Strategic Commitment and Lying: An
Experimental Study on the Interaction
between Entrepreneur and Underwriter

Abstract
The objective of this paper is to answer the problem “When and how
do people choose to lie?” through introducing strategic commitment bypotential liars. In order to consider the role of commitment, we focus on
an IPO setting and examine the interaction between an entrepreneur andan underwriter. Our theoretical and experimental findings suggest that theentrepreneur uses the ownership retention as a signal of commitment andmanages earnings upward. In addition, given that the entrepreneur retains
ownership, the underwriter optimistically assesses the reported earnings.

Keywords: IPO; earnings management; commitment; white lies; experiment
JEL Classification: D74; G02; M41

1

1

Introduction

The objective of this paper is to investigate the relationship between strategic commitment and lying. Numerous experimental studies consider lying behaviors in
diﬀerent economic environments and report that people have a tendency toward
lying aversion (e.g., Gneezy, 2005; Hurkens and Kartik, 2009; Lundquist et al.,2009; Sanchez-Pages et al., 2009; Erat and Gneezy, 2012; Gibson et al., 2013;
Gneezy et al., 2013; Lopez-Perez and Spiegelman, 2013). That is, people often
tell the truth even if they can increase their material payoﬀs by lying. This suggests that people are more honest than is predicted by the traditional economic
theories, which is based on the homo economicus assumption. Nonetheless casual
observations suggest that dishonest behaviors are frequently found in some economic settings. Accounting frauds, such as window-dressing and tax evasion, aretypical examples. So when and how do people choose to lie?
One of the factors which might aﬀect whether people tell lies or not is theconsequential outcomes for both the liar and the other. Gneezy (2005) argues
that people care about not only their own gains from lying; they also take into
account their partners’ payoﬀs. Erat and Gneezy (2012) classify the four typesof lies by the consequential outcomes from lying. (i) Selfish black lies: liars canincrease their own payoﬀs but partners suﬀer losses，(ii) spiteful black lies: bothliars and partners incur losses，(iii) altruistic white lies: liars incur losses but
partners’ payoﬀs increase，(iv) Pareto white lies: both liars and partners benefit
from lying．In addition, the experimental data of Erat and Gneezy (2012) suggests

2that people lie more frequently in the situation of “Pareto white lie” compared withthe situation such as “selfish black lie” and “altruistic white lie.”This paper answers the problem “When and how do people choose to lie?”through introducing strategic commitment by potential liars. In order to examine the role of commitment, we focus on a specific economic setting where an
entrepreneur is filing for an initial public oﬀering (IPO). More specifically, we
consider the situation where an entrepreneur (IPO firm) issues new shares and reports earnings, and then an underwriter assesses the earnings and sets the oﬀering
price.
In IPO research, two major problems are well-known as ‘IPO puzzles.’ First,
in the short-run, it is observed that the first listing price of an IPO firm is muchhigher than the oﬀering price set by the underwriter (Ibbotson, 1975; Ritter, 1984;
Loughran and Ritter, 1995; Loughran and Ritter, 2002; Ritter and Welch, 2002;
Loughran and Ritter, 2004). The diﬀerence between them is so-called ‘money
left on the table.’ Second, it is also observed that in the long-run the share pricebecomes much lower than the oﬀering price (Aggarwal and Rivoli 1990; Ritter,
1991; Loughran and Ritter, 1995; Ritter and Welch, 2002). That is often called‘long-run underperformance.’
It leads to a question ‘which is the fundamental value, the first listing priceor the oﬀering price?’ There are two main streams of research to answer thequestion. First, according to the traditional theories assuming that investors havehomogeneous expectation (Markowitz, 1952; Sharpe, 1964; Lintner, 1965; Blackand Scholes, 1973), it is argued that the first listing price is the fundamental value.
3

Hence the diﬀerence between them is ‘underpricing’ in that the IPO firm was underpriced by the underwriter. Second, according to the behavioral theories assuming that there is a divergence of opinions among investors (Miller, 1977; Shleifer,
1986; Chen, Hong, and Stein, 2002; Chatterjee, John, and Yan, 2012), it is argued
that the oﬀering price is the fundamental value. Hence the diﬀerence between
them can be interpreted as investors’ sentiment bubble.
Our research diﬀers from both the traditional theories and the behavioral theories in that neither the first listing price nor the oﬀering price is the fundamental
value. That makes us possible to explain why the IPO puzzles coexist.
Assuming that there is a divergence of opinions among investors, we havea conclusion that even the oﬀering price is distorted through collusion between
the entrepreneur and the underwriter. That is, the oﬀering price is already “overpriced.” Therefore the diﬀerence between the first listing price and the oﬀering
price represents investors’ sentiment bubble, and hence the share price will godown seriously as asymmetry of information between both the entrepreneur andthe underwriter and investors is mitigated after the IPO. That delivers the long-run
underperformance.
Our IPO context has some interesting features. First, according to Miller(1977), we assume that there is a divergence of investors’ opinions, and hence
the demand curve of the share is downsloping to right. That is a sharp contrast
to the traditional theories.1 Second, capital market perceives a higher ownership1

In the traditional theories (e.g. Sharpe (1964) and Lintner (1965)), there are no divergencesof investor’s opinions, and hence the demand curve is flat.

4

retention of the entrepreneur as good news. Namely, the demand curve shifts
upward as the level of the retained ownership increases.2 The settings make us
possible to explore the interactive mechanism of the demand and the supply.
In general, the entrepreneur prefers a higher oﬀering price because she wants
to obtain enough capital to expand her business or realize the founder’s profit.
Therefore, the entrepreneur might have an incentive to overstate earnings in orderto pretend that the firm has good performance and have the oﬀering price raised.
To some extent, the underwriter and the entrepreneur share mutual interests.
Since the underwriting fee generally increases in the capital raised, the underwriter might benefit from the higher oﬀering price. However, the underwriter
must also bear the risk. If the oﬀering price is too high for the shares to be soldout in the market, the underwriter will absorb the loss due to the unsold shares.
This might lead the underwriter to assess the reported earnings strictly and set theoﬀering price lower in order to avoid the risk.3 That is, when the demand for theshares is relatively low and the risk of loss due to the unsold shares is relatively
high, there is a conflict of interest between the entrepreneur and the underwriter.
We model the potential conflict situation above and conduct an experiment inorder to test the theoretical predictions. Basically, an experimental approach has
several advantages in testing them. First, researchers can freely create a controlled
economic environment that corresponds to the timeline and the information set
2This assumption is consistent with the empirical finding of Fan (2007) that ownership retention is positively related to valuation of IPO firms.
3See, for example, Baron (1982), Chen and Mohan (2002), and Deloof et al. (2008). In
particular, Deloof et al. (2008) argues that the final oﬀering price is decided taking into accountcurrent market conditions.

5

of the model. Second, researchers can directly observe people’s behaviors andcollect behavioral and psychological data. These characteristics make us possible
to directly verify the model.
Our theoretical and experimental findings are summarized as follows. First,
the entrepreneur increases the level of ownership retention and overstates earnings
to have the oﬀering price raised. Second, the underwriter overlooks the distorted
earnings and quote a higher oﬀering price especially in the case of a suﬃciently
high level of the ownership retention.4 This is because, given that investors perceive the higher ownership retention as good news, it increases the market demand for the shares. Therefore, the underwriter can reduce the risk of incurring
loss due to the unsold shares even if he sets the higher oﬀering price. In otherwords, the ownership retention works as a signal of commitment so that the interests of the entrepreneur and the underwriter are aligned. In this situation, boththe entrepreneur and the underwriter can benefit from overstating the earnings andsetting the oﬀering price “overpriced.”
This paper has several contributions to the academic research. First, to the bestof our knowledge, this is the first paper that argues IPO firms are “overpriced.”
We develop a theoretical model on the collusion between the entrepreneur andthe underwriter in an IPO setting on the assumption that there is a divergence of
opinions among investors and that the higher retention is perceived as good news
by them. The collusion is a typical example of ‘Pareto white lie’ situation. Our

4

In the model, the oﬀering price is an increasing function of ownership retention and earnings
after the assessment by the underwriter. The details of the model will be described in Section 2.

6

conclusion is a sharp contrast to those of prior research that argues IPO firms areunderpriced. Therefore, this paper could oﬀer a new insight to the IPO research.
Second, the intense interest has recently focused on the question of when andhow people lie. We develop a theoretical model in IPO settings and examine thepredictions of the model by laboratory experiment. Because IPOs are big businessevents that attract attention of many business people (e.g. investors, underwriters,
regulatory agencies and so on), our paper makes some contribution to business bysuggesting a clue to when and how people lie.
Third, the traditional theories assume that investors have homogeneous expectation and hence the demand curve is flat. However that is an unrealistic premisebecause it is hard to believe that investors have the same opinion about security
prices in an uncertain world. Therefore we develop the model on the assumptionthat there is a divergence of investors’ opinions, and hence the demand curve isdownsloping to right. This enables us to develop the plausible model that explains
reality.
Fourth, this paper provides a new insight into the literature by examining therole of commitment. Trueman (1986) assumes the information asymmetry between an entrepreneur and investors, and developed a model that she uses capital
investment and the ownership retention as signals in IPO settings. In our settings,
the level of ownership retained by the entrepreneur (potential liar) works as a signal of commitment and can change the underwriter’s behavior so that both theentrepreneur and the underwriter share mutual interests. This implies that, in theframework of Erat and Gneezy (2012), the entrepreneur can change the situation
7

of “selfish black lie” into that of “Pareto white lie” by raising the level of commitment. Our results suggest that people strategically create the situation of “Pareto
white lie” by means of commitment and lie.5
Finally, this paper also relates the experimental studies about IPOs and earnings management. In accounting, Mayhew et al. (2004) examine the retained
ownership as a signaling device in IPO. In their experiment which is based on
Datar et al. (1991) model, however, earnings management is not addressed. Other
studies explore the IPO auction mechanism. Zhang (2009) compares fixed priceoﬀerings with uniform price auction. Almeida and Leal (2011) examine three
IPO pricing methods, namely book building, the Dutch clock auction, and thecompetitive method. On the other hand, there are several experimental studies
which examine earnings management in various settings but not IPO contexts.
Hirst and Hopkins (1998) and Maines and McDaniel (2000) investigate the effect of disclosure format of comprehensive income on investors’ ability to detect
earnings management and their judgments about the firm performance. Tan andJamal (2006) examine whether managers smooth earnings through real discretion
when accounting discretion reduces. Some other studies focus on the relationship between earnings management and audit. For example, Hirst (1994) examine auditors’ judgments about the probability that a material misstatement exists
in contexts of a management buyout and earnings-based compensation plans. In
their recent study, Chen et al. (2012) investigate the eﬀects of changes in auditors’

5

In this paper, the term “Pareto white lie” is used in the sense that both players in the gamebenefit from lying. To discuss social welfare is beyond the scope of this paper.

8

actions on the deterrence of earnings management. To the best of our knowledge,
this paper is in experimental studies the first that investigates both the ownershipretention and the earnings management in the setting of IPO. Therefore, this paper can provide the possible explanation to the relationship between ownershipretention and earnings management in IPO.
The remainder of this paper is organized as follows. In section 2, we develop
the theoretical model which provides the basis for experimental tests. Section 3
describes the experimental design and Section 4 reports the results. In section
5, we extend the model by introducing earnings management costs. Section 6summarizes the paper.

2

Model

2.1

Settings of the model

We have a two-period model. In the first period (hereafter ‘period 0’), a riskneutral entrepreneur who owns all of the firm’s shares (N shares) decides to havethe firm go public at the beginning of the second period (hereafter, ‘period 1’). At
the IPO, she issues another N shares and sell S = (1 − w)N shares that she owns
(0 ≤ w ≤ 1).
Since her payoﬀ by selling the shares increases in the public oﬀering price P0
decided by an underwriter, she has an incentive to raise it by managing earnings
in financial statements she issues at the end of period 0. Let θ and µ be the true
earnings and an amount of the earnings management in period 0 respectively. The
9reported earnings e can be written ase = θ + µ.
We assume that 0 ≤ µ ≤ θ, that is θ ≤ e ≤ 2θ.
The firm has business activities in period 1. The probability of its successis p(0 < p < 1) and in case of the success the share price will go up to P1 =P0 + α (α > 0) at the end of period 1. However there is a risk that the earnings
management comes to light. We assume the probability is q (0 < q < 1). If
it does, the share price will go down by kµ (0 ≤ k ≤ 2) in period 16 . In caseof the business activities’s failure (with the probability 1 − p), the share pricewill go down to P1 = 0 at the end of period 1 irrelevant of whether the earnings
management comes to light or not.
Hence, the entrepreneur maximizes(1 − q)[P0 S + p(P0 + α)(N − S )] + q[P0 S + p(P0 + α − kµ)(N − S )]= N {[1 − (1 − p)w)]P0 + wp(α − qµk)} .

Since N is positive and constant, for simplicity we define her payoﬀ as
Ue = [1 − (1 − p)w)]P0 + wp(α − qµk).
6

We assume α > kµ to avoid the cases of P1 < 0.

10

According to Miller(1977), we assume that there is a divergence of investors’
opinions, and hence the demand curve of the share is downsloping to right shownin Figure 17 . Let a demand curve of the share be
P + D(P) = a + f (w)where P and D(P) are a share price and an inverse demand function of theshare respectively. a represents a degree of popularity of the firm and we assume
a > 2N 8 .
A higher ownership retention after the IPO is perceived as good news by investors because it is a signal that she may have private information about goodprospects of the firm, and shifts the demand curve upward shown in Figure 1.
That is,f (0) = 0, f (w)w,0 > 0, f ′ (w) > 0.
We assume that the marginal eﬀect of the retention on w is decreasing, f ′′ (w) ≤ 0.
Insert Figure 1 about here.
Generally an underwriter’s payoﬀ increases in a product of an oﬀering priceand how many shares (Q) he sells in a market. Hence, we define the underwriter’s
7

In the traditional theories (eg. Sharpe(1964) and Lintner(1965)), there are no divergences ofinvestor’s opinions, and hence the demand curve is flat.
8This is a typical assumption about demand curves.

11

payoﬀ as P0 Q for simplicity. It is clear that a higher oﬀering price makes his
payoﬀ higher as long as the demand of the shares exceeds the supply in the market.
However too high an oﬀering price makes the excess supply and makes his payoﬀ
lower.
We assume that the underwriter decides the oﬀering price considering two
factors. The first is earnings in period 0. Since he cannot observe the true earnings
but the reported earnings that might be managed by the entrepreneur, all he can dois to estimate it, in other words to estimate the earnings management. The larger
estimated earnings management leads him to quote a lower oﬀering price. The
second is the owner’s retention. Since he knows the higher ownership retention isperceived as good news by investors, it leads him to quote a higher oﬀering price.

Hence we assume that he decides the oﬀering price P0 according to
P0 = x + g(w) + e − bµ = x + g(w) + (θ + µ) − bµ
where x(> 0), θ(> 0), and bµ(≥ 0) are the firm value at the beginning of period
0, the true earnings in period 0, and the earnings management estimated by theunderwriter respectively, and where g(0) = 0, g(w)w,0 > 0, and g′ (w) > 0. We
further assume that g′ (w) is less than N 9 and the marginal eﬀect of the retention
on g(w) is decreasing, g′′ (w) ≤ 0.

9This assumption only implies that the curve g(w) is not very steep in 0 ≤ w ≤ 1.

12

Hence, the problem of the underwriter is to maximize Uu .





 P0 (N + S ) if N + S ≤ D(P0 )Uu = P0 Q =  P0 D(P0 )otherwise
if P0 ≤ a + f (w) − (N + S ) P0 (N + S )= P0 (a + f (w) − P0 )otherwise−(N + S )[bµ − (x + g(w) + e)]








if b
µ ≥ x + g(w) − f (w) + e − a + N + S


=
.




−[b
µ − (x + g(w) + e)][bµ − (x + g(w) − f (w) + e − a)]









otherwise.
Insert Figure 2 (a), (b) about here.

The intersections of Uu = P0 (N + S ) and Uu = P0 D(P0 ) are bµ1 = x + g(w) −f (w) + e − a + (2 − w)N and bµ2 = x + g(w) + e shown in Figure 2 10 . It is important
to note that the larger earnings management, the higher bµ1 and that the higher
retention, the lower b
µ1 .
∂b
µ1
= 1.
∂µ
∂b
µ1
= g′ (w) − f ′ (w) − N < 0 ( f ′ (w) > 0, 0 < g′ (w) < N).
∂w
We first solve the problem in a case without earnings management costs (k =In Figure 2, we assume that the axis of symmetry of Uu is greater than bµ1 . In Appendix A,
we show why this assumption is appropriate.
10130) for simplicity, since the implications are qualitatively same as in a case with theearnings management costs (k > 0). In the fifth section we show the solutions withthe earnings management costs as an extension by comparing with the solutions
without them.

2.2

Solutions without earnings management costs

We solve the problem by dividing it into three cases.
Case （I） A very popular firm with a ≥ x + 2θ + 2N
We call a firm with a ≥ x + 2θ + 2N a ‘very popular firm’ in that even if
the entrepreneur sells all the shares she owns (w = 0) and manages earnings to a
maximum degree (µ = θ),µb1 |w=0,µ=θ = x + 2θ − a + 2N ≤ 0.
Hence, the underwriter chooses bµ∗ = 0 shown in Figure 2(a).
Since P0 = x + g(w) + θ + µ,
Ue = {1 − (1 − p)w}(x + g(w) + θ + µ) + wpα.

Since ∂Ue /∂µ = 1 − (1 − p)w > 0, the entrepreneur chooses µ∗ = θ.

14

Hence, Ue can be written as
Ue = {1 − (1 − p)w}(x + g(w) + 2θ) + wpα.

dUe
= pα − (1 − p){g(w) + wg′ (w) + x + 2θ} + g′ (w) ≡ ϕ0H (w).
dw

Since g′ (w) > 0, g′′ (w) ≤ 0,
d2 Ue dϕ0H (w)== −2(1 − p)g′ (w) + {1 − (1 − p)w}g′′ (w) < 0.
dw2
dw
Hence, ϕ0H (w) is a strictly decreasing function of w.
∂ϕ0H (w)= α + g(w) + wg′ (w) + x + 2θ > 0.
∂p
∂ϕ0H (w)= p > 0.
∂αHence, the larger p and the larger α shift the curve ϕ0H (w) upward. Since ϕ0H (w)is a strictly decreasing function of w shown in Figure 3, the optimal retentions are
as follows:[A0 ] When p and/or α are large enough to hold ϕ0H (1) ≥ 0, w∗ = 1.
[B0 ] When p and/or α are such that hold ϕ0H (1) < 0 < ϕ0H (0), 0 < w∗ < 1.
15

[C0 ] When p and/or α are small enough to hold ϕ0H (0) ≤ 0, w∗ = 0.
Insert Figure 3 about here.
The implications of the solutions are twofold. First the entrepreneur whose
firm is very popular to investors before the IPO manages earnings to the maximum degree because she knows the underwriter chooses to estimate zero earnings
management. Second she nevertheless sells the shares when an expected loss fromholding the shares is enough larger than an expected return from the business activities11 .
Case （II） An unpopular firm with a < x + g(1) − f(1) + θ + N
We call a firm with a < x + g(1) − f (1) + θ + N an ‘unpopular firm’ in that even
if the entrepreneur holds all the shares she owns (w = 1) and does not manage
earnings at all (µ = 0),bµ1 |w=1,µ=0 = x + g(1) − f (1) + θ − a + N > 0.

Hence, the underwriter chooses bµ∗ = bµ1 shown in Figure 2(b).
Since P0 = x + g(w) + e − bµ∗ = f (w) + (w − 2)N + a,
Ue = {1 − (1 − p)w}{ f (w) + (w − 2)N + a} + wpα.

(1)

The expected return from the business activities is pα. Since the oﬀering price when w = 0 is
P0 = x +2θ, the expected loss is (1 − p)(x +2θ). In the extreme case that an expected loss is enoughlarger than an expected return, say ϕ0H (0) = pα − (1 − p)(x + 2θ) + g′ (0) < 0, the entrepreneur sells
all the shares she owns.
1116This implies the entrepreneur’s payoﬀ is irrelevant of the reported earnings.
Hence, she chooses µ∗ =any(0 ≤ µ∗ ≤ θ).
dUe= −(1 − p){ f (w) + w f ′ (w) + 2(w − 1)N + a} + f ′ (w) + N + pα ≡ ϕ0L (w).
dw

Since f ′ (w) > 0 and f ′′ (w) ≤ 0,
d2 Ue dϕ0L (w)== −2(1 − p){ f ′ (w) + N} + {1 − (1 − p)w} f ′′ (w) < 0.
2dw
dw
Hence, ϕ0L (w) is a decreasing function of w.
∂ϕ0L (w)= f (w) + w f ′ (w) + 2(w − 1)N + a + α > 0 (a > 2N).
∂p
∂ϕ0L (w)= p > 0.
∂αHence, the larger p and the larger α shift the curve ϕ0L (w) upward. Since ϕ0L (w)is a decreasing function of w shown in Figure 4, the optimal retentions are as
follows:[a0 ] When p and/or α are large enough to hold ϕ0L (1) ≥ 0, w∗ = 1.
[b0 ] When p and/or α are such that hold ϕ0L (1) < 0 < ϕ0L (0), 0 < w∗ < 1.
17

[c0 ] when p and/or α are small enough to hold ϕ0L (0) ≤ 0, w∗ = 0.
Insert Figure 4 about here
The implications of the solutions are twofold. First the entrepreneur whose
firm is unpopular to investors does not have an incentive to manage earnings,
because the underwriter focuses only on the components of the demand function(w, a, N) and does not use the reported earnings when deciding the oﬀering price.
Second the entrepreneur nevertheless holds the shares when an expected returnfrom the business activities is enough larger than an expected loss from holding
the shares12 .
Case （III） For a firm with x + g(1) − f(1) + θ + N ≤ a < x + 2θ + 2N
We call a firm neither very popular nor unpopular a ‘popular’ firm. We call ita ‘popular firm’. The sign of b
µ1 = x + g(w) − f (w) + e − a + (2 − w)N can be either
positive or negative depending µ and w.
We examine whether the entrepreneur can increase her payoﬀ by raising theownership retention. Suppose that for w = w1 , the underwriter chooses bµ∗ = bµ1 >0 (hereafter ‘unpopular equilibrium’) and that for w = w2 ≡ w1 + ∆w (∆w >0), he chooses bµ∗ = 0 (hereafter ‘very popular equilibrium’). In the unpopular
equilibrium,
Ue1 = {1 − (1 − p)w1 }{ f (w1 ) + (w1 − 2)N + a} + w1 pα
The expected return is pα. Since the oﬀering price when w = 0 is P0 = a − 2N , the expected
loss is (1 − p)(a − 2N). When the expected return is enough larger than the expected loss, say
ϕ0L (0) = −(1 − p)(a − 2N) + f ′ (0) + N + pα > 0 , the entrepreneur holds some or all of the shares.
1218

and in the very popular equilibrium,
Ue2 = {1 − (1 − p)w2 }{x + g(w2 ) + 2θ} + w2 pα.

The conditions that the entrepreneur can increase her payoﬀ by raising theownership retention are that in the very popular equilibrium she does not sell all
the shares she owns13 , in the unpopular equilibrium she does not hold all the shares
she owns14 , and her payoﬀ increases from the change in the equilibriums. That is,
ϕ0H (0) ≡ pα − (1 − p)(x + 2θ) + g′ (0) > 0.
ϕ0L (1) ≡ pα + f ′ (1) + N − (1 − p){ f (1) + f ′ (1) + a} < 0.
Ue2 ≡ {1 − (1 − p)w2 }{x + g(w2 ) + 2θ} + w2 pα> {1 − (1 − p)w1 }{ f (w1 ) + (w1 − 2)N + a} + w1 pα ≡ Ue1 .

Insert Figure 5 about here.
The shadowed area in Figure 5 satisfies all the conditions above, and for any
points (p, α) in the shadowed area, there exist w1 and ∆w (∆w > 0) that satisfy
0 ≤ w1 < w2 = w1 + ∆w ≤ 1. The proof is provided in Appendix B.
Taken together, there exist some cases that the payoﬀ of the entrepreneur
can be increased through changing the underwriter’s behavior by increasing theowner’s retention. Hence, we have a proposition.
13
14This is equivalent to [A0 ] or [B0 ] in Case(I).
This is equivalent to [b0 ] or [c0 ] in Case(II).

19

Proposition
Neither in a situation that p and/or α are not small enough for theentrepreneur in the very popular equilibrium to sell all the shares nor
in a situation that p and/or α are not large enough for the entrepreneurin the unpopular equilibrium to hold all the shares,
1. the entrepreneur raises the ownership retention and manages
earnings upward to a maximum degree, and2. the underwriter chooses to estimate no earnings managements.
Since the entrepreneur knows that in a higher retention case it is optimal forthe underwriter to decide the oﬀering price assuming she does not manage earnings at all, she chooses the higher retention and the maximum level of earnings
management. On the other hand, since the underwriter knows the higher retention
is perceived as good news by investors, he chooses to estimate no earnings management as far as the demand of the share exceeds the supply. This is a collusion
between the entrepreneur and the underwriter, and an typical example of Pareto
white lie to investors.
In a real world, a firm that is going public can be thought neither a very popular firm nor an unpopular firm, the proposition can explain the strategic interaction
between the entrepreneur and the underwriter. In the following section we examine the proposition by experiment.

20

3

Experimental Design

3.1

Experimental parameters and hypotheses

Based on the model analyzed in the previous section, we conduct an experimentin order to test the theoretical predictions. Since the implications in the case withthe earnings management costs are qualitatively same as those without the costs,
we conduct the experiment in the case of without them for simplicity. Especially,
we consider the “popular” case in the model. In the experiment, participants takethe role of either the entrepreneur or the underwriter. The entrepreneur is assumed
to own a hundred of shares of her firm and plan to issue an additional a hundredof shares (i.e., N = 100). She chooses the level of ownership retention w% andreported earnings e. Then, the underwriter observes and assesses the reported
earnings and chooses the corrected actual earnings, which is calculated by subtracting the underwriter’s estimation of earnings management from the reported
earnings (i.e., e − bµ).
The experimental parameters are deliberately specified so that we can create
the “popular” case in the model and the participants can easily understand thestructure of the game. In particular, the parameters used in the experiment are as21

follows.

Oﬀering Price (P0 )= 100 + 10 × Retention (w%) + Corrected Actual Earnings (e − bµ),Demand= −Oﬀering Price (P0 ) + 10 × Retention (w%) + 450,
Supply= 100 + 100 × (1 − Retention (w%)),
Stock Dealings = min {Demand, Supply}.

For simplicity, we assume that the business activities of the firm achieve success with probability 75% and the share price will go up to P1 = P0 + 100. On theother hand, the business activities fail with probability 25% and the share pricewill go down to P1 = 0. Therefore, the payoﬀ for the entrepreneur is calculated
as follows.
Ue = Oﬀering Price (P0 ) × 100 × (1 − Retention (w%))+ 0.75 × (Oﬀering Price (P0 ) + 100) × (Retention (w%) × 100).

The payoﬀ for the underwriter does not depend on the success in business and is
calculated as follows.
Uu = Oﬀering Price (P0 ) × Stock Dealings.
22

When the entrepreneur chooses the reported earnings e, she can manage earnings upward. More specifically, nature selects the true earnings θ from the set{80, 100, 120} and only the entrepreneur observes the realized one. Then, shechooses the reported earnings among (i) the true earnings (i.e., e = θ), (ii) 1.5
times of the true earnings (i.e., e = 1.5θ), and (iii) the double of the true earnings(i.e., e = 2θ). This means that (i) when e = θ, the earnings management µ = 0,(ii) when e = 1.5θ, µ = 0.5θ, (iii) when e = 2θ, µ = θ. For example, if the true
earnings is 100, then the entrepreneur chooses the reported earnings from the set{100, 150, 200}. Furthermore, she chooses the level of ownership retention w%
from the set {0%, 50%, 100%}.15
The underwriter observes the reported earnings e and the ownership retention
w%. He chooses the percentage from the set {0%, 25%, 50%, 75%, 100%} taking
into account that the entrepreneur might manage earnings upward. For example,
if the reported earnings is e = 200 and the underwriter chooses 75%, then theestimation of the earnings management bµ is calculated as (200 × 0.75) = 150.
Thus, the corrected actual earnings (e − bµ) is 200 − 150 = 50.
We focus on the “popular” case in the model. In this case, the conflict of interest between the entrepreneur and the underwriter might exist. This is because
if the entrepreneur manages earnings upward and the resulting oﬀering price becomes higher, then the underwriter might face the risk of incurring loss due tothe unsold shares. Hence, the underwriter will have an incentive to assess the15

For ease of participants, the experiment requires them to choose an amount of shares which
they sell.

23

reported earnings severely (i.e., lower the corrected actual earnings) and set theoﬀering price lower.
The entrepreneur, however, can enhance the market demand for the shares by
increasing the level of the ownership retention. This reduces the underwriter’srisk and can alter the situation from “selfish black lie” to “Pareto white lie.” Inother words, if the entrepreneur retains the ownership higher, then earnings management might also become beneficial to the underwriter. In our experimental
parameters, the probability of success in business is high enough for a risk-neutral
entrepreneur to retain the ownership. Therefore, we expect that the entrepreneur
uses the ownership retention as a signal of the commitment and manages the earnings upward. In addition, given that the entrepreneur retains ownership, we predict that the underwriter optimistically assesses the reported earnings because thehigher oﬀering price is beneficial for him. Taken together, the following hypotheses are tested.
Hypothesis 1 (the behavior of the entrepreneur) The entrepreneur increases theownership retention and manages earnings upward.
Hypothesis 2 (the behavior of the underwriter) The underwriter optimisticallyassesses the reported earnings if the entrepreneur retains the ownership higher.
Note that Hypothesis 1 and Hypothesis 2 correspond to Proposition 1 and
Proposition 2 in Section 2, respectively. Regarding Hypothesis 2, the conflictof interest between the entrepreneur and the underwriter is likely to arise in the24case where the reported earnings is above a certain level in our experimental parameters. Therefore, we expect that this relation between the assessment and theownership retention becomes pronounced when the entrepreneur reports higher
earnings.

3.2

Procedures

Following the experimental design discussed in the previous subsection, we ran
two sessions with the same parameters. Upon arrival at the lab, participants wererandomly assigned the role either the entrepreneur or the underwriter. The role
was unchanged throughout the session. In the lab, the participants were assigned
a computer screen and received a written instruction. Then, the experimenter read
aloud the instruction and the participants answered quizzes in order to check theunderstanding of the game. The instruction used an economic frame because ourexperimental setting is somehow complicated. We believe that the participants
can imagine the concrete situation which they face by appropriate framing. In addition, they can use both a payoﬀ calculator and a payoﬀ table in order to calculate
their payoﬀs.
In all the sessions, we used the strategy method, in which participants makecontingent decisions for all possible scenarios.16 In this method, first, participants
make contingent choices for every possible decision node; then they are matched;and, finally, the appropriate choices are carried out for the nodes that are reached,
and the other contingent choices are ignored (Casari and Cason, 2009, p.157).
16

See Brandts and Charness (2011) for the review about the strategy method.

25

Casari and Cason (2009) argue that this method has several advantages. First, researchers can collect a large volume of data because participants make decisions
for all possible situations. Second, compared to the standard game method, thestrategy method elicits more careful decisions. Third, providing monetary compensations based on the final matched outcome gives financial incentives to theparticipants. This ensures a certain level of internal validity.
In the experiment, each participant used a computer to access the website designated to their assigned role and responded to all the possible cases under our experimental parameters stated in the previous subsection. In addition, participants
whose roles were the entrepreneur were also required to answer their expectations
about underwriters’ estimations of earnings management, Ee (bµ), for each case. In
a similar way, participants whose roles were the underwriter were required to answer their expectations about true earnings, Eu (θ), for each case. These additional
data make the analysis of the experimental results in the following section richer.

4

Results

4.1

OutlineParticipants were the total of twenty-five undergraduate students in a Japanese
university. The average age of them was 19.5, the number of female was ten. The
total of thirteen were the role of entrepreneur, and the total of twelve were the roleof underwriter. The allocation of subjects to the roles was completely random.
The average reward was 2,096 JPY (about 17.5 US$). The average reward of the26role of the entrepreneur was 2,177 JPY (about 18.1 US$) and that of the role ofthe underwriter was 2,008 JPY (about 16.7 US$). The experiment sessions lasted
for approximately 80 minutes, including instructions.

4.2

Testing hypothesis 1: The behavior of the entrepreneur

In this subsection, we test the hypothesis 1. Table 1 provides descriptive statistics
for the results of the behavior of the entrepreneur.

Insert table 1 about here.

Earnings management ratio ( µθ ) is the amount of the earnings management (µ)
by an entrepreneur divided by true earnings (θ). When the true earnings is 100 andthe amount of the earning management is 50, for example, the ratio is 0.5. The
higher it is, the more egregious lie she is telling. Share holding ratio (w) is thenumber of shares which an entrepreneur continues to hold at IPO divided by the
number of shares she held before the IPO. When the total share of entrepreneurs
are 100 and the share which entrepreneurs continue to hold are 50, for example,
the ratio is 0.5. The higher it is, the higher the commitment level of entrepreneuris. Unreliability ratio ( Eeθ(bµ) ) is the expected amount by the entrepreneur for theunderwriter’s estimation of the earnings management (Ee (bµ) divided by the true
earnings (θ). This is the expectations for underwriters’ decision making by theentrepreneur.
Table 1 shows the tendency that the average earnings management ratio and27the average share holding ratio were high (over 50%). The result implies that theentrepreneur told a lie with the high commitment level of share holding. Table 1
also reports, on the other hand, that the average unreliability ratio were lower than
the average earnings management ratio. This result implies that the entrepreneur
thought that the underwriter would take a optimistic estimation of earnings management and permit her lie as long as the entrepreneur took a high commitment
level of share holding.

Figure 6 reports the scatter plot of the relation between the earnings management ratio and the share holding ratio.

Insert figure 6 about here.

Figure 6 shows that the participant who takes high rate of earnings management tends to have a higher commitment level of share holding. The rate of “Theearnings management ratio is 100% and the share holding ratio is also 100%” is
30.8%. The rate of “The earnings management ratio is 100% and the share holding ratio is 50%” is 28.2%. The total of them is 59.0%. The result also implies
that the entrepreneur told a lie with the high commitment level of share holding.
Table 2 focuses on the right column (the column in which earnings management ratio is 100%) of the figure 7, which is the number of observation of theparticipant who takes 100% of earnings management at each share holding ratio.

28

Insert table 2 about here.

Table 2 shows that the participant who takes 100% of earnings management
tends to have a higher commitment level of share holding. There is a statisticallysignificant diﬀerence among them (the Chi-squared test. χ2 (2) = 7.28, p value= 0.0026 < 0.01, eﬀect size w =0.539, power = 0.67). The result supports the
hypothesis 1.
Figure 7 and table 3 provide the average share holding ratio at the each earnings management ratio.

Insert figure 7 and table 3 about here.

Figure 7 and table 3 show the tendency that the entrepreneur who takes ahigher level of earnings management tends to hold the higher ratio of share, although there is not a statistically significant diﬀerence among the three groups(the Kruskal-Wallis test. χ2 (2, N = 39) = 2.531, p value = 0.282, eﬀect size =0.06).
Figure 8 and table 4 provide the average earnings management ratio at eachcommitment level of share holding.

Insert figure 8 and table 4 about here.

Figure 8 and table 4 show the tendency that the entrepreneur who takes a29higher commitment level of share holding tends to take the higher rate of earnings
management, although there is not a statistically significant diﬀerence among thethree groups (the Kruskal-Wallis test. χ2 (2, N = 39) = 2.520, p value = 0.284,
eﬀect size = 0.06).

In conclusion, the results of our experiment support the hypothesis 1. As
expected by our model, the entrepreneur told a lie with the high commitment levelof share holding since she anticipated that the underwriter would permit her lie.

4.3

Testing hypothesis 2: The behavior of the underwriter

In this subsection, we test the hypothesis 2. Table 5, 6, 7 and 8 provide descriptive
statistics for the results of the behavior of the underwriter.

Insert table 5 - 8 about here.

Earnings management estimation ratio ( bµe ) is defined as the level of estimationof earnings, which is defined as the amount of estimation of earnings management (bµ) divided by reported earnings (e). When reported earnings is 200 and theamount of estimation of earnings management is 50, for example, the ratio is 25%.
The expected true earnings (Eu (θ)) is defined as the amount of the true earnings(θ) that underwriter estimates. This is the expectations for entrepreneurs’ decision
making by the underwriters.
Table 5 reports the tendency that the amount of earnings management estioma30

tion ratio was totally low level, and the table 6 shows the tendency that the amountof ratio was especially low level when the share holding ratio was high (100%).
Table 7 shows the tendency that the underwriters estimated the true earnings
adequately, and table 8 implies that their estimation of the true earnings was adequate regardless of the commitment level of share holding by entrepreneurs.

Table 9 provides the number of the participants who take the zero estimationof earnings management at the each reported earnings and the share holding ratio.
Figure 9 shows the number especially when the reported earnings is 240.17

Insert table 9 and figure 9 about here.

There are two key points in table 9. First, when the reported earnings is 240(the true earnings is equal to 120 and earnings management ratio is 100%), there
is a bias of the number of the zero estimation among the share holding ratio: thehigher the share holding ratio becomes, the higher the number of zero estimation
is. Figure 10 shows this result. There is a statistically significant diﬀerence among
them (the Chi-squared test. χ2 (2) = 7.82, p value = 0.026 < 0.05, eﬀect size w=0.843, power = 0.707). Second, when the reported earnings is lower than 240,
there is not the bias of the number of the zero estimation among the share holding
ratio: the number of zero estimation is the same (about eight or nine, and the ratio
per observation is about 0.67 or 0.75). The result supports Hypothesis 2. In our
17

We extract the subsample in which the reported income is 240.

31

model, the underwriter tend to take a optimistic assessment, but when the true
earnings is higher level (e.g. 120), he choose an estimation level depending on theratio of share holding: the higher share holding ratio is, the more optimistic theassessment is.

Table 10 and figure 10 provides the average level of the permission of lie.

Insert table 10 and figure 10 about here.

µ
The level of the permission of lie ( Ee−b
) is defined as the corrected actualu (θ)

earnings (e − bµ) divided by expected true earnings (Eu (θ)), which is the level thatthe underwriter would permit the entrepreneurs’ lie. The higher the level is, themore permissive the underwriter is for the lie. When the expected true earnings is
100 and the corrected actual earnings is 150, for example, the level is 1.5. When it
is higher than 1, the underwriter permits the entrepreneurs’ lie. When the expectedtrue earnings is 100 and the corrected actual earnings is 100, for example, the levelis 1. When it is equal to 1, the underwriter does not permit the entrepreneurs’ lie.
When the expected true earnings is 100 and the corrected actual earnings is 50,
for example, the level is 0.5. When it is lower than 1, the underwriter does not
permit the entrepreneurs’ lie and punishes her for the lie.
Table 10 indicates two key points: First, the level is higher than 1 at the all
sample (1.23 on average). This implies that the underwriter is overall permissive
for the lie. Second, the higher the share holding ratio becomes, the higher the32

level is when reported earnings is relatively high. Figure 10 shows the tendency
that the higher share holding ratio becomes, the higher the level is. There is astatistically significant diﬀerence among the three groups at the 10% level (theKruskal-Wallis test. χ2 (2, N = 288) = 4.744, p value = 0.093 < 0.10). A posthoc test using Mann-Whitney tests with Holm correction showed the significant
diﬀerences between the group of 50% level of share holding and that of 100%level of share holding (p = 0.082 < 0.10, r = 0.13) and between the group of 0%
level of share holding and that of 100% level of share holding (p = 0.044 < 0.05,
r = 0.15).
This implies that the underwriter is permissive for the lie especially when theshare holding ratio is 100%. The result supports Hypothesis 2. In our model, theunderwriter tend to take a optimistic estimation of earnings management especially when share holding ratio is so high.

In conclusion, the results of our experiment support the hypothesis 2. As expected by our model, the underwriter tend to take a optimistic assessment especially when the share holding ratio is high, even though he knows the entrepreneur’s lie.
The reason why the underwriter permit the entrepreneur’s lie is supposed thathe thinks that his optimistic assessment would raise the stock value and he would
have a chance to get high profit. In short, the underwriter is not irrational but quiterational. Therefore, the underwriter rationally permits the entrepreneur’s “Pareto
white lie”.
33

5

Extension: Solutions with Earnings Management
Costs

We show the solutions with earnings management costs by comparing with thesolutions without them.
Case （I） A very popular firm with a ≥ x + 2θ + 2N
The underwriter chooses bµ∗ = 0 in the same way as in the case without earnings management costs shown in Figure 2(a). However, there are earnings management costs kµ in the entrepreneur’s payoﬀ in this case.

Ue = {1 − (1 − p)w}P0 + wp(α − qkµ)
= [1 − {1 − (1 − qk)p}w]µ + {1 − (1 − p)w}{x + g(w) + θ} + wpα.
∂Ue
= 1 − {1 − (1 − qk)p}w.
∂µ
The solutions of the entrepreneur are(θ, 1)(θ, 0 < w∗ < 1) (θ, 0) when ∂Ue /∂µ > 0






(µ∗ , w∗ ) = (any, 1) (any, 0 < w∗ < 1)
when ∂Ue /∂µ = 0 .







 (0, 1)(0, 0 < w∗ < 1)
when ∂Ue /∂µ < 0

The proof is provided in Appendix C.
The implications of the solutions are twofold. First the entrepreneur does not34

always manage earnings to the maximum degree because of the earnings management costs. Second when she sells all the shares that she owns, she manages theearnings to the maximum degree.
Case （II） An unpopular firm with a < x + g(1) − f(1) + θ + N
The underwriter chooses bµ∗ = bµ1 in the same way as in the case without
earnings management shown in Figure 2(b). The entrepreneur’s payoﬀ is
Ue = {1 − (1 − p)w}{ f (w) + (w − 2)N + a} + wp(α − qkµ).

Since ∂Ue /∂µ = −wpqk < 0, the entrepreneur chooses µ∗ = 0. Hence, Ue canbe written as
Ue = {1 − (1 − p)w}{ f (w) + (w − 2)N + a} + wpα.

Since this is the same as equation (1) in the case without the earnings management costs, the optimal retention can be obtained in the same way. The implications of the solutions are also the same as in the case without earnings management
costs18 .
Case （III） For a firm with x + g(1) − f(1) + θ + N ≤ a < x + 2θ + 2N
18

The only diﬀerence from the case without earnings management costs is that the entrepreneurchooses µ∗ = 0. However it does not change the implications that she does not have an incentive
to manage earnings because the underwriter does not use them when deciding the oﬀering price.

35

The entrepreneur’s payoﬀ is
Ue = {1 − (1 − p)w}P0 + wp(α − qkµ).

We examine whether the entrepreneur can increase her payoﬀ throughchanging the equilibriums by raising the ownership retention. Note that in thevery popular equilibrium,(θ, 1)(θ, 0 < w∗ < 1) (θ, 0) when ∂Ue /∂µ > 0






(µ∗ , w∗ ) = (any, 1) (any, 0 < w∗ < 1)
when ∂Ue /∂µ = 0 .







 (0, 1)(0, 0 < w∗ < 1)
when ∂Ue /∂µ < 0
Insert Figure 11 (a),(b),(c) about here.
The conditions that the entrepreneur can increase her payoﬀ by raising theownership retention are that in the very popular equilibrium she does not sell all
the shares she owns, in the unpopular equilibrium she does not hold all the shares
she owns, and her payoﬀ increases from the change in the equilibriums.
When the expected cost qk is so small that µ∗ = θ in the very popular equilibrium and that ϕ0L (1) = 0 locates above ϕH,max (0) = 0, the shadowed area in
Figure 11(a) and (b) satisfies all the conditions above, and for any points (p, α) in
the shadowed area, there exist w1 and ∆w (∆w > 0) that satisfy 0 ≤ w1 < w2 =w1 + ∆w ≤ 1. The proof is provided in Appendix F.
36

When the expected cost qk is so large that µ∗ =any(0 ≤ µ∗ ≤ θ) or 0 in the very
popular equilibrium, the shadowed area in Figure 11(c) satisfies all the conditions
above, and for any points (p, α) in the area, there exist w1 and ∆w (∆w > 0) thatsatisfy 0 ≤ w1 < w2 = w1 + ∆w ≤ 1 . The proof is provided in Appendix G.
Taken together, there exist some cases that the payoﬀ of the entrepreneur
can be increased through changing the underwriter’s behavior by increasing theowner’s retention. This conclusion is same as that of Section 2. Hence, the implications in the case without earnings management costs can be extended generally
to the case with them.

6

Conclusion

This paper answers the problem “When and how do people choose to lie?” throughintroducing strategic commitment by potential liars. In order to examine the roleof commitment, we focus on a specific economic setting where an entrepreneurplans to file for an initial public oﬀering (IPO). More specifically, we consider thesituation where an entrepreneur (IPO firm) issues new shares and reports earnings,
and then an underwriter assesses the earnings and sets the oﬀering price.
We develop a theoretical model on the assumption that there is a divergenceof investors’ opinions, and hence the demand curve of the share is downsloping
to right. We have predictions that the entrepreneur of a popular firm raises theownership retention and manages earnings upward to a maximum degree and thatthe underwriter chooses to estimate no earnings management because he knows

37higher ownership retention is perceived as good news by investors.
We test the predictions by laboratory experiment. In other words, the ownership retention works as a signal of commitment so that the interests of the entrepreneur and the underwriter are aligned. In this situation, both the entrepreneur
and the underwriter can benefit from overstating the earnings and setting thehigher oﬀering price.
To the best of our knowledge, this paper is in experimental studies the firstthat investigates both the ownership retention and the earnings management in thesetting of IPO. Therefore, this paper can provide the possible explanation to therelationship between ownership retention and earnings management in IPO. Our
research can be a milestone in this field. Our research can be extended to various
research examining when and how to lie in economic environments.

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Appendix A
The axis of symmetry of U s = −[bµ −(x+g(w)+e)][bµ −(x+g(w)− f (w)+e−a)]isbµa = x + g(w) + e −]1[f (w) + a .
2

Since bµ1 = x + g(w) − f (w) + e − a + (2 − w)N,b
µa − bµ1 =]
1[f (w) + a − 2(2 − w)N .
2

Consider a case of µba ≤ bµ1 and w = 1, that isa ≤ 2N − f (1).
Since a > 2N from the assumption of the demand function, there do not exist
any cases of b
µa ≤ bµ1 and w = 1. However in the real world, there exist IPO
firms in which entrepreneurs hold all the shares they own (w = 1). Hence, it isappropriate to assume bµa > bµ1 .
Appendix B
From ϕ0H (0) ≡ pα − (1 − p)(x + 2θ) + g′ (0) > 0,α>1(x + 2θ − g′ (0)) − (x + 2θ)
p

where

x + 2θ − g′ (0) > 0.

44

From ϕ0L (1) ≡ pα + f ′ (1) + N − (1 − p){ f (1) + f ′ (1) + a} < 0,α<1
{ f (1) + a − N} − { f (1) + f ′ (1) + a}pwhere f (1) + a − N > 0, f (1) + f ′ (1) + a > 0.
ϕ0H (0) = 0 represents a set of marginal points (p, α) that make the entrepreneurof the very popular firm sell all the shares she owns. ϕ0L (1) = 0 represents a set of
marginal points (p, α) that make the entrepreneur of the unpopular firm hold all
the shares she owns. Since for a certain p(0 < p < 1), α that satisfies ϕ0L (1) = 0 islarger than α that satisfies ϕ0H (0) = 0, the curve ϕ0L (1) = 0 locates above the curve
ϕ0H (0) = 0. Hence, the set of (p, α) that satisfies ϕ0H (0) > 0 and ϕ0L (1) < 0 is the
shadowed area in Figure 5.
We prove there exists (w1 , w2 = w1 + ∆w) that satisfies Ue2 > Ue1 in thatarea. Let P0H and P0L be oﬀering prices in the very popular equilibrium and in theunpopular equilibrium respectively. That is
P0H ≡ x + g(w2 ) + 2θ, P0L = f (w1 ) + (w1 − 2)N + a (P0H > P0L ).
Consider ∆w such that)
P0L
0 < ∆w < (1 − w1 ) 1 − H .
P0
(

(B1)

45

Since()
P0L(1 − w1 ) 1 − H < 1,
P0

)
P0L
0 < ∆w < (1 − w1 ) 1 − H < 1.
P0(

Hence,)(
P0L
w1 < w2 = w1 + ∆w < w1 + (1 − w1 ) 1 − H .
P0
Since
[

(

PL
1 − w1 + (1 − w1 ) 1 − H0
P0)]
= (1 − w1 )

P0L
≥ 0,
P0H

(
)
P0L
0 ≤ w1 < w2 = w1 + ∆w < w1 + (1 − w1 ) 1 − H ≤ 1.
P0

46

(B2)

From Ue2 > Ue1 and (1 − w1 )P0L − (1 − w2 )P0H < 0 19 ,w1 P0L − w2 P0H 1 (1 − w1 )P0L − (1 − w2 )P0Hα>+ ·w2 − w1p
w2 − w1LH(1 − w1 )P0L − (1 − w2 )P0H
w1 P0 − w2 P0< 0 and< 0.
where
w2 − w1
w2 − w1(B3)

From equation (B2) and (B3), there exists (w1 , w2 = w1 + ∆w) that satisfies
Ue2 > Ue1 in the shadowed area in Figure 5.
Appendix C
We find we solutions in the way as follows: First we find the optimal retention
in case µ∗ = θ, any(0 ≤ µ∗ ≤ θ), and 0. Next for each case we examine whether∂Ue /∂µ > 0, ∂Ue /∂µ = 0, and ∂Ue /∂µ < 0 holds.
(i) when µ∗ = θ, that is ∂Ue /∂µ > 0,
Ue = {1 − (1 − p)w}{x + g(w) + 2θ} + wp(α − qkθ).

∂Ue= −(1 − p){x + g(w) + 2θ} + {1 − (1 − p)w}g′ (w) + p(α − qkθ)∂w
= p(α − qkθ) − (1 − p){x + g(w) + wg′ (w) + 2θ} + g′ (w) ≡ ϕH,max (w).
19

(1 − w1 )P0L − (1 − w2 )P0H < 0 can be easily obtained from equation (B1).

47

Since g′ (w) > 0, g′′ (w) ≤ 0,
d2 Ue dϕH,max (w)== −2(1 − p)g′ (w) + {1 − (1 − p)w}g′′ (w) < 0.
dw2
dw
Hence, ϕH,max (w) is a strictly decreasing function of w.

∂ϕH,max (w)= α + x + g(w) + wg′ (w) + (2 − qk)θ > 0 (0 < q < 1, 0 < k ≤ 2)
∂p
H,max
∂ϕ
(w)
=p>0
∂α
∂ϕH,max (w)= −pkθ < 0∂q∂ϕH,max (w)= −pqθ < 0∂kHence, the larger p and the larger α shift the curve ϕH,max (w) upward, and thelarger q and the larger k shift the curve ϕH,max (w) downward. Note that ϕH,max (w)is a strictly decreasing function of w.
[Amax ]
When p and/or α are large enough and/or q and/or k are small enough to hold
ϕH,max (1) ≥ 0, w∗ = 1. Hence, there exist (p, α, q, k)(0 < p < 1, 0 < q < 1, 0 < k ≤2) that hold ∂Ue /∂µ|w∗ =1 = (1 − qk)p > 0.
[Bmax ]
When p, α, q, and k are such that hold ϕH,max (1) < 0 < ϕH,max (0), 0 < w∗ < 1.
48

Hence, there exist (p, α, q, k)(0 < p < 1, 0 < q < 1, 0 < k ≤ 2) that hold∂Ue /∂µ|0<w∗ <1 = 1 − {1 − (1 − qk)p}w∗ > 0. The proof is provided by Appendix D.
[Cmax ]
When p and/or α are small enough and/or q and/or k are large enough to hold
ϕH,max (0) ≤ 0, w∗ = 0. Since ∂Ue /∂µ|w∗ =0 = 1, any (p, α, q, k)(0 < p < 1, 0 < q <1, 0 < k ≤ 2) hold ∂Ue /∂µ|w∗ =0 > 0.
(ii) when µ∗ =any(0 ≤ µ∗ ≤ θ), that is ∂Ue /∂µ = 0, or µ∗ = 0, that is ∂Ue /∂µ < 0,
Ue = {1 − (1 − p)w}{x + g(w) + θ} + wpα.

∂Ue= −(1 − p){x + g(w) + θ} + {1 − (1 − p)w}g′ (w) + pα
∂w
= pα − (1 − p){x + g(w) + wg′ (w) + θ} + g′ (w) ≡ ϕH,any,0 (w).

Since g′ (w) > 0, g′′ (w) ≤ 0,
d2 Ue dϕH,any,0 (w)== −2(1 − p)g′ (w) + {1 − (1 − p)w}g′′ (w) < 0.
2
dw
dw

49

Hence, ϕH,any,0 (w) is a strictly decreasing function of w.
∂ϕH,any,0 (w)= α + x + g(w) + wg′ (w) + θ > 0∂p∂ϕH,any,0 (w)=p>0∂αNote that ϕH,any,0 (w) is a strictly decreasing function of w.
[Aany,0 ]When p and/or α are large enough to hold ϕH,any,0 (1) ≥ 0, w∗ = 1. Hence,
there exists (p, α, q, k)(0 < p < 1, 0 < q < 1, 0 < k ≤ 2) that holds ∂Ue /∂µ|w∗ =1 =(1 − qk)p = 0. There also exists (p, α, q, k)(0 < p < 1, 0 < q < 1, 0 < k ≤ 2) that
holds ∂Ue /∂µ|w∗ =1 = (1 − qk)p < 0.
[Bany,0 ]When p and α are such that hold ϕH,any,0 (1) < 0 < ϕH,any,0 (0), 0 < w∗ < 1.
Hence, there exist (p, α, q, k)(0 < p < 1, 0 < q < 1, 0 < k ≤ 2) that hold∂Ue /∂µ|0<w∗ <1 = 1 − {1 − (1 − qk)p}w∗ = 0. There also exist (p, α, q, k)(0 < p <1, 0 < q < 1, 0 < k ≤ 2) that hold ∂Ue /∂µ|0<w∗ <1 = 1 − {1 − (1 − qk)p}w∗ < 0. The
proof is provided by Appendix E.
[Cany,0 ]When p and/or α are small enough to hold ϕH,any,0 (0) ≤ 0, w∗ = 0. Since∂Ue /∂µ|w∗ =0 = 1, there does not exist any (p, α, q, k)(0 < p < 1, 0 < q < 1, 0 <k ≤ 2) that hold ∂Ue /∂µ|w∗ =0 ≤ 0.

50

From (i) and (ii), the solutions are(θ, 1)(θ, 0 < w∗ < 1) (θ, 0) when ∂Ue /∂µ > 0






(µ∗ , w∗ ) = (any, 1) (any, 0 < w∗ < 1)
when ∂Ue /∂µ = 0 .







 (0, 1)(0, 0 < w∗ < 1)
when ∂Ue /∂µ < 0Appendix D
For a certain p,q,k where 0 < p < 1 and 0 < qk < 1, we can select α large
enough to satisfy 0 ≃ ϕH,max (1) < 0. Then
0 < w∗ < 1 (w∗ ≃ 1).
∂Ue≃ (1 − qk)p > 0.
∂µAppendix E[Aany,0 ]For a certain p,α that satisfies ϕH,any,0 (1) ≥ 0, w∗ = 1.
For a certain q, k that satisfies qk = 1, ∂Ue /∂µ|w∗ =1 = (1 − qk)p = 0.
For a certain q, k that satisfies qk < 1, ∂Ue /∂µ|w∗ =1 = (1 − qk)p < 0.
[Bany,0 ]51

For a certain p, we can select α large enough to satisfy 0 ≃ ϕH,any,0 (1) < 0.
0 < w∗ < 1 (w∗ ≃ 1).
∂Ue≃ (1 − qk)p∂µ

In the vicinity of qk = 1, there exists (q, k) that satisfies ∂Ue /∂µ|0<w∗ <1 = 0.
Since 0 < qk < 2, (q, k) that satisfies qk ≃ 2 and qk < 2, ∂Ue /∂µ|0<w∗ <1 < 0.
Appendix F
The oﬀering price in the unpopular equilibrium is
x + g(w1 ) + θ − bµ1 ≡ P0L,0 .

The oﬀering price in the very popular equilibrium is
x + g(w2 ) + 2θ ≡ P0H .

Hence,
P0H > P0L,0 .

52

From Ue2 > Ue1 and (1 − w1 )P0L,0 − (1 − w2 )P0H < 0 20 ,w1 P0L,0 − w2 P0H + w2 qkθ 1 (1 − w1 )P0L,0 − (1 − w2 )P0Hα>+ ·w2 − w1p
w2 − w1
L,0
H(1 − w1 )P0 − (1 − w2 )P0
< 0.
where
w2 − w1

Appendix G
The oﬀering price in the unpopular equilibrium is
x + g(w1 ) + θ − bµ1 ≡ P0L,0 .

The oﬀering price in the very popular equilibrium is
x + g(w2 ) + θ ≡ P0H,0 .

Hence,
P0H,0 > P0L,0 .

(1 − w1 )P0L,0 − (1 − w2 )P0H < 0 is obtained in the same way as in the case without the earnings
management costs.
20

53

From Ue2 > Ue1 and (1 − w1 )P0L,0 − (1 − w2 )P0H,0 < 0 21 ,w1 P0L,0 − w2 P0H,0 1 (1 − w1 )P0L,0 − (1 − w2 )P0H,0α>+ ·w2 − w1p
w2 − w1L,0H,0(1 − w1 )P0L,0 − (1 − w2 )P0H,0
w1 P0 − w2 P0< 0 and< 0.
where
w2 − w1
w2 − w1(1 − w1 )P0L,0 − (1 − w2 )P0H,0 < 0 is obtained in the same way as in the case without the earnings
management costs.
21

54

55

56

57

58

59

60

Figure 6: Scatter plot of the relation between earnings management ratio and shareholding ratio

61

Figure 7: The average share holding ratio at the each earnings management ratio

62

Figure 8: The average earnings management ratio at the each commitment levelof share holding

63

Figure 9: The number of the zero estimation of earnings management at the eachcommitment level of share holding (when the reported income is 240)

64

Figure 10: The average level of permission of lie at the each commitment level ofshare holding

65

66

67

68

Table 1: The results of the behavior of the entrepreneur
Total
Observation
Earnings management ratio

Ave.
S.D.
Ave.
S.D.
Ave.
S.D.

Share holding ratio
Unreliability ratio

39
0.73
0.33
0.64
0.31
0.44
0.47

True earnings
80
100
120
13
13
13
0.88
0.76
0.65
0.21
0.31
0.41
0.73
0.57
0.61
0.31
0.26
0.34
0.41
0.51
0.41
0.49
0.51
0.38

Table 2: The number of observation of participants who takes 100% earnings
management at each commitment level of share holding

Observation(ratio)p value

Total
25

Share holding ratio
100
50
0
12
11
2
(0.48)(0.44)(0.08)
0.026

Table 3: Share holding ratio at each level of earnings management

Observation
AverageS.D.

earnings management ratio
100
50
0
25
10
4
0.70
0.55
0.50
0.31
0.26
0.35

69

Table 4: The average earnings management ratio at the each commitment level ofshare holding

Observation
Average
S.D.

100
15
0.86
0.29

Share holding ratio
50
0
20
4
0.73
0.63
0.33
0.41

Table 5: The results of the behavior of the underwriter(1): Earnings management
estimation ratio at the each reported earnings
Total
Observation
Average
S.D.

Reported earnings
240 200 180 160 150 120 100
80
288
36
36
36
36
36
36
36
36
0.18 0.29 0.23 0.20 0.17 0.15 0.16 0.13 0.11
0.28 0.30 0.31 0.32 0.28 0.25 0.27 0.23 0.20

Table 6: The results of the behavior of the underwriter(2): Earnings management
estimation ratio at the each share holding ratio

Observation
Average
S.D.

Share holding ratio
100
50
0
96
96
96
0.169
0.188
0.198
0.31
0.26
0.26

Table 7: The results of the behavior of the underwriter(3): The expected true
earnings at the each reported earnings
Total

Reported earnings
240
200
180 160150
120 100
80
Observation
288
36
36
36
36
36
36
36
36
Average100.7 113.9 101.1 113.9 85.0 100.6 108.9 98.3 83.9
S.D.
15.8 13.2
9.4 12.3 10.9
8.8 16.0 8.7 10.4

70

Table 8: The results of the behavior of the underwriter(4): The expected true
earnings at the each share holding ratio

Observation
Average
S.D.

Share holding ratio
100
50
0
96
96
96
99.2
101.9
101.0
16.8
14.2
16.2

71

Table 9: The number of the zero estimation of earnings management at the eachreported earnings and the share holding ratio

Reported earnings
240

200

180

160

150

120

100

80

Obs.
zero estimation
the ratioObs.
zero estimation
the ratioObs.
zero estimation
the ratioObs.
zero estimation
the ratioObs.
zero estimation
the ratioObs.
zero estimation
the ratioObs.
zero estimation
the ratioObs.
zero estimation
the ratio

72

Share holding ratio
100
50
0
12
12
12
8
1
2
0.67
0.08
0.17
12
12
12
8
7
3
0.67
0.58
0.25
12
12
12
8
8
7
0.67
0.67
0.58
12
12
12
8
9
7
0.67
0.75
0.58
12
12
12
8
8
8
0.67
0.67
0.67
12
12
12
8
8
8
0.67
0.67
0.67
12
12
12
9
8
8
0.75
0.67
0.67
12
12
12
9
8
9
0.75
0.67
0.75

Table 10: The average level of permission of lie at the each reported earnings andthe share holding ratio

Total

Obs.
Ave.
S.D.
hold 100 Obs.
Ave.
S.D.
hold 50 Obs.
Ave.
S.D.
hold 0 Obs.
Ave.
S.D.

Total
288
1.23
0.57
96
1.30
0.63
96
1.20
0.52
96
1.19
0.53

240
36
1.53
0.74
12
1.75
0.84
12
1.35
0.55
12
1.48
0.74

200
36
1.53
0.63
12
1.59
0.73
12
1.61
0.52
12
1.40
0.60

Reported earnings
180 160 150 120
36
36
36
36
1.28 1.60 1.27 0.92
0.51 0.58 0.39 0.31
12
12
12
12
1.42 1.67 1.29 0.99
0.44 0.59 0.46 0.38
12
12
12
12
1.22 1.62 1.23 0.88
0.55 0.54 0.39 0.26
12
12
12
12
1.19 1.50 1.28 0.91
0.49 0.60 0.29 0.28

73

100
36
0.88
0.24
12
0.88
0.32
12
0.88
0.20
12
0.89
0.17

80
36
0.86
0.23
12
0.85
0.29
12
0.85
0.21
12
0.90
0.15