Description
Value relevance studies, in particular international comparative studies, use market
values sampled at different dates relative to the fiscal year-end. This paper aims to contribute a
theoretical and empirical analysis of the relationship between value relevance and the month of market
value sampling.
Accounting Research Journal
Coincident and forecast relevance of accounting numbers
Karol Marek Klimczak Grzegorz Szafranski
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Karol Marek Klimczak Grzegorz Szafranski , (2013),"Coincident and forecast relevance of accounting
numbers", Accounting Research J ournal, Vol. 26 Iss 3 pp. 239 - 255
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Coincident and forecast relevance
of accounting numbers
Karol Marek Klimczak
Department of Finance, Kozminski University,
Warsaw, Poland, and
Grzegorz Szafranski
Department of Econometrics, Faculty of Economics and Sociology,
University of Lodz, Lodz, Poland
Abstract
Purpose – Value relevance studies, in particular international comparative studies, use market
values sampled at different dates relative to the ?scal year-end. This paper aims to contribute a
theoretical and empirical analysis of the relationship between value relevance and the month of market
value sampling.
Design/methodology/approach – The paper examines two components of value relevance,
coincident relevance and forecast relevance, which the paper develops on the basis of the Ohlson
model. The paper measures value relevance by estimating separate panel-data regressions for each of
the 12 months around ?scal year-end. The sample consists of companies listed in two continental
European countries, France and Germany, over the 1989-2008 period.
Findings – In both country panels, the paper ?nds that overall value relevance is higher when market
value is sampled before or close to ?scal year-end, but incremental value relevance varies
between domestic and International Financial Reporting (IFRS) accounting standards. Regression
results reveal signi?cant variations in coef?cients over the following months of market value in
French panel and its IFRS sub-sample only.
Research limitations/implications – The scope of the study is limited to the average value
relevance parameters of companies listed on stock exchanges in France and Germany. Future research
may be devoted to other countries and study additional determinants of value relevance.
Practical implications – The study shows that the selection of the month of market value sampling
can have signi?cant impact on value relevance regression results. Therefore, sensitivity analysis
needs to be included in research studies which rely on the value relevance approach.
Originality/value – The paper contributes the ?rst systematic analysis of the variation in value
relevance parameters in response to the selection of the month in which market value is sampled.
Keywords Value relevance, Accounting-based valuation, Panel regression, Residual income model
Paper type Research paper
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1030-9616.htm
The authors would like to acknowledge the helpful comments of Katerina Hellstro¨m, Ian Kwan,
Jeroen van Raak and the participants of the 2010 Annual Congress of the Association
Francophone de Comptabilite´, the Global Finance Conference in 2010, the 2011 FindEcon
Conference and the 2011 Annual Congress of the European Accounting Association. On the early
stages of inventing the concept of coincident and forecast relevance, the authors published
(under different titles) two papers in post-conference materials only. It was after the 2010 Annual
Congress of the Association Francophone de Comptabilite´ (Valuation Effects of Accounting
Information Availability) and FindEcon’2011 Conference (Divergent Patterns of Value
Relevance).
Accounting Research Journal
Vol. 26 No. 3, 2013
pp. 239-255
qEmerald Group Publishing Limited
1030-9616
DOI 10.1108/ARJ-09-2012-0076
Coincident and
forecast
relevance
239
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1. Introduction
The relevance of ?nancial statement information for the valuation of corporate equity
in ?nancial markets is one of the core research problems in accounting. The bulk of this
literature focuses on the properties of accounting numbers (Barton et al., 2010; Habib,
2010) or the properties of the reporting corporations and their information environment
(Aharony et al., 2010; Iyengar et al., 2010). The purpose of this paper is to look at the
value relevance question from a different angle and examine the methods of measuring
market value rather than the properties of accounting numbers. To this end we study
how Ohlson (1995) valuation model parameters change when market value is sampled
in different months around a ?scal year-end. We run a series of panel regressions on
samples of French and German stock-listed companies, changing the month of market
valuation while keeping annual accounting numbers constant, then we test for
differences in parameter estimates across monthly regressions and between country
samples. The results of our study have implications for the selection of the month for
market value measurement in international comparative studies.
Extant research provides little insight into the selection of the date for market value
sampling even though a number of alternative approaches are present in the literature.
In the ?rst wave of comparative value relevance studies, the authors sample market
value three months (Alford et al., 1993) or six months (Harris et al., 1994; Joos and Lang,
1994) after ?scal year-end. In the second wave of widely cited studies, which
introduced panel data regressions to accounting research, market value is usually
sampled at ?scal year-end (Arce and Mora, 2002; King and Langli, 1998). In the recent
studies, motivated by the worldwide adoption of the International Financial Reporting
Standards (IFRS), researchers tend to sample market value three months after ?scal
year-end (Devalle et al., 2010; Sahut et al., 2011; Lin et al., 2012), or even in later months
(Aharony et al., 2010; Clarkson et al., 2011).
Only a handful of value relevance papers include a discussion of the impact the
selection of the month in which market value is sampled has on regression results.
Hellstro¨m (2006) uses market prices from the end of March, but carries out sensitivity
analyses for December and June dates. Filip and Raffournier (2010), who use the
returns model, argue that in an inef?cient market accounting numbers are priced with
a lag. They report the results for returns measured over two different windows: over
the 12 months of the ?scal year and over 18 months starting at the beginning of the
?scal year. A different approach to the issue of market value sampling was taken by
Aboody et al. (2002), who use stock prices measured with a lead of one to three years
and then de?ate them by a proxy for realized systematic risk. The reasoning behind
this procedure is similar: the market reacts to earnings announcements with an error,
but this error is resolved with time.
This study contributes a systematic analysis of the impact of the month of market
value sampling on the results of comparative value relevance studies in the theoretical
and empirical aspect. First, we build on the Ohlson (1995) model to construct the
notions of coincident relevance and forecast relevance. Coincident relevance refers to
the association between accounting numbers and market value during the ?scal
year, that is, before the accounting numbers are published. Forecast relevance refers
to the association between accounting numbers and market value in the period after
the accounting numbers are published. Second, we provide empirical evidence of the
relative strength of the two elements of the value relevance relationship by regressing
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accounting numbers for ?scal year ended on the 31st of December of year t on market
value sampled in each of the months between July of year t and June of year t þ 1.
The study is set in the context of the continental accounting model. We study value
relevance of accounting numbers of companies listed in two European continental
countries, France and Germany, whose economies have a signi?cant impact on
international ?nancial markets. The two countries in our sample offer the bene?t of
economic and institutional proximity, which makes the comparison of results
meaningful. Over the two decades of the sample period, from 1989 to 2008, the two
countries have experienced strong economic integration, which limits the number of
uncontrolled material variables that could affect model parameters. The two countries
are highly correlated in terms of gross domestic product, interest rates and cost of
equity capital, the stock markets are of a comparable size and liquidity, and both
countries are subject to similar freedom of capital movement regulations as members
of the European Union. Both national ?nancial systems feature continental
characteristics: they put less weight on shareholders’ information needs and more
weight on the needs of creditors and tax authorities. In France, accounting is
characterized by the use of a standard chart of accounts (Delvaille et al., 2005). In
Germany, the same principles of accounting are used for reporting and for tax
purposes, and a liberal use of reserves is permitted in order to smooth earnings and
maintain dividend payout ratios at a stable level (Goldberg and Godwin, 2002).
Finally, this study takes into account the present research interest in the effects of
the mandatory adoption of the IFRS for the functioning of capital markets. While the
number of studies devoted to this topic is considerable and still growing, the results
are mixed (Devalle et al., 2010). Our results indicate that one reason for mixed results is
the selection of the month of market value sampling. In the two countries studied here,
the IFRS have been mandatory for consolidated ?nancial statements since 2005, but
local GAAP statements are mandatory for single entities (Mac? ´as and Muin˜o, 2011).
Before the adoption of IFRS, local accounting systems in both countries were highly
developed and contained a large number of detailed provisions divergent from IFRS
(Ding et al., 2006), which had an impact on the selection of options after IFRS adoption
(Haller and Wehrfritz, 2013).
2. Hypothesis development
This paper extends the analysis of value relevance by examining how the relationship
between accounting numbers and market value varies depending on the date when
market value is sampled, relative to ?scal year-end. We introduce the terms coincident
and forecast relevance to distinguish between the two research hypotheses. We de?ne
coincident relevance as the statistical relationship between accounting numbers for
the year and market value before the end of the reporting year. It represents the
interpretation of value relevance as the ability of accounting numbers to capture value
relevant information, which is connected with the correlation hypothesis (Francis and
Schipper, 1999). In contrast, we de?ne forecast relevance as the statistical relationship
between accounting numbers for the year and market value after their publication.
It represents the usefulness of accounting numbers as inputs to valuation methods and
as a basis for forming expectations by investors (Holthausen and Watts, 2001).
To develop the notions of coincident and forecast relevance we begin with a
simpli?ed setting. Assume that there exists a ?rm which closes its accounting books
Coincident and
forecast
relevance
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on the 31st of December each year and makes an immediate disclosure of the annual
?nancial statement. Further, the ?rm ful?lls the assumptions of the Ohlson model, so
its equity can be reliably valued with that model. The Ohlson (1995) model is an
extension of the residual income valuation model. The model allows market value to be
expressed in terms of coincident accounting numbers, because expectations of future
residual income are modeled using linear information dynamics. The model takes the
following form:
MV
t
¼ BV
t
þa
1
RI
t
þ a
2
v
t
;
where a
1
¼
v
1 þ r
e
2v
; a
2
¼
1 þ r
e
ð1 þ r
e
2vÞð1 þ r
e
2gÞ
ð1Þ
According to the model, when the ?rm discloses its accounting numbers for year t, the
market value of its equity at the end-of-year (MV
t
) is expected to adjust to the Ohlson
model value determined by its end-of-year book value (BV
t
), residual income over the
last ?scal year (RI
t
) and current non-accounting information on next year income (v
t
).
The parameters of the model depend on the autoregressive characteristics of residual
income (0 , v , 1) and of the non-accounting information variable (0 , g , 1), as
well as the cost of capital (r
e
). The Ohlson model remains the core theoretical
foundation for value relevance studies because it provides a direct link between
accounting numbers and market value of equity. Empirical tests of the model show
that it performs as well as alternative models (Dechow et al., 1999; Francis et al., 2000).
However, the other information variable can be omitted without a reduction in the
power of the model (Isidro et al., 2006).
In the context of our study it is important to note that in the Ohlson model both the
market value MV
t
and the accounting information variables (BV
t
, and RI
t
) are sampled
at the same moment in time. That moment is exactly the end of the reporting year: the
date when all value relevant information included in annual accounting numbers is
already known and discounted in market values. In reality, ?nancial statements are
published with a reporting lag of at least two or three months into the next reporting
year. Hence, at the time of publication, market values already re?ect new information
?ows into the market, which are not re?ected in accounting numbers. This observation
is the starting point for the development of our hypotheses about coincidence and
forecast relevance.
Let us now consider the valuation of the ?rm’s equity immediately before the
publication of its ?nancial statements, at time t 2 t, where t represents a fraction of a
year corresponding to the number of months to ?scal year-end (e.g. 0/12 for December,
6/12 for July). We refer to the statistical relationship between the annual accounting
numbers and market value calculated at time t 2 t as coincident relevance. If
coincident relevance is high, that would imply that in month t 2 t the market prices
the ?rm’s equity at a value close to the end-of-year Ohlson model value, even though
the accounting numbers are not yet known[1]. This is possible if investors predict
accounting numbers with enough precision, or if accounting numbers re?ect known
economic factors relevant to valuation.
Now, we turn to the period after accounting numbers are published to consider the
second effect, forecast relevance. After the publication of annual accounting numbers,
investors may use published accounting numbers as inputs to the residual income
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valuation model (1) at time t þ t and adjust their portfolios. As the reduced form of the
model stems directly from the autoregressive structure of future residual income, the
last year ?nancial data are value relevant as long as they allow investors to predict
future bene?ts from holding the ?rm’s equity. On the other hand, accounting numbers
contain only information available up to ?scal year-end, so the valuation model does
not re?ect new information, revealed after the ?scal year-end. As the year progresses,
the news will keep accumulating, thus decreasing the strength of forecast relevance.
Note, that the lag between ?scal year-end and the publication of annual ?nancial
statements introduces an interim period for which we cannot make clear predictions.
During this period accounting numbers are not available yet, but news concerning the
new ?scal year begin to accrue in market values. The way they accumulate in market
values may depend on the information environment of both country stock markets
(Christensen and Demski, 2003). For clarity of presentation in the empirical section we
refer to the entire period after ?scal year-end as forecast relevance.
3. Research design
The main focus of our study is to examine the variation in coincident and forecast
relevance of accounting numbers as a function of the month in which market values are
sampled. To this end, we perform separate regressions of annual accounting ?gures on
the average market value of equity measured in each of six months in the last part of a
?scal year from July to December (m ¼ 7,8, . . . , 12), and then in each month of the ?rst
six months of a new ?scal year from January to June (m ¼ 1,2, . . . , 6)[2]. Separate
regressions of the following type are run for each month of the year:
MV
i;t
m
¼ a
i:
þ a
:t
þ b
1
BV
i;t
þ b
2
RI
i;t
þ u
i;t
t
m
¼ t 2ð12 2mÞ=12 for m ¼ 7; 8; . . . ; 12
t
m
¼ t þ m=12 for m ¼ 1; 2; . . . ; 6
ð2Þ
where parameters a
i.
(i ¼ 1, . . . , N) denote individual effects (constant over time), and
a.
t
(t ¼ 1, . . . , T) represent time effects (common for all ?rms in a given period).
Variables u
it
denote idiosyncratic disturbances with zero-mean, which are uncorrelated
with the explanatory variables but possibly correlated in time and heteroskedastic.
We use the panel regression framework to exploit the bene?ts of full sample
information. Since samples of ?rm-year data are usually strongly unbalanced, one
cannot run separate time-series regressions for each company (Kothari and Shanken,
2003). Note that parameters of model (1) standing at residual income and
non-accounting information variable vary between individual companies because of
?rm-speci?c autoregressive coef?cients and risk-adjusted discount rates. However,
in the panel regressions, we treat all coef?cients in model (1) as homogeneous in
the cross-section to gain ef?ciency[3]. We also include ?rm and time ?xed effects
to minimize the risk of estimation bias[4]. This approach allows us to interpret
the common coef?cients from panel regressions as the estimates of the average value
of the individual (?rm-speci?c) coef?cients. The standard errors of the estimates,
which are corrected for heteroskedasticity and autocorrelation with a Newey-West
method (Wooldridge, 2007), indicate the degree of coef?cient heterogeneity across
the sample[5].
Coincident and
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Since the objective of this study is to analyze the value relevance of book value and
earnings through the variability of their respective regression coef?cients, we need to
apply statistical tests. We use the within R
2
statistic, which is a measure of the part of
temporal variability of the explained variable (market value) within individual ?rms
explained by the explanatory variables (accounting numbers), to compare overall value
relevance across monthly regressions, but following the arguments of Gu (2007) we do
not use it for comparisons across samples. We test for differences between coef?cients
by applying the Wald test for each monthly regression in relation to the December
regression. To examine if the differences between two country samples are signi?cant
we calculate the Wald statistic for common coef?cients in the two country samples for
each month of market value sampling.
To make the comparison of value relevance across countries meaningful we control
for a number of sample-speci?c factors. We eliminate the impact of unobservable
characteristics using ?rm- and time-speci?c variables in a two-way error component
model. We use the ?xed effects estimator[6] which allows us to treat those
unobservable effects as possibly correlated with accounting numbers. This reduces the
impact of variables that vary in the cross-section, such as size of industry sector, which
we include in robustness tests but not in the main results because their impact is
immaterial. However, we present results for sub-samples limited to companies
reporting in accordance with the IFRS. We do so for two reasons. First, we set this
study in the stream of recent research devoted to the effects of IFRS adoption. Second,
the results in the IFRS sub-samples are in fact signi?cantly different from those
observed in the full samples.
4. Sample composition
We analyze the relationship between accounting numbers and market values of
companies listed at the Paris Stock Exchange (Euronext Paris) in France (907 ?rms in
total) and Deutsche Boerse in Germany (940 ?rms) from January 1989 until December
2008. The explained variable is the market value of equity calculated as the number of
common outstanding shares times the monthly average of stock price. The daily
quotes come from the Compustat Global Security Daily Data Set. The sample starts at
1989 because of data availability and ends in 2008 before the full outset of the recent
?nancial crisis. Market values for each of the last six months of a ?scal year and the
?rst six months of the following year are separately regressed on the annual ?nancial
statement ?gures, which are obtained from Compustat Global Fundamentals Annual
Database supplied by Wharton Research Data Services.
Table I shows the sample selection process in terms of ?rm-year observations
dropped in each step. To facilitate our analysis, we selected ?rms with the same ?scal
year-end, 31st of December. Further reductions in the sample size are caused by the use
of lagged book values for calculating residual income[7] or lagged earnings for the
months after the ?scal year-end. The other sources criteria of sample selection are the
exclusion of ?rms from the ?nancial sector, of ?rms reporting negative book values,
?rms quoted fewer than ten times in a given month, ?rms with fewer than 36 monthly
quotes, and ?rms reporting in accordance with an accounting standard other than local
domestic or the IFRS. The last row of Table I shows the composition of the ?nal data
set for market values sampled in December. The data sets vary in size because of
market data availability for speci?c months from 3,580 (in May) to 4,216 (in December)
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?rm-year observations for France and from 4,087 (in February and April) to 4,670
(in January) ?rm-year observations for Germany.
Table II contains descriptive statistics of annual accounting data and market values
from December in full samples and in sub-samples of companies reporting according to
the IFRS. Tests for the equality of means show that companies in the two country
samples are similar in terms of average book value, residual income and market value.
There are however signi?cant differences between ?rms reporting according to the
IFRS and ?rms reporting according to local standards. Companies reporting according
France (889 ?rms) Germany (927 ?rms)
Number of
observations
In % of full
sample
Number of
observations
In % of full
sample
Full sample (Compustat 1989-2008) 6,922 100 7,666 100
þ Fiscal-year end in December 5,535 80 6,298 82
þ Non-?nancial sector 5,514 80 6,213 81
þ Non-negative book value 5,327 77 5,982 78
þ With market quotations in a
given month (December here) 5,065 73 5,779 75
þ Starting year for calculating
residual income 4,386 63 5,083 66
þ Accounting standards (local
domestic DS þ international DI) 4,216 61 4,637 60
Table I.
Cumulative sample
attrition in terms of
?rm-year observations
Variables MV BV RI MV BV RI
Descriptive
statistics
France: 4,216 ?rm-year observations Germany: 4,637 ?rm-year obs.
Mean 1,428.46 697.56 24.71 1,232.15 664.63 13.11
t-test (France
vs Germany)
– – – 1.56 0.55 2 1.82
*
Standard
deviation
6,683.83 2,801.25 604.65 5,138.80 2,773.98 271.40
International accounting standards IFRS only (DI)
Descriptive
statistics
France: 1,373 obs. Germany: 2,270 obs.
Mean 2,278.46 1,246.24 30.76 1,572.86 900.22 22.32
t-test (France
vs Germany)
– – – 2.92
* * *
2.74
* * *
0.76
Standard
deviation
229.96 105.07 10.06 126.51 74.96 6.11
t-test
(IFRS vs local
accounting
standards)
5.76
* * *
8.92
* * *
2.65
* * *
4.43
* * *
5.68
* * *
2.26
* *
Notes: p-value of a Student test is lower than
*
10,
* *
5 and
* * *
1 percent; variable codes: MV stands
for average market value in December of each ?scal year calculated as the average of daily market
values, BV stands for book value of shareholders equity, RI stands for residual income, t-test is a
standard t-Student statistics for equal means between sub-samples (i.e. between countries or
accounting standards)
Table II.
Descriptive statistics
by countries and
accounting standards in
millions of EUR
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1
:
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8
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4
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a
n
u
a
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2
0
1
6
(
P
T
)
to the IFRS are larger on average than those following local domestic accounting
standards. While a relatively larger proportion of companies ?le IFRS reports in
Germany (40 percent) than in France (30 percent), IFRS adopters in France are about
40 percent larger (in terms of MV or BV) than in Germany.
5. Empirical results
Estimation results for the two country samples (Table III) show that the model
explains between 39 and 61 percent of the within-?rm variance in the French sample
and between 45 and 75 percent in the German sample, depending on the month in
which market value is sampled (Figure 1). In the French sample, the highest value of
the R
2
, 61 percent, is observed in the January regression, and the lowest, 39 percent, in
the March regression. With the exception of January, overall value relevance is higher
before ?scal year-end than after, which indicates coincident relevance is stronger than
forecast relevance. In the German sample, the difference between coincident and
forecast relevance is clearer. The R
2
is above 70 percent in the regressions where
market value is sampled in August, September or October before ?scal year-end, which
is an indication of high coincident relevance. The R
2
decreases in November and
December regressions, then continues to decline to a low of 45 percent in the March
regression, which shows that forecast relevance is weaker.
The sources of differences in overall value relevance of accounting data can be
explained by the variation in coef?cients standing at book values and residual income
(Figure 2). In the French sample, the estimated coef?cients at book value tend to
increase around ?scal year-end with the maximum of 1.6 in January and the minimum
of 1.3 in June (the upper section of Table III). The book value coef?cients in other
monthly regressions are relatively stable, with values ranging from 1.4 to 1.5. Book
value variables are statistically signi?cant across the monthly regressions, while the
residual income coef?cients are statistically signi?cant only in those regressions where
market value is measured after ?scal year-end. When we consider the regression
coef?cients at residual income and if we focus only on these regressions where the
income variable is statistically signi?cant, we observe a growth from 0.4, in the ?rst
month of the ?scal year, up to 0.7 in the ?fth and the sixth month. The Wald test
con?rms there are signi?cant differences in coef?cients at book value across the year,
while signi?cant differences in the residual income coef?cients are found only for the
July and October regressions as compared to the December regression. When both
coef?cients are tested jointly, signi?cant differences are found in all months except for
March and June.
In the German sample, the book value coef?cients increase till December of the
?scal year to the value of 1.6, then they drop in January and later remain at a relatively
stable level of 1.5 until June (the lower section of Table III). In contrast, the residual
income coef?cients decrease steadily towards ?scal year-end from the maximum of 3.7
in the July regression, then they continue to decrease with the minimum value of 0.8 in
the February and March regressions, after which the values of coef?cients increase
again. The residual income variable is statistically signi?cant only in regressions for
the months before a ?scal year-end, from July till November, whereas the book value
variable is statistically signi?cant in all regressions across the months. When we limit
the analysis to the regressions where the residual income variable is statistically
signi?cant, the values of coef?cients exhibit a falling trend from 3.7 in July before ?scal
ARJ
26,3
246
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e
v
a
r
i
a
b
l
e
t
e
s
t
(
t
e
s
t
R
I
o
r
t
e
s
t
B
V
)
Table III.
Estimation results of
model (2) for ?rms with
local domestic and IFRS
accounting standards,
and non-negative BV
Coincident and
forecast
relevance
247
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
1
8
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
year-end, to 2.2 in November of the same year. The Wald test shows, however, that
parameters at residual income are not statistically different across the months around
?scal year-end as compared to the December regression, with the exception of the June
regression.
Results for the IFRS sub-samples, that is samples limited to ?rms reporting in
accordance with the IFRS, are distinct from the results for the full samples. Overall
value relevance, measured by R
2
, resembles the patterns found in the full sample
regressions (Figure 3). In the French IFRS sub-sample, the R
2
is lower than in the full
sample, with values ranging from 27 to 50 percent. The highest value is still reported in
the January regression, while the lowest is reported in the June regression. On the
average, coincident relevance is slightly stronger than forecast relevance, but the
difference is less pronounced than in the full sample. In the German IFRS sub-sample,
the R
2
statistics are lower as well, but the difference between coincident and forecast
relevance remains clear. The R
2
reported in regressions from July to December range
between 47 and 53 percent, while in regressions from January to June the values range
from 36 to 43 percent.
The coef?cients at book value and residual income also diverge from the ones found
in the full sample regressions (Table IV). In the French IFRS sub-sample, presented in
the upper section of Table IV, the residual income coef?cients increase towards the
?scal year-end, from 0.4 in July to 2.2 in December, but the variable is statistically
signi?cant only in the regressions from October until December. The coef?cients at
residual income tend to decrease to negative values after ?scal year-end, when they are
not statistically different from zero. The book value variable is signi?cant throughout
the year, but the regression coef?cients show more variation than in the full sample.
The coef?cient values are about 1.2 before ?scal year-end, then drop steadily to 0.8
after ?scal year-end. The Wald test shows the differences between residual income
coef?cients are statistically signi?cant in months from April till June after ?scal-year
end, while the test for the book value coef?cient shows signi?cant differences in all
Figure 1.
Comparison of within
R
2
by month of market
value sampling
Jul. Aug. Sept. Oct. Nov. Dec. Jan. Feb. Mar. Apr. May Jun.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
France: RSQ Germany: RSQ
Month of market value sampling
W
i
t
h
i
n
R
-
s
q
u
a
r
e
d
Note: Correlation is measured with within R
2
obtained in
equation (2)
ARJ
26,3
248
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
1
8
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
months except July through September. The joint test for the two coef?cients shows
signi?cant differences in all months except September, November and February.
In the German IFRS sub-sample, presented in the lower section of Table IV, we ?nd
residual income variable is statistically signi?cant in all the monthly regressions. The
coef?cient values ?uctuate from a low of 1.8 in the July regression, through a local
maximum of 3 in October, November and December, then they decrease to 2.6 in the
January and February regressions, and increase again in March to remain at a level of
about 3 in later months. The book value variable is also statistically signi?cant and the
coef?cient values range from 0.8 after ?scal year-end to 1.9 in the October and
November regressions. The Wald test does not indicate statistically signi?cant
differences between the coef?cient estimates, with the exception of two cases.
Finally, we compare the coef?cient estimates between the two country samples by
performing the Wald test. In the full sample estimations (Table III), results show that
Figure 2.
Comparison of regression
coef?cients for residual
income (RI) and book
value (BV) by month of
market value sampling
Jul. Aug. Sept. Oct. Nov. Dec. Jan. Feb. Mar. Apr. May Jun.
0
0.5
1
1.5
2
2.5
3
3.5
4
France: RI Germany: RI
Month of market value sampling
R
e
s
i
d
u
a
l
I
n
c
o
m
e
C
o
e
f
f
i
c
i
e
n
t
Jul. Aug. Sept. Oct. Nov. Dec. Jan. Feb. Mar. Apr. May Jun.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
France: BV Germany: BV
Month of market value sampling
B
o
o
k
V
a
l
u
e
C
o
e
f
f
i
c
i
e
n
t
Coincident and
forecast
relevance
249
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
1
8
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
a signi?cant difference exists in the October, November and June regressions. The ?rst
two monthly regressions show residual income coef?cients of 0.5-0.6 for French sample
(insigni?cant) and 2.2-2.9 for the German sample (signi?cant). The book value
coef?cients are 1.4 for the French sample, and 1.6 for the German sample (signi?cant in
all cases). In the June regression, the residual income coef?cients are 0.7 and 2.5,
respectively, for the French and German samples, while the book value coef?cients are
1.3 and 1.5 (signi?cant in all cases).
The results of the cross-country comparison for the IFRS sub-sample diverge from
the full sample ones. The Wald statistic is signi?cant in all regressions where market
value is sampled after ?scal year-end, while there are no statistically signi?cant
differences between the coef?cients when market value is sampled before ?scal
year-end. After ?scal year-end, the residual income coef?cients are lowand insigni?cant
in the French IFRS sub-sample, while inthe GermanIFRS sub-sample theyare as highas
3 and signi?cant. The book value coef?cients range from 0.8 to 1.1 in the French IFRS
sub-sample and from 0.8 to 0.9 in the German IFRS sub-sample (signi?cant in all cases).
The differences between coef?cients are not signi?cant in the regressions where the
highest and signi?cant values are found in the French IFRS sub-sample, because these
values are closer to the results found in the German IFRS sub-sample.
The results presented in Tables III and IV are robust to alternative model
speci?cations and the inclusion of control variables (Ruland et al., 2007). For simplicity
of exposition we do not tabulate the results of robustness checks. First, we introduce
limited heterogeneity in the coef?cients by including variables for industry sector and
?rm size, and their interactions with residual income and book value. Although some of
the control variables are signi?cant, these changes do not affect the Wald test results.
Second, we exclude ?rms reporting an accounting loss, which causes an increase of the
residual income coef?cient in the German sample. As a result, the Wald test for the
cross-country comparison returns a signi?cant value in all months before ?scal
Figure 3.
Comparison of within
R
2
by month of market
value sampling in IFRS
sub-samples
0
0.1
0.2
0.3
0.4
0.5
0.6
Jul. Sept. Nov. Jan. Mar. May
W
i
t
h
i
n
R
-
s
q
u
a
r
e
d
Month of market value sampling
France: RSQ Germany: RSQ
Note: Correlation is measured with within R
2
obtained in
equation (2)
ARJ
26,3
250
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
1
8
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
B
e
f
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s
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e
a
r
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n
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1
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3
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3
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2
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2
9
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1
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2
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5
N
_
g
3
6
7
3
6
3
3
6
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3
6
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3
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3
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3
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t
(
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0
:
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N
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g
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3
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Table IV.
Estimation results of
model (2) for ?rms with
IFRS accounting
standards and
non-negative BV
Coincident and
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251
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year-end, except for December. Third, we use full accounting income instead of residual
income in the regressions. This again causes changes in the German sample, where the
coef?cients at income become high and signi?cant not only before, but also after ?scal
year-end. The results of the Wald test indicate a signi?cant differences between the two
country samples exist in the July, August and October regressions.
6. Conclusions
The objective of this study is to assess the sensitivity of value relevance regression
results to the month in which market value is sampled. We ?nd signi?cant variation in
overall value relevance and in the incremental value relevance of residual income and
book value. The R
2
varies by up to 75 percent depending on the month of market value
sampling. The highest degree of coef?cient variation is present in the residual income
coef?cients, where variations of 50 percent are not uncommon. The book value
coef?cients are more stable, but exhibit signi?cant variations over the months as well.
Out of the two country samples, we ?nd the variations are greater in the French sample
than in the German sample.
We attribute the variations in coef?cients to the notions of coincident and forecast
relevance which we de?ne in the paper. Results indicate that coincident relevance is
stronger than forecast relevance, because the R
2
is generally greater in the regressions
where market value is sampled before ?scal year-end. However, the incremental
relevance of residual income depends on the country of listing and the accounting
standard. We ?nd that residual income has greater impact on forecast relevance in the
French sample, while in the German sample it affects coincident relevance. When we
limit the sample to IFRS-reporting companies, results point to coincident relevance of
residual income and book value in both country samples, although in the German
sample residual income is also forecast relevant.
The results of our study indicate the need for sensitivity testing in international
comparative studies. When we compare coef?cients between the two country samples,
we ?nd the results of the test depend on the month of market value sampling. In the full
sample regressions, we ?nd signi?cant differences in coef?cients between the two
country samples if market value is sampled from one to two months before ?scal
year-end, or six months after ?scal year-end. In the IFRS sub-sample regressions we
?nd signi?cant differences between the two country samples if market value is
sampled from one to six months after ?scal year-end. Thus, our results show that the
choice of the month determines the results of cross-country comparisons.
Results presented in this paper raise a number of interesting questions and offer
possible extensions concerning the variation in the relative strength of coincident and
forecast relevance. First of all, future studies may examine companies listed in
countries representative of other accounting and ?nancial market models than France
and Germany. Second, future research may be directed at ?nding the determinants of
changes in the relative strength of coincident and forecast relevance, such as the
adoption of IFRS, which is described in this study. These determinants may be found
in the changes of regulation, changes of market institutions and of the information
environment. Finally, the relative strength of coincident and forecast relevance
may vary with factors other than the country of listing or the accounting standard.
Further research is needed to identify these factors and determine whether they affect
inferences from comparative value relevance studies.
ARJ
26,3
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Notes
1. To be precise, under value relevance and time value of money hypotheses it is the forward
(for t 2 t) or backward (for t þ t) discounted market value that would be correlated with the
residual income valuation. Because the cost of capital for up to 6 months at rates prevailing
in the market is small, we remove the discount factor for simplicity.
2. The sample is limited to companies that report on the 31st of December each year.
3. While this approach does not allow for full variation of parameters, it is ef?cient, and it is
more robust to misspeci?cation problems than separate cross-sectional regressions.
4. Ignoring ?rm-speci?c effects as in pooled OLS regression approach or applying
Fama-MacBeth procedure may also lead to a downward bias in standard errors as
discussed by Petersen (2009).
5. Heteroskedasticity in idiosyncratic disturbances is possibly a result of using pooled
regression parameters, unscaled market values and accounting numbers, or it also may be
an effect of omitted explanatory variables. Autocorrelation may stem from omitting
non-accounting information variable (v
t
) from equation (2), which is autoregressive by
construction.
6. The Hausman test indicates that the ?xed effects model is preferable over the random effects
model.
7. Initially, we estimated residual income for each ?rm using the one-factor market model.
However, results remained unaltered when we used constant rate of cost of capital between
7 and 11 percent, which led us to adopt a single rate (9 percent) across the sample.
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About the authors
Karol Marek Klimczak is an Assistant Professor of ?nance, a member of the European
Accounting Association. His research interests include the role of accounting information in
market pricing and risk-based management control systems. Karol Marek Klimczak is the
corresponding author and can be contacted at: [email protected]
Grzegorz Szafranski is an Assistant Professor in the Chair of Econometrics, and he is a
Co-Editor of FindEcon Monograph. His empirical research is focused on ?nancial econometrics
and macroeconometrics.
Coincident and
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255
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doc_483598832.pdf
Value relevance studies, in particular international comparative studies, use market
values sampled at different dates relative to the fiscal year-end. This paper aims to contribute a
theoretical and empirical analysis of the relationship between value relevance and the month of market
value sampling.
Accounting Research Journal
Coincident and forecast relevance of accounting numbers
Karol Marek Klimczak Grzegorz Szafranski
Article information:
To cite this document:
Karol Marek Klimczak Grzegorz Szafranski , (2013),"Coincident and forecast relevance of accounting
numbers", Accounting Research J ournal, Vol. 26 Iss 3 pp. 239 - 255
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Coincident and forecast relevance
of accounting numbers
Karol Marek Klimczak
Department of Finance, Kozminski University,
Warsaw, Poland, and
Grzegorz Szafranski
Department of Econometrics, Faculty of Economics and Sociology,
University of Lodz, Lodz, Poland
Abstract
Purpose – Value relevance studies, in particular international comparative studies, use market
values sampled at different dates relative to the ?scal year-end. This paper aims to contribute a
theoretical and empirical analysis of the relationship between value relevance and the month of market
value sampling.
Design/methodology/approach – The paper examines two components of value relevance,
coincident relevance and forecast relevance, which the paper develops on the basis of the Ohlson
model. The paper measures value relevance by estimating separate panel-data regressions for each of
the 12 months around ?scal year-end. The sample consists of companies listed in two continental
European countries, France and Germany, over the 1989-2008 period.
Findings – In both country panels, the paper ?nds that overall value relevance is higher when market
value is sampled before or close to ?scal year-end, but incremental value relevance varies
between domestic and International Financial Reporting (IFRS) accounting standards. Regression
results reveal signi?cant variations in coef?cients over the following months of market value in
French panel and its IFRS sub-sample only.
Research limitations/implications – The scope of the study is limited to the average value
relevance parameters of companies listed on stock exchanges in France and Germany. Future research
may be devoted to other countries and study additional determinants of value relevance.
Practical implications – The study shows that the selection of the month of market value sampling
can have signi?cant impact on value relevance regression results. Therefore, sensitivity analysis
needs to be included in research studies which rely on the value relevance approach.
Originality/value – The paper contributes the ?rst systematic analysis of the variation in value
relevance parameters in response to the selection of the month in which market value is sampled.
Keywords Value relevance, Accounting-based valuation, Panel regression, Residual income model
Paper type Research paper
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1030-9616.htm
The authors would like to acknowledge the helpful comments of Katerina Hellstro¨m, Ian Kwan,
Jeroen van Raak and the participants of the 2010 Annual Congress of the Association
Francophone de Comptabilite´, the Global Finance Conference in 2010, the 2011 FindEcon
Conference and the 2011 Annual Congress of the European Accounting Association. On the early
stages of inventing the concept of coincident and forecast relevance, the authors published
(under different titles) two papers in post-conference materials only. It was after the 2010 Annual
Congress of the Association Francophone de Comptabilite´ (Valuation Effects of Accounting
Information Availability) and FindEcon’2011 Conference (Divergent Patterns of Value
Relevance).
Accounting Research Journal
Vol. 26 No. 3, 2013
pp. 239-255
qEmerald Group Publishing Limited
1030-9616
DOI 10.1108/ARJ-09-2012-0076
Coincident and
forecast
relevance
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1. Introduction
The relevance of ?nancial statement information for the valuation of corporate equity
in ?nancial markets is one of the core research problems in accounting. The bulk of this
literature focuses on the properties of accounting numbers (Barton et al., 2010; Habib,
2010) or the properties of the reporting corporations and their information environment
(Aharony et al., 2010; Iyengar et al., 2010). The purpose of this paper is to look at the
value relevance question from a different angle and examine the methods of measuring
market value rather than the properties of accounting numbers. To this end we study
how Ohlson (1995) valuation model parameters change when market value is sampled
in different months around a ?scal year-end. We run a series of panel regressions on
samples of French and German stock-listed companies, changing the month of market
valuation while keeping annual accounting numbers constant, then we test for
differences in parameter estimates across monthly regressions and between country
samples. The results of our study have implications for the selection of the month for
market value measurement in international comparative studies.
Extant research provides little insight into the selection of the date for market value
sampling even though a number of alternative approaches are present in the literature.
In the ?rst wave of comparative value relevance studies, the authors sample market
value three months (Alford et al., 1993) or six months (Harris et al., 1994; Joos and Lang,
1994) after ?scal year-end. In the second wave of widely cited studies, which
introduced panel data regressions to accounting research, market value is usually
sampled at ?scal year-end (Arce and Mora, 2002; King and Langli, 1998). In the recent
studies, motivated by the worldwide adoption of the International Financial Reporting
Standards (IFRS), researchers tend to sample market value three months after ?scal
year-end (Devalle et al., 2010; Sahut et al., 2011; Lin et al., 2012), or even in later months
(Aharony et al., 2010; Clarkson et al., 2011).
Only a handful of value relevance papers include a discussion of the impact the
selection of the month in which market value is sampled has on regression results.
Hellstro¨m (2006) uses market prices from the end of March, but carries out sensitivity
analyses for December and June dates. Filip and Raffournier (2010), who use the
returns model, argue that in an inef?cient market accounting numbers are priced with
a lag. They report the results for returns measured over two different windows: over
the 12 months of the ?scal year and over 18 months starting at the beginning of the
?scal year. A different approach to the issue of market value sampling was taken by
Aboody et al. (2002), who use stock prices measured with a lead of one to three years
and then de?ate them by a proxy for realized systematic risk. The reasoning behind
this procedure is similar: the market reacts to earnings announcements with an error,
but this error is resolved with time.
This study contributes a systematic analysis of the impact of the month of market
value sampling on the results of comparative value relevance studies in the theoretical
and empirical aspect. First, we build on the Ohlson (1995) model to construct the
notions of coincident relevance and forecast relevance. Coincident relevance refers to
the association between accounting numbers and market value during the ?scal
year, that is, before the accounting numbers are published. Forecast relevance refers
to the association between accounting numbers and market value in the period after
the accounting numbers are published. Second, we provide empirical evidence of the
relative strength of the two elements of the value relevance relationship by regressing
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accounting numbers for ?scal year ended on the 31st of December of year t on market
value sampled in each of the months between July of year t and June of year t þ 1.
The study is set in the context of the continental accounting model. We study value
relevance of accounting numbers of companies listed in two European continental
countries, France and Germany, whose economies have a signi?cant impact on
international ?nancial markets. The two countries in our sample offer the bene?t of
economic and institutional proximity, which makes the comparison of results
meaningful. Over the two decades of the sample period, from 1989 to 2008, the two
countries have experienced strong economic integration, which limits the number of
uncontrolled material variables that could affect model parameters. The two countries
are highly correlated in terms of gross domestic product, interest rates and cost of
equity capital, the stock markets are of a comparable size and liquidity, and both
countries are subject to similar freedom of capital movement regulations as members
of the European Union. Both national ?nancial systems feature continental
characteristics: they put less weight on shareholders’ information needs and more
weight on the needs of creditors and tax authorities. In France, accounting is
characterized by the use of a standard chart of accounts (Delvaille et al., 2005). In
Germany, the same principles of accounting are used for reporting and for tax
purposes, and a liberal use of reserves is permitted in order to smooth earnings and
maintain dividend payout ratios at a stable level (Goldberg and Godwin, 2002).
Finally, this study takes into account the present research interest in the effects of
the mandatory adoption of the IFRS for the functioning of capital markets. While the
number of studies devoted to this topic is considerable and still growing, the results
are mixed (Devalle et al., 2010). Our results indicate that one reason for mixed results is
the selection of the month of market value sampling. In the two countries studied here,
the IFRS have been mandatory for consolidated ?nancial statements since 2005, but
local GAAP statements are mandatory for single entities (Mac? ´as and Muin˜o, 2011).
Before the adoption of IFRS, local accounting systems in both countries were highly
developed and contained a large number of detailed provisions divergent from IFRS
(Ding et al., 2006), which had an impact on the selection of options after IFRS adoption
(Haller and Wehrfritz, 2013).
2. Hypothesis development
This paper extends the analysis of value relevance by examining how the relationship
between accounting numbers and market value varies depending on the date when
market value is sampled, relative to ?scal year-end. We introduce the terms coincident
and forecast relevance to distinguish between the two research hypotheses. We de?ne
coincident relevance as the statistical relationship between accounting numbers for
the year and market value before the end of the reporting year. It represents the
interpretation of value relevance as the ability of accounting numbers to capture value
relevant information, which is connected with the correlation hypothesis (Francis and
Schipper, 1999). In contrast, we de?ne forecast relevance as the statistical relationship
between accounting numbers for the year and market value after their publication.
It represents the usefulness of accounting numbers as inputs to valuation methods and
as a basis for forming expectations by investors (Holthausen and Watts, 2001).
To develop the notions of coincident and forecast relevance we begin with a
simpli?ed setting. Assume that there exists a ?rm which closes its accounting books
Coincident and
forecast
relevance
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on the 31st of December each year and makes an immediate disclosure of the annual
?nancial statement. Further, the ?rm ful?lls the assumptions of the Ohlson model, so
its equity can be reliably valued with that model. The Ohlson (1995) model is an
extension of the residual income valuation model. The model allows market value to be
expressed in terms of coincident accounting numbers, because expectations of future
residual income are modeled using linear information dynamics. The model takes the
following form:
MV
t
¼ BV
t
þa
1
RI
t
þ a
2
v
t
;
where a
1
¼
v
1 þ r
e
2v
; a
2
¼
1 þ r
e
ð1 þ r
e
2vÞð1 þ r
e
2gÞ
ð1Þ
According to the model, when the ?rm discloses its accounting numbers for year t, the
market value of its equity at the end-of-year (MV
t
) is expected to adjust to the Ohlson
model value determined by its end-of-year book value (BV
t
), residual income over the
last ?scal year (RI
t
) and current non-accounting information on next year income (v
t
).
The parameters of the model depend on the autoregressive characteristics of residual
income (0 , v , 1) and of the non-accounting information variable (0 , g , 1), as
well as the cost of capital (r
e
). The Ohlson model remains the core theoretical
foundation for value relevance studies because it provides a direct link between
accounting numbers and market value of equity. Empirical tests of the model show
that it performs as well as alternative models (Dechow et al., 1999; Francis et al., 2000).
However, the other information variable can be omitted without a reduction in the
power of the model (Isidro et al., 2006).
In the context of our study it is important to note that in the Ohlson model both the
market value MV
t
and the accounting information variables (BV
t
, and RI
t
) are sampled
at the same moment in time. That moment is exactly the end of the reporting year: the
date when all value relevant information included in annual accounting numbers is
already known and discounted in market values. In reality, ?nancial statements are
published with a reporting lag of at least two or three months into the next reporting
year. Hence, at the time of publication, market values already re?ect new information
?ows into the market, which are not re?ected in accounting numbers. This observation
is the starting point for the development of our hypotheses about coincidence and
forecast relevance.
Let us now consider the valuation of the ?rm’s equity immediately before the
publication of its ?nancial statements, at time t 2 t, where t represents a fraction of a
year corresponding to the number of months to ?scal year-end (e.g. 0/12 for December,
6/12 for July). We refer to the statistical relationship between the annual accounting
numbers and market value calculated at time t 2 t as coincident relevance. If
coincident relevance is high, that would imply that in month t 2 t the market prices
the ?rm’s equity at a value close to the end-of-year Ohlson model value, even though
the accounting numbers are not yet known[1]. This is possible if investors predict
accounting numbers with enough precision, or if accounting numbers re?ect known
economic factors relevant to valuation.
Now, we turn to the period after accounting numbers are published to consider the
second effect, forecast relevance. After the publication of annual accounting numbers,
investors may use published accounting numbers as inputs to the residual income
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valuation model (1) at time t þ t and adjust their portfolios. As the reduced form of the
model stems directly from the autoregressive structure of future residual income, the
last year ?nancial data are value relevant as long as they allow investors to predict
future bene?ts from holding the ?rm’s equity. On the other hand, accounting numbers
contain only information available up to ?scal year-end, so the valuation model does
not re?ect new information, revealed after the ?scal year-end. As the year progresses,
the news will keep accumulating, thus decreasing the strength of forecast relevance.
Note, that the lag between ?scal year-end and the publication of annual ?nancial
statements introduces an interim period for which we cannot make clear predictions.
During this period accounting numbers are not available yet, but news concerning the
new ?scal year begin to accrue in market values. The way they accumulate in market
values may depend on the information environment of both country stock markets
(Christensen and Demski, 2003). For clarity of presentation in the empirical section we
refer to the entire period after ?scal year-end as forecast relevance.
3. Research design
The main focus of our study is to examine the variation in coincident and forecast
relevance of accounting numbers as a function of the month in which market values are
sampled. To this end, we perform separate regressions of annual accounting ?gures on
the average market value of equity measured in each of six months in the last part of a
?scal year from July to December (m ¼ 7,8, . . . , 12), and then in each month of the ?rst
six months of a new ?scal year from January to June (m ¼ 1,2, . . . , 6)[2]. Separate
regressions of the following type are run for each month of the year:
MV
i;t
m
¼ a
i:
þ a
:t
þ b
1
BV
i;t
þ b
2
RI
i;t
þ u
i;t
t
m
¼ t 2ð12 2mÞ=12 for m ¼ 7; 8; . . . ; 12
t
m
¼ t þ m=12 for m ¼ 1; 2; . . . ; 6
ð2Þ
where parameters a
i.
(i ¼ 1, . . . , N) denote individual effects (constant over time), and
a.
t
(t ¼ 1, . . . , T) represent time effects (common for all ?rms in a given period).
Variables u
it
denote idiosyncratic disturbances with zero-mean, which are uncorrelated
with the explanatory variables but possibly correlated in time and heteroskedastic.
We use the panel regression framework to exploit the bene?ts of full sample
information. Since samples of ?rm-year data are usually strongly unbalanced, one
cannot run separate time-series regressions for each company (Kothari and Shanken,
2003). Note that parameters of model (1) standing at residual income and
non-accounting information variable vary between individual companies because of
?rm-speci?c autoregressive coef?cients and risk-adjusted discount rates. However,
in the panel regressions, we treat all coef?cients in model (1) as homogeneous in
the cross-section to gain ef?ciency[3]. We also include ?rm and time ?xed effects
to minimize the risk of estimation bias[4]. This approach allows us to interpret
the common coef?cients from panel regressions as the estimates of the average value
of the individual (?rm-speci?c) coef?cients. The standard errors of the estimates,
which are corrected for heteroskedasticity and autocorrelation with a Newey-West
method (Wooldridge, 2007), indicate the degree of coef?cient heterogeneity across
the sample[5].
Coincident and
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Since the objective of this study is to analyze the value relevance of book value and
earnings through the variability of their respective regression coef?cients, we need to
apply statistical tests. We use the within R
2
statistic, which is a measure of the part of
temporal variability of the explained variable (market value) within individual ?rms
explained by the explanatory variables (accounting numbers), to compare overall value
relevance across monthly regressions, but following the arguments of Gu (2007) we do
not use it for comparisons across samples. We test for differences between coef?cients
by applying the Wald test for each monthly regression in relation to the December
regression. To examine if the differences between two country samples are signi?cant
we calculate the Wald statistic for common coef?cients in the two country samples for
each month of market value sampling.
To make the comparison of value relevance across countries meaningful we control
for a number of sample-speci?c factors. We eliminate the impact of unobservable
characteristics using ?rm- and time-speci?c variables in a two-way error component
model. We use the ?xed effects estimator[6] which allows us to treat those
unobservable effects as possibly correlated with accounting numbers. This reduces the
impact of variables that vary in the cross-section, such as size of industry sector, which
we include in robustness tests but not in the main results because their impact is
immaterial. However, we present results for sub-samples limited to companies
reporting in accordance with the IFRS. We do so for two reasons. First, we set this
study in the stream of recent research devoted to the effects of IFRS adoption. Second,
the results in the IFRS sub-samples are in fact signi?cantly different from those
observed in the full samples.
4. Sample composition
We analyze the relationship between accounting numbers and market values of
companies listed at the Paris Stock Exchange (Euronext Paris) in France (907 ?rms in
total) and Deutsche Boerse in Germany (940 ?rms) from January 1989 until December
2008. The explained variable is the market value of equity calculated as the number of
common outstanding shares times the monthly average of stock price. The daily
quotes come from the Compustat Global Security Daily Data Set. The sample starts at
1989 because of data availability and ends in 2008 before the full outset of the recent
?nancial crisis. Market values for each of the last six months of a ?scal year and the
?rst six months of the following year are separately regressed on the annual ?nancial
statement ?gures, which are obtained from Compustat Global Fundamentals Annual
Database supplied by Wharton Research Data Services.
Table I shows the sample selection process in terms of ?rm-year observations
dropped in each step. To facilitate our analysis, we selected ?rms with the same ?scal
year-end, 31st of December. Further reductions in the sample size are caused by the use
of lagged book values for calculating residual income[7] or lagged earnings for the
months after the ?scal year-end. The other sources criteria of sample selection are the
exclusion of ?rms from the ?nancial sector, of ?rms reporting negative book values,
?rms quoted fewer than ten times in a given month, ?rms with fewer than 36 monthly
quotes, and ?rms reporting in accordance with an accounting standard other than local
domestic or the IFRS. The last row of Table I shows the composition of the ?nal data
set for market values sampled in December. The data sets vary in size because of
market data availability for speci?c months from 3,580 (in May) to 4,216 (in December)
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?rm-year observations for France and from 4,087 (in February and April) to 4,670
(in January) ?rm-year observations for Germany.
Table II contains descriptive statistics of annual accounting data and market values
from December in full samples and in sub-samples of companies reporting according to
the IFRS. Tests for the equality of means show that companies in the two country
samples are similar in terms of average book value, residual income and market value.
There are however signi?cant differences between ?rms reporting according to the
IFRS and ?rms reporting according to local standards. Companies reporting according
France (889 ?rms) Germany (927 ?rms)
Number of
observations
In % of full
sample
Number of
observations
In % of full
sample
Full sample (Compustat 1989-2008) 6,922 100 7,666 100
þ Fiscal-year end in December 5,535 80 6,298 82
þ Non-?nancial sector 5,514 80 6,213 81
þ Non-negative book value 5,327 77 5,982 78
þ With market quotations in a
given month (December here) 5,065 73 5,779 75
þ Starting year for calculating
residual income 4,386 63 5,083 66
þ Accounting standards (local
domestic DS þ international DI) 4,216 61 4,637 60
Table I.
Cumulative sample
attrition in terms of
?rm-year observations
Variables MV BV RI MV BV RI
Descriptive
statistics
France: 4,216 ?rm-year observations Germany: 4,637 ?rm-year obs.
Mean 1,428.46 697.56 24.71 1,232.15 664.63 13.11
t-test (France
vs Germany)
– – – 1.56 0.55 2 1.82
*
Standard
deviation
6,683.83 2,801.25 604.65 5,138.80 2,773.98 271.40
International accounting standards IFRS only (DI)
Descriptive
statistics
France: 1,373 obs. Germany: 2,270 obs.
Mean 2,278.46 1,246.24 30.76 1,572.86 900.22 22.32
t-test (France
vs Germany)
– – – 2.92
* * *
2.74
* * *
0.76
Standard
deviation
229.96 105.07 10.06 126.51 74.96 6.11
t-test
(IFRS vs local
accounting
standards)
5.76
* * *
8.92
* * *
2.65
* * *
4.43
* * *
5.68
* * *
2.26
* *
Notes: p-value of a Student test is lower than
*
10,
* *
5 and
* * *
1 percent; variable codes: MV stands
for average market value in December of each ?scal year calculated as the average of daily market
values, BV stands for book value of shareholders equity, RI stands for residual income, t-test is a
standard t-Student statistics for equal means between sub-samples (i.e. between countries or
accounting standards)
Table II.
Descriptive statistics
by countries and
accounting standards in
millions of EUR
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to the IFRS are larger on average than those following local domestic accounting
standards. While a relatively larger proportion of companies ?le IFRS reports in
Germany (40 percent) than in France (30 percent), IFRS adopters in France are about
40 percent larger (in terms of MV or BV) than in Germany.
5. Empirical results
Estimation results for the two country samples (Table III) show that the model
explains between 39 and 61 percent of the within-?rm variance in the French sample
and between 45 and 75 percent in the German sample, depending on the month in
which market value is sampled (Figure 1). In the French sample, the highest value of
the R
2
, 61 percent, is observed in the January regression, and the lowest, 39 percent, in
the March regression. With the exception of January, overall value relevance is higher
before ?scal year-end than after, which indicates coincident relevance is stronger than
forecast relevance. In the German sample, the difference between coincident and
forecast relevance is clearer. The R
2
is above 70 percent in the regressions where
market value is sampled in August, September or October before ?scal year-end, which
is an indication of high coincident relevance. The R
2
decreases in November and
December regressions, then continues to decline to a low of 45 percent in the March
regression, which shows that forecast relevance is weaker.
The sources of differences in overall value relevance of accounting data can be
explained by the variation in coef?cients standing at book values and residual income
(Figure 2). In the French sample, the estimated coef?cients at book value tend to
increase around ?scal year-end with the maximum of 1.6 in January and the minimum
of 1.3 in June (the upper section of Table III). The book value coef?cients in other
monthly regressions are relatively stable, with values ranging from 1.4 to 1.5. Book
value variables are statistically signi?cant across the monthly regressions, while the
residual income coef?cients are statistically signi?cant only in those regressions where
market value is measured after ?scal year-end. When we consider the regression
coef?cients at residual income and if we focus only on these regressions where the
income variable is statistically signi?cant, we observe a growth from 0.4, in the ?rst
month of the ?scal year, up to 0.7 in the ?fth and the sixth month. The Wald test
con?rms there are signi?cant differences in coef?cients at book value across the year,
while signi?cant differences in the residual income coef?cients are found only for the
July and October regressions as compared to the December regression. When both
coef?cients are tested jointly, signi?cant differences are found in all months except for
March and June.
In the German sample, the book value coef?cients increase till December of the
?scal year to the value of 1.6, then they drop in January and later remain at a relatively
stable level of 1.5 until June (the lower section of Table III). In contrast, the residual
income coef?cients decrease steadily towards ?scal year-end from the maximum of 3.7
in the July regression, then they continue to decrease with the minimum value of 0.8 in
the February and March regressions, after which the values of coef?cients increase
again. The residual income variable is statistically signi?cant only in regressions for
the months before a ?scal year-end, from July till November, whereas the book value
variable is statistically signi?cant in all regressions across the months. When we limit
the analysis to the regressions where the residual income variable is statistically
signi?cant, the values of coef?cients exhibit a falling trend from 3.7 in July before ?scal
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(
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V
)
Table III.
Estimation results of
model (2) for ?rms with
local domestic and IFRS
accounting standards,
and non-negative BV
Coincident and
forecast
relevance
247
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
1
8
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
year-end, to 2.2 in November of the same year. The Wald test shows, however, that
parameters at residual income are not statistically different across the months around
?scal year-end as compared to the December regression, with the exception of the June
regression.
Results for the IFRS sub-samples, that is samples limited to ?rms reporting in
accordance with the IFRS, are distinct from the results for the full samples. Overall
value relevance, measured by R
2
, resembles the patterns found in the full sample
regressions (Figure 3). In the French IFRS sub-sample, the R
2
is lower than in the full
sample, with values ranging from 27 to 50 percent. The highest value is still reported in
the January regression, while the lowest is reported in the June regression. On the
average, coincident relevance is slightly stronger than forecast relevance, but the
difference is less pronounced than in the full sample. In the German IFRS sub-sample,
the R
2
statistics are lower as well, but the difference between coincident and forecast
relevance remains clear. The R
2
reported in regressions from July to December range
between 47 and 53 percent, while in regressions from January to June the values range
from 36 to 43 percent.
The coef?cients at book value and residual income also diverge from the ones found
in the full sample regressions (Table IV). In the French IFRS sub-sample, presented in
the upper section of Table IV, the residual income coef?cients increase towards the
?scal year-end, from 0.4 in July to 2.2 in December, but the variable is statistically
signi?cant only in the regressions from October until December. The coef?cients at
residual income tend to decrease to negative values after ?scal year-end, when they are
not statistically different from zero. The book value variable is signi?cant throughout
the year, but the regression coef?cients show more variation than in the full sample.
The coef?cient values are about 1.2 before ?scal year-end, then drop steadily to 0.8
after ?scal year-end. The Wald test shows the differences between residual income
coef?cients are statistically signi?cant in months from April till June after ?scal-year
end, while the test for the book value coef?cient shows signi?cant differences in all
Figure 1.
Comparison of within
R
2
by month of market
value sampling
Jul. Aug. Sept. Oct. Nov. Dec. Jan. Feb. Mar. Apr. May Jun.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
France: RSQ Germany: RSQ
Month of market value sampling
W
i
t
h
i
n
R
-
s
q
u
a
r
e
d
Note: Correlation is measured with within R
2
obtained in
equation (2)
ARJ
26,3
248
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
1
8
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
months except July through September. The joint test for the two coef?cients shows
signi?cant differences in all months except September, November and February.
In the German IFRS sub-sample, presented in the lower section of Table IV, we ?nd
residual income variable is statistically signi?cant in all the monthly regressions. The
coef?cient values ?uctuate from a low of 1.8 in the July regression, through a local
maximum of 3 in October, November and December, then they decrease to 2.6 in the
January and February regressions, and increase again in March to remain at a level of
about 3 in later months. The book value variable is also statistically signi?cant and the
coef?cient values range from 0.8 after ?scal year-end to 1.9 in the October and
November regressions. The Wald test does not indicate statistically signi?cant
differences between the coef?cient estimates, with the exception of two cases.
Finally, we compare the coef?cient estimates between the two country samples by
performing the Wald test. In the full sample estimations (Table III), results show that
Figure 2.
Comparison of regression
coef?cients for residual
income (RI) and book
value (BV) by month of
market value sampling
Jul. Aug. Sept. Oct. Nov. Dec. Jan. Feb. Mar. Apr. May Jun.
0
0.5
1
1.5
2
2.5
3
3.5
4
France: RI Germany: RI
Month of market value sampling
R
e
s
i
d
u
a
l
I
n
c
o
m
e
C
o
e
f
f
i
c
i
e
n
t
Jul. Aug. Sept. Oct. Nov. Dec. Jan. Feb. Mar. Apr. May Jun.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
France: BV Germany: BV
Month of market value sampling
B
o
o
k
V
a
l
u
e
C
o
e
f
f
i
c
i
e
n
t
Coincident and
forecast
relevance
249
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
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V
E
R
S
I
T
Y
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t
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6
(
P
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)
a signi?cant difference exists in the October, November and June regressions. The ?rst
two monthly regressions show residual income coef?cients of 0.5-0.6 for French sample
(insigni?cant) and 2.2-2.9 for the German sample (signi?cant). The book value
coef?cients are 1.4 for the French sample, and 1.6 for the German sample (signi?cant in
all cases). In the June regression, the residual income coef?cients are 0.7 and 2.5,
respectively, for the French and German samples, while the book value coef?cients are
1.3 and 1.5 (signi?cant in all cases).
The results of the cross-country comparison for the IFRS sub-sample diverge from
the full sample ones. The Wald statistic is signi?cant in all regressions where market
value is sampled after ?scal year-end, while there are no statistically signi?cant
differences between the coef?cients when market value is sampled before ?scal
year-end. After ?scal year-end, the residual income coef?cients are lowand insigni?cant
in the French IFRS sub-sample, while inthe GermanIFRS sub-sample theyare as highas
3 and signi?cant. The book value coef?cients range from 0.8 to 1.1 in the French IFRS
sub-sample and from 0.8 to 0.9 in the German IFRS sub-sample (signi?cant in all cases).
The differences between coef?cients are not signi?cant in the regressions where the
highest and signi?cant values are found in the French IFRS sub-sample, because these
values are closer to the results found in the German IFRS sub-sample.
The results presented in Tables III and IV are robust to alternative model
speci?cations and the inclusion of control variables (Ruland et al., 2007). For simplicity
of exposition we do not tabulate the results of robustness checks. First, we introduce
limited heterogeneity in the coef?cients by including variables for industry sector and
?rm size, and their interactions with residual income and book value. Although some of
the control variables are signi?cant, these changes do not affect the Wald test results.
Second, we exclude ?rms reporting an accounting loss, which causes an increase of the
residual income coef?cient in the German sample. As a result, the Wald test for the
cross-country comparison returns a signi?cant value in all months before ?scal
Figure 3.
Comparison of within
R
2
by month of market
value sampling in IFRS
sub-samples
0
0.1
0.2
0.3
0.4
0.5
0.6
Jul. Sept. Nov. Jan. Mar. May
W
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a
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e
d
Month of market value sampling
France: RSQ Germany: RSQ
Note: Correlation is measured with within R
2
obtained in
equation (2)
ARJ
26,3
250
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Table IV.
Estimation results of
model (2) for ?rms with
IFRS accounting
standards and
non-negative BV
Coincident and
forecast
relevance
251
D
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year-end, except for December. Third, we use full accounting income instead of residual
income in the regressions. This again causes changes in the German sample, where the
coef?cients at income become high and signi?cant not only before, but also after ?scal
year-end. The results of the Wald test indicate a signi?cant differences between the two
country samples exist in the July, August and October regressions.
6. Conclusions
The objective of this study is to assess the sensitivity of value relevance regression
results to the month in which market value is sampled. We ?nd signi?cant variation in
overall value relevance and in the incremental value relevance of residual income and
book value. The R
2
varies by up to 75 percent depending on the month of market value
sampling. The highest degree of coef?cient variation is present in the residual income
coef?cients, where variations of 50 percent are not uncommon. The book value
coef?cients are more stable, but exhibit signi?cant variations over the months as well.
Out of the two country samples, we ?nd the variations are greater in the French sample
than in the German sample.
We attribute the variations in coef?cients to the notions of coincident and forecast
relevance which we de?ne in the paper. Results indicate that coincident relevance is
stronger than forecast relevance, because the R
2
is generally greater in the regressions
where market value is sampled before ?scal year-end. However, the incremental
relevance of residual income depends on the country of listing and the accounting
standard. We ?nd that residual income has greater impact on forecast relevance in the
French sample, while in the German sample it affects coincident relevance. When we
limit the sample to IFRS-reporting companies, results point to coincident relevance of
residual income and book value in both country samples, although in the German
sample residual income is also forecast relevant.
The results of our study indicate the need for sensitivity testing in international
comparative studies. When we compare coef?cients between the two country samples,
we ?nd the results of the test depend on the month of market value sampling. In the full
sample regressions, we ?nd signi?cant differences in coef?cients between the two
country samples if market value is sampled from one to two months before ?scal
year-end, or six months after ?scal year-end. In the IFRS sub-sample regressions we
?nd signi?cant differences between the two country samples if market value is
sampled from one to six months after ?scal year-end. Thus, our results show that the
choice of the month determines the results of cross-country comparisons.
Results presented in this paper raise a number of interesting questions and offer
possible extensions concerning the variation in the relative strength of coincident and
forecast relevance. First of all, future studies may examine companies listed in
countries representative of other accounting and ?nancial market models than France
and Germany. Second, future research may be directed at ?nding the determinants of
changes in the relative strength of coincident and forecast relevance, such as the
adoption of IFRS, which is described in this study. These determinants may be found
in the changes of regulation, changes of market institutions and of the information
environment. Finally, the relative strength of coincident and forecast relevance
may vary with factors other than the country of listing or the accounting standard.
Further research is needed to identify these factors and determine whether they affect
inferences from comparative value relevance studies.
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Notes
1. To be precise, under value relevance and time value of money hypotheses it is the forward
(for t 2 t) or backward (for t þ t) discounted market value that would be correlated with the
residual income valuation. Because the cost of capital for up to 6 months at rates prevailing
in the market is small, we remove the discount factor for simplicity.
2. The sample is limited to companies that report on the 31st of December each year.
3. While this approach does not allow for full variation of parameters, it is ef?cient, and it is
more robust to misspeci?cation problems than separate cross-sectional regressions.
4. Ignoring ?rm-speci?c effects as in pooled OLS regression approach or applying
Fama-MacBeth procedure may also lead to a downward bias in standard errors as
discussed by Petersen (2009).
5. Heteroskedasticity in idiosyncratic disturbances is possibly a result of using pooled
regression parameters, unscaled market values and accounting numbers, or it also may be
an effect of omitted explanatory variables. Autocorrelation may stem from omitting
non-accounting information variable (v
t
) from equation (2), which is autoregressive by
construction.
6. The Hausman test indicates that the ?xed effects model is preferable over the random effects
model.
7. Initially, we estimated residual income for each ?rm using the one-factor market model.
However, results remained unaltered when we used constant rate of cost of capital between
7 and 11 percent, which led us to adopt a single rate (9 percent) across the sample.
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About the authors
Karol Marek Klimczak is an Assistant Professor of ?nance, a member of the European
Accounting Association. His research interests include the role of accounting information in
market pricing and risk-based management control systems. Karol Marek Klimczak is the
corresponding author and can be contacted at: [email protected]
Grzegorz Szafranski is an Assistant Professor in the Chair of Econometrics, and he is a
Co-Editor of FindEcon Monograph. His empirical research is focused on ?nancial econometrics
and macroeconometrics.
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