firmls expected payoff in t + 1 as a function of at and the disclosure action taken by the firm, ηt + /D ...... V Journal of Accounting Research 38: 137$162. Teoh, S.
Information Relevance, Reliability and Disclosure Xiao-Jun Zhang1 University of California, Berkeley Current version: June 2010
1 This
paper bene…ted from comments and suggestions of Ron Dye, John Fellingham, Jonathan Glover, Nicole Johnson, Thomas Pfei¤er, Shyam Sunder, Marco Trembetta and seminar participants at Ohio State University, Universität Wien, Univeristy of Fribourg, and the 2nd Interdiciplinary Accounting Conference.
Abstract This paper studies the relationship between information’s properties (e.g., reliability, relevance) and public disclosure policy.
It is shown that the optimal accounting system of-
ten involves a carefully balanced combination of mandatory and voluntary disclosure, with mandatory reporting focused on reliable information. The emphasis on reliability causes the welfare-maximizing mandatory report to consistently lag the …nancial market in incorporating certain value-relevant information. It is also demonstrated that the …nancial reporting as a whole (mandatory as well as voluntary disclosure) exhibits asymmetric timeliness in capturing good versus bad news.
1
Introduction
One of the major challenges faced by accountants is the lack of reliable measures that can be used to e¤ectively gauge certain economic events and transactions, especially concerning the impact on a …rm’s future cash ‡ows. The current practice in dealing with this issue often involves simply leaving "unreliable" information unreported. Such a method of accounting has drawn heavy criticism.
For instance, a company’s reported earnings is shown to sig-
ni…cantly lag its stock price in incorporating value-relevant information (Ball and Brown [1968]). This is perceived by many as an indication that the …nancial reporting system is defective and incapable of providing timely information to investors (Wallman [1995], Lev and Zarowin [1999]). Various proposals have been made to improve accounting by including more timely measures of gains/losses.1
Such proposals, however, often bring up heated
debates which inevitably lead to the core issue of …nancial reporting, i.e., how to balance the reliability and relevance of accounting information (He¤es [2005]).2 In this paper we study the relation between the various properties of information (e.g., relevance and reliability) and mandatory disclosure policy. The lack-of-reliability problem stems from the insu¢ cient knowledge possessed by investors, auditors, and the regulatory agencies. Even though the manager of a …rm may have superior information regarding the future outcome of a company, investors often do not know exactly what data and/or model the manager used in his deliberation. Hence investors cannot ensure truthful disclosure by having the data veri…ed by auditors. In other words, such information becomes unveri…able. In this situation, we argue that mandatory reporting can take on an added role: inducing …rms to disclose more. If investors and the regulatory agencies do not have enough knowledge to force …rms to credibly convey certain information, why not let the …rms show how such information can be credibly communicated? For instance, if the regulatory agency can not mandate truthful disclosure because it is not clear whether the …rm actually possesses any 1
Statement of Financial Accounting Standards (SFAS) No. 142 "Goodwill and Other Intangible Assets" (2001), SFAS No. 123R "Stock-Based Payment" (2004), SFAS No. 157 "Fair Value Measurements" (2006), Financial Accounting Standards Board, Norwalk, CT. 2 Relevance refers to the information’s ability to "make a di¤erence in a decision by helping users to form predictions about the outcomes of past, present, and future events." Reliability is the "faithfulness with which a measure represents what it purports to represent" (Pages 5-6, SFAC No. 2, Financial Accounting Standards Board, Norwalk, CT, May 1980.)
1
superior information, then why not design the accounting in such a way that the …rm will voluntarily reveal its possession of the information? The idea of designing a more e¤ective mandatory reporting system by factoring in any induced change in voluntary disclosure is appealing. However, relying on voluntary disclosure to solve the lack-of-reliablity problem in mandatory reporting may seem implausible or even self-contradictory.
Mandatory reporting policy, almost by de…nition, deals with
information which …rms choose not to disclose voluntarily. We argue that such a presumption is unjusti…ed.
A …rm’s incentive to disclose changes with the implementation of a
mandatory reporting system. We show that even with the mandatory reporting of a rather noisy signal, a …rm’s incentive to voluntarily disclose can changes signi…cantly. A carefully designed mandatory reporting policy, which takes advantage of this mechanism, can indeed cause …rms to disclose more and improves social welfare. Because of the added role of inducing voluntary disclosure, we show that the optimal accounting policy tends to focus on ex ante veri…able information. This is because when there exists signi…cant uncertainty regarding how certain economic events can be measured, any induced disclosure is often conditional, meaning that the …rm’s incentive to disclose varies with the outcome of the mandatory report. As a result, it is generally better to leave such disclosure voluntary as opposed to mandatory.
The optimal reporting system thus consists
of a carefully balanced combination of mandatory and voluntary disclosure.
In such an
environment with multiple sources of information, our result suggests that it is important to let certain value-relevant information reach the market via alternative (and more suitable) channels besides mandatory …nancial statements. Restricting the scope of mandatory reporting by focusing on reliable information actually increases the overall amount of information ‡ow. The tendency to emphasize reliability in setting accounting rules, although it increases social welfare, is also shown to reduce the value-relevance of the mandatory …nancial reports. This implies that having mandatory disclosure that lags the market in incorporating certain information is actually desirable. The analysis further reveals that the optimal accounting system exhibits asymmetric timeliness in capturing good and bad news. This asymmetry is
2
not caused by accounting conservatism. Instead it is due to the availability of other channels for certain types of information to reach the market. An exception to the above result occurs when the ex ante reliable information provides a rather accurate measure, that is, when the impact of unveri…able information seems relatively minor. In that case we show that it is better to mandate …rms to report both reliable as well as unreliable information. This is because under such a circumstance the …rm’s incentive to voluntarily disclose is so strong that the …rm will truthfully disclose the additional information no matter what the mandatory report shows.
As a result a comprehensive
mandatory reporting, which includes both reliable as well as unreliable information, is more welfare enhancing. Overall, our analysis suggests that whether the scope of mandatory reporting should be restricted to reliable information or not depends on the relative amount of information such reliable data can provide. Interestingly, it is when reliable information seems to be missing a signi…cant portion of the …rm’s private information that mandatory reporting should be restricted to the reliable data.
Traditional arguments for the exclusion of less reliable
information rely on the idea that such information is too noisy and hence generates very little bene…t. Our argument di¤ers fundamentally in that we approach the problem from the angle of inducing the informed …rms to voluntarily improve information reliability. The traditional argument often has di¢ culty justifying the complete exclusion of less reliable information since it is often argued that such information, no matter how noisy it might be, can still be useful to investors. Our reasoning, however, suggests that exclusion of less reliable information is desirable because by doing so we can achieve superior total disclosure ex post. After a brieft literature review in Section 2, we carry out our analysis in four steps. First, in sections 3 and 4, we set up a model featuring multi-…rm, multi-product with Cournot competition to model the demand for information.3
Although the proprietary nature of
information may prevent informed parties from voluntarily disclosing all information, prior research has shown that the mechanism that drives the "unraveling" result of Grossman 3
Our model can be easily expanded to explicitly incorporate demand for information in the …nancial market. See footnote 21 for more details.
3
[1981] and Milgrom [1981] can also induce full disclosure in settings with production (Darrough and Stoughton [1990], Wagenhofer [1990]). It is demonstrated in these two sections that demand correlation among di¤erent products often leads to nondisclosure equilibria. An important feature of these nondisclosure equilibria is that the size of the demand shock does not need to be extreme.
This provides a setting to study mandatory disclosure of
noisy information, which is not highly signi…cant in nature, and causes only minor revisions in users’ expectations.
Next, in sections 5 to 8, we analyze how proper public disclosure
policy relates to properties of information.
Mandatory disclosure of noisy information is
shown to be capable of disproportionately increasing the overall amount of information via its impact on a …rm’s voluntary disclosure behavior. In addition, we show that mandatory accounting based on reliable information is generally more preferable.
Last, in section 9,
we show how emphasizing information reliability leads to reduction in the price-relevance of mandatorily disclosed information and asymmetry in the way di¤erent news is captured.
2
Related Literature
This paper builds on prior research in three areas: closure and informational properties.
the social value of information, dis-
Social value of information research addresses the
issue of when information in general and mandatory disclosure in particular improves social welfare (e.g. Demski [1973], Demski [1974], Hakansson et. al. [1982], Diamond [1985], Dye [1990], Teoh [1997], Admati and P‡eiderer [2000]). This paper studies the welfare impact of information in the presence of several alternative sources of information. It contributes to the literature by showing how information quality measures play a role in determining the optimal disclosure policy. The paper also extends the literature on disclosure.
Grossman [1981] and Milgrom
[1981] established the "unraveling" result whereby lack of disclosure is taken as bad news, forcing the informed parties to reveal their information in equilibrium.
Dye [1985] and
Verrecchia [1983] went further showing how uncertainty about information or proprietary costs limit voluntary disclosure.
Darrough and Stoughton [1990], Wagenhofer [1990], and
4
Clinch and Verrecchia [1997] study more speci…c proprietary cost models and show that the "unraveling" mechanism can still lead to full voluntary disclosure.4 This study demonstrates how correlated information signals about di¤erent segments of operation can limit voluntary disclosure and lends support to mandatory reporting.
More important, this paper shows
how uncertainty about the existence and reliability of information creates an inductive role for mandatory reporting, which aims at motivating …rms to make more voluntary disclosure. Arya, Frimor, and Mittdorf [2008] also study a model with signal correlation and proprietary disclosure cost.
They examine the issue of aggregation in voluntary disclosure.
Even
though we also study the issue of voluntary disclosure, our main focus in on mandatory reporting. Gigler and Hemmer [1998] study a stewardship setting and show that an increase in frequency of mandatory disclosures can reduce the amount of voluntary disclosure and hence reduce overall price e¢ ciency. Unlike Gigler and Hemmer [1998], this paper shows that expansion in mandatory disclosure requirements can increase voluntary disclosure and hence increase total information available to investors.
The main di¤erence between this paper
and Gigler and Hemmer [1998] is the timing and the relative importance of mandatory versus voluntary disclosure. In their paper mandatory disclosure exists only to "con…rm" voluntary disclosure, which acts as the timely source of information.
In our setting, mandatory
disclosure serves as the primary source of information. It "induces" voluntary disclosure that takes place after (or concurrently with) mandatory reporting. Einhorn [2005] also studies the interaction between mandatory disclosure and voluntary disclosure. Unlike this paper, Einhorn [2005] focuses on a capital market setting where a manager is assumed to maximize …rm price by exercising discretion in voluntary disclosure. The disclosure cost, as well as the information that is disclosed mandatorily versus voluntarily, is exogenously …xed in her analysis. Although the settings di¤er, some of the results of this paper complement those of Einhorn [2005].5 It is shown that even though voluntary disclosure exists in equilibrium, it does not negate the need for mandatory reporting requirements. In addition, we study the question of the how to optimally match the type of information with the format of disclosure, 4
See Fried [1984], Gal-Or [1985], Shapiro [1986], Darrough [1993], among others, for more analysis of strategic information transfer among Duopoly/Oligopoly competitors. 5 Because of the endogenous disclosure cost, our results regarding how the content and the accuracy of mandatory reporting a¤ects the likelihood of voluntary disclosure di¤er from those of Einhorn [2005].
5
i.e., mandatory versus voluntary reporting. Finally, the study contributes to the literature on informational properties. This line of research addresses how properties of information (for example, reliability, veri…ability, relevance) a¤ect the design of mandatory disclosure rules.
It is commonly believed that
reliability and veri…ability are desirable because they reduce measurer error in recording economic events (Moonitz [1961], Paton and Littleton [1940]). This paper demonstrates how reliability helps to induce …rms to disclose other relevant information. There seems to be considerable support among accounting professionals for the view that reliability should be the dominant quality of the information conveyed in …nancial statements, even at the expense of relevance.6 This paper provides justi…cation for this view. The paper complements two other works on soft information.7 Dye and Sridhar [2004] model the relevance and reliability trade-o¤ in the setting where manipulation by the manager leads to, in certain cases, desirable withholding of unreliable information from investors.
Liang and Zhang [2006] show how
soft information can exacerbate the adverse selection problem in the …nancial market. This paper adds to this line of argument by showing that excluding certain ex ante unreliable information increases welfare when there are other (more suitable) channels for disseminating such information.
3
Model
References to information properties such as relevance and reliability have a long history in the professional accounting literature. According to the Statement of Financial Accounting Concepts No. 2, relevance refers to the ability of information to "make a di¤erence in a decision" while reliability is the "faithfulness with which a measure represents what it purports to represent." The fact that standard setters often need to tradeo¤ information relevance and reliability when evaluating alternative accounting measures reveals two key features of the problem. (i) The …rst-best case of enforcing disclosure of one measure which 6
See, for example, paragraph 44 of SFAC No. 2, FASB, Norwalk, CT. A piece of information is considered to be soft if its interpretation varies across di¤erent parties (Ijiri [1975]). 7
6
is both highly relevant and highly reliable is usually not attainable, at least ex ante. (ii) The …rms are not forthcoming in voluntarily disclosing the information.
To capture these
fundamental aspects of the problem, we use the following model in our analysis.
3.1
Production
Consider two …rms formed by risk neutral investors who compete in two product markets: 1 and 2.8 Demand for these products follows a downward-sloping curve: (e y1t
pe1t ; ye2t
pe2t ), t = 1; 2; :::
where pe1t and pe2t are the prices of the two products at time t.
ye1t and ye2t are random
with mean y > 0. For simplicity both …rms are assumed to have the same cost function.9
Productions take place in every period, starting in period 1, with total production cost of …rm f (f = 1; 2) in period t equal to qef21t + qef22t , f = 1; 2
where qef 1t (e qf 2t ) denotes …rm f ’s output of product 1 (2).10 It is assumed that there is no inventory holding so that the product market clears at the end of each period:
ye1t
pe1t =
2 X f =1
qef 1t and ye2t
pe2t =
2 X f =1
qef 2t
Let e cf t denote …rm f ’s net pro…t from selling these products in period t, i.e., e cf t = (e p1t qef 1t
qef21t ) + (e p2t qef 2t
qef22t )
We use the above duopoly model with Cournot competition to capture demand for 8
Results of this paper can be easily extended with a …nite number of …rms. See Shapiro [1986], among others, for cases where …rms have di¤erent production cost functions. 10 Quadratic cost function ensures that the optimal production level of each …rm is …nite. The essence of the results remain if the cost function is changed to other similar forms, such as (qf at + qf bt )2 . 9
7
mandatory disclosure and to study the externality problem concerning information distribution. Changing the setup to a Bertrand competition will a¤ect the speci…c conditions under which the informed …rm withholds information (Darrough [1993]). However the main results of the paper, including how restricting mandatory reporting is needed to balance mandatory disclosure and other sources of information, remain unchanged.
3.2
Information
Assume that
where
(e y1t+1 ; ye2t+1 ) = (y; y) +
(e; ke) + (e "y1t+1 ; e "y2t+1 )
t
can be considered as a measurement, or simply a statistic.
t
(1) equals 1 or
1 with
equal probability. e "y1t+1 and e "y2t+1 are independently and identically distributed noise terms with zero-mean.11
e and k are constants known to all participants. The magnitude of e
(> 0) indicates how the new information ( t ) can update the belief about demand relative to the prior, y. k 2 ( 1; 1) re‡ects the extent to which products 1 and 2 complement or substitute for each other.12;13 As will be seen from our analysis, k plays an important role in determining the extent to which proprietary cost prevents the informed …rm from voluntarily disclosing its information. There is a signal of
t
in the sense that when , where
1
1 2
0). It could also re‡ect a shift in consumer demand from desktops to laptops(k < 0). 13 When k = 1 asymmetric information with respect to demand does not lead to asymmetric information about …rm value (this will become clear from analysis later in the paper), thus we exclude this special case from our analysis.
8
revelation of
t.
However, unlike , whether such added information ( t ) can be credibly
veri…ied and communicated to outsiders at time t is known only by …rm 1. Note that the above assumption regarding …rm 1’s possession of information
can be easily modi…ed to
incorporated ex ante uncertainty. That is, perhaps more realistically, we can assume that …rm 1 may or may not have signal , with some positive probability. All our results hold with minor modi…cations. The two signals (
and ) di¤er in their reliability. More formally, let
the knowledge needed to have signal
(
( ) reliably veri…ed and communicated.
denote the relevant information set of …rm 1 at time t, and let
t
) denote Let
0
t
denote the corresponding
set of public information. We use Dt = (Dtm ; Dtv ) to denote the public disclosure made by the informed …rm at time t.
It includes a mandatory component (Dtm ), and a voluntary
component (Dtv ). If the …rm chooses not to make any voluntary disclosure, then Dtv = ;. Let Dm denote the set of information that …rms are mandated to disclose. We make the simplifying assumption that veri…cation cost is negligible so that, whenever investors and auditors know how to verify certain information, such information will be veri…ed and hence truthfully conveyed. That is, if reported value of 2
0
while
a
t.
2 =
Similarly, if 0.
2 Dm and
2
2 Dm and
In other words,
t,
2
then t,
then
m t
= m t
t
=
where t.
m t
denotes the
It is assumed that
can be reliably communicated ex ante while
can not. To illustrate the di¤erence between
and
, consider two issues in accounting: the
fair value measurement of trading securities and employee stock options.
For trading
securities such as treasury bonds, investors and regulators know how to verify the fair value information. In contrast, the way to verify the fair value measure of employee stock options is not as clear.
Auditors usually do not know how to test key inputs into the valuation
functions, such as the projected volatility of future stock returns. Management are often better informed regarding the future performance of a …rm, but the auditors do not know how to verify such information. In other words, compare with ,
is less veri…able and less
reliable. Note, however, that the extent to which a piece of information can be veri…ed depends
9
on the technology and knoweledge available to the general public.
When internet …rms
started to emerge in the 80’s and 90’s, most people consider the valuation of such …rms extremely subjective and judgemental. However, as time goes by, companies and analysts started to share information using measures such as the number of "hits" and the number of unique visitors. These measures are shown to sign…cantly correate with future revenues of the internet …rms, rendering the prediction of sales more reliable (Trueman et. al. [2000]). As another example, it used to be almost impossible to determine the exact number and location of inventories for large businesses before computers were used. Now, with the help of computer networks and Radio Frequency Identi…cation (RFID), inventory numbers and locations can be determined instantaneously with extreme precision. The point is that, with the arrival of new technology and new knowledge of how certain information can be veri…ed, what used to be thought of as unreliable can become reliable. To capture the above aspect of the problem, we di¤erentiate between the ex ante and the ex post veri…ability of signal . For simplicity we assume that with probability 1 even the informed …rm, …rm 1, does not know how to have information and communicated. That is, with probability 1
,
2 =
0
0.
>0
credibily veri…ed
In that case, information
is entirely unveri…able. This assumption re‡ects the fact some times unreliable information takes the form of a simple "hunch," which is hard to quantify and di¢ cult to credibly communicated. However, with strictly positively probability
That is, even
though in this case the general public does not know how to have information
veri…ed, the
informed …rm does. In this case, information …rm 1 reveals . That is,
2
0
0.
> 0,
is only unveri…ablity ex ante.
Ex post, if
to the general public, then the auditor and the public will be able to verify becomes veri…able ex post.
Throughout the paper we refer to …rm 1’s private information regarding how to credibly communicate
(i.e.,
) as private knowledge, to di¤erentiate from the case where
private information only includes the realization of knowledge
t.
This distinction is important. The
determines whether a signal can be reliably communicated. Hence spreading
the knowledge of
will change the veri…ability of a signal.
For example, once investors
know the underlying data items of , auditors can verify such data and make the measure
10
more reliable.
Alternatively, the credibility of disclosure about
can be enhanced if
reveals how future data can be used to discipline management’s truthful reporting. Either way, the amount of knowledge possessed by the public a¤ects the reliability of information. Accordingly, reliability is not exogenously …xed in our model.
Instead it is determined
endogenously. Analysis of asymmetric distribution of knowledge (
and
) is the key to
our analysis. Note that the lack of ex ante reliability does not prevent regulators from mandating its disclosure.
Even though we do not know how to veri…y …rm’s claim regaridng the
projected stock return volatity, …rms are still required to disclose the fair value estimates of their outstanding employee stock options (SFAS 123R). The main focus of our analysis is whether mandatory reporting should be limited to ex ante reliable measures, such as , or should include measures that are not as reliable, such as .
3.3
Gain from disclosure
When the informed …rm does not fully disclose its private information (for reasons to be discussed in the next section), the production will be ine¢ cient. Compared with the full information case, …rm 1 (2) over (under) produces when the demand is higher (lower) than the average.
In addition, the market-clearing price may be too high relative to the full
information case, and the consumers su¤er. The following social welfare function captures the impact of disclosure: 1 X t=1
ft (D )] = R E0 [W t
m
1 X t=1
+
Z R E0 [ t
Z
0
0
qe12t +e q22t
qe11t +e q21t
(e y2t
(e y1t
q)dq
q)dq
2 2 (e q11t + qe21t )
(2)
2 2 (e q12t + qe22t )]
The right-hand side of equation (2) captures the total of producer and consumer surplus. Firms are assumed to choose their voluntary disclosure strategies as well as production plans optimally, conditional on the mandatory disclosure requirement (Dm ).14 Note that the 14
Note that the usual criteria of Pareto e¢ ciency is not used in this paper. Prior studies (e.g., Demski [1974]) have shown that, since alternative accounting standards often lead to di¤erent wealth distributions
11
individual …rm does not capture the entire surplus from production –a portion of it is enjoyed by the other …rm as well as consumers. This real externality problem creates the need for disclosure regulation (Dye [1990]).
Note also that our analysis focuses on the product
market to highlight the operational costs that prevent a …rm from voluntarily disclosing all its information. The model can be easily extended to incorporate the externality problem in the …nancial market, which further give rise to the need for mandatory reporting (Admati and P‡eiderer [2000]). For instance, we can use jE[e yt+1 j
t]
E[e yt+1 j
0 t ]j
to capture the
amount of social loss in the …nancial market due to information asymmetry, and assume a portion of that is not internalized by the …rm owner.
All our results hold with minor
revisions.15 .
3.4
Time line and equilibrium
Overall, after the mandatory disclosure rule (Dm ) is chosen, the sequence of events is as follows: t = 0: Firm 1 obtains information about (e y11 ; ye21 ) and then makes disclosure D0 .
t = 1: Both …rms produce and sell their products. The market clears and cash ‡ow c1 realizes. In the meantime, …rm 1 obtains information about (e y12 ; ye22 ) and makes
disclosure D1
t > 1: The above transaction cycle repeats. Each transaction cycle spans two periods: in the …rst period, after observing private information, the …rm makes the mandatory as well as voluntary disclosure. Production and sales take place in the next period. To simplify the analysis and exposition, it is assumed among individuals, using the criterion of strict Pareto improvement often does not yield much insight when comparing alternative accounting standards. The measure of social welfare used in (2) is equivalent to measuring the ex ante average welfare of society. 15 Using other functional forms such as (E[e yt+1 j 1t ] E[e yt+1 j t ; Rtm ])2 can yield additional interesting results such as …rms having incentives to voluntarily disclose when mandatory disclosure provides the "wrong" signal.
12
that demand is not correlated over time Corr(e yt ; ye ) = 0 for all t 6=
Even though the transaction cycles are independent of each other, the existence of multiple transaction cycles a¤ect …rms’equilibrium disclosure behaviors. Throughout the paper the analysis focuses on Perfect Bayesian Equilibrium where, at any stage, …rms’strategies are optimal given their beliefs, and their beliefs are obtained from equilibrium strategies and observed signals using Bayes’Rule. Speci…cally, let Dv (Dm ;
0
)
denotes the voluntary disclosure decision of the informed …rm, which is the function of the mandatory reporting policy (Dm ) and the …rm’s private information ( 0 ).
qe1 ( 0 ) =
q1 ( 0 ) + e "q1 and qe2 ( ; D) = q2 ( ; D) + e "q2 denote the production of …rms 1 and 2 based on each …rm’s total information, where e "q1 and e "q2 are independent and identically distributed random noise in produciton.
For simplicity, assume that these noise terms are normally
distributed with mean zero, variance
2 q,
and zero covaraince with other shocks (such as e "y ).
We use " " to denote the conjectured decision functions by other parties. De…nition: An equilibrium is characterized by fDv (Dm ;
0
); q1 ( 0 ); q2 ( ; D); Dv (Dm ;
0
);
q1 ( 0 ); q2 ( ; D); g where (1) Firm 1 chooses the optimal disclosure and production strategy Dv and q1 to maximize its total expected pro…t, conditional on a conjectured production plan of …rm 2 (q2 ). (2) Based on available public information, …rm 1’s disclosure, and a conjectured disclosure strategy of …rm 1 (Dv ), …rm 2 updates its belief regarding future demand using the Bayes’ rule. (3) Based on the updated belief and the conjectured production plan of …rm 1 (q1 ), …rm 2 chooses optimal production q2 to maximize its expected pro…t. (4) Both …rms’conjectures need to be correct in equilibrium: Dv = Dv , q1 = q1 , q2 = q2 .
13
4
Lack of voluntary disclosure
Before comparing the welfare e¤ect of alternative accounting rules, it is necessary to establish the need for having such mandatory reporting requirements in the …rst place. Existence of asymmetric information, as described in section 3.2, does not necessarily create the need for disclosure regulation. For instance, the informed …rm often …nds it appealing to voluntarily disclose its private information, rendering any mandatory disclosure rule redundant (Dye [1990]).
The …rms determine their production quantities by solving the following pro…t-
maximizing problems:16 8
8(1 + k) y 9(1 + k 2 )
(4)
Proof. All proofs are in the Appendix. When condition (4) does not hold, the informed …rm would voluntarily disclose its private information . To illustrate, consider the simple case when k = 0. Since both …rms share the same information regarding the demand for product 2, both …rms will produce the same pro…t-maximizing quantity in the standard duopoly game (i.e., y=5). However, for product 1, …rm 1 has better information regarding its demand.
When such private information
indicates that future demand is likely to be low (i.e., E[e y1t+1 j
0 t]
=y
e), the informed …rm
16 Note that the function in (3) does not equal to the expected cash ‡ows in t + 1. The two di¤ers by a constant which is a function of 2q .
14
would prefer to credibly disclose this "bad" news.
This way its competitor (i.e., …rm 2)
will lower its output, which in turn increases the market clearing price of the product and hence increases the informed …rm’s pro…t. However, in the case when demand is expected to be high, i.e., E[e y1t+1 j
0 t]
= y + e, …rm 1 would want to keep this information private and
increase its production accordingly. Otherwise the other …rm would also increase its output and take away some of the pro…t from high demand. Let c1t+1 ( t ; t ) denote the informed …rm’s expected payo¤ in t + 1 as a function of …rm,
t
t
and the disclosure action taken by the
2 fD; N Dg. D and N D stand for disclosure and nondisclosure respectively. The
informed …rm’s future payo¤ has the following ranking: Et [e c1t+1 (
t
= 1; N D)] > Et [e c1t+1 (
t
= 1; D)] > Et [e c1t+1 (
t
=
1; D)] > Et [e c1t+1 (
t
=
1; N D)]
As we would expect, the payo¤ changes monotonically as the private signal changes from "good" (
t
= 1) to "bad" (
t
=
but makes the …rm worse o¤ when possess information
Disclosure makes the …rm better o¤ when
1). t
t
=
1,
= 1. In this case if the informed …rm is known to
, the uninformed …rm will rationally interpret any nondisclosure by
…rm 1 as an indication of high expected demand, thereby increasing its output and forcing the informed …rm to fully disclose. This leads to a fully revealing equilibrium. However, when condition (4) holds, the informed …rm’s payo¤ has a di¤erent ranking: Et [e c1t+1 (
t
= 1; N D)] > Et [e c1t+1 (
t
= 1; D)] > Et [e c1t+1 (
t
=
Nondisclosure can make the …rm better o¤ in both cases (i.e.,
1; D)] < Et [e c1t+1 (
t
=
1 and
t
t
=
1; N D)]
= 1). The
intuition can be best illustrated with k < 0. When demand for production a is expected to be low, the informed …rm may not want to share such information with its competitor because doing so would cause its competitor to shift its production e¤ort to the "right" sector (i.e., to produce more of b whose demand is going to be high). Thus …rm 1 will tend to withhold the information. Lemma (1) brings out an important insight. In many cases, a …rm’s information cannot be simply classi…ed "good" or "bad": a piece of information may help the …rm in some way
15
and at the same time hurt the …rm in another way. Thus outsiders normally cannot simply interpret withholding information by the informed …rm as an indication of "good" or "bad" news. This leads to the prevalence of nondisclosure equilibria. Condition (4) ensures that …rm 1’s bene…t of withholding the information outweighs its cost. Multiply both sides of (4) by (1 + k 2 )e, we get (1 + k 2 )e2 > 89 (1 + k)ye. The left hand side, which is a function of e2 , represents the bene…t from "monopolizing" information on unexpected demand. The cost of keeping the information private is captured on the right hand side (as a function of ye). For the product whose demand is less than expected, not sharing the information means that the competitor will over-produce, reducing the equilibrium price and the informed …rm’s pro…t. Correlation between demands for products a and b (i.e., k) plays an important role in determining the equilibrium disclosure behavior of …rms. When k = 0, condition (4) can only be satis…ed when e > 98 y, which means that the relative magnitude of the demand shock (e), as compared to the average demand (y), needs to be very large. E[e y1t+1 j t ] = y
In that case, when
e, both the market clearing price of product a as well as the informed …rm’s
optimal production quantity will be negative. In other words, the informed …rm will need to consume rather than to produce.17
With non-negative production quantity, condition
(4) will be violated and only disclosure equilibria exist. Since …rms will voluntarily disclose their information, any mandatory disclosure requirement becomes redundant. The situation changes when k 6= 0. When k is less than 0, condition (4) can be satis…ed even when e is very small.18 Such a feature ensures that the equilibrium production quantity in the nondisclosure equilibrium is positive.
More importantly, this enables us to study mandatory disclosure
of noisy information, which does not have to be extremely signi…cant in nature, and whose disclosure only induces minor revision in users’beliefs. Lemma 2 Assume that the production quantities are non-negative and that the informed …rm does not voluntarily disclose information . Then k < 0. 17
This is consistent with the result of Clinch and Verrecchia [1997]: nondisclosure equilibrium occurs only at the very extreme. 18 When k > 0, correlation between products will exacerbate the informed …rm’s tendency to voluntarily disclose, increasing the likelihood of fully revealing equilibrium.
16
The rest of the analysis focuses on the cases where production quantities are non-negative and where condition (4) holds with k < 0. Since the informed …rm withholds information regarding demand in the nondisclosure equilibrium, production is not e¢ cient. In addition, consumers su¤er due to the informed party’s desire to safeguard the information.
These
social welfare losses lead to consideration of mandatory disclosure policy, which is the subject of the remaining analysis.
5
Inducing voluntary disclosure with mandatory reporting
To assess the potential gain from imposing mandatory disclosure requirements, the following benchmark case is analyzed where mandatory reporting can achieve full disclosure. Lemma 3 Suppose mandatory reporting regulation can achieve full disclosure such that
t
is completely revealed. Implementation of such an accounting will be welfare-enhancing. This lemma provides the necessary condition for further analysis, i.e., it is indeed socially bene…cial to have such information widely disseminated. Full disclosure, however, is rarely achievable.
Even though a …rm manager knows how to better measure certain economic
events, outside investors, auditors, and standard setters often do not have such knowledge. This puts limits on the ability of auditors to verify disclosure, rendering the …nancial reports noisy. More speci…cally, since
2 =
0,
the public does not know how any claim regarding
can be veri…ed. In this case whether the …rm should still be mandated to disclose
or
not becomes an issue. To illustrate, consider the typical situation where investors would like to know, for instance, a …rm’s future cash ‡ows and its fair value. Investors know that the …rm’s managers may be better able to forecast the …rm’s future performance, but they do not know exactly what model and data the managers use in their forecast. Given this situation, one way to set up accounting policy would be to mandate disclosure based on things that investors do know about, for example, the historical cost of assets. The way to obtain such a measure 17
is common knowledge, and hence can be more easily veri…ed. In our setting, this can be represented by a policy mandating disclosure of
only. We denote this policy as:
Dm = f g With accounting policy Dm accounting purports to measure only , just as historical cost accounting purports to measure nothing but the cost the …rm incurred to purchase the asset. An alternative approach to accounting policy setting is to target the accounting measure as providing the most useful information to investors.
We use the following notation to
capture such an accounting Dm = f ;
; g
Comparing this accounting with Dm , it is easy to see that the accounting measure relevant, but less reliable ex ante. We include
is more
in Dm to make it clear that Dm
Dm .
In other words, our analysis is not the compare two mutually exclusive accounting signals. Instead, we are interested in the choice among two accounting methods where the scope of one is strictly larger than the other, due to the inclusion of less reliable information. course, If the …rm chooses not to disclose
Of
by simply claims that it does not posses such
knowledge, investors will only get reliable information .19
Nonetheless, advocate of this
approach argues that in cases when the …rm does decide to communicate more relevant information besides , it would be helpful to investors to have such information re‡ected in the …nancial statements. Firms may be required to disclose whatever information is deemed relevant for predicting future cash ‡ows.20 Such an accounting is in the spirit of the recent pronouncements made by FASB ([2002], [2005], [2006]).21 Recall that
represents the credible communication of . The informed …rm may reveal
either to the auditor, to directly to the investors. The revelation can also take di¤erent forms.
For instance, …rms may reveals the data and the model used by the manager to
19 Note that when 2 = t , auditors will ensure that the disclosure is consistent with the veri…able information . 20 For arguments in favor of such an accounting approach, see Wallman [1995]. 21 For example, to value stock options, the accounting rules do not specify exactly how to forecast future stock volatility. Instead managers are supposed to come up with their best estimates.
18
forecast future outcomes. Auditors can then verify the data to ensure the accuracy of the reported
. In this case, credibility comes from independent veri…cation.
…rm 1 may simply report
Alternatively,
without any supporting evidence. Credibility of such disclosure
may come from the implicit assumption that the manager cares about potential damage to his/her reputation if such claims turns out ex post veri…ably false.22 In this case, credibility comes from ex post con…rmation. Regardless of the exact format of
, without it, the lack
of reliabilility will prevent investors from enforcing full disclosure of . Any disclosure of by …rm 1 will remove such uncertainty. As we have shown in Lemmas (1) and (2), the informed …rm tends not to voluntarily disclose its private information. Given this, will …rm 1 ever has incentive to credibly disclose if the …rm is required to report
? In the following proposition we show that in deed
mandatory disclosure can provide some incentive for the informed …rm to disclose more. Proposition 1 With the mandatory disclosure of and
, which are functions of e; k; and y.
will not disclose
. When
t,
there exist two threshold levels of ,
When
, the
= 1.
To understand the mechanism that causes the informed …rm’s disclosure incentive to change, consider the case (2
(y
1)e; y
.
Since the expected demand in period t + 1 equals
1)e) (conditional on
k(2
production equal to ( y
>
(2 5
1)e y k(2 ; 5
1)e
t
=
1), the uninformed …rm would set
). In this case, when
t
=
1, the informed …rm’s
cash ‡ow from operation will be 2 (y 25 22
(2
1)e)2 +
2 (y 25
k(2
1)e)2 +
1 + k2 2
2 2
e
2(1 + k) (y 5
(2
Note, of couse, that ex post ver…ciation is needed in order for such a scheme to work.
19
1)e) e
4
2 q
if the …rm does not make any voluntary disclosure. If the informed …rm does make additional disclosure and credibly convey
t
=
2 (y 25
1, its payo¤ will be e)2 +
2 (y 25
ke)2
4
2 q
Hence the …rm’s net gain from not disclosing equals 1 1 4 2 (1 + k 2 )e2 + (1 + k 2 )e2 (1 + k)e2 ] + (2 1)[ (1 + k)ey 25 8 5 25 1 1 9 1 + (1 + k)ye + (1 + k)e2 ] + (1 + k 2 )e2 (1 + k)ye 5 5 200 25 (2
1)2 [
Let Z ( ) denote the above quadratic function in
and e
9 200
(1 + k 2 )e2
1 (1 + k 2 )e2 4
1 (1 25
+ k)ye.
It can be shown that Z ( ) = (2 Therefore, as
2 ) e
41 (1 200
1)e2
41 (1 + k 2 ) 200
40 (1 + k) 200
increases, the bene…t from non-disclosure diminishes at an accelerating speed.
Z ( ) reaches its minimum at and e2
(2
+ k2)
of (1=2; 1). We use
40 (1 200
3 4
+ 4[ 41 (1+k2 )e 200
40 (1+k)]e2 200
. Since Z (1=2) = e > 0, Z (1) = 0,
+ k) > e , equation Z ( ) = 0 has a unique solution in the range
to denote this solution. When
>
the informed …rm’s cash ‡ow
from operations in period t + 1 would be larger with credible disclosure of . Given that the …rm may have incentive to disclose more, it seems sensible to make mandatory reporting more comprehensive by including information that seems unreliable ex ante (i.e., ). Next we study the e¤ect of accounting policy Dm in details.
6
Comprehensive mandatory reporting (Dam)
With accounting policy Dm , the mandatory report includes all relevant information in the …nancial report. However, since
is unknown to the public at time t = 0, it is not clear
how investors should react to any disclosure made by the …rm. In this section we show how two factors a¤ect the equilibrium disclosure of : (a) the communication of
20
, and (b) the
accuracy of the reliable signal (i..e, ).
6.1
Disclosure of
Without the knowledge of how
can be veri…ed, or more broadly speaking, how
be credibly communicated (i.e.,
2 =
), any disclosure of
can
may become "cheap talk."
Nonetheless, as shown in Crawford and Sobel [1982], such communication can be credible when the incentives of the sender and the receiver of a message are properly aligned. Proposition (1) reveals that the informed …rm does have incentive to credibly communicate the accuracy of
(i.e.,
) exceeds certain thresholds.
once
In the next Lemma we examine
whether such incentive actually leads to credible communication of . Lemma 4 Consider the case
2 =
t.
In equilibrium any disclosure regarding
t
will be
ignored. When …rm 1 simply make a claim about
without attaching any credibility to it (for
example, without any audit or any implicit guarantee of accuracy by the management), the above lemma shows such claim, in equilibrium, will be ignored by investors. The reason is intuitive. Since the informed …rm does not disclose
a,
market participants can only rely
on the informed …rm’s incentive to gauge the reliability of the disclosed signal
t.
However,
even when investors know that the informed …rm has incentive to credibly communicate , i.e., when the accuracy of
exceeds
, it turns out investors cannot simply rely on the
disclosed . This is because if investors do use the disclosed informed …rm’s incentive to disclose changes.
to update their belief, the
In equilibrium, the …rm no longer has the
incentive to truthfully convey . This, in the end, renders the disclosure of unreliable.
Thus in equilibrium any disclosure of
completely
by the informed …rm will simply be
ignored. That is, only the "babbling" equilibrium exists in this cheap talk game.
21
6.2
Accuracy of the reliable information ( ) and the disclosure of
Lemma (4) shows that if the informed …rm ever wants to disclose
, it is important to
communicate such information in a credible way. However, in doing so, the informed …rm essentially reveals to the public how
can be credibly communicated (i.e.,
proposition we show that the informed …rm will truthfully disclose of signal
). In the next
only when the accuracy
is high enough.
Proposition 2 Consider accounting policy Dm . Suppse that truthfully discloses
by setting
m
=
2
0
0.
The informed …rm
if and only if the accuracy of the reliable signal ( )
and the discount rate (R) are high such that (5) and R where
1>
9(1 + k 2 ) 41k 2 40k + 1
, which is function of by e; k; y, and R, exceeds
When the informed …rm credibly communicates
(6) .
to maximize the current pro…t, the
disclosure also impacts the …rm’s future pro…t. Since accounting policy mandates disclosure of Dm , investors will force the …rm to truthfully disclose
in the future once
is known
publicly. For example, once the public knows how to verify , the …rm will no longer be able to claim that it does not possess such information. Taking this into consideration, the informed …rm will choose to truthfully convey
only when two conditions are met. First,
the …rm needs to discount the future cash ‡ows deeply enough so that condition (6) holds. Second, the accuracy of
needs to be high.
This is because, as Proposition (1) shows,
the informed …rm’s current period cash ‡ow is only favorably a¤ected by the disclosure of when the accuracy of
exceeds certain thresholds. When
impact of disclosing a more accurate signal
becomes accurate, the negative
on the …rm’s future cash ‡ows is reduced.
22
6.3
Welfare e¤ect of accounting policy Dam
Since the informed …rm’s disclosure behavior is a¤ected by the accuracy of , the impact of the accounting policy on social welfare will also be a function of . Corollary 1 Suppose
2
0
0.
When condition (6) holds, the average social surplus in each
period equals ft!1 (Dm )] = E0 [W
12 2 y 25
5 67 + (1 + k 2 )e2 [ 32 + 800 (2 12 2 5 67 2 2 y + (1 + k )e [ 32 + 800 (2 1)2 + 25
1)2 ] 3 2q when 67 (1 )] 3 200
2 q
< when (7)
When condition (6) does not hold, ft!1 (Dm )] = 12 y 2 + (1 + k 2 )e2 [ 5 + 67 (2 E0 [W 32 800 25 This welfare e¤ect is plotted in Figure 1. When becomes more accurate. However, once
exceeds
1)2 ]
3
2 q
(8)
, the social surplus increases as
> > < ; when 2 t and ( t = 1 or ( t = 1 and t = 1)) v Dt = > > f t = 1; g with probability (1 ) when 2 t and ( > > > > : ; otherwise
When
>
t
1 and
=
t
=
1) (9)
,
8 > > f t ; g when 2 = t and [( t = 1, t = 1) or ( t = 1, t = 1)] > > > > > > ; when 2 t and [( t = 1 and t = 1) or ( t = 1 and t = 1)] > < Dtv = f t = 1; g with probability (1 ) when 2 t and ( t = 1 and t = > > > > > f t = 1; g with probability (1 when 2 t and ( t = 1 and t = 1) > ) > > > : ; otherwise
1)
(10)
Note that the private information held by the informed …rm will not be completely revealed.
When the public signal
=
t
1 is reported, the uninformed …rm knows that
the informed …rm has the incentive to disclose when the true state is E[(e y1t+1 ; ye2t+1 )j (y
e; y
ke), i.e.,
t
=
0
t]
=
1. However, if the informed …rm does not make any disclosure, the
uninformed …rm can not simply infer that the true state is E[(e y1t+1 ; ye2t+1 )j
0
t]
= (y+e; y+ke).
This is because if the uninformed …rm takes such a strategy, the informed …rm will no longer have the incentive to disclose when
…rm to make the wrong inference (
t
=
t
1 since not disclosing can induce the uninformed
= 1).
Thus, in equilibrium, upon observing no
disclosure, the informed …rm can only update its belief regarding 24
t
by an amount that
makes the informed …rm indi¤erent to voluntarily disclosing or not. That is, the informed …rm will take the following selective disclosure strategy: when (
t
=
1;
t
=
1), with
probability (1 the informed …rm will convey
and con…rm
rest of the time. Similarly, when will voluntarily disclose voluntarily disclosing
t
t
=
) =
t
1. The …rm will remain silent for the
crosses the second threshold level,
= 1 with probability 1 with probability
(1 (1
) )
when
t
=
, the informed …rm t
= 1, in addition to
. In all other cases, the …rm will only
make the required mandatory disclosure. The selectiveness in the informed …rm’s voluntary disclosure behavior is key to the establishment of the equilibrium.
The possibility that the informed …rm will remain silent
in some cases prevents the investors from interpreting the lack of voluntary disclosure as t
In fact, upon observing no voluntary disclosure and a mandatory disclosure
= 1.
Dtm = f
t
=
1g, the uninformed …rm will apply the Bayes’ rule and attach the follow-
ing probability to Et [(e y1t+1 ; ye2t+1 )] = (y
[1
(1
e; y (1
) + [1
ke) : )
]
(1
That is, the uninformed …rm interprets the signal disclosure as if the signal was of quality
)
]
t
=
=
1 with no additional voluntary
. This presents an interesting result: when the
informed …rm discloses more information voluntarily, the quality of disclosure (Dtm and Dtv ) increases since investors obtain additional information about
t.
However, when the …rm
chooses not to do so, the perceived quality of the mandatorily disclosed signal is actually lower (since
< ). The reason for this result is that investors are uncertain whether lack
of additional disclosure is due to withholding "bad" or "good" news. Thus the additional disclosure actually increases uncertainty when such disclosure is not made. Overall it is unclear whether investors are better o¤ with the added voluntary disclosure from the informed …rm. The following corollary addresses this issue.
25
Welfare e¤ect of accounting policy Dm
7.2
Corollary 2 With accounting policy Dm , the average social surplus in each period equals
ft!1 (Dm )] = E0 [W
8 > > > > > > > > > < > > > > > > > > > :
12 2 y 25
5 + (1 + k 2 )e2 [ 32 +
67 (2 800
1)2 ]
12 2 y 25
5 + (1 + k 2 )e2 [ 32 +
67 (2 800
1)2
+
67 ( 400
12 2 y 25
+
)(1
5 + (1 + k 2 )e2 [ 32 +
67 ( 400
)(1
and
2 q
67 (2 800
)+
when
when
> ( y 5be (1 4b)e ; y 5kbe k(1 4 b)e ) when t = 1, t = 1 > > > > < ( y be + (1+b)e ; y kbe + k(1+b)e ) when = 1, t = 1 t 5 4 5 4 = (1+b)e y+kbe k(1+b)e e > > ; 5 ) when t = 1, t = 1 ( y+b > 5 4 4 > > > : ( y+be + (1 b)e ; y+kbe + k(1 b)e ) when = 1, t = 1 t 5 4 5 4
Substitute this into (2) we get
38
(20)
When
2 ft (Dm )] = 12 y 2 + 5(1 + k ) e2 + 67 (1 + k 2 )(2 E0 [W 25 32 800
1)2 e2
3
2 q
is revealed, both …rms will produce according to
qt+1
8 < ( y e ; y ke ) when 5 5 = : ( y+e ; y+ke ) when 5
5
t
= t
1
=1
Hence the average surplus equals
2 ft (Dm )] = 12 y 2 + 6(1 + k ) e2 E0 [W 25 25
3
2 q
(21)
Next, consider the case when the informed …rm does not have information
. In this
case, it is easy to show that ft (Dm )] = E0 [W
67 12 2 5(1 + k 2 ) 2 e + (1 + k 2 )(2 y + 32 800 25
Last, we average the case when …rm 1 posses
1)2 e2
3
2 q
and the case when …rm 1 does not. Note
that, as shown in Proposition (2), the informed …rm will reveal its possession of information when conditions (5) and (6) hold. As t ! 1, the probability that the uninformed …rm knows about the informed …rm’s possession of
approaches 1. Therefore the average welfare
can be calculated as in (21). When condition (6) holds and ft!1 (Dm )] = 12 y 2 + (1 + k 2 )e2 [ 5 + 67 (2 E0 [W 25 32 800 12 2 5 67 = y + (1 + k 2 )e2 [ + (2 25 32 800 On the other hand, if
67 (1 b2 )] 800 67 1)2 + (1 )] 200 1)2 +
then
ft!1 (Dm )] = 12 y 2 + (1 + k 2 )e2 [ 5 + 67 (2 E0 [W 25 32 800 Proof of Proposition 3
39
1)2 ]
3
2 q
3
2 q
3
2 q
(1) Consider the case
. Since (16) > 0, the informed …rm will choose not to make
.
( y+(2 5 1)e ; y+k(2 5 1)e ) if Dtm = f t = 1g and Dtv = f;g > > > > < ( y (2 1)e ; y k(2 1)e ) if Dm = f = 1g and Dv = f;g t t t 5 5 = y+ke y+e > ( ; > ) if Dtm = f t = 1g and Dtv = f ; t = 1g > 5 5 > > > : ( y e ; y ke ) if Dm = f = 1g and Dv = f ; = 1g t t t t 5 5
Proof of Corollary 2
With policy Dm , we can calculate the social surplus according to (2). First consider the case when …rm 1 possesses information
. We know from Proposition (3) that the informed
…rm will reveal its possession of information when
t
=
1 and
t
1. Hence as t ! 1
=
the probability that such information becomes public approaches 1. Therefore, after some simpli…cation, the average welfare equals
8 12 2 5 67 > > y + (1 + k 2 )e2 [ 32 + 800 (2 1)2 ] > 25 > > > 67 12 2 5 > > y + (1 + k 2 )e2 [ 32 + 800 (2 1)2 > 25 > > > < + 67 (1 )( )] 3 2q when 400 m ft!1 (D )] = E0 [W 12 2 5 67 > > y + (1 + k 2 )e2 [ 32 + 800 (2 1)2 > 25 > > > 67 67 > > )( ) + 400 (1 )( > + 400 (1 > > > : when 42
3
2 q
when
0 implies
conclude
@ @R
< 0.
> @ W @
. In addition, @
1)
(1 + k 2 )e2
=@R = 0, and @
=@R < 0. Therefore, we
> 0 follows directly from Proposition (4).
Proof of Corollary 4 First consider policy Dm . When
t
1 is revealed, the …rm’s expected cash ‡ow in
=
period t + 1 equals 2 (y 25
(2
1)e)2 +
2 (y + k(2 25
1)e)2
Change in stock price as a result of this report can be calculated as Pt (
t
=
=
2 2 (y (2 1)e)2 + (y k(2 25 25 4 2 2 1 y + (1 + k 2 )(2 1)2 e2 + (1 (2 25 25 8
1) = R 1 [
4 R 1 (1 + k)y(2 25
Similarly, when 2 1)e)2 + 25 (y +k(2
t
1 1)e)2 + (1 8
(2
1)2 )(1 + k 2 )e2
1)2 )(1 + k 2 )e2 ]
1)e
= 1, the …rm’s expected cash ‡ow in period t + 1 equals 1)e)2 , which causes the stock price to increase by
2 (y 25
+ (2
4 R 1 (1+k)y(2 25
1)e.
Therefore, Corr( Pt ;
t)
=1
The mandated, reported accounting data is highly correlated with stock price changes. Next we examine policy Dm . When
t
=
1 is disclosed, price may move di¤erently
depending on whether the …rm voluntarily discloses more information. The expected value
44
of cash ‡ow in period t + 1 equals 2 (y + (2 25
2 1 (y + k(2 1)e)2 + (1 (2 1)2 )(1 + k 2 )e2 25 8 1 2 2 2 1 + ( (y e)2 + (y ke)2 + ( (y (2 1)e)2 2 1 25 25 1 25 2 1 + (y k(2 1)e)2 + (1 (2 1)2 )(1 + k 2 )e2 )) 25 8 4 2 1 2 = y + (1 + k 2 )(2 1)2 e2 + (1 + k 2 )e2 (1 (2 1)2 ) 25 25 8 9 (1 + k 2 )e2 (1 )( ) 100 1 2
Et [e c1t+1 ] =
1)e)2 +
When voluntary disclosure is made, Pt = R 1 [
2 (y 25
e)2 +
9 (1 + k 2 )e2 (1 100
2 (y + ke)2 25 )(
(
4 2 2 y + (1 + k 2 )(2 25 25
1 1)2 e2 + (1 + k 2 )e2 (1 8
))]
In contrast, when no voluntary disclosure is made Pt = R 1 [
2 (y 25
(2
1)e)2 +
4 2 2 y + (1 + k 2 )(2 25 25 9 (1 + k 2 )e2 (1 )( 100
(
In addition, when
t
2 (y 25
k(2
1 1)e)2 + (1 8
1 1)2 e2 + (1 + k 2 )e2 (1 8
1)2 )
1 (1 8
(2
(2
1)2 )
= 1 is disclosed, change in price equals
2 2 (y + (2 1)e)2 + (y + k(2 1)e)2 + 25 25 4 2 2 1 ( y + (1 + k 2 )(2 1)2 e2 + (1 + k 2 )e2 (1 25 25 8 9 (1 + k 2 )e2 (1 )( ))] 100 >
(2
2)2 )(1 + k 2 )e2
))]
Pt = R 1 [
Therefore, when
(2
1)2 )(1 + k 2 )e2
, Corr( Pt ;
t)
(1
t]
)
t]
= (y; y)
(e; ke)) =
1 2
(1
)
and Pr(Et [e yt+1 j
. Therefore
= (y; y) (e; ke)) Pr(Et [e yt+1 j (1 )( ) = 2(1 )(1 )
t]
= (y; y) + (e; ke))
, we conclude Pr(Et [e yt+1 j
t]
= (y; y)
(e; ke)) > Pr(Et [e yt+1 j
46
t]
= (y; y) + (e; ke))
t]
=
12
Illustration
The following …gures show the value of welfare functions (7), (8) and (11). values are y = 10, e = 1, k =
Parameter
0:9, and =0.9. Black, dotted line shows the benchmark
case with no mandatory reporting (Dm = ;). The red, thin line show the welfare with a comprehensive mandatory reporting system (Dm ). The blue, thick line shows the welfare with mandatory reporting of reliable information only.
12.1
Figure 1 - Welfare e¤ect of comprehensive mandatory reporting (Dm ) welfare 48.43
48.4
48.38
48.35
48.33
48.3
48.28 0.5
0.625
0.75
0.875 phi
47
12.2
Figure 2 - Welfare e¤ect of mandatory reporting of reliable information (Dm ) welfare 48.43
48.4
48.38
48.35
48.33
48.3
0.5
0.625
0.75
0.875
1 p
12.2.1
Figure 3 - Comparing alternative accounting systems welfare 48.43
48.4
48.38
48.35
48.33
48.3
48.28 0.5
0.625
0.75
0.875
1 p
48
References Admati, A. and P. P‡eiderer. 2000. "Forcing Firms to Talk: Financial Disclosure Regulation and Externality." Review of Financial Studies (Fall): 479-519. Arya, A., H. Frimor, and B. Mittendorf. 2008. "Discretionary Disclosure of Properietary Information in a Multi-Segment Firm." Working Paper, Ohio State University, University of Aarhus, and Yale School of Management. Ball, R. and P. Brown. 1968. "An Empirical Evaluation of Accounting Income Numbers." Journal of Accounting Research (Autumn): 159-178. Basu, S. 1997. "The Conservatism Principle and the Asymmetric Timeliness of Earnings." Journal of Accounting and Economics 24: 3-37. Clinch, G. and R. Verrecchia. 1997. "Competitive Disadvantage and Discretionary Disclosure in Industries." Australian Journal of Management 22: 125-137. Crawford, V. and J. Sobel. 1982. "Strategic Information Transmission." Econometrica 50: 1431-51. Darrough, M. 1993. "Disclosure Policy and Competition: Cournot vs. Bertrand." The Accounting Review (July): 543-561. Darrough, M. and N. Stoughton. 1990. "Financial Disclosure Policy in an Entry Game." Journal of Accounting and Economics: 219-43. Demski, J. 1973. "The General Impossibility of Normative Accounting Standards." The Accounting Review (October): 718-723. Demski, J. 1974. "Choice Among Financial Reporting Alternatives." The Accounting Review (April): 221-232. Diamond, D. 1985. "Optimal Release of Information By Firms." Journal of Finance: 10711094.
49
Dye, R. 1985. "Disclosure of Nonproprietary Information." Journal of Accounting Research 23: 123-145. Dye, R. 1990. "Mandatory Versus Voluntary Disclosures: the Case of Financial and Real Externalities." The Accounting Review (January): 1-24. Dye, R. and S. Sridhar. 2004. "Reliability-Relevance Trade-o¤s and the E¢ ciency of Aggregation." Journal of Accounting Research (42): 51-88. Einhorn, E. 2005. "The Nature of the Interaction between Mandatory and Voluntary Disclosures." Journal of Accounting Research 43 (September): 593-621. Financial Accounting Standards Board. 2002. "Proposal: Principles-Based Approach to U.S. Standard Setting." File Ref. #1125-001. Financial Accounting Standards Board. 2004. SFAS 123R "Stock-Based Payment." Financial Accounting Standards Board. 2005. "Project Updates: Revenue Recognition." Financial Accounting Standards Board. 2006. SFAS 157 "Fair Value Measurements." Fried, D. 1984. "Incentives for Information Production and Disclosure in a Duopolistic Envirornment." Quarterly Journal of Economics 99 (May)"367-81. Gal-Or, E. 1985. "Information Sharing in Oligopoly." Econometrica 53 (March): 329-43. Gigler, F., and T. Hammer. 1998. "On the Frequency, Quality, and Informational Role of Mandatory Financial Reports." Journal of Accounting Research: 117-147. Grossman, S. 1981. "The Informational Role of Warranties and Private Disclosure about Product Quality." Journal of Law and Economics: 461-483. Hakansson, N., G. Kunkel, and J. Ohlson. 1982. "Su¢ cient and Necessary Conditions for Information to Have Social Value in Pure Exchange." Journal of Finance: 1169-81. He¤es, E. 2005. "The Relevance of Reliability: An Update on the FASB and IASB Joint Conceptual Framework Project." Financial Executive (December): 15-18. 50
Ijiri, Y. 1975. "Theory of Accounting and Measurement." Studies in Accounting Research #10. Sarasota, FL: American Accounting Association. Lev, B. and P. Zarowin. 1999. "On Boundaries of Financial Reporting and How to Extend Them." Journal of Accounting Research (Autumn): 353-385. Liang, P. and X. Zhang. 2006. "Accounting Treatment of Uncertainty and the Capital Structure of the Firm." Journal of Accounting Research (March): 145-176. Milgrom, P. 1981. "Good News and Bad News: Representation Theorems and Applications." Bell Journal of Economics 12: 380-391. Moonitz, M. 1961. "The Basic Postulates of Accounting." Accounting Research Study No. 1. AICPA. Paton, W. and A. Littleton. 1940. "An Introduction to Corporate Accounting Standards." American Accounting Association Monograph No. 3. Shapiro, C. 1986. "Exchange of Cost Information in Oligopoly." Review of Economic Studies (July): 433-446. Trueman, B., F., Wong, and X. Zhang. 2000. The Eyeballs Have it: Searching for the Value in Internet Stocks." Journal of Accounting Research 38: 137-162. Teoh, S. 1997. "Information Disclosure and Voluntary Contribution of Public Goods." Rand Journal of Economics: 385-406. Verrecchia, R. 1983. "Discretionary Disclosure." Journal of Accounting and Economics: 179194. Wagenhofer, A. 1990. "Voluntary Disclosure with a Strategic Opponent." Journal of Accounting and Economics 12: 341-63. Wallman, S. 1995. "The Future of Accounting and Disclosure in an Evolving World: The Need for Dramatic Change." Accounting Horizon (September): 81-91.
51
