It

Hence, the restriction that E{e St * it} 0, Vs y i.

2See, for example, Sharpe (40, 41, and 42], Lintner [30 and 31], Fama[13 and 15], Jensen [26], and Markowitz [34, p. 100].

Throughout this paper,variances and covariances will be used as

measures of "risk."

3The natural logarithm of the price relative represents the one-periodrate of return under continuous compounding.

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Of particular interest for this report are the estimates of systematic

risk that may be secured via (1). The estimated residual variance from (1),

var{E. }, is an indicant of the variability in the ith security's price relativeitthat is not associated with general market factors (represented by I t). Also,by the restriction E{.it * }ik} Vk p t, the regression residuals are supposed

to evidence no systematic movements over time. The systematic variability ofththe log of the i firm's price relative, denoted by Rit. is defined to be

that part of its total estimated variability, Var{R it1, that is associated

with movements in It, i.e., 1 - (Var{ it}/Var{R it). This, of course, is the

estimated squared coefficient of correlation from (1). Note that, within the

context of portfolio theory, Var{ it} is that part of a security's total varia-

bility that may be diversified away, whereas the systematic variability is the

part that cannot be eliminated by diversification. Moreover, the relative con-

tribution of the i th security to the risk of a well-diversified portfolio iseffectively determined by the estimated S i.

The reported income number series associated with a firm's operations

may be treated in a manner that is analogous to the manner in which the market

model, (1), treats market-determined rates of return. Presumably, the account-

ing numbers issued by a firm reflect (to some extent) events that have affected

the firm's operations. These events include (1) those that occurred within thefactor input markets regarding which the firm is a transactor and (2) those that

occurred within the output markets of the firm. These events may be specific

to a particular industry or they may be economy-wide events. Finally, some

of the events that influence a firm's operations may be specific to that par-

ticular firm. Thus, for estimation purposes, we may conceive of the total

variability of a firm's income-number series as consisting of a systematic

component and individualistic component. The systematic component would be the

part of the total variability of the number series that is associated with

economy-wide and/or industry-wide factors. The individualistic component would

be the part of this total variability that is associated with the unique

attributes of the firm's operations. Evidence on this perspective of a firm's

income-number series is provided in Brealey [9] and Brown and Ball [10] and

Gonedes (25].4

Several estimation models were used in this study for accounting income-

numbers:

(2.1) Income Levels

it=li +li t li t + lit; E{Y . }i E{Y i .Cl }0

4The underlying economic motivation for using models based upon thisperspective of a firm's operations is discussed at greater length in Gonedes [25]

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(2.2) First Differences

it Y2i 2i t +2i AYt + 2it; E{AYt c2itI = E{A t 2it =

(2.3) Scaled Income Levels

A Y3i 3i AE 3i Ii 3it I.i X {3iit ,t * t ytA yi +6 i -E -i I i A }

E3it -I

Ait At A At At t

(2.4) Scaled First Differences

AY Y = AYe Am AYF

AYo- 4i + 64i _E t1w4i .I. + e4it;E c4t ~ ei I. 0A _ 1 1E

it = c wmtA

tA

kit kit ki kit kip kit kjt

k = 1, 0.., 4;

where (letting tilde denote a random variable):th

Yt = the income number of the i firm for period t,

= the economy-wide income number for period,5t

-I. th=t

= the industry income number, for the industry to which the ifirm belongs, for period t,

At = the total-asset number of the i firm at the beginning of period t,E = the economy-wide total asset number at the beginning of period t, andt

AI th th=tetotal-asset number for the industry-grouping of the i firm

at the beginning of period t.

For each firm in my sample and for each of the above income-number

models, I obtained estimates of the systematic variability (i.e., the multiple

correlation coefficients) associated with the number series used in each model.

The final stage of th,is study involved an examination of the correlation be-

tween the estimates of systematic variability provided by (2.1) - (2.4) and

the estimate of systematic variability provided by the market model, (1), for

5The methods used (1) to compute the economy-wide and industry numbersand (2) to adjust the industry numbers for the effects of economy-wide factorsare discussed in Section IIC.

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the ith firm.6 The cross-sectional correlation between these estimates pro-

vides one (operational) indicant of the correlation between the risk-information

impounded in market prices and the risk-information conveyed by accounting

income number series. A "low" estimated correlation would suggest that the

risk-information conveyed by these accounting numbers is but a small part of

all the risk-information that is impounded in stock prices and that determinesthe market-based estimates of systematic variability. The opposite conclusion

would be suggested by a "high" correlation. These inferences are, of course,

conditional upon the models examined.

An additional (though not independent) test of the association between

market-based and accounting-based estimates of systematic variability was

based upon the estimated regression coefficients of models (2.3) and (2.4) and

the estimated S.-coefficients from the market model, (1). Since the income

numbers in models (2.3) and (2.4) are scaled, they may be used in cross-sectional comparisons. Now, consider the construction of a "portfolio" of

Y.t Yfirms' income number series: - or - . As in the case of a portfolio

Ait Aitof securities each firm's contribution to the variability of such a combined

series would be determined primarily by the estimated regression coefficients

63i and w3i (for model (2.3) or 64i and wi (for model (2.4)). And, these

estimates are functions of the estimated systematic variability of the i

firm's number series. The residual (unsystematic) variability -- e.g.,

VAr { 3it} for model (2.3) -- is the part of the total variability of each

firm's number series that may be eliminated via diversification. In effect,

the estimates of 63. W 6 and w fulfill roles similar to that of the3V 3i 4i' 4iestimated S.-coefficients from the market model. So, an additional test of

the correlation between market-based and accounting-based estimates of sys-

tematic variability is provided by examining the correlation between (1) the

estimated regression coefficients, 63iFw3iV 644i

and4W

and (2) estimated

a.-coefficients from the market model.7

B., Samle of Firms

The models introduced above were applied to a random sample of 99 firms

taken from the set of all firms that satisfied the following conditions:

6This approach was also used in Ball and Brown (1].

7Results from a related approach (involving different estimation methods)are among those discussed in Beaver, Kettler, and Scholes (4]. As will beseen later, my results cast some doubt on the generality of their results.

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(a) Monthly price-relative data were available for the firm from the

C.R.S.P.8 Price-Relative Tape for the period January 1946-

June 1968 and the following data were available for the firm from

the University of Chicago's Annual Industrial COMPUSTAT apes for

the years 1946-1968: (1) Net Income, (2) Available for Common,

(3) Total Assets, and (4) Common Equity.(b) The firm is a member of a two-digit Standard and Poor's industry

grouping with at least 15 member firms.

The results presented in this report are based upon Net Income and Total

Assets.9 The second condition, (b), was imposed so that the industry indices

used in models (2.1) - (2.4) would be based upon a "reasonable" number of firms.

The two-digit code was used so that the admissible industry groupings (i.e.,

those with at least 15 member firms) would not be too few in number; obviously

the number of firms within a Standard and Poor's industry and the scope of the

industry definition vary directly. Admittedly, these criteria are arbitrary

(though not necessarily useless). A list of the 99 firms in the random sample

and a list of the industry codes represented in the sample appear in the

Appendix.

Economy-wide and industry-wide indices were constructed using data for

firms selected from the set of all firms represented on the COMPUSTAT apes.

The firms selected for each index were as follows:

Economy-Wide Index for a Given Year: All firms for which data wereavailable for all of the years 1946-1968.

Industry Index for a Given Industry and a Given Year: All firms in theindustry for which data were available for all of the years 1946-1968.

8Center for Research in Security Prices, University of Chicago.

9The other number series, Available for Common Equity, were used in orderto determine whether the results presented below are sensitive to the types ofincome numbers and scaling factors employed. Operating Income, which was avail-able for all the firms satisfying condition (a), was used for the same purpose(with Total Assets as the scaling factor). There were no essential differencesamong the results based upon these different income number series. The dataused for this study were secured from a merged COMPUSTAT tape, rather than theavailable tapes taken individually (each of which covers a different sequenceof consecutive years). I am indebted to Ross L. Watts for making this tapeavailable to me. Extended COMPUSTAT definitions of the required number seriesmay be found in Gonedes [23, Appendix I] or in Standard Statistics Company'sCOMPUSTAT nformation Manual.

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Thus, the indices are based upon data for "continuously listed" firms, relative

to the period 1946-1968.10

When each of the income number models was applied to a given firm's

income-number series, that firm's data were excluded from the economy-wide

and industry indices required by the model. For example, if N firms were

accepted for computation of the economy-wide index for year t and if model (2.2)was being applied to firm k, then the economy-wide index for (2.2) was computed

using the following:

N N_ _ i t k -A A ,Vt,kt i=l itVtki=l it

ifk ijEk

Furthermore, in order to attack the potential problem of multicollinear-

ity vis-a-vis the economy-wide indices and the industry indices, the original

industry indices were regressed on the economy-wide indices. Thence, the

residuals from this regression provided the industry numbers actually used in

applications of models (2.1) - (2.4). For example, in applying model (2.1),-Ii -Ethe original industry index, Kt , was first regressed on Yt via the model

(3) Kt '1 + 2r c tI I ~~I. I_~~~~ 2 t

then I set Yt 3t, where ct are the estimated residuals from (3). This

procedure serves to adjust the industry number series for the association be-

tween the industry number series and the economy number series.

Industry indices were included in the income-number models essentially

because there was no available evidence with which to infer the unimportance

of these indices for models (2.1) - (2.4). And including the indices at least

provides information for such inferences. With regard to the model (1), how-

ever, available evidence (see King [283) suggests that, on average, industry

factors account for a small portion (approximately 10 percent) of the varia-

bility in securities' rates of return. Thus, no industry indices were included

1OResults from an alternate index-construction scheme were also examined.Under the alternative scheme, firms were selected as follows: (1) Economy-wideindex for a given year -- all firms for which data were available for the givenyear. (2) Industry Index for a given industry and a given year -- all firms inthe industry for which data were available for the given year. The indicesconstructed under this scheme reflect entry and exit of firms (relative to allfi-rms on the COMPUSTAT apes) and changes in industry membership.

The empirical results reported in this paper were essentially the sameas those based upon the alternative index-construction scheme. Complete resultsfor the alternative scheme are in Gonedes [231.

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in the market model; only a general market index was used. Fisher's Arithmetic

Index, described at length in [17], was used for this purpose.

III. Intermediate Estimation Results and Problems

A. Market Model

Application of the market model, (1), to securities' price relatives inorder to estimate "systematic variability" raises issues of model specifica-

tion. Does the linear relationship depicted in (1) have descriptive validity?

Are the residuals uncorrelated over time (for a given firm) and across firms

(at a given time). Are the residuals homoscedastic? The test results of Fama,

Fisher, Jensen, and Roll (16] and my results answer these questions in the

affirmative. But my results also suggest that the parameters of the market

model are not stationary over time, i.e., that structural changes in the rela-

tionships considered by the market model do occur.11 Such changes can ad-versely affect the validity of the description sought via (1). That is,

for example, if the "true" ai and Si regression coefficient from model (1)

changes from, say, 1946-1955 to 1956-1965, then estimates of ai and i based

upon data from 1946-1965 will be biased estimates of the 1946-1955 and 1956-1965

regression coefficients.

In order to test for the occurrence of structural changes, model (1) was

applied to the data of different time periods using Ordinary Least Squares12

procedures. Then prediction tests were conducted using the estimated models.

All estimated models were used to predict the same observations, and the obser-

vations to be predicted were not used in estimating the parameters of model (1).

The rationale underlying this approach may be seen by considering the properties

of estimates from model (1). fi-.it

Ditit}s in Section II, let Rit =n and t Zn {It The market

it-lmodel is, as before,

Rit 3.i + Si Xt + it

lNonconstancy of the estimated regression coefficients of the marketmodel is also suggested in Blume (8] and Fisher (18].

12Note that the probability plots of the residuals from my regressionsmanifested the kinds of outliers that usually characterize rates of return oncommon stocks; see Fama [12] and Blume (7]. The justification for usingOrdinary Least Squares estimators when the underlying data exhibit suich out-liers is provided by the theoretical results of Wise [43], which indicate that

such estimators (in the context of these outliers) are unbiased and consistent,though not efficient. A useful related paper is Blattberg and Sargent [6].

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where the estimated parameters a. and Si are:13

n2 (t - W)(R. - R)

6 ==1.-

a =i Ra C En i)1 1 _" =-n 2 it3. -, ~~~2 t=ln- i2: (0 -t

t=l

plim = S plim a a. pliM a a23. .

Also, we have the following estimates for the variances and covariances

of ai and $ ..

n -2 2 A2

Est. Var (a.} = = Est. Var {S} - a= n __-3. a n -2 nn 2 (0 -0) 2 (0-)

t=l t=l

A2-aY

Est. Coy {.it 5i} aa, n 22

(t-0)t=l

n 2 A~2 -A2 ^2and as n c , 2 (0 t-) + Sn, where S is a constant, and a + a -r a + 0.

t=l a ,The final set of limiting relationships provides a strong motivation for

letting the number of observations used for estimating (1) become as large as

possible. As the number of observations increases, ceteris paribus, the preci-

sion of the (unbiased) estimates, ai and Xi, increases. This increase in

precision has a clear effect on predictions made with these estimates since,

letting Ri be a prediction of R. at time k, k > n, we have for the mean-tig ik beapeito if3ksquared prediction error (conditional on 0k):

P - - 2 2 2~~~~~~~2~~~2 .2 -2(4)E{ik ik E{(a a.) +( -C) 0k - k} = 0ka + 2$a2 +o2 + a2

which, upon rearrangement becomes,

P 2 -~2 2 1) A2 A.2 k(5) E{Ri Rk (0 -0)O + ( + )a =a Ll + n+mikik k n C. s:n

The mean-squared prediction error is a decreasing function of n: asp -2 Ala2

n+ooE{R.-

R. a.

Also, and of importance for finite samples, theik 3.k s.

13See, e.g., Mood [36, Chapter 13], and Kendall and Stuart [27,Chapters 26 and 28].

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2 2 A2mean-squared prediction error is a decreasing function of Ca, aa, and a(where the latter quantities are also decreasing functions of n).

Suppose that, as we are increasing n in a time series analysis problem,

we begin to include data that were generated under different structural con-

ditions. Then (ignoring the effect of increasing n on sampling error for a

moment), the expected squared error will increase, relative to (5), by squares

and cross products of bias terms. For example, in the case of an unbiased

estimate Xi, we have

2 A 2 -2E{a} Xi and i -i] = E[3. - E{f3 H = a

If, however, E{ai} # i' then1

1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~aa1A(6)

i E{i}]+

[E{3} aX+E{ I

In such a case, the other parameter variance and covariance terms that would

emerge from (4) would be:

A- 2 -^2 2(7) Eci.A = a + [E{ai} - ai] and

A A A2 A {A(8) E[ci( ai i i-

=a, + E{ai} [E{0i} - Xi] + E{f3} [E{i} - a ]

+ [E{ai.}-

aiE][E{.}-

The variance and covariance terms for the parameters would appear in (4)^2 ^2 ^2where a aa' and a now appear. Of course, as suggested above, increasing

n induces reductions in sampling error. Hlowever, if increasing n results in the

use of data generated under different structural conditions, then such reduc-

tions must contend with the disadvantageous effects of the bias terms. In

effect, it would seem that increasing the number of observations in a time

series analysis increases the probability that bias terms will be important

because of the impact of the increasingly "dated" observations that may be

acquired as one moves farther backward in time. Using this perspective one may

view the expected squared prediction error as a "total cost" magnitude that is

composed of two major components: (1) the sampling variability of the parameter

estimates and (2) the biases of the parameter estimates. As n is increased

by going farther backward in time, the relative weight of the first component

tends to decrease and the (potential) weight of the second component tends to

increase.(I

use theadjective

"potential" because the second component's

existence depends upon the existence of structural changes, in our case. And

such changes need not always exist within some time interval.)

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Suppose that we want to use model (1) in order to describe the structure

of a period of time [t1, t2]. Suppose also, and just for a moment, that the

structural relationships within the interval ft , t2] are unchanged. Then

estimating model (1) via Least Squares would provide unbiased estimates for

ft1 t2]. Furthermore, suppose that we also want to consider using data from

[t, t2I, t < tl, in estimating model (1) for the purpose of describing Et1, t2]Select some observations from ft , t2 that were not used in estimating model

(1) and consider predicting these observations using: (a) the estimates from

regressing on [t , t2], excluding the observations to be predicted, and (b) the

estimates from regressing on It, t21, excluding the observations to be pre-

dicted. Given the specifications of the model, if the estimates based upon

ft, t21 are also unbiased estimates for ft1, t2 ], then the predictions using

these estimates should be more efficient (in, say, the mean-squared-error

sense) than the predictions using the estimates based only on the data from

fti, t2] simply because the variability of the estimates ("sampling error")

should be less (due to the larger sample size). If, in fact, the former pre-

dictions are less efficient, then the existence of bias in these estimates is

suggested (relative to the relationships of ft , t21); see equations (4)-(8).

Tne preceding remarks ignore the effects of, for example, heteroscedasticity

and serial correlation on predictive efficiency, because my results did not

suggest that such specification violations were statistically significant

(as indicated below).

In this study, I am interested in describing rates of return on securi-

ties, via the market model, for the period 1946-1968. The question to be

answered is: Were there any structural changes within this period? If so,

how many consecutive observations may be used for each set of estimates based

upon a subperiod of 1946-1968 so that the effects of structural changes are

avoided, or at least reduced?

The approach I used in dealing with these questions is based upon my

preceding remarks regarding the effects of more observations in a time series

regression. First, I reserved the first six monthly observations from 1960 and

the first six from 1968 for prediction tests. Then, I estimated the parameters

of the market model using consecutive monthly observations (except for the

reserved observations) from the following periods:

Three-Year Intervals

1950-19521957-1959 (*)1965-1967 (**)

Five-Year Intervals

1948-1952

1955-1959 (*)1963-1967 (**)

Seven-Year Intervals

1946-19521953-1959 (*)1961-1967(**)

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Ten-Year Intervals

1950-1959 (*)1958-1967 (**)

rwent5-One-Year Interval

1946-1967 (excl. 1960) (*), (**)

The estimates based upon all intervals characterized by (*) were used to

predict the six reserved observations from 1960, conditional upon the observed

values of the log of the market index, Ot, for the corresponding months. The

estimates characterized by (**) were used to predict the six reserved observa-

tions from 1968, conditional upon the log of the observed values of the market

index. Note that the estimates based upon 1946-1967 (excluding 1960) were used

to predict both sets of reserved observations. Since the first prediction

period, 1960, falls within this observation period (and around the center of

it), one might expect the prediction test results for 1960 to evidence a strong

advantage for the 1946-1967 estimates, relative to the subinterval regression's

estimates. This was, however, not the case.

For each prediction month and for each firm the following prediction

error was computed:

p p(9) C.. R.. - R

13 13 1

where Ri. is the predicted one-period rate of return for the ith firm at time

j, and R.. is the actual rate of return. The following cross-sectional summary

statistics based upon the prediction tests are presented: (a) deciles for theaverage prediction errors, e , (b) deciles for the mean-squared errors,(Ci

and (c) deciles for the mean absolute errors, lclj, where (letting K equal the

number of predictions):

(10) P 1 K p(12) C.il = K E C.. I

419

j=1

P 2 1 K P 2

(11) ~~~~(C)=

E (C..and

i K =

(12) 1 =l 1

In addition, the following overall averages are reported (where N 99

is the nLumber of firms in the sample):

1 N-p(13) Overall Average Prediction Error= -

Ns.C

N =l

419



15/38

1 P 2(14) Overall Mean-Squared Error = z (C.) , and

i=l

N -(15) Overall Mean-Absolute Error = N E

i=l

Cross-sectional summary statistics are presented in Table 1 (more

detailed tables appear in [23]). Indicants of predictive efficiency, in the

mean-squared-error sense, appear in the upper part of Table 1. A comparison

of the means and medians indicates that the error distributions are not

symmetric. H-ience, I use primarily the means and medians in order to evaluate

the results. The pattern manifested by the means and medians is of particular

interest. For the 1960 predictions, it appears that decreasing the number of

observations used for estimation results in improved predictive efficiency

until one encounters the five-year and three-year regression results, which

suggest reduced predictive efficiency. The results from the seven-year regres-

sion show the greatest predictive efficiency. The prediction test results of

1968 are similar to those of 1960, with the major exception being the similarity

of the overall means and the medians (across models) until the five-year and

three-year regression results are encountered, at which time predictive effi-

ciency decreases. These results also suggest that, for the aggregate and "on

average," the seven-year observation period provides a (relatively) better set

of estimates. Nlote that the similarity between the 1968 median predictive

efficiency for the seve-n-year model and the twenty-one and ten-year models does

not mean that the estimates fron these models are equivalent. If the specifi-

cation of the market model were satisfied equally as well over each of these

three intervals, then the twenty-one-year and ten-year regression models'

predictive efficiency should have been greater than the seven-year models'

predictive efficiency simply because of the reduced sampling error in the models

with more observations, as indicated earlier. The magnitudes of the differences

in predictive efficiency are not huge, but the systematic pattern of changes

is evident. And this pattern is not wholly consistent with that which one would

expect in the absence of misspecifications.

In order to determine whether the pattern of the results in Table 1 is

primarily due to extreme errors, I also computed mean-absolute prediction errors,

which are less affected by extreme errors than the mean-squared prediction

errors. Cross-sectional summary statistics for the mean-absolute errors are

provided in the lower part of Table 1. These results are consistent with those

420



16/38

TABLE 1

CROSS SECTIONAL UMMARY TATISTICS FOR PREDICTION ERRORS FROMMARKETMODEL; SIX PREDICTIONS PER PREDICTION NTERVAL;

PREDICTION NTERVALS: 1960/1-1960/6 and 1968/1-1968/6-/

DecilesAverage

1 5 9

Mean Squared Prediction Errors

Prediction Interval: 1960

Models

1946-1967 (excl. 1960) .00424 .00096 .00324 .009351950-1959 .00416 .00102 .00317 .009361953-1959 .00413 .00090 .00318 .009531955-1959 .00415 .00087 .00348 .009731957-1959 .00425 .00087 .00328 .00970


Models

1946-1967 (excl. 1960) .00638 .00128 .00360 .012621958-1967 .00636 .00103 .00362 .013771961-1967 .00628 .00109 .00361 .014161963-1967 .00630 .00102 .00365 .012791965-1967 .00647 .00089 .00371 .01301

Mean Absolute Prediction Errors


Models

1946-1967 (excl. 1960) .04892 .02449 .04764 .072821950-1959 .04902 .02526 .04770 .072211953-1959 .04881 .02461 .04377 .072151955-1959 .04909 .02457 .04704 .07408

1957-1959 .04950 .02421 .04684 .07555


Models

1946-1967 (excl. 1960) .05598 .02833 .04761 .092561958-1967 .05593 .02667 .04769 .092531961-1967 .05501 .02615 .04738 .092611963-1967 .05544 .02574 .04910 .092691965-1967 .05626 .02487 .05059 .09501

aNinety-nine cross-sectional observations.

421



17/38


18/38

TABLE 2

CROSS-SECTIONAL UMMARY TATISTICS FOR PARAMETER STIMATES FOR MARKETMODEL-/

b/ Durbin-

il d(Wi) i | pt(i) R2 Watson

Statistic

1946-1967 (excl. 1960)

Mean -.0005 .7212 .9806 11.47 .33 2.15Standard Deviation .0033 .5665 .2659 2.57 .09 .15Deciles 1 -.0052 .0969 .6549 8.32 .21 1.92

5 -.0001 .5646 .9500 11.60 .34 2.189 .0036 1.6966 1.3648 14.66 .46 2.33

1946-1952

Mean .0001 .7889 .9827 8.17 .42 2.19Standard Deviation .0058 .5798 .3093 2.27 .13 .23Deciles 1 -.0090 .1583 .5804 4.92 .21 1.91

5 .0013 .6451 .9815 8.24 .44 2.189 .0067 1.6450 1.4222 11.45 .61 2.47

1953-1959

Mean .0002 .9215 1.0323 5.80 .27 2.15Standard Deviation .0073 .8449 .3659 2.01 .13 .26Deciles 1 -.0096 .1079 .5085 3.04 .09 1.82

5 .0005 .7580 1.0296 5.75 .27 2.169 .0084 1.9895 1.5204 8.76 .47 2.49

1961-1967

Mean -.0023 .8767 .9485 6.25 .31 2.16Standard Deviation .0070 .7497 .3056 1.57 .10 .23Deciles 1 -.0117 .1258 .5776 4.03 .15 1.86

5 -.0035 .6880 .9093 6.24 .31 2.169 .0053 2.0591 1.4233 8.38 .45 2.50

a- Ninety-nine cross-sectional observations.

b/ 2R adjusted for degrees-of-freedom.

423



19/38

regarding the market model. A "larger" number of observations is desirable

because of lower sampling error. Yet, as we increase the number of observations

by moving over time, we may acquire observations generated under different

structural conditions. So, it may be that the larger number of observations

is not desirable. In order to make some inferences regarding this issue, I

used (once again) prediction tests. Before discussing these tests, I shallconsider additional details on the estimation methods used.

The accounting income number models (2.1)-(2.4) allow for the effects

of economy-wide events and industry-wide events. In the case of the income

levels model (2.1), there seemed to be no need for an industry index and an

economic index because of the high correlation coefficients (typically in

excess of .80) between these indices for each time period of interest. The

magnitudes of the correlations were such that, on average, the incremental

explanatory power gained by, say, including an industry index in the model

after including the economy-wide index (and after adjusting the industry index

for its correlation with the economic index) was statistically unimportant. So,

I used only the economic index in the income levels model for all firms and for

all time periods.15

In the cases of (a) scaled income levels, (b) first differences in income

numbers, and (c) scaled first differences, the industry indices were not uni-

formly highly correlated with the economic index. This result was not dependent

upon the firms used in computing the indices. The magnitudes of the correla-

tion coefficients for scaled income levels, first differences, and scaled first

differences were similar (typically less than .30 in absolute value). Since

the correlation coefficients for these number series did not suggest that, on

average, one of the indices would serve as a substitute for the other, both

indices were used in estimating the parameters of (2.2) - (2.4). As indicated

in Section II, industry indices were adjusted for their correlations with the

economic index whenever both indices were used in estimating the parameters of

any accounting number model; the adjustment procedure employed is described

in Section IIC.

Prediction tests were conducted with the accounting income number models

using 1960 and 1968 as the prediction years. The objective of these tests was

15There were lOout of 48 (12 industries x 4 time-intervals) instancesfor which the correlation coefficients betweer indices were less than .66. Inorder to determine whether inclusion of both indices would have been necessaryin these instances, I applied the accounting number model, (2.1), with (a) the

economic index only, and (b) both indices to the data of the firms within theaffected industries and for the time intervals associated with the "low" cor-relation coefficients. The estimation results from the regression using bothindices were essentially the same as those from using only the economic index.

424



20/38

to determine whether the estimates from the accounting number models suggested

the existence of structural changes, such as those suggested by the estimates

from the market model (see Section IIIA). The procedures used for these tests

were the same as those used for the market model, with one major exception:

for the unscaled number series (income levels and first differences) the pre-

diction errors for each firm had to be scaled so that interfirm (cross-sectional)

comparisons could be made. In the absence of a scaling factor, the prediction

errors for these series would be influenced by the size of the firm and cross-

sectional results would he meaningless, relative to our objective. The scaling

factor used for a firm was the standard error of estimate from that firm's

1946-1967 (excluding 1960) regression. For convenience, this scaling technique

was used for all accounting number results.

Cross-sectional summary statistics from the prediction tests are pre-

sented in Table 3. The definitions of the summary statistics are the same as

those used for the market model tests (see (9)-(15), Section IIIA) with the

number pf predictions, K, equal to one.

For model (2.2) -- first differences in income numbers -- the predictive

efficiency of the 1946-1968 regression is greater than the seven-year reares-

sions for both prediction years, 1960 and 1968. This result characterizes the

predictive efficiency defined in the mean-squared error sense and the mean

absolute-error sense (which is less affected by extreme errors). The same

conclusion is suggested for model (2.3) -- scaled income levels. For model

(2.1), and for the prediction year 1960, the 1960 medians of the distributions

are favorable towards the 1946-1968 model. For 1968, the medians are favorable

towards the seven-year regression. But examination of the 1968 deciles indi-

cates that the seven-year regression admits of more extreme errors (see the

upper deciles). So, in general, it appears that for model (2.1) the 1946-1968

regression has more predictive efficiency. The results for model (2.4) --

scaled first differences -- are similar to those for model (2.1), except that

for (2.4) the 1968 prediction results for the seven-year regression evidence a

lower frequency of extreme errors relative to the model (2.4) 1968 prediction

results from the 1946-1967 regression (compare the relationships between the

last deciles for model (2.4) with the counterpart relationships for model

(2.1)).

Consideration of the prediction test results for all of the models sug-

gests that, in general, 1946-1967 (excluding 1960) regressions have greater

predictive efficiency.The major qualification needed for this conclusion is

in regard to the 1968 prediction test results for model (2.4), for which the

mean-squared and mean-absolute error distributions reflect favorably upon the

425



21/38

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426



22/38

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23/38

seven-year regression, 1961-1967, except for the last deciles of these

distributions.

Table 4 contains cross-sectional summary statistics for the accounting

number models for 1946-1967 (excluding 1960) and, for purposes of comparison,

1953-1959. Looking only at the R 's, it appears that the results are consis-

tent with the propositions advanced in Section II: the accounting income numbersmay be viewed as reflecting economy-wide events, industry-wide events, and

events specific to individual firms.16 But note that not all of the models

satisfy their specifications equally as well. In particular, for the 1946-1967

period, models (2.1) and (2.3) seem to be characterized by serilaly correlated

residuals. (This result was also suggested by plots of estimated residuals.)

In this regard the first-differences models, (2.2) and (2.4), seem to be the

best specified models. Note also that the distributions of estimated regres-

sion coefficients for model (2.3) for 1946-1967 contain several extremelylarge values. Such extreme values do not appear in the 1953-1959 results,

which are similar to those for 1960-1967. They did appear however in the

1946-1952 results (see (23] for detailed tabulations).

It might seem appropriate to drop models (2.1) and (2.3) from this study

because they appear to be ill-specified. Yet, including them is not without

benefit. If these models are ill-specified and if income numbers do convey

information about risk, then the association between estimates of risk from

the market model and those from models (2.2) and (2.4) should not be less than

the association between estimates from the market models (2.1) and (2.3). Not

observing this would make our results somewhat puzzling.

IV. Market-Based and Accounting-Based

Estimates of Systematic Variability

A. Estimates of the Correlation between the Estimates from the Market Model

and the Estimates from the Accounting Number Models.Recall that the estimated coefficients of determination, R 's, from the

market model provide estimates of firms' systematic risk (or "systematic varia-

bility"). The estimated coefficients of determination from the accounting

income number models also provide estimates of the systematic variability

associated with firms' overall operations. In order to evaluate the association

between the risk-information impounded in security prices and the risk-

information in accounting income numbers, I computed cross-sectional correlation

16For additional evidence in this regard, see Brealey (9, Chapter 9] and,especially, Brown and Ball (10].

428



24/38

coefficients between the estimates of systematic variability based upon the

market model and the estinmates of systematic variability based upon each

accounting income nuniber model.

The results of my prediction tests regarding the aarket model suggested

that the estimates based upon seven-year observation periods had greater

descriptive validity. Tihe prediction test results for the accounting-numbermodels suggested that the estimates based upon the twenty-one-year observation

period, 1946-1967 (excluding 1960), had greater descriptive validity, relative

to the estimates based upon the seven-year observation period.17 So, in

comrputing correlation coefficients between market-based and accounting-based

estimates of systematic variability, the estimation results from the twenty-

one-year accounting models were of primary interest. But the results from

applying the accounting number models to the seven-year observation periods

are not completely useless; they can serve as a means of "validating" the

correlation coefficients based upon the twenty-one-year estimates of systematic

variability. The prediction-test results suggest that (for tlle number of

observations at hand) the accounting-number models do not reflect the structural

changes reflected by the market model. Additionally, my prediction test results

suggest that the twenty-one-year accounting models have rnore "descriptive

validity" than the seven-year accounting models. Accordingly, the estimated

correlation coefficients between accounting-based and market-based estimates

of systematic variability should, on average, not be lower for the twenty-one-

year accounting-based estimates than they are for the seven-year estimates.

This relationship should hold whenever there is a statistically significant

relationship between the market-based estimates of systematic variability and

the twenty-one-year accounting-based estimates. If the correlation coefficients

for the latter estimates are not statistically significant, then the reasoning

that I just used would have no empirical validity and, consequently, the pre-

dicted relationship should not be expected.

In Section IIA, I suggested that an additional (though not independent)

test of the correlation between market-based and accounting-based estimates of

systematic variability may be conducted with the estimated regression coeffi-

cients of the accounting-income number models (2.3) and (2.4) and the estimated

ai-coefficients from the market model. So, the same correlation analysis

applied to the coefficients of determination from the market model and the

17It is important to remember that the parameters of the market modelwere estimated using monthly data, whereas the parameters of the accountingincome number models were estimated using annual data.

429



25/38

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26/38

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431



27/38

accounting-number models was applied to the estimated regression coefficients

of these models.18

The correlation coefficients that resulted from these analyses appear

in Table 5. The numbers in parentheses are Spearman Rank Correlation Coeffi-

cients; the other numbers are first-order Pearsonian Correlation Coefficients

(adjusted for degrees of freedom). The letters "M" and "A" denote the sourcesof the estimates that were used in the correlation analyses; "M" refers to

the market model and "A" refers to the accounting-number model named at the

side of the table. The subscripts on M and A denote the observation period

upon which the estimates are based; the denotations of these subscripts are:

Subscripts for M and A Observation Periods

1 1946-1967 (excluding 1960)

2 1946-1952

3 1953-1959

4 1961-1967

Selection of the above observation periods was based upon the prediction test

results discussed in Sections and

First, consider the results on the left-hand side of Table 5. These

results pertain to the estimates from the three seven-year market models and

the twenty-one-year accounting number models. In general, these results indi-

cate that one cannot reject the hypotheses that there is no correlation between(1) market-based estimates of systematic risk and (2) accounting-based esti-

mates of systematic risk from model (2.1) -- levels of income numbers -- and

model (2.3) -- scaled income levels. In general, the opposite conclusion is

suggested regarding model (2.2) -- first differences in income numbers --

and (2.4) -- scaled first differences. These conclusions also apply to (1) the

correlation coefficients between the estimated coefficients of determination of

the market model and the accounting models and (2) the correlation coefficients

among the estimated regression coefficients of these models.The correlation coefficients presented on the right-hand side of Table 5

pertain to the estimates from the three seven-year market models and the three

seven-year accounting-numier models. The relationship between these results

and these on the left-hand side of the table is consistent with my earlier

assertion: in general, the correlation coefficients from the seven-year

accounting models' estimates should not be higher than the coefficients for the

18As indicated in Section IIA, the estimated regression coefficients ofmodels (2.1) and (2.2) are affected by firms' sizes. Hence, they were not usedin cross-sectional analyses.

432



28/38

twenty-one-year models, if the correlation coefficients for the latter are

statistically significant. The support for this assertion constitutes one kind

of "validation" for my interpretations of the results on the left-hand side of

the table.

Using the left-hand side of Table 5, one may infer that the association

between 64iand

S3is

stronger than that between w4iand

i.. This is an intui-tively reasonable result because both 64i and Si pertain to economy-wide (or

market-wide) indices, whereas w4i pertains to industry-wide indices.

It is important to note that all of the estimated correlation coeffi-

cients presented in Table 5 are biased downward because of measurement errors

in the variables employed in the correlation analyses.19 One may assert, a

priori, that these variables contain measurement errors because they are

estimates of parameters and, as such, they measure the parameters with error.

Consequently, those correlation coefficients that are "almost statisticallysignificant" (e.g., R = .16 or R = .19) may be indicative of a relationship

that is "statistically significant." The impact of this bias on the results

for the seven-year accounting models may be quite severe because of the small

number of observations used for the estimated parameters of these models

(hence, the potentially large amount of sampling error). But the general in-

significance of the results in the right-hand side of Table 5 cannot be attri-

buted solely to measurement errors. If this were the case, all of the estimated

correlation coefficients based upon the twenty-one-year accounting models'estimates snould be sharply higher than those based upon their seven-year

counterparts. And this is not evident in the table.

According to the results presented, there is (in general) a statistically

significant relationship between market-based and accounting-based estimates of

systematic risk if the accounting-based estimates are derived from first dif-

ferences in income numbers or scaled first differences. This finding does

suggest that accounting income numbers, if appropriately transformed, do reflect

a statistically significant amount of the information impounded in market prices

of securities (traded on the N'ew York Stock Exchange).20 Presumably, the trans-

formations induce "better" specifications- of the underlying stochastic pro-

cesses, a result that is consistent with the finding that models (2.1) and

(2.3) seemed to evidence misspecifications (see Section IIIB). Observe, however,

19See, e.g., Cochran (111, Kendall and Stuart (27, Chapter 29], andGoldberger [20]. A consideration of measurement errors and analyses based uponestimates from the market model, in particular, appears in Miller and Scholes[35].

20As indicated earlier, the results for other income numbers series(Income Available for Common, Net Operating Income) were essentially the same asthose presented here (all of which are based upon COMPUSTAT's Net Income series).

433



29/38

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31/38

that all estimated correlation coefficients in Table 5 (left side) are less

than R = .45. This suggests that much of the information impounded in security

prices is not reflected in accounting income numbers. More generally, it is

consistent with the proposition that accounting numbers, as sources of informa-

tion for market transactors, function within a context of competing information

sources.21

B. Remarks

The accounting-based estimates of systematic variability are estimates

of the covariability of firms' income numbers. In a recent report by Beaver,

Kettler, and Scholes [4], it is asserted that there is a strong relationship

between such accounting-based estimates, in particular those corresponding to

the regression parameters of accounting model (2.3), and the Xi-coefficients

of the market model. An examination of Table 5 suggests that there is nostrong association between these estimates. At first, this appeared to be an

inexplicable inconsistency. The accounting-based estimates used by these

authors were derived from scaled income levels; the market-based estimates were

derived from the market model. The accounting model (2.3) also used scaled

income levels; the market-based estimates that I used are also based upon the

rnarket model. Why the strikingly different results? To be sure, the samples

used are different. Also, Beaver, Kettler, and Scholes did not select their

observation periods on the basis of prediction tests. So, some differences

are to be expected. I conjecture that these methodological differences are

not the primary reasons for the differences in our results. Instead, I suspect

that our results differ primarily because of differences in the scaling methods

used for the income numbers. I scaled income numbers by another accounting

number, viz., total assets. Beaver, Kettler, and Scholes scaled income numbers

with market prices. But market prices also appear in the variables of the

market model; consequently, the estimated aI-coefficients of the market model

are functions of market prices. I suppose that the "significant associations"

reported by Beaver, Kettler, and Scholes are direct results of the fact that

their so-called "accounting-based" estimates of earnings covariability are

actually functions of market prices because they used market prices to scale

income numbers. Hence, their results may simply reflect "spurious correlation,"

a phenomenon that occasionally characterizes results from regression analyses

21An analysis supporting this statement, which is predicated upon thetheory and evidence regarding the efficient capital markets model, is presentedin Gonedes [24].

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involving ratios.22 The same phenomenon may be reflected in some of the

results in Ball and Brown [1], results that were also based upon income numbers

scaled by market prices.23

22See, e.g., Madansky [33], Kuh and Meyer [29], and Pearson (39].

23Ball and Brown explicitly recognized this possibility, as well asproblems associated with the nature of the generating processes of incomenumber series.

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APPENDIX

LIST OF COMPANIES

CRSP Ind. Co.Code Code Code Name

003VOA 3570 4000 Addressograph--Multigraph Corp.OOCN8A 2800 13000 Allied Chemical Corp.OOE88A 3522 14600 Allis Chalmers Manufacturing Co.

OOELQA 3241 15000 Alpha Portland Cement

0OH94A 2051 17700 American Bakeries Co.

OOK4GA 3221 19600 American Can Co.

OOM30A 2063 21600 American Crystal Sugar Co.

OORCGA 2830 M6000 American Hlome Products

OOV04A 3711 29700 American Motors Corp.

012COA 3731 35200 American Ship Building Co.

012J8A 1000 35400 American Smelting & Refining Co.

013SUA 2062 36700 American Sugar Co., N1. J.

016SGA 3331 39760 Anaconda Co.O1BELA 2093 44500 Archer Daniels Midland Co.

O1DNGA 3310 46800 Armco Steel Corp.

O1G4LA 5311 49300 Associated Dry Goods Corp.

01N3JA 2085 55410 Austin NicholsOlQlQA 3721 57400 Avco Corp.02764A 3725 72900 Beech Aircraft

0291GA 3721 74800 Bendix Corp.02AUUA 3310 76700 Bethlehem Steel Corp.

02JNUA 2020 84700 Borden, Inc.

03UD8A 3310 127400 Carpenter Steel Co.

042M8A 3321 133800 Central Foundry04D22A 2844 144450 Chemway Corp.

04R40A 3531 156800 Clark Equipment0501UA 2841 163900 Colgate Palmolive Co.

055P4A 3511 169700 Combustion Engineering Inc.

05Q2LA 3560 188500 Cooper Industries05R1UA 3310 189500 Copperweld Steel

065BLA 3721 202100 Curtiss Wright Corp.06B40A 3522 208000 Deere & Co., Del.

06L6LA 2085 217300 Distillers Corp. Seagrams, Ltd.

0738QA 2899 232728 Eagle Picher Industries, Co.

076IGA 2800 236400 Eastman Kodak07F54A 3610 244900 Emerson Electric Co.

0800SA 5311 262170 Federated Department Stores, Inc.

08NRUA 3511 285500 Foster Wheeler08U8UA 3713 291100 Fruehauf Corp.0939UA 3400 298300 General Cable Corp.

097V2A 3711 303010 General MotorsO9A4LA 3297 305300 General Refractories Co.

O9AEAA 3670 305610 General Signal Corp.

O9DWGA 3721 309200 General Tire & Rubber Co.

09JE8A 5311 313800 Gimbel Brothers, Inc.

09SW4A 3310 322500 Granite City Steel

O9T7GA 5331 322800 Grant, W. T.

OAU7QA 2063 356600 Holly Sugar Corp.OBIVGA 3310 378800 Inland Steel Co.

OBJ3QA 3331 379000 Inspiration Consolidated Copper Co.

OBLQEA 3310 381710 Interlake Steel Corp.

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CRSP Ind. Co.Code Code Code Name

OBNA4A 3522 383300 International Harvester Co.OBQM4A 2800 385700 International Salt Co.OBSOUA 5311 387100 Interstate Department Stores, Inc.OC588A 3310 398600 Jones & Laughlin Steel Corp.

OCD28A 3331 406600 Kennecott CopperOCKVOA 2800 413600 Koppers Co.ODODOA 3714 426400 Libby-Owens-Ford Glass Co.ODOG4A 2030 426500 Libby McNeill and LibbyOD8KGA 3241 434800 Lone Star Cement Corp.ODETGA 3310 441200 Lukens SteelODJF4A 5311 444900 R. H. Macy and Co., Inc.ODW'FGA 2950 457200 Masonite Corp.OEOSGA 5311 459600 May Department StoresOE268A 3630 461000 Maytag Co.OECSUA 3560 471900 Mesta Machine Co.OEUQ8A 3340 488200 Monarch Machine Tool Co.

OEXG2A 2800 491010 Monsanto Co.OF7UGA 5331 499600 G. C. Murphy and Co.OFFAOA 2052 507200 National BiscuitOFHIWCA 2085 509900 National Distillers & Chemical Corp.OFQR4A 3310 516900 National Steel Corp.OFR2GA 2062 517200 National Sugar Refining Co.OGX8CA 3221 556300 Owens Illinois, Inc.OJ8MCA 2841 598700 Procter and Gamble Co.OJG94A 2912 606500 Quaker State Oil Refining Corp.OJSBOA 3310 616800 Republic Steel Corp.OJT40A 3400 617600 Revere Copper & Brass, Inc.OJTDCA 3334 617900 Reynolds Metals

OKBSPA 3570 634711 SCM Corp.OKDFGA 1031 636400 St. Joseph LeadOKL40A 2085 643200 Schenley Industries, Inc.OKMFQA 2600 644600 Scott PaperOL13LA 2912 656500 Shell Oil Co.OLW6UA 2912 686300 Standard Oil Company, IndianaOLWD4A 2913 686500 Standard Oil Company, New JerseyOM5BOA 2830 693600 Sterling Drug, Inc.OM6A8A 3569 694600 Stewart Warner Corp.QMFN8A 2010 704200 Swift & Co.OMWILA 3714 718900 Timken Roller BearingONCULA 2800 734100 Union Carbide Corp.ONSJ4A 2950 748100 United States GypsumONW62A 3400 751810 U. S. Smelting Refining and MiningONWAJ8A 3310 752200 U. S. SteelOPCSGA 2085 766800 Walker Hiram Gooderham & Worts, Ltd.

OPDG2A 3540 767490 Wallace-Murray Corp.OPE34A 2051 768100 Ward Foods, Inc.

OQOHQA 3713 787000 White Motor

OQB38A 2070 797800 William Wrigley, Jr. Company

439



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REFERENCES

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Evidence on the Information Content of Accounting Numbers 1973

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