Discussion Papers In Economics
And Business

The Relationships between Mandatory andVoluntary Disclosures: Unobservable
Precision Choices by Management
Toru Ishikawa
Discussion Paper 15-09

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANThe Relationships between Mandatory andVoluntary Disclosures: Unobservable
Precision Choices by Management
Toru Ishikawa
Discussion Paper 15-09
May 2015

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANThe Relationships between Mandatory andVoluntary Disclosures: Unobservable
Precision Choices by Management∗
Toru Ishikawa†

Abstract
This paper examines the eﬀects of mandatory disclosure informationon unobservable precision choices by management of voluntary disclosure.
Prior research articles investigate the precision of information disclosed bymanagement, but they do not consider the relationships between mandatory
and voluntary disclosure information. In this paper, I focus on the relationships and analyze precision choices under the situation that there are mandatory and voluntary disclosure. I find that mandatory disclosure informationinfluences precision choices of voluntary disclosure.

Key words: Mandatory Disclosure; Voluntary Disclosure; Unobservable; Precision choice; Relationship
JEL Classification: M41; M48∗ I am deeply grateful to Tatsushi Yamamoto who provided helpful comments and suggestions.

I would also like to thank Atsushi Shiiba and Katsuhiko Muramiya whose comments made enormous contribution to my work. I would like to thank the Handai Accounting Research Seminer
participants. All errors are my own.
† Graduate School of Economics, Osaka University, 1-7, Machikaneyama, Toyonaka, Osaka
560-0043, Japan; E-mail: u757296g@ecs.osaka-u.ac.jp.

1

Introduction
Since accounting standards do not require firms to disclose full information,

they disclose only a part of it. However, I can easily consider that the information
which is not disclosed is useful for investors to make a decision. Thus, voluntary disclosure is one of the important fields in accounting, and there are many
researches about voluntary disclosure.1 On the other hand, there are researches
about precision of information disclosed by management. It is diﬃcult for outsiders to verify the precision of the information, because there is not a distinct
criteria about the precision. If investors cannot verify the precision, it is probablethat they cannot estimate the firm value properly. Therefore, it is important tostudy the precision of disclosed information.
Thus, there are some researches about precision of mandatory disclosure information but there is no research, to my best knowledge, about the precision ofvoluntary disclosure by management. I consider that the research is a very important research area, because there are no regulations of voluntary disclosure bymanagement. Subramanyam (1996) examines the market reaction to information
when the information precision is uncertain and exogenous. Penno (1996) investigates precision choices by management in financial reporting when the precision
choices are endogenous and unobservable. This shows that the precision choices
depend on prior information in financial reporting. It is natural to assume that the
precision is endogenous and unobservable, because the management understandthe cost of gathering and disclosing information.2 Thus, I focus on the precision

1There are many researches that study firm’s voluntary disclosure. Verrecchia (2001) and Dye(2001), for example, investigate voluntary disclosure comprehensively.
2Hughes and Pae (2004) assume that the precision of mandatory disclosure is exogenous andprivate information of the management. They examine the decision of disclosing the informationby the management.

1

of voluntary disclosure information, assuming the precision is endogenous andunobservable.
Most literatures about voluntary disclosure focus on the decision of whether or
not disclosing information, but there are few literatures which examine the decision under the situation that there are both mandatory and voluntary disclosure. I
consider that the reason is that the two disclosure schemes are not interdependent.
While firms are even more required to disclose additional information by accounting regulation, firms voluntarily disclose information more and more. Einhorn(2005) studies the management disclosure decision with and without disclosure
regulation.3 This research shows that the number of firms which disclose information voluntarily becomes larger when there is a disclosure regulation. This isbecause mandatory disclosure information and voluntary disclosure are not alternative but complementary. Therefore, prior researches which do not consider the
relation have the weak implication to accounting standard-setting bodies.
Prior researches which examine the precision of disclosed information do nottake into account the relation between mandatory disclosure and voluntary disclosure. Therefore, I extend the basic precision model examined by Penno (1996) totake into account the relationships between mandatory disclosure information andvoluntary disclosure information. Assuming that the management chooses theprecision of voluntary disclosure information, I introduce mandatory disclosure
information exogenously to the model.
The main contribution of this paper is to provide a theoretical framework ofunobservable precision choices under the situation that there are mandatory andvoluntary disclosure. This paper explains that the precision by the management is

3Bagnoli and Watts (2007) also examines the management disclosure decision under the situation that there are mandatory disclosure and voluntary disclosure information. They assume thatthe two information are complementary.

2determined by mandatory information required by the regulations and prior information about the contents of voluntary disclosure information. When both theseinformation and mandatory are good news or bad news, I get similar result to theprior research. That is, the precision choices mainly depend on the prior information (good news or bad news). On the other hand, when the two information are
diﬀerent respectively (e.g., one is good news, the other is bad news), the precision
choices are determined by both mandatory information and the prior information.
This shows that the role of mandatory disclosure varies by the quality of the priorinformation of voluntary disclosure information.
The rest of this paper is organized as follows. Section 2 presents the model.
Section 3 presents the result. Section 4 presents the conclusion.

2

The modelThis model is an extension of Penno’s (1996) unobservable precision choices

model. While Penno’s(1996) model assumes there is only one public signal, I
assume that there are two public information, where one is media information andthe other is mandatory information. I assume a risk-neutral market. My model
considers management who chooses precision of voluntary disclosure information
to maximize expected end-of-period firm value. After observing the two public
signals, the management chooses precision of voluntary disclosure information,
which is unobservable for investors. These signals are credibly disclosed, andinvestors (the market) use all the public information to price the firm at expectedvalue.
Next, I explain the timeline.I consider five steps in this model. The value of thefirm is Ṽ , which is a random variable and normally distributed with mean µ andvariance σV2 , i.e., Ṽ ∼ N (µ, σV2 ). In the first step , media information is publicly

3

observed, denoted by z̃.
In the second step, mandatory disclosure information is publicly observed,
designated by s̃, where s̃ = δṼ + θ̃. The variable θ̃ is identically independent andnormally distributed, with zero mean and variance σθ2 , i.e., θ̃ ∼ N (0, σθ2 ). Here,δ is a variable that represents how much information of the firm value is included
in mandatory disclosure information, i.e., δ ∈ [0, 1]. This means that mandatory
disclosure information is a part of the firm’s value, and white noise.
In the third step, the management privately chooses the precision ρ of voluntary disclosure information, after observing media information and mandatory
disclosure information. The precision variable ρ ∈ [ρ L , ρ H ], 0 < ρ L < ρ H is acontinuous choice variable by the management, and the cost of precision choices
can be represented as c ρ, where c > 0. Thus, the value of the firm after choosing
precision is Ṽ − c ρ.
In the fourth step, voluntary disclosure information t˜. The voluntary disclosure information of the firm value is represented as t( ρ) = (1 − δ)V + ε ρ − c ρ,
where ε ρ is identically independent and normally distributed, with mean zero andprecision 1/ρ. That is, voluntary disclosure information consists of a part of thefirm value which is not included in mandatory disclosure information, noise basedon precision by the management, and the precision cost,
In the fifth step, investors (the market) price this firm at it’s expected value
conditional on the prior information. That is, the price of the firm is equal toconditional expected value of the firm value after choosing precision, P = E[V −c ρ|z, s,t( ρ)].
I adopt Penno (1996) approach. That is, "media information is a garbling of
the least informative information". When choosing ρ′ and ρ′′ (ρ L ≤ ρ′ < ρ′′ ≤ρ H ) , I assume that there exists a random variable λ̃ such that:4t˜( ρ′ ) + c ρ′ = t˜( ρ′′ ) + c ρ′′ + λ̃
where λ̃ is an identically independent and normal random variable with mean
zero. This means that t˜( ρ′ ) + c ρ′ is a garbling of t˜( ρ′′ ) + c ρ′. Thus, we canrepresent that z = t( ρ L ) + c ρ L + ψ = (1 − δ)Ṽ + ε ρ L + ψ̃, where ψ̃ is an identicallyindependent and normally distributed white noise term with mean zero i.e.,ψ̃ ∼N (0, σψ2 ). So, z̃ is normally distributed with a µ mean and variance σ 2z = σV2 +σ 2ρ L + σψ2 .

3Results

3.1

Basic case

The price of the firm P(s,t, z) is represented by equation (1).4 The management chooses the precision of voluntary disclosure to maximize the expected valueof the firm value at the third step. The expected value of the firm value is represented by equation (2) . Therefore, the management maximizes the expected valueof the firm price conditional on media information and mandatory disclosure information (E[ P̃(s, t˜, z)|z, s]).5
P(s,t, z) = E[V − c ρ|z, s,t( ρ)]ρ,t )Cov( s̃,t )Cov(Ṽ − c ρ, s̃) − Cov(Ṽ −c
V ar (t˜)˜= E[Ṽ − c ρ] +˜s̃,t ))V ar ( s̃) − (Cov(
V ar (t˜)2ρ,s̃)Cov( s̃,t )Cov(Ṽ − c ρ, t˜) − Cov(Ṽ −c
V ar ( s̃)˜(s − E( s̃))˜+

s̃,t˜))V ar (t˜) − (Cov(
V ar ( s̃)

4See the appendix.
5See the appendix.

52(t − E(t˜))(1)

E[ P̃(s, t˜, z)|z, s] = E[E[[Ṽ − c ρ|s,t( ρ), z]|z, s]ρ,t )Cov( s̃,t )Cov(Ṽ − c ρ, s̃) − Cov(Ṽ −c
V ar (t˜)˜= E[Ṽ − c ρ] +˜s̃,t ))V ar ( s̃) − (Cov(
V ar (t˜)ρ,s̃)Cov( s̃,t )Cov(Ṽ − c ρ, t˜) − Cov(Ṽ −c
V ar ( s̃)2˜(s − E( s̃))˜+

s̃,t˜)) 2
V ar (t˜) − (Cov(
V ar ( s̃)(E(t˜|s, z) − (1 − δ) µ + c ρ M (s, z))(2)

There exists one Nash equilibrium, where the management chooses the precision to maximize the expected value. Let ρ∗ be such that the management chooses
to maximize the object function. Furthermore, let ρF B be such that management
choose to maximize without precision constraints.6 From the assumption, the precision choices by management are unobservable, so the market conjecture theprecision. The market conjecture is denoted by ρ M . This model provides a uniqueequilibrium. The equilibrium depends on the realized value of the media information and mandatory disclosure information. Here, I define the realized value ofthe information that is higher than the mean of the information as "Good news",
and the realized value of the information that is lower than the mean of the information as "Bad news". If both the media information and mandatory disclosure
information are Good news or Bad news, I call them "same direction", otherwise"diﬀerent direction".
6The precision which mamize the object function without constraints is√
V ar ( s̃)(z − E(z)) − Cov( s̃, z̃)(s − E(s))
FBρ=.
{(Cov( s̃, z̃) 2 − V ar ( z̃)V ar ( s̃)}c
The detail of this is in appendix.

6

3.1.1

Diﬀerent direction of the media information and mandatory disclosure information

Here, I show the precision choices by the management in the case of diﬀerent
direction of media information and mandatory disclosure information, In this case,
we obtain the similar results of the prior research. In particular, the precision
choices by the management are same of the prior research., when the value of
media information is Good news (z > E(z)).

PROPOSITION 1(1) When the value of media information is Bad news (z < E(z)), the equilibrium precision strategy by management isρL, if ρF B ≤ ρ L < ρ H






ρ∗ = 
ρF B , if ρ L < ρF B < ρ H







 ρ H , if ρ L < ρ H ≤ ρF B .

In this case, the object function is shown in figure1.
(2) When the value of media information is Good news (z > E(z)), the equilibrium precision strategy by management isρ∗ = ρ L .
In this case, the object function is shown in figure2.

7

In the case of (1), the management expects that the low realized value of themedia information is realized by a noise term.
On the other hand, in the case of (2), mandatory disclosure information does
not influence the precision choices by management. The management expects thatthe low value of the information realized. If the management chose high precision, it would be likely that the lower value of voluntary disclosure information isrealized. Therefore the management chooses the lowest precision.

3.1.2

Same direction of the media information and mandatory disclosure
information

Here, I show the precision choices by management in the case of same thedirections. I show that the precision choices by management is dependent on thevalue of both media information and mandatory disclosure information.

PROPOSITION 2
When the value of media information is lower than the expected value of themedia information conditional on mandatory disclosure (z < E[z|s]), the equilibrium precision strategy by management isρL, if ρF B ≤ ρ L < ρ H






ρ∗ = 
ρF B , if ρ L < ρF B < ρ H







 ρ H , if ρ L < ρ H ≤ ρF B .

In this case, the object function is shown in figure1.

8

When the value of media information is higher than the expected value ofthe media information conditional on mandatory disclosure (z > E[z|s]), theequilibrium precision strategy by management isρ∗ = ρ L .
In this case, the object function is shown in figure2.

Thus, the precision choice by management is aﬀected by the value of mandatory disclosure information in these cases. This is because that the management
can not find the cause of the value of media information. That is, the observed
value of media information is realized by whether the firm value or noises. So,
the management would find the cause by using the value of mandatory disclosure
information. When the value of media information is lower than the expectedvalue of the information conditional on mandatory disclosure, the management
considers that the low value of the information is realized by a noise term.
On the other hand, when the value of media information is higher than the
expected value of the information conditional on mandatory disclosure information, the management considers that the high value of the information realized bynoises. Therefore, the management does not choose the high precision.

9

P

P

Ρ

Ρ

Figure 1: case(1)

3.2

Figure 2: case(2)Particular caseIn this section, we examine the precision choices by management, when precision cost is zero (c = 0). The aim of this section is to show when the management
has an incentive to choose high precision.
PROPOSITION 3(3) When the realized value of media information is higher than the expectedvalue of the media information conditional on mandatory disclosure information(E[z|s] <z), the management chooses the lowest precision.
ρ∗ = ρ L
In this case, the object function is shown in figure3.

(4) When the realized value of media information is lower than the expectedvalue of the media information conditional on mandatory disclosure information(E[z|s] >z), the management chooses the highest precision (ρ H ).
ρ∗ = ρ H

In this case, the object function is shown in figure4.
10

Thus, the precision choices by management depend on whether the value ofthe media information is higher or lower than the expected value of the information conditional on the value of mandatory disclosure information. When the valueof media information is higher than the expected value of the information conditional on mandatory disclosure information (E[z|s] < z), management does nothave a incentive to choose high precision, because the object function decreases inprecision. When the value of media information is lower than the expected valueof the information conditional on mandatory disclosure information (E[z|s] > z),
management has a incentive to choose high precision, because the object function
increases in precision.

P

P

Ρ

Ρ

Figure 3: case(3)Figure 4: case(4)114Conclusion
This paper provides an extension model of the basic precision model. Assum-

ing that the management chooses the precision of voluntary disclosure information, I introduce mandatory disclosure information to the model. This paper examines the influence of mandatory disclosure information on the precision choices
by management. I observe that mandatory disclosure information has influence on
the precision choices. In particular, I focus on the incentives of precision choices
by management. When the two public information (media and mandatory) are in
diﬀerent directions (Good or Bad), I observe the similar results of the prior research. In this case, the incentive of precision choices depends on the direction ofmedia information. However, I observe diﬀerent results, when the two public information are in the same direction. That is, the incentive depends not only on the
direction of media information but also on the direction of mandatory disclosure
information.
This research contributes to accounting standard-setting bodies, because it offers a theoretical framework of unobservable precision choices under the situationthat there are both mandatory and voluntary disclosure. It is more natural to assume that the precision is endogenous and unobservable under the situation. Thus,
I consider that my model can be applied to various contexts.
However, there is room for improvement. The property of mandatory disclosure is exogenous, but I can not observe the influence of incentive change on themarket in this model. This is a topic for my future research.

12

APPENDIX A
The price of the firmThis appendix provides price function. The price of the firm is equal to conditional expected value of the firm value after choosing precision. Thus, the pricefunction isP(s,t, z) = E[V − c ρ|z, s,t( ρ)]ρ,t )Cov( s̃,t )Cov(Ṽ − c ρ, s̃) − Cov(Ṽ −c
V ar (t˜)˜= E[Ṽ − c ρ] ++˜s̃,t ))V ar ( s̃) − (Cov(
V ar (t˜)ρ,s̃)Cov( s̃,t˜)
Cov(Ṽ − c ρ, t˜) − Cov(Ṽ −c
V ar ( s̃)˜s̃,t ))V ar (t˜) − (Cov(
V ar ( s̃)

2

˜

2

(s − E( s̃))(t − E(t˜)).

The expected value of this price of the firm
The expected value of this price of the firm is equal to conditional expectedvalue of the firm value before voluntary disclosure information is disclosed. Thatis, the expected value of this price of the firm is the expected value of the firm
price conditional on media information and mandatory disclosure information.

E[ P̃(s, t˜)|z, s] = E[E[[Ṽ − c ρ|z, ,t( ρ)]|z, s]ρ,t )Cov( s̃,t )Cov(Ṽ − c ρ, s̃) − Cov(Ṽ −c
V ar (t˜)˜= E[Ṽ − c ρ] +˜s̃,t ))V ar ( s̃) − (Cov(
V ar (t˜)ρ,s̃)Cov( s̃,t )Cov(Ṽ − c ρ, t˜) − Cov(Ṽ −c
V ar ( s̃)2˜(s − E( s̃))˜+

s̃,t˜)) 2
V ar (t˜) − (Cov(
V ar ( s̃)

13(E(t˜|s, z) − (1 − δ) µ + c ρ M (s, z))The precision which maximize the object function without constraints
From above results, to maximize the object function is equal to maximizing
the expected value of the voluntary disclosure information conditional on media
information and voluntary disclosure information (E[t˜|s, z]).

E[t˜|s, z]s̃,z̃)
Cov(t˜, s̃) − Cov(tV,z̃)Cov(ar (t˜)˜= E[t˜] +s̃,z̃))V ar ( s̃) − (Cov(
V ar ( z̃)= (1 − δ) µ ++2s̃,z̃)
Cov(t˜, z̃) − Cov(Vt ,s̃)Cov(ar ( s̃)˜(s − E( s̃)) +s̃,z̃))V ar ( z̃) − (Cov(
V ar ( s̃)2(z − E(z))

V ar ( s̃)(z − E(z)) − Cov( s̃, z̃)(s − E(s)) 1− cρρV ar ( z̃)V ar ( s̃) − (Cov( s̃, z̃) 2

V ar ( s̃)(z − E(z)) − Cov( s̃, z̃)(s − E(s))[(1 − δ) 2 + δ(1 − δ)]σV2
V ar ( z̃)V ar ( s̃) − (Cov( s̃, z̃) 21− c ρ + αδ(1 − δ)]σV2 ,ρV ar ( s̃)(z − E(z)) − Cov( s̃, z̃)(s − E(s))
where α =V ar ( z̃)V ar ( s̃) − (Cov( s̃, z̃) 2= (1 − δ) µ + α

Thus, the expected value of the voluntary disclosure information conditionalon media information and voluntary disclosure information (E[t˜|s, z]) is a functionof the precision by management. When the α > 0, there exists the precision thatmaximize the function. So, the precision which maximize the object function
without constraints is
ρF B =√V ar ( s̃)(z − E(z)) − Cov( s̃, z̃)(s − E(s)).
{(Cov( s̃, z̃) 2 − V ar ( z̃)V ar ( s̃)}c

14

Table 1: Main notations
variableṼ

firm valueṼ ∼ N (µ, σV2 )θ̃white noiseθ̃ ∼ N (0, σθ2 )δthe weightδ ∈ [0, 1]

ρ precision by management

0 < ρL ≤ ρ ≤ ρHε̃ ρcontrollable noiseε̃ ρ ∼ N (0, 1/ρ)z̃

media information(1 − δ)Ṽ + ε ρ L + ψ̃s̃

mandatory disclosure informationt˜ voluntary disclosure information15

δṼ + θ̃(1 − δ)Ṽ + ε̃ ρ − c ρREFERENCES
References[1] Bagnoli, M. and G. S. Watts. (2007). Financial Reporting and Supplemental Voluntary Disclosures

Journal of Accounting Research, Vol.45, No.5.

pp.885-913.
[2] Dye, R. (2001).

An Evaluation of Essays on Disclosure and the Disclosure

Literature in Accounting.

Journal of Accounting and Economics, Vol.32,

Issues 1-3, pp. 181-235.
[3] Einhorn, E. (2005).

The Nature of the Interaction between Mandatory andVoluntary Disclosures. Journal of Accounting Research, Vol. 43, No.4, pp.
593-621.
[4] Hughes, J., and S. Pae.(2004).
tion.

Voluntary Disclosure of Precision Informa-

Journal of Accounting and Economics, Vol. 37, No. 1, pp. 261-289.

[5] Penno, M. (1996). Unobservable Precision Choices in Financial Reporting.
Journal of Accounting Research, Vol. 34, No. 1, pp. 141-149.
[6] Subramanyam, K. R.(1996). Uncertainty Precision and Price Reactions toInformation.

The Accounting Review,Vol.71, No.2, pp.207-220.

[7] Verrecchia, R. E. (2001).

Essays on Disclosure.

and Economics,Vol. 32, Issues 1-3, pp. 97-180.

16

Journal of Accounting