Market Efficiency, Role of Earnings Information, and Stock
Returns: A Vector Autoregressive Model Approach*K K†H T

Graduate School of Strategic Management
CHUO UNIVERSITY

Graduate School of Finance, Accounting and Law
WASEDA UNIVERSITY

ABSTRACTis paper investigates how the information content contained in components of earnings
is impounded into stock prices and provides new evidence on market efficiency for firms
listed on the Tokyo Stock Exchange First and Second Sections. First, we conduct aconventional pooled Mishkin test to examine whether stocks are rationally priced or not,and claim how this particular test can result in misleading observations if we erroneously
pool the data for the overall sample period by completely disregarding the time-series
properties of accounting numbers. Next, we conduct time-series analyses on properties of
the components of accounting earnings and cast doubt on the forecasting equation usedin conventional Mishkin tests. In order to fully investigate the degrees of market efficiency
and examine interrelationships between components of accounting earnings, we employ avector autoregressive approach and propose a new framework to test rational pricing of theaccounting information. We find that for 82% of firms listed on the Tokyo Stock Exchange
the hypothesis of rational pricing cannot be rejected. is result implies that pooled
estimation of the forecasting equation, which disregards the interacting structure among
relevant variables, may lead us to incorrect inferences about the degree of informational
efficiency in capital markets. e paper further confirms the robustness of our estimation
results with some simulations studies.
JEL Classifications: M41; G14; C32; C52
Key Words: Accounting Accruals; Rational Expectations; Mishkin Test;
Augmented Dickey-Fuller Test; Impulse Response Functions* is paper was presented at the 2011 Nippon Finance Association Annual Meeting and the 2011 Japanese Accounting Review
Conference, and the authors thank Takashi Obinata and Shyam Sunder for their helpful comments. Also, by any means the author
would like to acknowledge the continuous and heated discussion with late Kazuyuki Suda without whom we could not have
explored this interesting and important topic in the positive accounting research field. Moreover, the authors also acknowledge
helpful discussion with George Constantinides, Zhaoyang Gu, Yuji Ijiri, Ramesh Rao, Srinivasan Sankaraguruswamy, Kenji Wada,
and Takeshi Yamada. e authors thank financial support from the Grant-in-Aid for Scientific Research ((A) 21243029) from
the Ministry of Education, Culture, Sports, Science and Technology of Japan. All remaining errors are our own.
† Corresponding Author. Address Chuo University 1-13-27, Kasuga, Bunkyo-ku, 112-8551, Tokyo, JAPAN.
Telephone +81 (3) 3817-7478 E-mail kekubota@tamacc.chuo-u.ac.jp.
Received June 23, 2011; accepted August 26, 2011
Copyright©2011 Research Institute for Economics & Business Administration - Kobe University.

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e Japanese Accounting Review, 1 (2011), 17-37

1. Introduction
ere are a large number of empirical studies which have tested mispricing phenomena obtained
from accrual components of accounting earnings for U.S. data (Sloan (1996) and Xie (2001) among
others). ese studies find that the market misjudges implications from accounting accruals andthat there exists market mispricing which is resolved by the time the next years’ earnings become
available to capital market participants.1 However, comparable studies with Japanese accounting
accruals data are relative few although they have been increasing (Kubota, Suda, and Takehara, 2010).
In the current study, we focus on the information content of accounting accruals vis-à-vis cash flows
information and earnings numbers for the sample of Tokyo Stock Exchange (denoted TSE) firms
with a new research framework we propose below.
Under the efficient capital market hypothesis in a semi-strong form, all publicly available
information is instantaneously and accurately impounded into stock prices. However, evidence
against the efficient market hypothesis has recently increased in the U.S (Shleifer (2000) and
Lakonishok, Shleifer, and Vishny (1994), for example). Kubota, Suda and Takehara (2009) find thatthe “value-to-price ratios” defined by Frankel and Lee (1998) help investors earn excess returns after
controlling for the three risk factors by Fama and French (1993) for Japanese data and thus present
evidence against market efficiency.
In this paper we focus, in particular, on the time-series properties of accounting numbers. We
conduct the Mishkin test employed in the accounting literature, which was first proposed by Sloan(1996) and used by Xie (2001), to the pooled sample of the firms listed on the First and Second
Sections of the Tokyo Stock Exchange. First, we examine whether these stocks are rationally priced
or not with this conventional approach. Next, we estimate the detailed stochastic processes ofaccounting numbers at the individual firm level and conduct the Augmented Dickey and Fuller (ADF)
test. Finally, we employ a vector autoregressive model approach to explicitly take into consideration
the interacting structure among the components of earning numbers in a simultaneous equation
system of the forecasting/valuation equations based on the original Mishkin (1983) book,2 andtest the hypothesis of rational pricing with this new framework. Furthermore, we conduct somesimulations to confirm the robustness of our results.
Section 2 motivates our research methodology in terms of the market efficiency hypothesis.
Section 3 explains the method for constructing the components of accounting accruals. Section 4
describes our new testing method of rational pricing and the data we use. After reporting empiricalresults from the Mishkin and ADF tests, in Section 5 we demonstrate the estimated structureof the vector autoregressive model and results from the test of rational pricing. In Section 6 wefurther investigate the cross-sectional and time-series inter-relationship between the components ofaccounting earnings by employing the impulse response function (IRF) analysis and also report theresults from simulation studies. Section 7 concludes.

Such evidence is with respect to the components of accounting accruals. Sloan (1996) points out that the post-announcement
drifts of earnings numbers found by Bernard and omas (1990) are only limited to quarterly reports. Kubota, Suda, and Takehara(2010) find that the return anomaly found in fiscal year end reports begins to disappear around the time when semi-annual reports
are disclosed for the Japanese sample.
2
Mishkin (1983, p. 2) recommends his testing method as a simpler method of testing the rational expectations hypothesis rather
than the full scale test by Hansen and Sargent (1981). We also employ this Mishkin testing methodology. See also Sargent (1973)
for the definition of rational expectations vis-à-vis one of adaptive expectations.
1

Kubota and Takehara: Market Efficiency, Role of Earnings Information, and Stock Returns

19

2. Market Efficiency and Accounting Reporting
In order to examine whether market participants rationally price accounting numbers or not, theMishkin test is often times used. Mishkin (1983) developed this cross-equation testing framework
for the purpose of examining the rational expectations hypothesis in macroeconomics, and Sloan(1996) employed this framework to test the rational pricing of accounting numbers. is method has
become a de facto standard tool among accounting researchers.
As we will discuss in detail in Section 4, the Mishkin test uses the system of equations composedof the ‘forecasting equation’ and the ‘valuation equation’. In the ‘forecasting equation’ market
participants forecast the next year’s earnings by using components of earnings (such as cash flows
from operations and accounting accruals) in the current year, and, in the ‘valuation equation,’ they try
to associate components of earnings with future stock returns. e hypothesis tested in the Mishkintest is whether estimated parameters in the forecasting equation are different from estimatedparameters in the valuation equation. If the parameter values turn out to be different, it forms
evidence that the market is not fully utilizing the information content of components of earnings in arational manner; i.e., the asset market is inefficient.
By using this Mishkin test the majority of empirical studies in accounting in early dates tend
to reject market efficiency with respect to components of accounting numbers for U.S. data. For
example, Sloan (1996) concludes that accounting accruals are less persistent than cash flows fromoperations and that the market overprices accruals information. Xie (2001) decomposes total
accruals into normal and abnormal accruals after applying the cross-sectional vresion of Jones model
as proposed by DeFond and Jiambalvo (1994), and concludes that abnormal accruals are the least
persistent among components of earnings and that the market overprices abnormal accruals to alarger extent than normal accruals.
However, most of these previous studies which rejected rational pricing used the pooled sample
estimation method in conducting the Mishkin test. According to our view, two serious problems arise
using the Mishkin test in this way. First, the result from the Mishkin test may be misleading, if weerroneously pool all the data during the overall sample period by completely disregarding time-series
properties of accounting numbers. For example, relating to the problem caused by pooling all thesamples, Teets and Wasley (1996) show that earnings response coefficients estimated using pooleddata are downward biased. Second, the base model used in Sloan (1996) and Xie (2001) disregards
the interacting structure among the components of earnings related information of our interest in
their system of equations. As Chan, Jegadeesh and Sougiannis (2004) have clearly pointed it out, thepredictability of future earnings can be improved significantly by employing the vector autoregressivemodel, which explicitly takes into consideration time-series interactions between components ofearnings. Note that we can also further explore the dynamic impact of random disturbance terms
in the system of components of earnings by analyzing impulse response functions with the vector
autoregressive approach.
In the current study, we carefully examine the persistency of individual firm's earnings numbers
as well as their components. We will conduct unit-root tests and demonstrate that abnormal accruals
are more persistent than cash flows from operations and normal accruals. Based on results from these
unit-root tests, we construct a vector autoregressive model with lag one, which explicitly takes into
consideration the interacting structure of components of earnings when testing forecasting/valuation
equations, and propose a new framework to test the rational pricing of accounting numbers, based on
the very original formulations by Mishkin (1983, p.13, lines 11-12).

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e Japanese Accounting Review, 1 (2011), 17-37

3. Construction of Accruals from Financial Statements in Japan
We use the net income after tax wherein extraordinary gain and losses are added back (denoted
EBEI below) as a base line income number for our analysis. is income concept, so called “current
earnings after tax,” is the bottom line net income number which financial analysts in Japan often
times follow and predict. is net income number contains the performance from financing decisionsof firms except for items of other comprehensive income, which are currently directly charged to theequity account as dirty surplus in accordance with Japanese accounting standards.
is earnings number, EBEI, can be decomposed into cash flows from operations (CFO) andtotal accounting accruals (ACC). We use total assets at the beginning of the period as a common
divisor to construct all variables, as it is more conventional in the literature (Sloan (1996, fn.7))
instead of the market value of common equity. Also, since cash flows statements are not available
before fiscal year 2000 in Japan, we compute the four components accruals, Δ COA, Δ COL, Δ NCOL
and DEPR from the balance sheet and income statement items in individual financial statements asfollows.3

Δ COA = (changes in current assets – changes in cash and deposits)
Δ COL= – (changes in current liabilities – changes in financing items)
ΔNCOL= – ( changes in loss allowances for accounts receivable+ changes in reserve for bonus payable and salary payable+ changes in short-term reserve accounts+ changes in allowance for future retirement bonus+ changes in long-term reserve accounts+ changes in amortization)
DEPR = – (depreciation)

(1)
(2)
(3)

(4)

Changes in financing items in equation (2) are composed of changes in short-term borrowing,changes in outstanding commercial papers, changes in long-term debt due within one year, andstraight bonds and convertible bonds due within one year. Note that Δ COL, Δ NCOL, and DEPR
are defined as negative numbers throughout the paper so that the amount of total accruals, ACC,
becomes larger (smaller) as these numbers become larger (smaller).
By using notations defined in equations (1) through (4), total accounting accruals, ACC, used inthis study are defined as follows.
ACC = Δ COA + Δ COL +Δ NCOL + DEPR

(5)

Because total accruals (ACC) are the gaps between accounting earnings (EBEI) and cash flows fromoperations, cash flows from operations (CFO) is defined as
CFO = EBEI − ACC.

(6)

All variables appear in equation (6), EBEI, ACC and CFO, are standardized by a divisor at the
beginning of the period book-value of total assets as mentioned above. All of the above procedures
are standard in earnings management-related empirical studies, which have been conducted for U.S.
3

After fiscal year 2003 we switch to the items from the consolidated financial statements to compute the component of accruals.

Kubota and Takehara: Market Efficiency, Role of Earnings Information, and Stock Returns

21

data (see Dechow et al. 1995, and Sloan, 1996).
Next, we decompose total accruals into so-called “normal (non-discretionary)” and “abnormal(discretionary)” sub-components. In order to estimate normal and abnormal accruals, we use the
CFO modified-Jones model proposed by Kasznik (1999). For each sample firm-year we estimate thefollowing cross sectional model:
ACCj,p = α p + β 1,pΔ ADJREVj,p + β 2,p PPEj,p + β 3,pΔ CFOj,p + ε j,p(7)

where Δ ADJREV is the change in sales revenues (adjusted for the change in receivables), PPE is thegross property, plant and equipment, and Δ CFO is the change in cash flows from operations. esubscript j denotes the firm index for the number of firms within each estimated portfolio p. Basedon the 33 industry classifications of the Tokyo Stock Exchange, we then classify all non-financial
firms into 27 sectors and define each sector portfolio as sector p. All explanatory variables for eachfirm in equation (7) are deflated by total assets at the beginning of the fiscal year.4
Finally, the fitted values from OLS estimation are used as normal accruals (NAC), which
represent the normal accounting accrual level for each firm, and the deviations from these fitted
values are used as abnormal accruals (ABNAC), which represent firm specific accrual components. We
decompose the accrual component into the normal component and the abnormal component in thisway and investigate the persistency and variability of these numbers potentially managed by company
managers and controllers in order to test the rational pricing of stock prices in capital markets.

4. Testing Methods and the Data
4.1 e Mishkin Test
Mishkin (1983) developed a new framework to test the rational expectations hypothesis inmacroeconomics. en Sloan (1996) employed this Mishkin test for the first time to examine whether
the components of accounting earnings are priced rationally or not. is framework proposed by
Sloan (1996) has been extensively used as the de facto standard among accounting researchers.
e rational expectations hypothesis asserts that the subjective probability distribution of any
variable held by market participants is identical to the objective distribution of the same variableconditional on all available past information (Mishkin 1983, and Sargent 1973). With respect to the
expected value of asset future values, Fama (1970) states this as the market efficiency hypothesis (seealso Lehman (1991)).
For any given economic variable X, the rationality conditions can be written as
Em[Xt|Ft–1] = E[Xt|Ft–1],(8)

where Ft–1 is the information set publicly available at time t–1, Em[·|Ft–1] is the subjective expectations
assessed by the market and E[·|Ft–1] is the objective expectations conditional on Ft–1. Let rt denote
the return from holding a security from t–1 to t. en the rational expectation hypothesis as defined4

We computed with the Jones model, the modified Jones model, the CFO Jones model and the CFO modified Jones model. Basedon these four estimation models, we estimated abnormal accruals not only by conducting industry-wide cross-sectional regression
analyses, but also by conducting time-series regression analyses using individual firm’s accounting data. us, we confirmed thatthe likelihood ratios reported in Table 3 are less susceptible to the choice of estimation methods for abnormal accruals. e resultsfrom these tests are available upon request from the authors.

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e Japanese Accounting Review, 1 (2011), 17-37

in equation (8) implies the following condition to hold:E[rt – Em(rt|Ft–1)|Ft–1] = 0.

(9)Because the above condition is too general to be testable,5 one must specify the market equilibrium
condition that relates Em(rt|Ft–1) to some subset of past information, Ωt–1,6Em(rt|Ft–1) = f (Ωt–1) = rt*.

(10)

Combining equations (9) and (10) we obtain the following efficient market conditions.
E[rt – rt*|Ft–1] = 0.

(11)

is condition implies that the term (rt – rt*) should not be correlated with the past information
set Ft–1. at is, any forecasts based on the information set have to be orthogonal to the above term.
Let us denote Yt as any set of variables which is relevant to the pricing of security at time t. As
shown by Mishkin (1983, p.11), a model which satisfies the efficient market condition in (11) isrt – rt* = (Yt – Ytopt)t β + ε t,(12)where Ytopt is the one-period-ahead optimal forecast of Yt , ε t is the disturbance with the property
E[ε t |Ft–1] = 0, and β is a vector of slope coefficients. Note we suppressed for firm subscript i in theabove and will in the following equations for simplicity.
In the test framework proposed by Sloan (1996) the value relevance variable Yt is the accounting
earnings, EBEI, of firms. Following Freeman, Ohlson and Penman (1982), Sloan (1996) assumes thatthe future earnings performance can be expressed as:
EBEIt = γ 0 + γ 1EBEIt–1 + ν t.

(13)

Combining the above forecasting equation (13) with the rational pricing model (12), we can obtainthe following system of equations:
EBEIt = γ 0 + γ 1EBEIt–1 + ν t,
rt – rt* = (EBEIt – γ 0* – γ 1*EBEIt–1) β + ε t.

(14)

e first equation is called a forecasting equation and the second equation a valuation equation. eslope coefficient vector β in the valuation equation is called the earnings response coefficient (ERC).
Because the following identity equation holds by definition,
EBEIt = CFOt + ACCt = CFOt + NACt + ABNACt ,(15)

combining equation (15) with system (14) gives us the following two alternative versions of thee limitations from testing any asset pricing theory with the subset of conditional information are discussed in Cochrane (2001,
pp. 145-146).
6
Or with no arbitrage conditions (Lehmann, 1991).
5

Kubota and Takehara: Market Efficiency, Role of Earnings Information, and Stock Returns

23

extended models.
EBEIt = γ 0 + γ 1CFOt–1 + γ 2 ACCt–1 + ν t ,rt – rt* = β (EBEIt – γ 0* – γ 1*CFOt–1 – γ 2*ACCt–1) + ε t.

(16)

EBEIt = γ 0 + γ 1CFOt–1 + γ 2 NACt–1 + γ 3ABNACt–1 + ν t ,rt – rt* = β (EBEIt – γ 0* – γ 1*CFOt–1 – γ 2*NACt–1 – γ 3*ABNACt–1) + ε t.

(17)

e first model (16) was proposed by Sloan (1996) and the second model (17) was by Xie (2001). In
these systems of equations, whenever the rationality assumption holds, γ s has to coincide with γ * selement by element (Mishkin, 1983).
With the use of the correctly specified asset pricing theory, computations of abnormal returns(rt – rt*) in this valuation equation require risk adjustments of normal returns, rt*. For this purpose
we use Fama and French’s (1993) three factor model as a benchmark model for our data following
Jagannathan, Kubota, and Takehara (1998), and estimate Jensen’s alpha for each firm. In the
regression equation (18), we regress 12 monthly returns of firm j on Fama and French’s three risk
factors in the same period from July of year t through June of year t+1 and obtain Jensen’s alpha α j,tas the estimates of this regression equation.
rj,t,k – r f,t,k = α j,t + β j,t (rM,t,k – r f,t,k )+ γ j,t SMBt,k+ δ j,t HMLt,k+ ε j,t,k, k =1,...,12,

(18)

+

In the next step, the abnormal return, rj,t, – r*j,t,, can be constructed as the annualized Jensen’s alpha(=12 α j,t ).
As Mishkin (1983) originally proposed, in the first stage we estimate the parameters of themodel with no equality constraints on γ s and γ * s, and in the second stage we estimate the modelwith equality constraints, (γ i = γ i*, i = 0,..., l), l =2 or 3. en, the likelihood ratio statistics LR are
constructed as 2N ln(SSRc / SSR u) , in which N is the number of observations, SSRc, SSR u are
the sums of squared residuals from constrained regressions in the first stage and unconstrained
regressions in the second stage, respectively. Mishkin (1983) further proves that these LR statistics
are asymptotically distributed as χ 2(k) variables, and hence the null hypothesis of rational pricing forcomponents of earnings is rejected, whenever the LR statistics are sufficiently large.
4.2 Unit-Root Tests of Accounting Numbers
Although there is ample evidence for U.S. data for time-series properties of accounting
numbers, there are only a few for Japanese firms. In this paper we present evidence of the first-order
autocorrelations using OLS estimation and conduct the Augmented Dickey and Fuller unit root test
(Hamilton, 1994).
Xt = a + ρ ·Xt–1 + ut

(19)

We use the sample that covers at least consecutive 10 years of observations. In the above equation
ut s are assumed to be distributed with Gaussian white noise and the initial value X0 is assumed
to be zero. When the true ρ is close to one, it is well known that the estimated ρ from the OLS
regression is underestimated (Harvey (1981)). Accordingly, in the case that the true ρ equals one,e Japanese Accounting Review, 1 (2011), 17-37

24

the distributions of ρ are not well defined in a normal manner, and alternative Augmented Dickey
and Fuller tests are called for, for which the numerator is the chi-square distributed variable and thedenominator is the normally distributed variable.
If the unit root hypothesis is not rejected, the model becomes a random walk model, and wesay that the accounting numbers are highly “persistent” in the sense of Kormendi and Lipe (1986).7
On the other hand, if the null hypothesis of the unit-root is rejected and the AR (1) model is
implied, it is called “less persistent”. is is the reason why we test the existence of unit roots for eachcomponent of accounting numbers.
4.3 On Vector Autoregressive Model Approache Mishkin test based on the models (16) or (17) have been used in the past with a pooled
sample method for the purpose of testing rational pricing of accounting numbers, and there is awide spread belief that abnormal accruals are the least persistent among the component of earnings.
However, a number of recent studies have made critical attacks on these models as well as on theinterpretation of the empirical results obtained by Sloan (1996) and Xie (2001). For instance, Kraft,
Leone and Wasley (2007) point out the imminent ‘omitted variable problems,’ and demonstrate thatrational pricing of accruals is not rejected, if the additional explanatory variables are included in theforecasting/valuation equations. Another study which reports the evidence against Sloan (1996) is
the one by Francis and Smith (2004). ey evaluate persistence using firm specific time-series based
estimations and demonstrate that more than 85% of firms in the U.S. do not show any evidence that
accruals are less persistent than cash flows.
As we will show in the next section, the distributions of first order auto-correlations andcorresponding probability values from the Augmented Dickey Fuller test demonstrate that abnormal
accruals are more persistent than cash flows and normal accruals in Japan. ese findings along withprevious studies on U.S. data can give us an important clue that time-series properties of earnings
components may not be captured in an appropriate manner by models (16) and (17). If that werethe case, we would have to build an alternative model for forecasting and valuing, which can welltake into consideration interactions among components of earnings in current and future time
periods. ose being the reasons, we employ a vector autoregressive model in the same way as Chan,
Jegadeesh and Sougiannis (2004) proposed.
We assume that cash flows from operations, normal accruals, and abnormal accruals are all
relevant variables in explaining and predicting stock returns. In this case the variable, Yt in equation(12) becomes a three dimensional vector, consisting of CFOt, NACt, and ABNACt. We assume
these variables are well represented by a first order vector autoregressive process based on our priorunivariate time series tests. Under these assumptions the VAR (1) forecasting equation can be
described as follows:
Yt =

γ01
γ 11 γ 12 γ 13
CFOt
NACt = γ02 + γ 21 γ 22 γ 23
γ03
γ 31 γ 32 γ 33
ABNACtv1t
CFOt-1
NACt-1 + v2t = Γ0 + ΓYt-1 + vt.
v3t
ABNACt-1(20)

Because Yt*, the optimal forecast of Yt, is given by Γ0 + ΓYt-1, the valuation equation paired with theforecasting equation (20) becomes the following (21).
7

As for the definition of the earnings quality, see the literature review by Shipper and Vincent (2003).

Kubota and Takehara: Market Efficiency, Role of Earnings Information, and Stock Returns

rt – rt* = (Yt – Γ*0 – Γ*Yt-1)tβ + ε t

25

(21)

e vector β in the valuation equation (21) is named ‘Component Earnings Response Coefficients’(Component ERC) in this study, because these coefficients denote estimated relationships between
the unanticipated changes in components of earnings and stock returns. Note in this formulation
we assume that investors form their expectations on the components of earnings separately; i.e., one
for normal accruals and another for abnormal accruals. e former will be based on their forecastsof the industry-wise economic conditions and latter of the individual unsystematic conditions. en,if the information contained in the stochastic process of Yt is rationally priced in the stock market,
the intercept Γ0 has to coincide with Γ*0 and the slope matrix Γ also has to coincide with Γ* element
by element. Since there are 12 overall parameters in the forecasting equations, the likelihood ratio
statistics are asymptotically distributed as χ 2 (12) under the null hypothesis.
4.4 Data
e primary source for accounting variables of the Tokyo Stock Exchange First and Second
Sections firms is the Nikkei NEEDS database supplied by Nihon Keizai Shinbun Inc. e primarysource for monthly return data is the Nikkei PortfolioMaster Database. For each EBEI, CFO, ACC,
NAC and ABNAC variable, we exclude the top 0.5% and bottom 0.5% of the sample as an outlier.
e sampling period in the study is from 1978 through 2008, and the number of total pooled sample
observations after excluding the extreme observations is 30,438 firm-years. e minimum yearlyobservation is 653 for 1979 and the maximum is 1,304 for 2005, with an average of 982 firms peryear.
We limit our sample to non-financial firms listed on the First and Second Sections of the Tokyo
Stock Exchange and exclude financial firms due to the reason that representations of these firms arequite different from non-financial firms. Since most Japanese firms’ fiscal year end March 31st, we
compute the next year’s portfolio returns starting July 1st, while in previous research for the U.S.,
market portfolio returns were usually computed starting April 1st for firms with a December 31st
fiscal year end. In order to align calendar days, we also exclude firms whose fiscal years are not at theend of March, which consists of less than 10 percent of the total sample.

5. Empirical Results
5.1 Basic Observation
In Table 1 we report descriptive statistics for the pooled sample data from fiscal year 1978
through 2008. e average value of abnormal accruals (ABNAC) computed from the CFO modifiedJones model (Kasznik, 1999) should be zero since ABNAC is the residual term from the regression
equation (7). However, note the estimated average value of ABNAC is slightly different from zero
because of the exclusion of outliers every period as mentioned above. While the estimated standard
deviation of earnings (EBEI) is relatively low at 2.925, standard deviations of both cash flows fromoperations (CFO) and total accruals (ACC) are quite high at 5.672 and 5.144, respectively. We inferthat it may be evidence from earnings-smoothing behavior because the earnings are the simple sumof cash flows and total accruals by definition.
Table 2 reports the correlation matrix for cash flows, earnings and their components. ee Japanese Accounting Review, 1 (2011), 17-37

26

EBEI

Mean

T 1: D S
S.D.

1stQu.

Median3rdQu.

5.672

1.615

4.993

8.442

2.309

2.925

ACC

-2.753

5.144-5.797-2.855

ABNAC-0.0043.391-2.052

0.006

CFO

NAC

5.062

-2.748

4.264

0.839

2.019

-5.315-2.827

3.702
0.201

-0.2542.028

Note: e sample consists of 30,798 firm-years between 1978 and 2008. Firm characteristics are defined
as follows: EBEI: earnings before extraordinary items; CFO: cash flows from operations; ACC: total
accruals; NAC: normal accruals; ABNAC: abnormal accruals. All variables are divided by total assets atthe beginning of the period. Mean, S.D., 1st Qu., Median and 3rd Qu. denote sample means, standard
deviations, first quintiles, medians, and third quintiles, respectively.

EBEI
CFO
ACC
NAC
ABNAC

EBEI
0.430
0.000
0.094
0.000
0.000
0.955
0.144
0.000

T 2: C M
CFO
0.419
0.000

-0.8580.000-0.6850.000-0.440
0.000

ACC
0.046
0.000
-0.843
0.000
0.756
0.000
0.567
0.000

NAC
-0.0090.125-0.660
0.000
0.734
0.000
-0.111
0.000

ABNAC
0.085
0.000
-0.416
0.000
0.531
0.000
-0.1080.000

Note: e sample consists of 30,798 firm-years between 1978 and 2008. Firm characteristics are defined
as follows: EBEI: earnings before extraordinary items; CFO: cash flows from operations; ACC: total
accruals; NAC: normal accruals; ABNAC: abnormal accruals. All variables are divided by total assets at the
beginning of the period. e figures in the above diagonal matrix are Spearman’s rank correlations and thenumbers in below the diagonal matrix are Pearson’s correlation. e figures shown in italics in lower cells
are corresponding significance probabilities (p-values ).

correlation between cash flows (CFO) and total accruals (ACC) is negative with a very high numberof –0.843 for Spearman’s rank correlation and even higher with –0.858 for the Pearson correlation.
e result may indicate that the higher the cash flows the lower the earning management behavior,
for which firm managers and accountants try to boost their corporate earnings. e correlation
between cash flows and abnormal accruals is lower at -0.416 and -0.440, respectively. e correlation
between normal and abnormal accruals is also low at -0.108 and -0.111, respectively, which indicatesthat these two components may be proxies for different accrual accounting behavior. In a later subsection of this paper we present evidence which demonstrates that abnormal accruals contain its
unique information in comparison with the other two accruals components. e total accruals (ACC)and normal accruals (NAC) are highly correlated at 0.734 and 0.756, respectively, and this result
reveals the relatively large weight normal accruals have among accruals components.
5.2 e Result from the Mishkin Teste results from the market efficiency test as proposed by both Sloan (1996) and Xie (2001) areKubota and Takehara: Market Efficiency, Role of Earnings Information, and Stock Returns

27T 3: N G L S E (M T)  CFO, ACC, NAC 
ABNAC  R  O-Y A E   R M P
Panel A: Market Pricing of Earnings Components with Respect to One-Year Ahead Earnings.
Model 1.

Parameter

γ 0(Intercept)
γ 1(CFO)γ 2(ACC)β (ERC)

Forecast

0.683

Model 2.

Valuation

0.647
---

Forecast

Valuation

γ 1(CFO)

0.656

0.655

-0.304γ 0(Intercept)

0.675

γ 2(NAC)

0.673

0.625

Parameter

2.162

γ 3(ABNAC)
β (ERC)

0.677
0.639
0.626

---

-0.376
0.612
0.746
2.189

Note: Model 1 is first proposed and examined by Sloan (1996) and Model 2 is proposed by Xie (2001), in
which total accruals are decomposed into normal and abnormal components. e sample consists of 30,798
firm-years between 1978 and 2008. ERC denotes the estimated earnings response coefficient.
Model 1. (Equation (16))
EBEIt = γ 0 + γ 1CFOt-1 + γ 2 ACCt-1 + ν t.
Abnrett = β (EBEIt – γ 0*– γ 1*CFOt-1– γ 2*ACCt-1) + ε t.
Model 2. (Equation (17))
EBEIt = γ 0 + γ 1CFOt-1 + γ 2 NACt-1 + γ 3 ABNACt-1 + ν t.
Abnrett = β (EBEIt – γ 0*– γ 1*CFOt-1– γ 2*NACt-1– γ 3 ABNACt-1) + ε t.

Panel B: Tests of Rational Pricing of Components of Earnings
Null Hypothesis
Model 1.
Model 2.

CFO, ACC (γ 0*=γ 0, γ 1*=γ 1, γ 2*=γ 2)

CFO, NAC, ABNAC (γ 0 =γ 0, γ =γ 1, γ =γ 2, γ =γ )
*

*
1

*
2

*
3

Likelihood Ratio
Statistic

250.431291.470

Marginal
Significance Level

0.000
0.000

Note: Likelihood ratio statistics = 2N·ln (SSR / SSR ) where N is the number of observations,
SSRc, SSR u are the sum of squared residuals from the constrained regressions in the first stage andunconstrained regressions in the second stage (Mishkin, 1983, p. 19).
cureported in Table 3. Model 1 in equation (16) corresponds to the case in which both CFO and ACC
are used and Model 2 in equation (17) corresponds to the case in which all CFO, NAC, and ABNAC
variables are used in simultaneously estimating the forecasting and valuation equations. As discussed
in the foregoing, the market efficiency condition implies that γ estimates equal to γ * estimates element
by element. Sloan (1996) constructed a null hypothesis in which the persistence of current earnings isdecreasing in the magnitude of accruals and increasing in the magnitude of cash flows, which meansthat estimated γ 1 should be larger than γ 2 and γ 1* larger than γ 2* in two equations.
Panel A of Table 3 reports the estimated parameter values in forecasting and valuation equations.
In Model 1 the estimated coefficient for γ 1 in the forecasting equation is 0.647 and is larger than 0.625
for γ 2 . is indicates that the total accruals series is less persistent than cash flows. Moreover, in thevaluation equation γ 2* is slightly larger than γ 1* at 0.675 in comparison to 0.673. is suggests thatthe market overprices accruals information to some extent. ese findings are also similar in the caseof Model 2, wherein we find that the abnormal accruals variable is the least persistent and the most28

e Japanese Accounting Review, 1 (2011), 17-37

overpriced (0.746 vs. 0.655 and 0.612) among different specifications of components of the earnings.
e latter finding seems to be in accordance with previous findings for U.S. data by Sloan (1996) andXie (2001).
From Panel B of Table 3 we find that the hypothesis of rational pricing is rejected for our data
both for Model 1 and Model 2 with corresponding likelihood ratios and the significance level asshown in Panel B. Accordingly, there is clear evidence against rational pricing for Japanese data
similar to previous evidence for U.S data.8
Accordingly, if the model framework and the estimation method proposed by Sloan (1996)
were indeed appropriate to test the rational pricing of accounting accruals, our results could havesuccessfully demonstrated that abnormal accruals are the least persistent among the components ofearnings and the stock market overprices abnormal accruals information for the Japanese market andwe overall reject the rational pricing hypothesis.
However, the fundamental query we raise here is whether one-period ahead earnings forecasts
can be rationally or even in an adaptive sense, (Sargent 1971) predicted correctly by the use of asingle equation AR (1) specification as in equation (13).9 In other words, we cast doubt whether thepooling of the sample is indeed allowed in the rationality test of accounting earnings numbers.
In order to formally answer this important but not yet explored question for Japanese data we
extensively investigate time-series properties of cash flows, earnings, and their components in thenext sub-section. Based on this result we then propose a vector autoregressive version of the Mishkintest originally formulated by Mishkin (1983, p.13, lines 11-12) and proceed to test the rational
pricing hypothesis.
5.3 Unit-root Tests of Accounting Number Series
In previous empirical accounting literature, the word “persistency” generally meant the estimatedtime-series regression coefficients of candidate accounting numbers on the lagged one series of thesame variable. As was shown by Kormendi and Lipe (1987), if a univariate autoregressive model canbetter approximate the market expectations of earnings, it leads us to the prediction that the higher
the persistency of accounting earnings, the larger the influence of unanticipated changes in earnings
upon stock returns.
e upper panel of Table 4 reveals sampling distributions of first order autocorrelation
coefficients of earnings, cash flows, total accruals, normal accruals, and abnormal accruals. eresults suggest the possible persistency of earnings and their components as follows. As for EBEI
and ABNAC, some of the first order autocorrelations are high and close to 1.0. For example, the 90
percentile estimates for EBEI and ABNAC are 0.738 and 0.518, respectively, and are much higher
than the ones for CFO, ACC, and NAC. Accordingly, from this result the EBEI and ABNAC series
seem more persistent than other three series, as can be also observed from Figure 1.
However, it is also well known that the regression coefficients of the variable on the lagged one
variable are downwardly biased from one even when the model is in fact a random walk (Harvey
1981, p. 29). Accordingly, the usual use of the univariate time-series regression coefficients applied toeach firm is not recommended, nor can we conclude about the estimated coefficients shown above.
us, in order to assess correctly the nature of the stochastic processes of these accounting
numbers, we conduct the Augmented Dickey-Fuller test and the corresponding test statistics (t-values)
Chordia et al. (2010) present evidence that the stock market was somewhat inefficient in the U.S. and recently has become more
efficient with respect to the information set including accounting accruals.
9
Although there may be an omitted variable problem with this specification, we do not deal with this problem in this paper andonly investigate the joint time-series properties per se of the three variables of our interests, CFO, NAC, and ABNAC.
8

Kubota and Takehara: Market Efficiency, Role of Earnings Information, and Stock Returns

29T 4: S S  A  D-F S
Panel A: Distribution of First Order Auto-Correlation
EBEI
CFO
ACC
10%ile0.053-0.311-0.363
1st Qu.
0.249-0.170-0.215Median0.452
0.004-0.049
Mean
0.420
0.008
-0.0433rd Qu.
0.621
0.186
0.125
90%ile
0.738
0.343
0.294

NAC
-0.529-0.400-0.260-0.236-0.0920.081

ABNAC-0.020
0.121
0.267
0.257
0.407
0.518

Panel B: Distribution of Dickey-Fuller t Statistics
EBEI
CFO
ACC
10%ile-3.975-6.543-6.968
1st Qu.
-3.152-5.459-5.839Median-2.423-4.394-4.638Mean-2.491-4.502-4.779
3rd Qu.
-1.786-3.396-3.61590%ile-1.206-2.653-2.820%H 0 Rejected
28.53182.18685.238NAC-8.541-7.330-5.853-5.989-4.533-3.54894.180ABNAC-4.716-3.998-3.255-3.325-2.615-2.05957.559Note: e summary of the estimation results of autocorrelation coefficients and Augmented Dickey-Fuller
t statistics with 1,409 sample firms for which the time-series observations for accounting numbers wereavailable for at least 10 consecutive years. e observation years are between 1978 and 2009. CFO is cash
flows from operations, ACC is total accruals, NAC is normal accruals, ABNAC is abnormal accruals, and
EBEI is earnings after tax and before extraordinary items. ‘%H0 Rejected’ is the percentage of the firms on
which a null hypothesis of unit-root is rejected.

are reported in the lower panel of Table 4. In ADF tests we set the minimum requirement for thenumber of annual observations for each firm sample at 10, while most of our data had 32 years ofobservations. We have 1,409 firm samples which satisfy these conditions within our accounting data
set. As for earnings, EBEI, we find that only in 28.53 percent of the cases the random walk modelis rejected, as shown in the upper most to the left bottom row of the table. e results suggest that
EBEI series are the most persistent among these five series.10
As for abnormal accruals, the same fraction is 57.559 percent, and thus there is a 42.441
percent chance that the underlying model follows a random walk model and a 57.559 percent
chance that it follows a mean-reverting process. Hence, this series is the next persistent. Note themean reversing process is called “less persistent” by the definition of Schipper and Vincent (2003).
On the other hand, as for cash flow series, for 82.186 percent of the sample the estimated t-values
reject the random walk hypothesis, 85.238 percent for accruals, and 94.180 percent for normal
accruals, respectively. In sum, we conclude that the latter three series, CFO, ACC, and NAC follow
mean-reverting processes with a very high chance. Note among these variables that the most meanreverting is the normal accruals series. Because accounting deferral or the accrual process has to revert
itself most of the time within one period (Francis and Smith, 2005) , this finding is not surprisingand also it re-confirms the mechanism which works for the accrual and deferral processes for our
data.
10

It may be the case that possible earnings management causes earnings series to be persistent for Japanese data, whose point we will
not explore further in the paper.

e Japanese Accounting Review, 1 (2011), 17-37

30F 1: C   E D F  F O A-C
 EBEI, CFO, ACC, NAC, ABNAC

���
�����

���

����

���

���

���

�������������� �� �� �� �

�� �

�� �

�� �

Note: Non-parametric estimates of the probability density of the first order autocorrelation of earnings,
cash flows, total accruals, normal accruals and abnormal accruals are depicted. e observation years are
between 1978 and 2009 and there are 1,409 sample firms for which the time-series observations foraccounting numbers were available for at least 10 consecutive years.

5.4 Results from the Mishkin Test based on Vector Autoregressive Model
Once we estimate the VAR (1) models for each firm, we are able to test the rational pricingof accounting numbers by the framework proposed by Mishkin (1983, p. 15). If the market prices
rationally all the information contained in the components of accounting earnings, the estimatedparameters in forecasting equation (20) must coincide with those in valuation equation (21). In thiscase the null hypothesis H0 becomes a joint hypothesis that Γ0 = Γ0*, Γ = Γ*.
However, before conducting the Mishkin test on the system of equations (20) and (21), we
compare estimated parameters in forecasting equation (20) to those in valuation equation (21) as our
first diagnosis check. We estimate the system of equations (20) and (21) for each firm which has atleast 10 consecutive years of accounting data. e numbers of firms which satisfy this criterion are
1,264. Table 5 reports distributions of estimated parameters in the system of equations (20) and (21).
When we compare the median values of parameters in the forecasting and the valuation equation,
we find that these are quite similar. However, by reading through the percentile statistics, we findthat distributions are more widely dispersed for the valuation equation with its extreme 90 percentile
and 10 percentile values larger in absolute values than for the forecasting equation. Figure 2 reports
distributions of marginal significance of estimated likelihood ratios as defined by Mishkin (1983,

Kubota and Takehara: Market Efficiency, Role of Earnings Information, and Stock Returns

31T 5: D  E P   VAR(1) M

Panel A: Forecasting Equation

Panel B: Valuation Equation
10%ile-2.403-2.956-2.689-1.872-2.028-2.594-2.120-1.925-2.125

1st Qu. Median Mean 3rd Qu. 90%ile-0.860 0.281 0.111 1.371 2.817-1.010 0.247 -0.106 1.388 2.917-0.703 0.518 0.406 1.655 3.149-0.435 0.370 0.459 1.229 2.556-0.778 0.090 0.498 1.041 2.683-1.044 -0.196 -0.273 0.733 2.286-0.812 -0.082 -0.064 0.654 2.017-0.620 0.225 0.050 1.064 2.481-0.629 0.208 0.333 1.036 2.403

Note: We estimate the firm-specific parameters in the VAR (1) forecasting equation (20) and the valuation
equation (21) with 1,264 sample firms, for which time-series observations for accounting numbers wereavailable for at least 10 consecutive years. Distributions of the estimates of firm specific parameters Γ in(20) are shown in Panel A and Γ* in (21) is shown in Panel B.
Yt = Γ0 + ΓYt-1 + ν t
rt – rt* = (Yt – Γ0 + ΓYt-1) β + ε t

(20)
(21)

�

��

���

���

F 2: D  M S L  LR T S

���������

γ 11
γ 12
γ 13
γ 21
γ 22
γ 23
γ 31
γ 32
γ 33

10%ile 1st Qu. Median Mean 3rd Qu. 90%ile-0.826 -0.179 0.301 0.259 0.717 1.227-0.961 -0.290 0.245 0.225 0.783 1.392-0.726 -0.092 0.442 0.433 0.995 1.580-0.351 0.016 0.336 0.385 0.706 1.099-0.789 -0.361 0.020 0.057 0.401 0.885-0.947 -0.562 -0.200 -0.143 0.196 0.646-0.722 -0.398 -0.091 -0.132 0.160 0.492-0.438 -0.088 0.222 0.199 0.517 0.900-0.426 -0.091 0.240 0.195 0.547 0.856

�� �

�� �

�� �

�� �

�� �

�� �

���������������������������

�
Note: e number of firms for which we conduct a Mishkin test based on VAR (1) structure is 1,264. enumber of firms whose marginal significance level (p-value corresponding to the LR test statistic) is lessthan 0.05 is 224. It means that for 82.3% of the firms listed in the TSE the rational pricing of accounting
numbers is not rejected at the 5% level.

e Japanese Accounting Review, 1 (2011), 17-37

32

T 6: D  E C ERCs

β 1 (CFO)
β 2 (NAC)
β 3(ABNAC)
β 1 –β 2
β 1 –β 3
β 2 –β 3

10%ile-6.378-8.047-7.232-4.314-4.903-6.936

1st Qu.
-1.866-2.670-2.060-2.237-2.298-3.514

Median
2.457
2.311
2.320
-0.153
0.116
0.258

Mean
2.859
2.908
2.532
-0.0500.326
0.376

3rd Qu.
1.371
1.388
1.655
2.037
2.861
3.842

90%ile
2.817
2.917
3.149
4.424
5.762
8.251

t-value-------0.427
2.176
1.773

p-value------0.669
0.030
0.076

Note: Distributions of the estimates of firm-specific Component ERCs are shown. e lower panel reports
the paired t- test statistics (t-value) along with the corresponding probability values (p-value) as well as the
sample means and percentile figures of the estimated component ERCs.

p. 19), in which we use p-values to summarize the results. Surprisingly we find that rational pricing
cannot be rejected for 82.3 percent of the firm samples at the 5 percent significance level.
Next, Table 6 reports distributions of the “Components ERC” which are defined as the estimatedvector valued β in valuation equation (21). Table 6 also reports simple paired t-test results for thedifferences between estimated β s for each firm in the lower panel. From the upper panel, we find thatboth median values are 2.457, 2.311, and 2.320, and average values are 2.859, 2.908, and 2.532 withthe consecutive sequences of the CFO, NAC, and ABNAC variable, respectively. In comparison withthe univariate time-series model case in Table 4 for which ERC was 2.162, we find that Components
ERC is larger. More importantly, when we read the percentile numbers of these vector-valued betas,
we find that distributions are skewed to the left, and there is more concentration of the probability
mass above these high median values.
e lower panel of Table 6 reports the paired t-test results for the differences between
components ERC for each firm. From p-values shown in the upper-most right column we find that
there is no difference in the size of responses between cash flows and normal accruals in the valuation
equation. However, the difference of responses of the valuation equation between cash flows andabnormal accruals is significant at the 5 percent level and the one between the normal and abnormal
accruals is significant at the 10 percent level. Accordingly, we infer from these results that market
responses to abnormal accruals are somewhat different from ones to cash flows and normal accruals.
We further investigate this point and explore how the response to abnormal accruals is different byanalyzing impulse response functions in the next section.

6. Impulse Response Function Analysis
Impulse response functions trace the effects of a unit shock to one of the components ofearnings onto other components in the VAR. Because we employ a first order vector autoregressivemodel, the relation between the Yt and k period lead variable Yt+k is described as in the equation(22). From (22) we see that the unit shock to Yt-1 is conveyed through the matrix Γk and the impulse
response function is identical to this Γk.
Yt = Γ0 + ΓYt-1 + vtkΣΓYt+k = I +

j=1

j-1

k

ΣΓ v

Γ0 + Γ k+1Yt-1 + vt+k +

j=1

k

t+k-j

(22)

Kubota and Takehara: Market Efficiency, Role of Earnings Information, and Stock Returns

33T 7: D  P C A  C  E
CFO-ACC
CFO-NAC
CFO-ABNAC
NAC-ABNAC

10%ile-0.987-0.874-0.723-0.449

1st Qu.
-0.972-0.811-0.619-0.275Median-0.935-0.735-0.480-0.101Mean-0.896-0.708-0.450-0.1043rd Qu.
-0.865-0.635-0.3130.080

90%ile-0.752-0.518-0.1340.229

Note: e sample means and percentile figures of Pearson moment correlations among cash flows (CFO),
normal accruals (NAC), and abnormal accruals are reported for1,409 individual firms for which CFOs,
NACs and ABNACs are available for at least 10 consecutive years and Pearson correlations were estimated.

First, as a guide to the intuition of the results, Table 7 shows distributions of Pearson correlations
between each paired variable. is is the result computed from individual data rather than resultsfrom pooled data that we previously reported in Table 2, where we criticized the use of pooled data.
It is noteworthy that cash flows and total accruals have strongly negative correlations with medianvalue -0.935. Cash flows and normal accruals are also strongly and negatively correlated with -0.735.
Although somewhat weaker, cash flows and abnormal accruals are also negatively correlated with
-0.480. In addition, we find that the correlation between normal and abnormal accruals is close tozero (mean -0.104 and median -0.101).
e final Table 8 reports the result from estimated impulse response functions, and Figure
3 depicts oscillation and convergence patterns of these response functions over time. As for thepersistence of shocks, from Panel A and Figure 3 we find that cash flows shocks diminish rather
slowly (onto CFO, the median is 0.301 in year 1 and 0.163 in year 2 and so forth). Also, from Panel
B and C and Figure 3, we find that the shock from abnormal accruals takes a shorter time to decay,
but takes longer than the shock from normal accruals.
As for the prediction of abnormal accrual, we find the current increase of cash flows increaseabnormal accruals in the next year as shown in median values (0.442 in year 1 and 0.111 in year2). On the other hand, the current increase in normal accruals will result in a decrease of abnormal
accruals in the next year (-0.200 in year 1). Because we know that cash flows and normal accruals arestrongly and negatively correlated (-0.735), when the cash flows amount is increased, the abnormal
accruals amount will be increased in a following year, and the concurrent decrease of normal accruals
may further amplify the amount of abnormal accruals in relative terms. On the other hand, for thereason the autocorrelations of abnormal accruals may become high as was the case for cash flows,
because these numbers are negatively and highly correlated, and the dissipation of abnormal accruals
shocks takes time.
Table 9 reports the results from our simulation experiments for 100 years based on our VAR
estimates obtained for each firm. Here we report distributions of the first order autocorrelations
computed from simulation paths for all sample firms. We find that the VAR (1) model we haveestimated above indeed succeeded in replicating well the actual autocorrelation coefficients reported
in Table 4. For example, median values of earnings are 0.452 (Table 4) vs. 0.508 (Table 9); cash
flows, 0.004 vs. 0.282; total accruals, -0.049 vs. 0.230; normal accruals, -0.260 vs. 0.073; and finally,
abnormal accruals, 0.267 vs. 0.367.
ese simulation results confirm that our initially estimated VAR model, which was neverconducted for Japanese data at individual firm levels for such a long series, can indeed well replicate
actual time-series distributions at the univariate level for cash flows, earnings, and components ofearnings, which in fact support rational pricing of accounting data for Japan. us, we find that ourestimation results and the tests of hypotheses are robust, and the evidence supports market efficiency

e Japanese Accounting Review, 1 (2011), 17-37

34

T 8: D  I R U   Y

Panel A: Impulse Response From CFO
To:

25%ileCFO
Median75%ile25%ileNAC
Median75%ile25%ile
ABNAC Median
75%ileYear 1 2
3
4
5
6
7
8
9
Year 10-0.179 -0.106 -0.048 -0.008 -0.010 -0.002 -0.003 -0.001 -0.001
0.000
0.301
0.163
0.094
0.063
0.026
0.018
0.007
0.005
0.002
0.001
0.717
0.450
0.303
0.215
0.140
0.105
0.069
0.048
0.033
0.025
-0.290 -0.116 -0.015 -0.026 -0.005 -0.006 -0.001 -0.002
0.000
0.000
0.245
0.113
0.107
0.040
0.031
0.011
0.008
0.003
0.002
0.001
0.783
0.417
0.328
0.183
0.147
0.088
0.070
0.042
0.034
0.020
-0.092 -0.096 -0.054 -0.021 -0.008 -0.004 -0.003 -0.002 -0.001
0.000
0.442
0.111
0.063
0.041
0.025
0.012
0.006
0.003
0.002
0.001
0.995
0.430
0.264
0.196
0.136
0.086
0.058
0.040
0.028
0.018

Panel B: Impulse Response From NAC
To:

25%ileCFO
Median75%ile25%ileNAC
Median75%ile25%ile
ABNAC Median
75%ileYear 1 2
3
4
5
6
7
8
9
Year 100.016 -0.074 -0.061 -0.043 -0.014 -0.012 -0.005 -0.004 -0.001 -0.001
0.336
0.092
0.038
0.013
0.014
0.004
0.003
0.001
0.001
0.000
0.706
0.283
0.147
0.083
0.062
0.036
0.026
0.015
0.011
0.006
-0.361 -0.121 -0.096 -0.022 -0.027 -0.005 -0.008 -0.002 -0.003 -0.001
0.020
0.093
0.018
0.029
0.005
0.007
0.002
0.002
0.000
0.000
0.401
0.325
0.134
0.111
0.053
0.043
0.024
0.017
0.009
0.008
-0.562 -0.087 -0.064 -0.040 -0.023 -0.009 -0.006 -0.003 -0.002 -0.001-0.200
0.094
0.034
0.014
0.007
0.005
0.002
0.001
0.000
0.000
0.196
0.338
0.155
0.081
0.055
0.038
0.023
0.015
0.010
0.006

Panel C: Impulse Response From ABNAC
To:

25%ileCFO
Median75%ile25%ileNAC
Median75%ile25%ile
ABNAC Median
75%ileYear 1 2
3
4
5
6
7
8
9
Year 10-0.398 -0.205 -0.095 -0.060 -0.040 -0.022 -0.014 -0.006 -0.004 -0.002-0.091
0.037
0.019
0.006
0.000
0.001
0.000
0.000
0.000
0.000
0.160
0.300
0.166
0.096
0.054
0.038
0.020
0.015
0.008
0.006
-0.088 -0.207 -0.090 -0.056 -0.036 -0.019 -0.011 -0.006 -0.004 -0.002
0.222
0.039
0.008
0.006
0.003
0.001
0.001
0.000
0.000
0.000
0.517
0.312
0.160
0.095
0.060
0.036
0.020
0.015
0.009
0.006
-0.091 -0.217 -0.076 -0.047 -0.032 -0.018 -0.011 -0.006 -0.003 -0.002
0.240
0.029
0.030
0.017
0.003
0.002
0.001
0.001
0.000
0.000
0.547
0.295
0.185
0.108
0.060
0.039
0.023
0.016
0.009
0.007

Note : Based on the firm-specific estimates of the transition matrix Γ in the VAR(1) forecasting equation(20), we compute the impulse responses from the current period one unit shock in the component of
earnings to itself and other components in future periods. e number of firm samples is 1,264, and 25
percentile, median and 75 percentile numbers are reported.

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Kubota and Takehara: Market Efficiency, Role of Earnings Information, and Stock Returns
35e Japanese Accounting Review, 1 (2011), 17-37

36

T 9: S S   F O A C  S S PDistribution of First Order Auto-Correlation
EBEI
CFO
ACC
10%ile0.052-0.269-0.335
1st Qu.
0.294-0.021-0.079Median
0.508
0.282
0.230
Mean
0.455
0.257
0.197
3rd Qu.
0.672
0.570
0.505
90%ile
0.802
0.749
0.697

NAC
-0.418-0.186
0.073
0.067
0.318
0.557

ABNAC
-0.058
0.138
0.367
0.348
0.584
0.752

Note: Based on firm-specific estimates of transition matrix Γ in the VAR (1) forecasting equation (20), we
simulate the forecasting model for each firm and re-compute the first order autocorrelation of earnings andits components from these simulated paths. Sample means and percentile figures of 1,264 firms are shownin the table.

of components of earnings information for Tokyo Stock Exchange firms.

7. Conclusion
is paper investigates how the information content contained in components of earnings
numbers is impounded into stock prices and provides new evidence on the market efficiency for thefirm sample listed on the Tokyo Stock Exchange. First, we conduct a conventional pooled Mishkintest to examine whether stocks are rationally priced, and suggest how this particular test result canbe misleading if we erroneously pool the data for the entire sample period by disregarding timeseries properties of accounting numbers. Next, we conduct time-series analyses on the properties ofcomponents of accounting numbers and cast doubt on the forecasting equation used in conventional
Mishkin tests, a first in the accounting literature for Japanese data. en we employ a vector
autoregressive model approach and proposed a new framework to test rational pricing of accounting
information. We find that for 82% of the firms listed on the Tokyo Stock Exchange, the hypothesisof rational pricing is not rejected. is implies that the pooled estimation of the forecasting equation,
which disregards the interacting structure among the value-relevant variables, may lead us toincorrect inferences about the degree of information efficiency in the Japanese capital market. epaper also reconfirms the robustness of our estimates by conducting simulations for 100 years.

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