ACCOUNTING WORKSHOP
On Market Concentration and Disclosure
By
Edwige Cheynel*
&
Amir Ziv
Columbia Business School
Columbia University
Thursday, May 12th, 2016
1:20 – 2:50 p.m.
Room C06
*Speaker
Paper Available in Room 447
On Market Concentration and Disclosure
Edwige Cheynel and Amir Ziv∗
Abstract
The empirical literature uses market concentration as a surrogate for competition,
and provides inconsistent, and at best weak, support for the relationship between
market concentration and disclosure. Indeed, existing theory suggests competition
should affect companies’ disclosure choices; however, it never defines competition
as market concentration. We investigate whether market concentration is associated
with firms’ disclosures under the different market structure and informational environments in standard competition models. We show that concentration is irrelevant
in explaining equilibrium disclosure levels. A change to market concentration
(exogenous or endogenous) does not cause more or less disclosure. We suggest,
however, that other dimensions of competition might affect disclosure choices. In
particular, we predict that competitive environments with ongoing entry feature less
disclosure relative to environments in which the number of firms is stable.
∗
Edwige Cheynel is an Assistant Professor and Amir Ziv is a Professor of Professional Practice, both
at Columbia Business School. Contact author: E. Cheynel, Columbia Business School, Columbia University, 3022 Broadway, New York, NY 10027. Email address: [email protected]. We thank Charles
Angelucci, Jeremy Bertomeu, Thomas Bourveau, Jon Glover, Moritz Hieman, Xiaojing Meng, and seminar participants at the Dartmouth Accounting Research Conference and at Columbia Business School for
helpful feedback.
1
1
Introduction
In this study, we ask whether market concentration is a good proxy for competition,
when disclosure choices are considered. Existing theory is of little help, as under theoretical models “more competition” means a change in a technological determinant of
competition, such as the type of competition, asset substitution, or entry cost, rather than
a change in the number of competitors.1 Unfortunately, these theoretical definitions of
competition do not easily map to clear empirical proxies. To mitigate the issue, studies
introduced auxiliary assumptions about the relevant observable measure of competition.
The empirical literature has often used concentration, such as the Herfindahl-Hirschman
index, as a surrogate for competition.
The documented results on the relationship between disclosure and concentration are
weak or mixed (see section 2). A possible reason for such a lack of results is related to
the limitations of methods and proxies used for the parameter of interest — concentration. Indeed, the flow of no-results has triggered much debate on research design. We
propose an alternative perspective on this issue: even if the concentration construct were
perfectly measured, the initial premise that concentration and disclosure should be related is invalid. Our approach, which covers most classic theoretical frameworks used
in the empirical literature, provides support for this alternative explanation. The claim
implies that improvements in existing measures of concentration might offer little benefit,
and further empirical tests of the theory should be conducted with other dimensions of
competition.
A vast empirical literature refers to the work of Verrecchia (1983) and of Darrough and
Stoughton (1990) to support the hypothesis that competition relates to observed disclosure
behavior (see column 6 of Table 1). Indeed, Verrecchia (1983) derives the proprietarycost hypothesis in which higher disclosure costs, stemming from lost competitive advantage (due to rivals’ ability to fine tune their strategies when better informed), reduce a
company’s level of disclosure. Darrough and Stoughton (1990) obtain a different prediction. They note that “competition encourages voluntary disclosure” (p. 221), where
competition is defined in terms of entry costs. For example, they write, “Since low entry
costs leads to a higher entry probability, full disclosure ensues under competitive pressure.” (p. 239). However, neither Verrecchia (1983) nor Darrough and Stoughton (1990),
nor other theories mentioned in Tables 1 and 2, relate the number of firms to competition. For example, Gal-Or (1985) and Darrough (1990) show that how firms compete
1
To our knowledge, the only study in which the number of firms decreases disclosure is Bertomeu and
Liang (2015), but only in the context of smaller industries in which tacit collusion may occur.
2
(i.e., Cournot, or Bertrand, on common-demand level or individual-cost level) matters for
disclosure, but their analyses do not consider the number of firms in a given industry as a
measure of competitiveness.
We explore various Cournot-Nash models, examining the number of firms in the industry, an obvious measure of concentration, as the variable of analysis. We remain open
to the two primary models of competition used in the literature and referenced by empirical work, namely, competition between existing rivals and competition induced by
entry of potential rivals. We also examine environments in which the manager commits
to an information system ex ante, or strategically decides whether to disclose ex post.
We further refine the firm manager’s objective that maximizes either long-term cash-flow
realizations or short-term market price. Lastly, we change the source of uncertainty from
common information, namely, demand, to firm-specific information, namely, cost. Each
of these settings implies different optimal disclosure policies; hence, competition does
matter for disclosure. However, none of the settings predicts an empirical association
between concentration and disclosure.
Our work aims to investigate whether theory predicts a relation between concentration
and disclosure. In building the case for the lack of such a relation, we also generate a few
additional theoretical implications that could support new empirical predictions. Environments with equilibrium entry typically feature less disclosure relative to environments
with a fixed number of firms. We also predict that managers with pure discretionary disclosure tend to disclose more information. Managers with short-term motives disclose
less, but only if the industry features endogenous entry. Further, prior literature has conjectured that the source of uncertainty, that is, common versus firm-specific uncertainty,
is of relevance primarily in models of existing competition, showing that fewer incentives
exist to disclose information about demand. Our integrated model reveals these results
largely carry over to endogenous entry, unifying the two approaches. Finally, we also
show that in the context of ex-post disclosures, the standard unraveling argument does not
hold in an entry model with a manager maximizing short-term price.
The organization of the paper is as follows. Section 2 summarizes the empirical evidence for the relationship between disclosure and concentration. In section 3, we develop
our formal model and consider ex-ante disclosure of a common parameter - the demand
intercept. Section 4 provides the analysis for the same model, under ex-post disclosure.
In section 5, we change the nature of the firm’s private information from a common parameter to an individual one — the cost of production. Section 6 provides empirical
predictions, concluding remarks, and avenues for additional research. Highlights of the
proofs appear in the Appendix.
3
2
The evidence
Our research question stems from a meta-study of the existing empirical evidence. Table 1 results from a systematic search of all articles relating disclosure to concentration,
published in the five leading accounting journals.2 For the dependent variable, we used
a broad definition of disclosure – any proxy for transmission of information to outsiders.
Our search involves information contained in earnings, forecasts and other voluntary
disclosures, special items, and indirect evidence from market reactions to information.
For the independent variable, we searched for the keywords “Herfindahl-Hirschman,”
“Herfindahl,” “HHI,” “concentration ratio,” or “CR4.”
A quick scan of the evidence presented in Table 1 reveals that about half of the empirical studies find no significant relation between concentration and disclosure, and for
each study with a significant relationship in one direction, another study exists with a
significant relationship in the other direction.
Nearly all studies using more than one disclosure proxy find inconsistent results in the
same sample, with one proxy being significant while the other is either insignificant or
significant in the other direction. For example, although frequency and accuracy of management forecasts are both proxies for disclosure, they tend to have a different association
with concentration. Among significant results, another fact is worrisome. The dominant
argument in the empirical literature is that competition reduces disclosure, with most of
the papers referring to a single theory, rather than comparing and contrasting alternative
theories. Column (5) reveals that studies that specifically seek to confirm a single theory
tend to find more significant negatives, whereas studies that use concentration as a control
variable tend to find more significant positives.
The flow of results has triggered much debate about the limitations of the methods
and proxies, as if insignificance necessarily indicates a problem in a proxy rather than a
possible more primitive issue: Does the theory actually predict the tested relationship? In
other words, researchers assumed a theory exists that connects disclosure and concentration, and that needs to be validated.
2
We have searched the Journal of Accounting and Economics, the Journal of Accounting Research, the
Accounting Review, Contemporary Accounting Research, and the Review of Accounting Studies. We also
searched Accounting, Organization and Society, but did not find any study that qualified according to our
search criteria. See Table 1 (notes) for details of our search criterion.
4
(1 )
Product market competition and conditional conservatism, D.
Dhaliwal, S. Huang, I. K. Khurana and R. Pereira, Review of
Accounting Studies (Dec., 2014).
B usiness strategy , financial reporting irregularities, and audit
effort, K. A. B entley , T . C . O mer and N . Y . Sharp,
C ontemporary Accounting Research (J un., 2013 ).
C orporate disclosures b y family firms, A. Ali, T .Y . C hen and S.
Radhakrishnan, J ournal of Accounting and E conomics (Sep.,
2007 ).
O vervaluation and the choice of alternative earnings management
mechanisms, B . A. B adertscher, T he Accounting Review (Sep.,
2011).
Accounting conservatism and the temporal trends in current
earnings’ ab ility to predict future cash flows versus future earnings:
evidence on the trade- off b etween relevance and reliab ility , S. P.
B andy opadhy ay , C . C hen, A. G . Huang and R. J ha, C ontemporary
Accounting Research, (J un., 2010).
Does earnings q uality affect information asy mmetry ? E vidence
from trading costs, N . B hattachary a, H. Desai and K.
V enkataraman, C ontemporary Accounting Research (J un., 2013 ).
Type of
disclosure
(2 )
C on cen t ra t ion
prox y
(3 )
-
Y es
V 8 3 , DS9 0,
C V 9 7
earnings
(irregularities)
HHI
-
N o
N one
earnings
(q uality )
HHI
+
N o
N one
earnings
(q uality )
HHI
insignificant
N o
N one
earnings
(q uality )
HHI
+
N o
N one
earnings
(q uality )
HHI
insignificant
N o
N one
HHI
insignificant
N o
N one
PIC : R& D+ HHI
-
N o
V 8 3
HHI/ C R4
- (sometimes
weak)
Y es
V 8 3 , DS9 0,
C V 9 7
C R4
+
N o
V 8 3
+ (q uantity )
and (accuracy )
Y es
DS9 0, W 9 0,
B 9 3 , G 9 4,
C V 9 7
-
N o
N one
forecasts
(management,
AIM R)
T he impacts of product market competition on the q uantity and
q uality of voluntary disclosures, X . L i, Review of Accounting
Studies (Sep., 2010).
forecasts
HHI (composite)
(management)
C E O ab ility and management earnings forecasts, B . B aik, D. B .
F arb er and S. L ee, C ontemporary Accounting Research (Dec.,
2011).
Serial correlation in management earnings forecast errors, G .
G ong, L . Y . L i and J . J . W ang, J ournal of Accounting Research
(J un., 2011).
C redib ility of management forecasts, J . L . Rogers and P. C .
Stocken, T he Accounting Review (O ct., 2005 ).
forecasts
C O N C (ratio of top
(management)
5 sales)
forecasts
(management)
HHI
- (weak)
N o
N one
forecasts
(management)
HHI
+ (q uantity )
and
insignificant
N o
N one
forecasts
(management)
forecasts
(management)
T he effect of ex ante management forecast accuracy on the postforecasts
earnings- announcement drift, L . Z hang, T he Accounting Review
(management)
(Sep., 2012).
C over me: managers' responses to changes in Analy st C overage
forecasts
in the post- Regulation F D period, D. Anantharaman and Y . Z hang,
(management)
T he Accounting Review (N ov., 2011).
T he association b etween management earnings forecast errors
forecasts
and accruals, G . G ong, L . Y . L i and H. X ie, T he Accounting
(management)
Review (M ar., 2009 ).
F orecasting without C onseq uence? E vidence on the Properties of
forecasts
Retiring C E O s' F orecasts of F uture E arnings, C .A. C assell, S. X .
(management)
Huang, and J . M . Sanchez , T he Accounting Review (N ov., 2013 ).
M anagement earnings forecast disclosure policy and the cost of
eq uity capital, S. P. B aginski and K. C . Rakow J r., Review of
Accounting Studies (J un., 2012).
(6 )
HHI
F irm Disclosure Policy and the C hoice B etween Private and
Pub lic Deb t, D. S. Dhaliwal, I. K. Khurana and R. Pereira,
C ontemporary Accounting Research (M ar., 2011).
Do managers alway s know b etter? T he relative accuracy of
management and analy st forecasts, A. P. Hutton, L . F . L ee and
S. Z . Shu, J ournal of Accounting Research (Dec., 2012).
C it ed
Th eory
earnings
(conservatism)
T ime- vary ing earnings persistence and the delay ed stock return
earnings
reaction to earnings announcements, C . C hen, C ontemporary
(q uality )
Accounting Research (J un., 2013 ).
M anagers' E PS forecasts: nickeling and diming the market? , L . S.
earnings
B amb er, K. W . Hui and P. E . Y eung, T he Accounting Review
(unrounded
(J an., 2010).
E PS)
Industry concentration and corporate disclosure policy , A. Ali, S.
forecasts
Klasa and E . Y eung, J ournal of Accounting and E conomics
(management,
(N ov.– Dec., 2014).
AIM R)
C apital market conseq uences of managers' voluntary disclosure
sty les, H. I. Y ang, J ournal of Accounting and E conomics (F eb Apr., 2012).
(4 )
Test of
com pet it ion
h ypot h esis
(5 )
R ela t ion
forecasts
(management)
5
HHI
insignificant
N o
N S9 3
HHI
insignificant
N o
N S9 3
HHI
insignificant
N o
V 8 3
HHI
insignificant
N o
V 8 3
HHI
insignificant
N o
N S9 3
HHI
insignificant
N o
N one
HHI
+
N o
N one
(1 )
D o declines in bank health affect borrowers’ voluntary disclosures?
Evidence from international propagation of banking shocks, A. K .
L o, Journal of Accounting Research (M ay, 2014).
T y p e of
d i sc l osu r e
(2 )
C on c en tr a ti on
p r ox y
(3 )
R el a ti on
(4 )
forecasts
(management)
HHI
forecasts
(management)
insignificant
(forecasts), weak (textual)
HHI
item
(segments)
T est of
c om p eti ti on
h y p oth esi s
(5 )
C i ted
T h eor y
(6 )
N o
N one
- (weak)
N o
N one
HHI
- (weak)
Y es
HL 9 6
item
(segments)
HHI
insignificant
Y es
V 8 3, HL 9 6
items
(advertising)
HHI
+ (weak)
N o
V oluntary nonfinancial disclosure and the cost of equity capital:
the initiation of corporate social responsibility reporting, D . S.
D haliwal, O . Z . L i, A. Tsang and Y . G . Y ang, The Accounting
Review (Jan., 2011).
P roprietary costs and the disclosure of information about
customers, J. A. Ellis, E. F ee and S. E. Thomas, Journal of
Accounting Research (Jun., 2012).
The fair value of cash flow hedges, future profitability, and stock
returns, J. L . Campbell, Contemporary Accounting Research,
forthcoming.
items
(corporate
social
responsibility)
B 8 3, D S9 0,
W 9 0, D 9 3,
N S9 3, G 9 4,
HL 9 6
HHI
insignificant
N o
N one
HHI
insignificant
Y es
items
(hedging)
HHI (top quantile)
+
N o
V 8 3, G 8 5,
D S9 0, W 9 0,
AM 07
N oncompliance with mandatory disclosure requirements: the
magnitude and determinants of undisclosed permanently
reinvested earnings, B . C. Ayers, C. M . Schwab and S. U tke, The
Accounting Review (Jan., 2014).
items
(permanently
reinvested
income)
Soft-talk management cash flow forecasts: bias, quality, and
stock price effects, M . D ambra, C.E. W asley and J.S. W u,
ontemporary Accounting Research (Jun., 2013).
M anagers' motives to withhold segment disclosures and the effect
of SF AS no. 131 on analysts' information environment, C. A.
B otosan and M . Stanford, The Accounting Review (Jul., 2005).
D iscretionary disclosure in financial reporting: an examination
comparing internal firm data to externally reported segment data,
D . A. B ens, P . G . B erger, and S. J. M onahan, The Accounting
Review (M ar., 2011).
The joint effects of materiality thresholds and voluntary disclosure
incentives on firms’ disclosure decisions,
S. Heitz man, C. W asley and J. Z immerman, Journal of
Accounting and Economics (F eb., 2010).
Redacted disclosure, R. E. V errecchia and J. W eber, Journal of
Accounting Research (Sep., 2006).
P erceived competition, profitability and the withholding of
information about sales and the cost of sales, E. D edman and C.
L ennox, Journal of Accounting and Economics (D ec., 2009 ).
Segment profitability and the proprietary and agency costs of
disclosure
P . G . B erger and R. N . Hann, The Accounting Review (Jul., 2007 ).
Contagion of accounting methods: evidence from stock
option expensing, D . A. Reppenhagen, Review of Accounting
Studies,
(Sep., 2010).
O rganiz ed labor and information asymmetry in the financial
markets, G . Hilary, Review of Accounting Studies (D ec., 2006).
items
(customers)
items (nonredactions)
HHI
+
Y es
V 8 3, D S9 0
HHI
insignificant
N o
W 9 0, V 8 3
HHI
+
Y es
HHI
insignificant
Y es
V 8 3, C8 3,
D S9 0, D 9 3,
CV 9 7 , C8 3,
AM 07 , B 09
HHI
+
N o
N one
HHI
insignificant
N o
N one
HHI (above
median)
-
N o
N one
HHI
-
N o
G 9 4
HHI
insignificant
N o
N one
HHI
insignificant
Y es
V 8 3, W 9 0,
D S9 0, G 9 4
HHI
insignificant
N o
N one
qualitative
(textual)
HHI
+
N o
N one
various
HHI
N o
AM 07
items (sales
and cost of
sales)
items
(segments)
items (stock
option
expense)
market
(liquidity)
Accounting Conservatism and Stock P rice Crash Risk: F irm-level
market (non
Evidence, J. B . K im and L . Z hang, Contemporary Accounting
crash risk)
Research, forthcoming.
M anagement forecast credibility and underreaction
market
to news, J. N g, I. Tuna, R. V erdi, Review of Accounting Studies
(reaction to
(D ec., 2013).
forecasts)
M arket reaction to the adoption of IF RS in Europe, C. S.
market
Armstrong, M . E. B arth, A. D . Jagolinz er and E. J. Riedl, The
reaction (IF RS
Accounting Review (Jan., 2010).
adoption)
D oes Silence Speak? An Empirical Analysis of D isclosure
qualitative
Choices D uring Conference Calls, S. Hollander, M . P ronk, and E.
(conference
Roelofsen, Journal of Accounting Research (Jun. 2010).
calls)
Annual report readability, current earnings, and earnings
qualitative
persistence, F . L i, Journal of Accounting and Economics, V ol. 45,
(textual)
N o. 2– 3 (Aug., 2008 ).
L arge-sample evidence on firms’ year-over-year M D & A
modifications, S. V . B rown and J. W . Tucker, Journal of
Accounting Research (M ay, 2011).
Employee ownership and firm disclosure, F . B ova, Y . D ou and O .
K . Hope, Contemporary Accounting Research, forthcoming.
N one
+
V 8 3, D S9 0,
N S9 3, G 9 4
Notes: This table lists all papers published in Journal of Accouting and Economics, The Accounting Review, Journal of Accounting Research,
Contemporary Accounting Research and Review of Accounting Studies that meet the following two conditions (a) refer to ``concentration" and
include ``HHI," "concentration ratio," or "CR4" as an independent variable, (b) include at least one dependent variable that is information-related
(excluding executive compensation). Column (1) is a bibliograpgic reference. Column (2) refers to the type of disclosure proxy. Column (3) refers
to the concentration proxy. HHI is the Herfindahl-Hirschman index, that is, the sum of the squared market share of the 40 largest firms in an
industry. CR4 is the Concentration Ratio 4 and is calculated as the sum of the market share of the four largest firms. Column (4) states the
primary empirical relation, where we denote weak situations where significance is only at the 10% level. In ambiguous cases, we present the
analysis by proxy and, otherwise, select the most frequent result. In column (5), we use judgment to decide whether a paper tests the
competition hypothesis, generally based on the objective of the title and abstract (this classification is rarely ambiguous). In column (6), we
reference all cited theory that refers to proprietary costs, tags are explicitly referenced in Table 2.
6
Table 1: Empirical research on concentration and disclosure
But does the referenced theory suggest using concentration as the measure of competition? References to formal theory are summarized in column (6) of Table 1, with details
for each reference in Table 2. About half the studies use concentration with no guidance
from theory, implicitly assuming a connection is self-evident. For others, the most widely
referenced paper is Verrecchia (1983). Although this classic paper offers a foundation
for strategic disclosure, it does not suggest using concentration as a proxy for proprietary
cost.
tag
Title
(1 )
(2 )
Da r r o u g h a n d
DS90
St a u g h t o n ( 1 990)
V 8 3
(3 )
e n try
V e r r e c c h i a ( 1 98 3 ) u n s p e c i f i e d
C V 97
G 94
H L 96
N S93
W 90
D93
C 8 3
B 09
A M 07
G 8 5
Type of competition
C lin c h a n d
e x is t in g ( C o u r n o t V e r r e c c h i a ( 1 997 ) d e m a n d )
G i g l e r ( 1 994 )
H a y e s a n
L u n d h o lm
N e w m a n
Sa n s i n g (
W a g e n h o
( 1 990)
Da r r o u g h
C la r k e
B o a rd
A ry a a
M it t e n
G a l- O
T h is p
d
( 1 996 )
a n d
1 993 )
fe r
( 1 993 )
e x is t in g ( C o u r n o t d e m a n d )
u n s p e c if ie d
e n try
e n try
e x
e x
( 1 98 3 )
d e
e x
( 2 009)
d e
n d
e x
d o r f ( 2 007 ) d e
e x
r ( 1 98 5 )
d e
e n
a p e r
(C
d e
is t in g
is t in g
m a n d
is t in g
m a n d
is t in g
m a n d
is t in g
m a n d
try a n
o u rn o
m a n d
)
( v a r io u s )
(B e rtra n d )
(B e rtra n d -
t
)
(C o u rn o t(C o u rn o t-
)
d e x is t in g
/c o s t)
M anager ' s
h or iz on
(4 )
s h o r t / lo n g
te rm
Timing
(5 )
e x -p o s t
C r ed ib ility
(6 )
tru th fu l
C ompetition
M eas u r e of
v s .
N b . of fir ms
competition
d is clos u r e
(7 )
(8 )
(9 )
+
s h o rt te rm
e x -p o s t
tru th fu l
lo n g t e r m
e x -p o s t
tru th fu l
e x -p o s t
c h e a p t a lk
+
c h e a p t a lk
+
lo n g / s h o r t
te rm
lo n g t e r m
s h o r t / lo n g
te rm
s h o rt te rm
e x -p o s t
e x -p o s t
e x -p o s t
tru th fu l
tru th fu l
s h o rt te rm
e x -a n te
tru th fu l
lo n g t e r m
e x -p o s t
tru th fu l
lo n g t e r m
lo n g t e r m
lo n g t e r m
s h o r t / lo n g
te rm
e x -a n te
e x -p o s t
e x -a n te
e x -a n te
/e x -p o s t
tru th fu l
tru th fu l
tru th fu l
tru th fu l
-
e n try c o s t
1 -2
s u b s t it u t io n
2
u n s p e c if ie d
-
1
m o n o p o ly v s
d u o p o ly
-
s u b s t it u t io n
+ /-
e n try c o s t
e n try c o s t
+ /-
s u b s t it u t io n
-
s u b s t it u t io n
n o d is c lo s u r e n o n e
-
2
2
1 -2
1 -2
2
n
s u b s t it u t io n
2
n o d is c lo s u r e n o n e
2
+ /-
n b . o f f ir m s
n
n
Table 2: Referenced research on concentration and disclosure
In Table 2, we list theory papers explicitly referenced in any of the papers in Table 1.
We organized this list around several distinctive aspects of the theoretical models:
1. The type of competition under consideration (column (3)): whether it refers to entry
by potential rivals or to existing competition. Models may also involve Cournot
or Bertrand competition, or common versus firm-specific information, which the
literature labels as demand versus cost information.
2. The horizon of the manager (column (4)): the manager may maximize the perceived
7
market value of the firm conditional on disclosure (short term) or the expected final
cash flows (long term).
3. The timing of the disclosure decision (column (5)): the manager may have to set up
an information system before receiving information (ex ante), or can decide whether
to voluntarily disclose after observing the realized signal (ex post).
4. The truthfulness of the reports (column (6)): the manager may be restricted to report
information truthfully or withhold, or may communicate an unverifiable message
(cheap talk).
Most of the literature referred to in Table 2 adopts the assumptions of existing competition, long term horizon, ex ante and truthful reporting; in fact, nearly all of the extensive
economic literature in this area, as surveyed by Raith (1996), adopts these assumptions.
The accounting literature is broader, although it tends to favor ex-post reporting.
The literature as a whole tends to favor Cournot-Nash competition with demand uncertainty. Two studies consider Bertrand-Nash competition, also with demand information.
The only study in this list that jointly considers multiple forms of competition is Darrough
(1993), but it does so by construction, because her research design is precisely to observe
the effect of the nature of competition. Among the three studies cited from the economics
literature, two accommodate n firms and, therefore, although their focus is not on concentration and disclosure, are suitable to the analysis of exogenous changes to concentration.
In both studies, n does not have any effect on the optimal disclosure.
In the accounting literature, all studies involving an existing number of rivals consider
only a duopoly and do not intend to offer implications about concentration. Analyzing the
implications of entry models is somewhat more difficult, because the number of firms, n,
is endogenous. To our knowledge, none of these studies claims to offer predictions about
concentration and, instead, their focus is on different measures of competition (column
(9)). In fact, we could not find any study in this group that explicitly makes predictions
about concentration. From column (10), these models examine industries that are monopolies or duopolies and were designed to parsimoniously capture the effect of entry, not to
predict the number of firms in an industry.
In our study, we cover a selection of settings from Table 2, with the restriction that
we focus on the (tractable) Cournot setting.3 We examine the prediction of the model
3
The (differentiated) Bertrand setting, as is known in this literature, tends to become intractable and ambiguous with more than two rivals. For example, in her treatment of this question, Gal-Or (1986) examines
Bertrand competition with two rivals only, and we are not aware of any other study since then that analyzes
disclosure in a Bertrand setting with more than two firms.
8
if the number of rivals is exogenous or is the result of entry, and with demand or cost
information. We also vary the assumptions regarding whether the firm implements an
information system ex-ante or information is disclosed ex-post, and whether the manager
cares about short-term stock prices or may wait until cash flows realize.
Our study adds to the fertile recent literature on competition and disclosure. This literature has largely contributed to clarifying the relationship between various aspects of
the industrial organization – different from market concentration – and disclosure. For
example, in the context of voluntary disclosures, Arya et al. (2010) study the strategic
disclosure choice of an incumbent firm operating in multiple segments and facing competition from a new entrant, whereas Bagnoli and Watts (2010) look at disclosure choices
in a duopoly setting in which firms can bias their reports at a cost. Arya and Mittendorf
(2013) consider the effect of disclosure in industries with imperfect competition along
vertical production chains. In the follow-up literature, this question has been the object
of considerable research featuring strategic relationships in complex production chains
(see, e.g., Guo et al. 2014 and Arya et al. 2014). Corona and Nan (2013) show that
competition can affect firms’ incentives to disclose information in a timely manner in order to gain a competitive advantage. Suijs and Wielhouwer (2014) focus on mandatory
disclosure, showing that the optimal mandatory disclosure is a function of the competition’s characteristics. Guenther and Sansing (2012) further investigate the consequences
of LIFO repeal on a firm’s value in imperfectly competitive markets. This literature exists
to guide researchers toward clear settings and appropriate measures of competition, and
away from one-size-fits-all proxies, such as concentration. In this light, our study also
serves to motivate the need for a proper understanding of the institutional details of an
industry.
3
Ex-ante disclosure
In this section, we introduce our model and examine the role of concentration in the
presence of demand uncertainty, and when the informed firm can implement its preferred
information system ex ante (e.g., as an industry standard, a reporting policy, etc.). In Table
2, the setting of this section corresponds to the class of models with Cournot-demand and
ex-ante.
9
3.1 Existing rivals
Consider a standard oligopoly model in which the number of firms in the industry is
given. The manager maximizes the perceived market value of the firm conditional on
either disclosure (short term) or on the expected final cash flow (long term). As will
become apparent, this distinction is irrelevant here, because when a disclosure decision is
made ex-ante, the expected cash flow is equal to the expected market price.
Assume n ≥ 2 risk-neutral firms compete. Each firm has a technology that produces
differentiated goods at a fixed marginal cost c and faces an inverse demand
Pi (qi ; (qj )i6=j ) = a − bqi − bt
X
qj ,
(1)
j6=i
where Pi is the price paid for the goods of firm i, a is a common-market demand intercept,
qj represents each firm’s output, and b > 0 (resp., bt > 0) is the sensitivity of the price
to the firm’s (resp., rivals’) output. Note the parameter t ∈ [0, 1] represents the degree of
product differentiation, ranging from zero when the goods are independent to 1 when the
goods are perfect substitutes. Firm i = 1 will be privately informed about the demand
intercept a, where a is a random variable with p.d.f. f (.) and c.d.f. F (.). All other
parameters are common knowledge.
The timeline is as follows. At time 0, firm i = 1 chooses an information system
to report a. In this setting, we model the optimal choice before receiving information.
In prior research, this choice is usually modeled as one of variance (Clarke 1983, GalOr 1985, Darrough 1993). We update this assumption using the more recent formulation
as an optimal ex-ante information system, which Kamenica and Gentzkow (2011) refer to
as Bayesian persuasion. Our model does not require a restriction to normally-distributed
noise and even turns out to be simpler to solve.4
The information system may truthfully report or withhold the realization of a. Let
θ(a) ∈ {0, 1} be a function equal to 1 if the information system reports a, denoted I = a,
and zero if a is withheld, denoted as I = N D. Firm 1 chooses θ(.) optimally at time 0,
prior to receiving any information.
At time 1, each firm observes its post-disclosure information Ii , where I1 = a and
Ii = I for i ≥ 2. That is, the informed firm always knows a, and its uninformed rivals
know a only if it is disclosed. Conditional on available information, each firm (simulta4
All of our results carry over to normally-distributed random variables and a choice of variance. Another
reason for not using the normal setting is aesthetic, because (later on) entry and ex-post models cannot be
solved with normally-distributed noise, because an ex-post disclosure might depend on the realized signal.
10
neously) chooses its production quantity qi∗ , where
qi∗ ∈ argmaxq
E(Pi (q; (qj∗ )j6=i )q − cq|Ii ).
(2)
The first-order condition of this problem implies
qi∗
= E(
a − c − bt
P
j6=i
2b
E(qj∗ |Ij )
|Ii ).
In a symmetric equilibrium, q ∗ ≡ qj∗ for any j ≥ 2. Solving this system of equations,
q1∗ =
(a − c)
(a − E(ã|I2 ))(n − 1)t
+
,
b(2 + (n − 1)t)
2b(2 + (n − 1)t)
qi∗ =
E(ã|I2 ) − c
.
b(2 + (n − 1)t)
(3)
For these equations to be exact, keep in mind that quantities, and prices, must remain
positive. Otherwise, we might sometimes be predicting an informed firm choosing a
negative quantity against a low demand and, in doing so, achieving a higher profit than
during a period of high demand. To avoid such issues, we assume a is suitably bounded
so that q1∗ > 0 for any I2 .5
As is intuitive, the informed firm’s output q1∗ is decreasing in the number of existing competitors. Closer inspection reveals this effect is the result of a trade-off between
two forces. The first term in q1∗ is decreasing in n, because a greater number of rivals
shrinks the per-firm available demand, decreasing quantity produced. The second term
in q1∗ is ambiguous because it represents how the informed firm adjusts output to the
beliefs of competitors. If uninformed competitors have unfavorable beliefs, that is, if
a − E(ã|I2 ) > 0, they tend to under-produce relative to what they would have produced
if informed. Then, a high n magnifies the aggregate under-production and encourages the
informed firm to produce more. Naturally, this effect reverses when the informed firm has
unfavorable information a − E(ã|I2 ) < 0.
Although the number of rivals changes quantities produced, it does not alter disclosure
preferences. For any information system, the profit of the informed firm conditional on a
5
A sufficient condition that guarantees positive quantities is where ã has support on [a, a], and
(a − c)
(a − a)(n − 1)t
+
> 0.
b(2 + (n − 1)t) 2b(2 + (n − 1)t)
Note that the Normal setting used in prior literature occasionally leads to negative quantities, which makes
the implied analysis inherently an approximation rather than an exact argument, that is, assuming the mean
is large enough so that negativity is not too frequent (Liang and Wen 2007). Our approach offers a simple
alternative to this approach because it does not require normality.
11
demand a is
π1 (a) = q1∗ P1 (q1∗ ; (qj∗ )i6=j ) − q1∗ c = b(q1∗ )2 .
Substituting the optimal quantity from (3) into π1 (a), the profit of the informed firm
as follows:
(i) if a is disclosed, that is, θ(a) = 1,
π1 (a) =
b(q1∗ )2
(a − c)2
=
, and
b(2 + (n − 1)t)2
|
{z
}
(4)
≡π1d (a;n)
(ii) if a is withheld, that is, θ(a) = 0,
π1 (a) = b(q1∗ )2 =
(2(a − c) + (a − E(ã|N D))(n − 1)t)2
.
4b(2 + (n − 1)t)2
|
{z
}
(5)
≡π1nd (a;n)
We are now equipped to derive the ex-ante optimal information system. Recall the informed firm chooses the information system θ(.) to maximize its expected profits. Therefore, the information system solves the following program:
θ∗ (.) ∈ argmaxθ
V = E(θ(ã)π1d (ã; n) + (1 − θ(ã))π1nd (ã; n)).
(6)
The informed firm’s disclosure faces a trade-off. On the one hand, the disclosure informs
the competitors about the firm’s payoff from the product market. In particular, if the firm
discloses a low demand, the competitors learn that a relatively low output is profitable.
Thus, disclosure of a low-demand intercept discourages supply by its competitors.
On the other hand, if the informed firm discloses information to its competitors, it also
informs them about its behavior in the product market. Specifically, if the firm discloses
a low demand, it signals to the competitors that it will produce less aggressively than
an uninformed firm. Therefore, disclosing low demand implies a cost because it makes
the competitors optimistic about the competitive pressure, and thereby encourages them
to supply more to the market. As we show next, the resolution of this trade-off is no
disclosure.
Proposition 1 Under existing (Cournot-demand) and ex ante, the informed firm always
prefers no disclosure (θ(a) = 0 for all a) regardless of the number of firms in the industry
and whether its objective is short-term or long-term.
12
Note that the optimal disclosure policy does not vary as the number of rivals changes.
To gain some further intuition for the irrelevance of n, consider the difference between
the expected profit of the informed firm under no disclosure π1nd and its profit under full
disclosure π1f d , and observe it increases in n:
π1nd − π1f d =
V ar(ã)
4
).
(1 −
4b
(2 + (n − 1)t)2
Each rival uses the disclosure to maximize its profits, causing the full-disclosure profit
of the informed firm to decrease. The effect is stronger when the number of rivals increases. Because no disclosure is preferred under n = 2, it must be preferred for any
number of rivals.
The result of Proposition 1 is not new and, indeed, generalizes the observation in
Clarke (1983), Gal-Or (1985), and Darrough (1993). In these models, the demand intercept is normally-distributed and the information system must involve the choice of a
variance. We extend this result to any continuous distribution for the demand shock and
to information systems that may not be symmetric (as in a choice of variance).
The rationale behind these results is as follows: revealing information about “common
value” information leads to more correlated output because each competitor sees the same
demand instead of the expected value. In Cournot competition, competitive firms prefer
uncorrelated output because of the convexity of the profit function with respect to prices.
3.2 Potential rivals
Next, we derive the optimal disclosure under the assumption the potential rivals’ optimal decision to enter the market determines the number of firms in the industry. That
is, we consider n to be an endogenous variable. Specifically, this environment can be described as entry (Cournot-demand), long term and ex ante. Hereafter, we leave aside any
special issue of discreteness of entry, although we note that it may matter for industries
that are small and could accommodate few entrants.6
Consider the timeline as in the previous subsection and add a time period between
t = 0 and t = 1, in which a large pool of potential rivals can decide to enter for a fixed
cost K > 0.7 When deciding whether to enter, a potential rival j ≥ 2 only knows the
6
This assumption is common in the literature (Mankiw and Whinston 1986). We impose it here to rule
out sophisticated disclosure strategies that are solely meant to change the number of firms in the industry
by a single firm. See also Heinle and Verrecchia (2009) for a recent example of free-entry in a model of
pure financial reporting.
7
We implicitly assume K is not too large; in particular, it is not larger than a monopolist’s profits in this
market. Otherwise, any entry will never occur, and our research question could not be addressed.
13
public disclosure I. Let n(I) define the equilibrium number of competitors given a public
signal I ∈ {N D, a}. After entry, all uninformed firms achieve their Cournot profit, as
given by
(E(ã|I) − c)2
π(I) = b(q ∗ )2 =
.
(7)
b(2 + (n(I) − 1)t)2
Rivals decide to enter if they expect to make a positive profit. Hence, competitive
entry implies the expected profit from entry must be zero for any public information I,
π2 (n(I)) − K = 0.
Substituting in equation (7), and solving for n(I2 ) yields a number of competitors8
n(I) =
E(ã|I) − c t − 2
√
.
+
t
t bK
(8)
Equation (8) is key to our analysis. The disclosed information affects entry because,
for example, reporting a low a will reduce entry conditional on that report and, vice-versa,
reporting a high a will increase entry. But, does disclosure affects entry in expectation?
To answer this question, let us apply the law of iterated expectations to equation (8),
implying that the expected entry is
E(n(I)) = E(
E(ã|I) − c t − 2
E(ã) − c t − 2
√
+
+
)= √
,
t
t
t bK
t bK
that is, expected entry does not depend on the information system chosen by the manager
and is the same regardless of how the manager discloses.
One might conclude the informed firm will be indifferent to any disclosure policy
given that such a policy does not decrease expected entry. This claim is not correct,
because the informed firm’s profits are not proportional to entry; indeed, the informed
firm would prefer to manage entry conditional on the demand realization, reducing it
when market demand is strong and the profit potential is higher. Full disclosure fails to
achieve this effect, because full disclosure tends to increase entry conditional on high
market demand. Therefore, the informed firm is better-off with a maintained policy of
withholding.
Next, we make this intuition formal. Reinjecting the number of competitors in (8), we
8
We do not model here the individual decision of all potential rivals or the coordination needed to get
the exact number of entrants into the market. Strictly speaking, assuming a randomized strategy for each
potential entrant, the number of firms we find in (8) represents the expected number of entrants.
14
find a withholding informed firm achieves a profit
π1nd (a, n(N D)) =
√ 2
a − E(ã|N D) + 2 bK
.
(9)
V ar(ã|N D)
,
4b
(10)
4b
Taking expectations over (9), withholding yields a profit
E(π1nd (ã; n(N D))|N D) = K +
where V ar(ã|N D) ≡ V ar(ã|θ(ã) = 0) denotes the variance conditional on no disclosure.
On average, the informed firm obtains an incremental profit, above the entry cost, that
is proportional to the residual variance in the private information V ar(ã|N D). Intuitively,
absent any informational advantage, the informed firm would earn the same profit as all
entrants, which, with endogenous entry, is equal to the cost of entry.
Furthermore, equation (10) suggests a simple trade-off. A policy of disclosing certain
market demands will, conditional on the disclosure being made, reduce the profit of the
informed firm to the entry cost K. But, disclosure of, say, intermediate market demands,
will tend to increase the variance conditional on non-disclosure. For example, this conditional variance V ar(ã|N D) tends to be greatest if only the highest and lowest realizations
of ã are withheld.9
Below, we compare each side of this trade-off by calculating the informed firm’s expected profit:
V
= E(θ(ã)π1d (ã; n(ã)) + (1 − θ(ã))π1nd (ã; n(N D)))
V ar(ã|N D)
= K + E(1 − θ(ã))
.
4b
(11)
In the next proposition, we show this profit function is always maximized under no
disclosure. That is, even though disclosure might increase the conditional variance – at
the cost of decreasing the probability of non-disclosure – it is never desirable.
Proposition 2 Under entry (Cournot-demand), long term and ex ante, the informed firm
always prefers no disclosure (θ(a) = 0 for all a).
9
In market settings, certain forms of disclosure such as withholding information about extreme values
tend to increase ex post uncertainty, which may sometimes lead to an increase in information asymmetry at
an ex ante stage (Cheynel and Levine 2015).
15
4
Ex-post disclosure
So far, we have considered ex-ante disclosure choice, whereby the firm implements its
preferred information system prior to receiving private information. We find the informed
firm prefers to withhold information regardless of the number of rivals. However, the
firm needs the ability to commit to an information system. We now extend the analysis to
settings in which the firm does not commit but instead chooses to disclose after observing
the information. In Table 2, this section corresponds to the class of models with Cournotdemand and ex post disclosure.
Before we lay out the formal analysis, note that models of product market competition
do not meet the conditions for the unraveling theorems as in, say, Milgrom (1981). Strictly
speaking, the unraveling theorems apply to truthful communication games in which (a)
the utility of the discloser depends only on post-disclosure market expectation, and not
directly on the discloser’s observed information, and (b) disclosure does not involve a
cost.
Both of these requirements are violated in a competition game. First, the profit of the
informed firm depends on both competitors’ expectations and on the firm’s own information (see equation (5)), because the information is used to choose production quantity.
Second, disclosure does involve an endogenous proprietary cost – in that the discloser is
better-off not disclosing (as shown in Propositions 1 and 2). Indeed, Verrecchia (1983)
proves disclosure costs tend to prevent unraveling. We make these preliminary remarks
because we demonstrate the unraveling property actually extends — often but not always— to product market competition with ex-post disclosure.
4.1 Long-term motives
Existing rivals
Consider the setting with existing (Cournot-demand), long term and ex post, in which
managers have a long-term horizon and value-realized cash flows. Because the informed
firm may always voluntarily disclose information, it must hold that, for any withheld
information a, the firm is better-off not disclosing, or π1d (a; n) ≤ π nd (a, n). We ask
whether such a potential proprietary cost is sufficient to rationalize an equilibrium in
which some information is withheld.
We conjecture that some market demands are withheld or, more precisely, that withholding occurs with non-zero probability. Then, we should find withheld market demand
16
a strictly below the expected withheld market demand, that is, a < E(ã|N D). Evaluating
the profit of the informed withholding firm at this market demand implies
(2(a − c) + (a − E(ã|N D))(n − 1)t)2
4b(2 + (n − 1)t)2
(a − c)2
<
= π1d (a; n),
b(2 + (n − 1)t)2
π1nd (a, n) =
(12)
where the inequality follows from the fact that, for quantities to be positive, 2(a − c) +
(a − E(ã|N D))(n − 1)t > 0.
We thus conclude that, in any equilibrium with some withholding, all informed firms
with below-average market demand would wish to disclose it. Intuitively, disclosing unfavorable information reduces the quantity chosen by competitors, leading to greater future
profits. All below-average non-disclosers shift to disclosure, implying that, in any equilibrium, all information is disclosed.
Proposition 3 Under existing (Cournot-demand), long term and ex post, the informed
firm always chooses full disclosure (θ(a) = 1 for all a) regardless of the number of firms
in the industry.
Although the informed firm faces a (proprietary) cost from disclosure, which tends
to reduce profits in expectation, this cost is not structured in a manner that would prevent unraveling. The intuition for the result is the following: the proprietary cost, in the
competition game, is not a fixed cost that would depend only on the presence of disclosure. Instead, this cost varies as a function of the information of the informed firm. And
although the cost is positive in expectation (the firm achieves lower surplus under full
disclosure), it will turn negative, becoming a benefit, if the information available is unfavorable relative to competitors’ prior beliefs. The transformation of the expected cost
into a benefit, for any below-average information, is what causes all below-average firms
to prefer disclosing, which in turn leads to unraveling. As for the role of concentration, in
this setting, the chosen optimal disclosure is always full disclosure and does not depend
on the number of rivals.
Potential rivals
We next extend the previous approach to the case in which the number of entrants is
endogenous, because a rival enters when expecting a profit greater than the entry cost
17
K. This setting corresponds to modeling an environment with entry (Cournot-demand),
where the manager has long term motives, and reports ex post.
If the informed firm discloses, all firms achieve the same profit, and hence the informed firm achieves a profit equal to K. If the informed firm does not disclose, it
achieves a profit given by equation (9). Thus, information is disclosed if
K≥
√ 2
a − E(ã|N D) + 2 bK
4b
.
(13)
What does the withholding region look like with the ex-post incentive compatibility
condition (13)? Under the (maintained) assumption of positive quantities, the right-hand
side of equation (13) is increasing in a, attaining K at a market size a = E(ã|N D). Hence,
any below-average withholding firm will be better off disclosing, yet again independently
of the number of rivals that enter in equilibrium.
Proposition 4 Under entry (Cournot-demand), long term, and ex post, the informed firm
always chooses full disclosure (θ(a) = 1 for all a).
4.2 Short-term motives
Existing rivals
Under some circumstances, managers may feature a short-termist bias and maximize
expected value after a disclosure is made. Below, we extend the analysis and consider
short-term reporting motives. That is, we assume the manager cares about the perceived
market value of the firm before cash flows realize – the case of existing (Cournot-demand)
competition, short-term motives, and ex-post reporting. In the formal analysis, we change
the expected cash flow π1nd (a, n) into the market perception of the expected cash flow
π̂1nd = E(π1nd (ã, n)|N D), because now the market prices the firm based on public information. The manager should consider two (contradicting) forces: on one hand, s/he wants
to disclose bad news in order to reduce competitors’ quantities, whereas on the other hand,
s/he also wants to disclose good news to increase market perceptions.
A manager observing a discloses if and only if the firm’s market price upon disclosure
is greater than the price under no disclosing; that is,
∆1 (a) = π1d (a; n) − π̂1nd ≥ 0.
18
The function ∆1 (a) is increasing in a because a higher market demand – although it
causes rivals to produce more – is nevertheless good news in terms of future cash flows.
Thus, the information is disclosed if demand exceeds some threshold a ≥ τ . Because
disclosure may induce a loss of surplus to competitors, especially when favorable information is reported that induces competitors to produce more, an interior threshold τ might
exist, and then this threshold might be a function of the number of rivals.
However, as we show below, an interior threshold does not occur in equilibrium. Note
that an interior threshold would make the firm at a = τ indifferent between disclosing
and not disclosing; that is,
∆1 (τ ) = π1d (τ ; n) − π̂1nd = 0.
Denoting aN D = E(ã|ã ≤ τ ),
(τ − c)2
(2(ã − c) + (ã − aN D )(n − 1)t)2
−
E(
|ã ≤ τ )
b(2 + (n − 1)t)2
4b(2 + (n − 1)t)2
E((ã − c)2 |ã ≤ τ )
(τ − c)2
−
> 0;
=
b(2 + (n − 1)t)2
b(2 + (n − 1)t)2
∆1 (τ ) =
that is, an average non-disclosing firm, would always be better off changing its nondisclosure action to disclose. As before, no equilibrium in which some firms withhold
information is sustainable.
Proposition 5 Under existing (Cournot-demand), short term, and ex post, the informed
firm always chooses full disclosure (θ(a) = 1 for all a) regardless of the number of firms
in the industry.
Potential rivals
With endogenous entry (entry (Cournot-demand), short-term and ex-post), the firm
discloses if the expected profit when disclosing, K, is greater than the expected profit (the
market price) when withholding:
K ≥ E(π1nd (ã; n(N D))|N D) = K +
V ar(ã|N D)
.
4b
(14)
Obviously, the firm always prefers to withhold.
Proposition 6 Under entry (Cournot-demand), short term, and ex post, the informed firm
always chooses no disclosure (θ(a) = 0 for all a).
19
This result might seem, at first sight, surprising, given that settings with short-term
reporting and ex-post disclosure are part of the required assumptions for the unraveling
theorem. But we do not find unraveling here; rather, we find that reporting motives serve
to provide the manager with incentives not to disclose ex-post. Similar to the earlier
intuition, disclosure actually creates proprietary costs. A withholding manager is not fully
penalized for low market demands (because the market does not know this information),
which, in turn, provides incentives to credibly follow the non disclosure policy.
We note that short-term motives actually reduce disclosure. That is, whereas the manager would have chosen full disclosure under entry (Cournot-demand), long term, and
ex post, changing the manager’s horizon to short-term has caused the optimal disclosure
policy to shift to non-disclosure.
5
Cost uncertainty
We now turn to a class of models in which the source of uncertainty is a firm’s individual
cost of production, whereas the demand intercept a is common knowledge. The informed
firm knows its own cost c̃1 , with probability density function g(c1 ) and a cumulative
density function G(c1 ). The remaining competitors have an identical cost c ≡ cj for
j ≥ 2, that is common knowledge.10
5.1 Existing rivals
We begin the analysis under the assumption of ex-ante disclosure, with a pre-existing set
of rivals, that is, existing (Cournot-cost), long term, and ex ante. As before, the firm
implements an information system θ(c) equal to 1 when the cost is disclosed, and we
denote the public information as I ∈ {c1 , N D}. The informed firm knows I1 = c1 while
competitors i ≥ 2 know the public signal Ij = I = {c1 , N D}:
qi∗ ∈ argmaxq
E(Pi (q; (qj∗ )j6=i )q − ci q| Ii ).
(15)
Solving this maximization, the quantity each firm chooses is
qi∗
=
a − ci − bt
P
2b
10
j6=i
E(qj |Ii )
(16)
This assumption is common in the literature (Darrough 1993), although one might wonder what would
occur if (i) costs were different across competitors, or (ii) competitors had their own private costs. Unfortunately, these models seem to become very intractable and ambiguous given too much heterogeneity on the
cost parameter.
20
Let q ∗ denote the quantity chosen by all uninformed rivals. Solving the system of equations in (16) implies the following cost-uncertainty analogue to (3):
a − c1 (n − 1)t(2(a − c) − t(a − E(c̃1 |I)))
−
,
2b
2b(2 − t)((n − 1)t + 2)
2(a − c) − (a − E(c1 |I))t
=
.
b(2 − t)((n − 1)t + 2)
q1∗ =
(17)
q∗
(18)
The lower rivals’ expectation about the informed firm’s cost, the higher their chosen quantities. As before, to avoid the occurence of negative quantities, we require c̃1 to be be
bounded.
Let π1 (c1 ) denote the informed firm profit conditional on the disclosure decision I ∈
{c1 , N D}. Reinjecting (17),
π1 (c1 ; I) =
(t(a − c1 ) − t(c − E(c̃1 |I))(n − 1)) − 2(a − E(c̃1 |I)))2
.
b(2 − t)2 ((n − 1)t + 2)2
(19)
In what follows, we denote π1d (c1 ; n) as the profit conditional on disclosure I = c1 ,
and π1nd (c1 ; n) as the profit conditional on withholding I = N D. The optimal information
system then solves the following program:
θ∗ (.) ∈ argmaxθ
V = E(θ(c̃1 )π1d (c̃1 ; n) + (1 − θ(c̃1 ))π1nd (c̃1 ; n)).
(20)
Proposition 7 concludes the analysis by deriving the optimal information system.
Proposition 7 Under existing, (Cournot-cost), long-term, and ex-ante, the informed firm
always prefers full disclosure (θ(c1 ) = 1 for all c1 ) regardless of the number of firms in
the industry.
We do not delve into this result, because, like its Cournot-demand analogue, it is
a generalization of prior results (Gal-Or 1985, Darrough 1993) to arbitrary information
systems and distributions. When disclosure is firm-specific information, disclosing leads
to more uncorrelated output because competitors learn the real value instead of forming an
expectation. Again, because of the convexity of the profit function in prices, the informed
firm prefers uncorrelated output and hence prefers full disclosure.
However, note that we show this result (in the Appendix) in a strong sense: whereas
prior literature shows that increasing the noise in a signal is beneficial – a form of withholding – we show here that, regardless of which signals would be withheld, disclosing
them would always increase the informed firm’s expected profits. For our purpose, a key
21
observation is that, in this setting, the choice of the optimal disclosure does not change as
a function of the number of rivals.
5.2 Potential rivals
Next, we alter the setting to endogenous entry, that is, with entry (Cournot-cost), long
term, and ex ante. In equilibrium the optimal number of entrants depends on whether the
established firm has disclosed its information.
If the informed firm discloses c1 , a rival will achieve a profit post-entry equal to b(q ∗ )2 .
Developing q ∗ from equation (18), the expected profit of a rival entering must be equal to
the cost of entry, implying
b(q ∗ )2 =
(2(a − c) − (a − c1 )t)2
= K,
b(2 − t)2 ((n(c1 ) − 1)t + 2)2
(21)
where n(c1 ) is the entry conditional on a disclosure I = c1 . Substituting in the equilibrium entry n(c1 ) from equation (21) into equation (19),
π1 (c1 ; c1 ) =
2
√
(2 − t) bK + c − c1
b(2 − t)2
.
(22)
This equation is the analogue to π1 (a, a) = K in the case of Cournot-demand; however,
under Cournot-cost, the informed firm is no longer symmetrical to all rivals, even after a
disclosure, so that it typically does not achieve a profit equal to the cost of entry.
If the informed firm withholds information, rivals will use their expected beliefs about
c1 . Then, the profit of an entering rival must satisfy b(q ∗ )2 = K. After substituting q ∗
from (17),
(2(a − c) − (a − E(c̃1 |N D))t)2 + t2 V ar(c̃1 |N D)
= K.
(23)
b(2 − t)2 ((n(N D) − 1)t + 2)2
Substituting in n(N D) into equation (19), and taking expectations, the informed firm
achieves an expected profit conditional on a non-disclosure equal to
(E(c̃1 |N D) − c)2 + V ar(c̃1 |N D)
b(2 − t)2
√
−2(2 − t) bK(E(c̃1 |N D) − c)
+
.
b(2 − t)2
E(π1 (c1 ; N D)|N D) = K +
As can be seen from equation (22), this expected profit is always smaller than the expected
22
profit when disclosing E(π1 (c˜1 ; c˜1 )|c̃1 ∈ N D). Hence, for any possible choice of withholding, changing all withheld information into a disclosure will increase the expected
firm’s profit. It follows that the preferred policy is one of full disclosure:
Proposition 8 Under entry (Cournot-cost, long term, and ex ante, the informed firm always prefers full disclosure (θ(c1 ) = 1 for all c1 ).
We have shown that the optimal reporting policy in a model with an existing set of
entrants — full-disclosure — remains the optimal policy in a model with endogenous
entry. To see why (and why this case is different from the case of uncertain demand),
note that the benefit in using disclosure to manage entry as a function of the realized
information is no longer clear. Instead, the informed firm needs to coordinate competitors
not to over-produce if it has a lower cost, and thus prefers to be in a situation featuring
full disclosure. Lastly, the expected number of entrants is no longer independent of the
disclosure policy.
5.3 Ex-post disclosure
We return next to the problem involving ex-post disclosure, that is, when the manager
decides to disclose after observing the information. Ex-post disclosure imposes the additional ex-post incentive-compatibility condition that a manager cannot credibly commit
to withhold information if doing so is not ex-post desirable. However, note that this issue
of ex-post incentive compatibility does not exist in all models that are Cournot-cost and
ex-post, because a policy of full-disclosure is already the one that maximizes the firm’s
utility ex-ante. The equilibrium in which the firm fully discloses remains an equilibrium
with ex-post incentive compatibility. If a firm were to deviate from its (preferred) equilibrium in which it is expected to fully disclose, making an off-equilibrium move to withhold
information, a set of beliefs exists that would make such a deviation unprofitable.11 Therefore, we conclude, below, that the informed manager prefers full-disclosure under ex-post
reporting.
Proposition 9 Under Cournot-cost, and ex-post, the informed firm always prefers full
disclosure (θ(c1 ) = 1 for all c1 ) regardless of the number of firms in the industry.
This last result is still in line with our underlying theme that, in this setting as well, the
number of rivals fails to relate to the disclosure policy.
11
In fact, this argument can be made stronger: in most settings, no equilibrium exists in which the firm
would withhold information.
23
6
Empirical Predictions
We have shown, across all settings, that a comparative static on the number of entrants
or on economic primitives that affect the equilibrium number of entrants, does not alter
the optimal disclosure policy. Hence, according to our theory, concentration levels should
have no explanatory power for whether a firm discloses. Put differently, concentration is
not the right variable to test the proprietary-cost hypothesis or the relationship between
disclosure and competition.
On the other hand, our analysis still generates numerous empirical implications. That
is, other observable dimensions of competition are likely to offer theory-motivated testable
implications of the proprietary-cost hypothesis. Table 3 summarizes the optimal disclosure in the different competition environment, sorting (with overlap) on four empirical
predictions.
The first determinant of the optimal disclosure choice is whether the manager discloses with the sole objective of maximizing short-term price (Verrecchia 1983), or has
long-term motives and discloses to maximize long-term cash flows (Gal-Or 1985, Darrough
1993). The reporting objective is likely to vary across firms: to give a few examples, managers with many exercisable stock options, an upcoming retirement, or with firms that are
more liquidity-constrained or are engaging in new security offerings, are likely to more
greatly favor short-term prices over long-term cash flows. We predict that managers with
short-term motives disclose less, but only if the industry features endogenous entry. The
latter may be proxied by changes to the number of firms or to concentration ratios. By
contrast, in industries with a relatively exogenous set of firms, we do not find any effect
of managerial motives on entry. In short, proprietary costs may be found in models with
entry in their interaction with proxies for the manager’s objectives.
The second determinant of the optimal disclosure is whether a manager commits to a
disclosure policy or discloses on a purely discretionary basis. We predict that managers
with pure discretionary disclosure tend to disclose more information. A good empirical setting to test this prediction is unbundled (or sporadic) versus bundled management
forecasts, because these forecasts tend to be unexpected and, comparably, are more discretionary. Our model predicts, therefore, that managers disclose more incremental information in their unbundled forecasts. By contrast, bundled forecasts are often interpreted
as implicit commitments to a regular reporting policy, possibly because the strategic interruption of a forecasting behavior could be used as part of a lawsuit. This effect occurs
weakly in all settings; to increase the power of this test, we also predict the effect will not
occur (i.e., no effect) in settings with endogenous entry and short-term motives, because
24
the optimal disclosure is the same regardless of the assumption about commitment.
The third determinant of the optimal disclosure policy is whether the industry features
endogenous entry or an established number of entrants. Across all settings, we find that
industries with endogenous entry feature weakly less disclosure than (more established)
industries with an exogenous number of firms. This prediction might be tested via changes
to the number of firms or the concentration levels, or in terms of the industry cycle (e.g.,
older, mature industries feature less entry). Cross-referencing with the other determinants,
the effect of endogenous entry should be found in settings with short-term motives and
discretionary disclosures.
Finally, the fourth determinant of the optimal disclosure policy is whether the disclosure is about common (demand) or firm-specific (cost) information. We might consider
testing this prediction by examining setting in which disclosed information might have a
larger effect on competitors because, beyond the competitive effects, disclosure about demand may reflect additional commonalities in the information. This distinction between
disclosure about demand and disclosure about cost may also be directly tested by considering the association between revenue across members of the industry, because common
shocks are usually tied to demand information. Prior literature has conjectured this distinction is of relevance primarily in models of existing competition, showing that fewer
incentives exist to disclose information about demand. Our integrated model reveals that
this intuition largely carries over to endogenous entry, unifying the two approaches. We
also predict the effect should not exist in settings with pure discretionary disclosure (no
commitment) and if the manager maximizes long-term cash flows. Note the degree of
product differentiation does not alter the disclosure choice regardless of the nature of the
competition, the manager’s motives, or whether the number of entrants is already established or is changing.
25
26
(c) Entry vs existing competition
(a) Long-term vs short-term
Table 3: Summary of the results
(d) Cournot demand vs Cournot Cost
(b) Commitment vs no commitment
Conclusion
To investigate this relation between market concentration and disclosure, we explore
several common models of competition. We are unable to find or predict any relationship
between concentration and disclosure. Perhaps a future model might predict such an
association, but we argue that, as of now, theory offers no guidance about the appropriate
settings in which such an association might be found. We also argue the absence of
a relationship seems to be the most neutral interpretation of the inconclusive evidence
documented in the empirical literature, when taken as a whole.
More generally, the nature of the industry organization does affect disclosure, and
our setting, in the continuation of a large body of research, strongly supports a connection between competition and disclosure. Separate from concentration, many industry
characteristics are key to the optimal disclosure and, by moving the focus away from
concentration, we hope to refocus empirical research designs on more suitable measures.
Yet, maybe the question itself could be reversed. Concentration might not cause disclosure but perhaps a shock to disclosure might be a key determinant of concentration.
In its own way, this question might be of greater practical interest because it is likely
to explain the role of disclosure as a factor in industrial organization rather than – as it
is currently understood – a consequence of it. Indeed, many accounting standards have
specific consequences on particular industries in which, for example, stock-option disclosures allowed a much more precise evaluation of the true costs of labor, or changes to the
management disclosure and analysis sections have moved to a greater emphasis on future
demand.
This direction, which takes disclosure as a determinant, may also help find the right
settings in which a shock to disclosure might have led to significant consequences for
concentration. It may also help regulators think about disclosure practices as part of their
model to evaluate the competitiveness of an industry, or even think about using accounting
disclosures as a tool to promote fair product market competition, above and beyond its
current stated focus on investors.
27
Appendix
Proof of Proposition 1: Simplifying the objective function, the optimal information system solves the following maximization:
Z
max 4(n − 1)t (a − c)(a − E(ã|N D))(1 − θ(a))f (a)da
Z
Z
2 2
2
2 2
+(n − 1) t
a (1 − θ(a))f (a)da − 2(n − 1) t E(ã|N D) a(1 − θ(a))f (a)da
Z
2 2
2
+(n − 1) t E(ã|N D)
(1 − θ(a))f (a)da.
θ∈[0,1]
We first determine two derivatives with respect to θ(a) that will be proven to be useful for
the maximization problem:
∂E(ã|N D)
=
∂θ(a)
and
∂
A=
∂θ(a)
0
R
a(1 − θ(a))f (a)da
a − E(ã|N D)
R
,
= −R
(1 − θ(a))f (a)da
(1 − θ(a))f (a)da
E(ã|N D)
2
Z
(1 − θ(a))f (a)da
= −2aE(ã|N D) + E(ã|N D)2 .
Then, taking the first-order condition on the objective function:
−4(n − 1)t(a − c)(a − E(ã|N D)) + 4(n − 1)t
Z
(a − c)(1 − θ(a))f (a)da
∂E(ã|N D)
∂θ(a)
−(n − 1)2 t2 a2 + 2aE(ã|N D)(n − 1)2 t2 + 2(n − 1)2 t2 A.
After simplifying,
−4(n − 1)t(a − E(ã|N D))2 − (n − 1)2 t2 (a − E(ã|N D))2 < 0.
Hence, it is always desirable to (locally) reduce the probability of disclosure and nondisclosure always must be preferable to any other policy. 2
Proof of Proposition 2: The informed firm’s objective function can be restated as
V =K+
R
(1 − θ(a))V ar(a|N D)f (a)da
.
4b
28
We maximize
Z
Z
Z
2
2
a f (a)(1 − θ(a))da − ( af (a)(1 − θ(a))da) /( f (a)(1 − θ(a))da)
Taking the first order condition (F.O.C) yields:
R
R
R
−2( af (a)(1 − θ(a))da)( f (a)(1 − θ(a))da)af (a) + f (a)( af (a)(1 − θ(a))da)2
R
.
−a −
( f (a)(1 − θ(a))da)2
2
Rearranging,
=
Z
Z
Z
Z
−a2 ( f (a)(1 − θ(a))da)2 + 2a( f (a)(1 − θ(a))da)( af (a)(1 − θ(a))da) − ( af (a)(1 − θ(a)))2
Z
Z
−(a f (a)(1 − θ(a))da − af (a)(1 − θ(a))da)2 < 0.
Hence, it is always desirable to reduce disclosure and a policy of non-disclosure is preferable to the informed firm.2
Proof of Proposition 7: The informed firm achieves an expected profit conditional
on a non-disclosure equal to
E(π1 (c1 ; N D)|N D) =
V ar(c1 |N D)
4b
(t(a − cn + c + E(c1 |N D)(n − 2)) − 2a + 2E(c1 |N D))2
+
.
b(t − 2)2 ((n − 1)t + 2)2
The expected profit when disclosing is:
E(π1 (c˜1 , c˜1 )|c̃1 ∈ N D)
V ar(c1 |N D) (t(a − cn + c + E(c1 |N D)(n − 2)) − 2a + 2E(c1 |N D))2
=
+
b(t − 2)2
b(t − 2)2 ((n − 1)t + 2)2
The expected profit conditional on a non-disclosure is always smaller than the expected profit when disclosing E(π1 (c˜1 ; c˜1 )|c̃1 ∈ N D). Hence, for any possible choice
of withholding, changing all withheld information into a disclosure will increase the expected firm’s profit. It follows that the preferred policy is one of full disclosure..2
29
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