Research in Economics 63 (2009) 11–21

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Research in Economics

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Strategic managerial dishonesty and financial distressDamien Besancenot a, Radu Vranceanu b,∗a CEPN and University of Paris 13, 92 rue Jean-Baptiste Clément, 93430 Villetaneuse, Franceb ESSEC Business School, BP 50105, 95021 Cergy, France

a r t i c l e i n f o

Article history:Received 9 August 2007Accepted 10 December 2008

Keywords:Financial distressBankruptcy costsDisclosureCorporate regulationHybrid Bayesian equilibrium

a b s t r a c t

This paper analyzes the effect of stricter sanctions against fraudulent disclosure in aneconomy where commercial lenders have only an imperfect information about the typeof the firm they trade with. In the hybrid Bayesian equilibrium, some managers runningfragile firms claim that their firm is solid only to benefit of better commercial credit terms.The default premium charged by the supplier over the normal cost can be interpreted hereas an indirect bankruptcy cost. When the sanction gets heavier, both the default premiumand the frequency of defaulting firms go up. Under given circumstances, these perverseeffects might be offset by a decline in direct bankruptcy costs.

© 2008 University of Venice. Published by Elsevier Ltd. All rights reserved.

1. Introduction

Shareholder capitalism is a ubiquitous feature of all contemporary developed economies. While this separation betweenfirm ownership and firm control would bring about substantial gains in terms of allocative efficiency, it has long beenacknowledged that objectives of managers and shareholders can sometimes diverge. One extreme development of thisconflict of interests between owners and managers is the latter’s fraud. In general, overheated economies provide the mostprolific ground for frauds. In the early 2000s, criminal investigations in the United States pointed out that during the ITbubble years, some CEOs committed such abuses. In particular, a few top executives manipulated earnings just in order topush up the share value of their company, then cashed the overvalued stock before the collapse of the company (Demski,2003; Hall, 2005). Such abuses threw the blame on the CEO profession and shifted the regulatory mood in favor of toughersanctions against fraudulent managers. For instance, one main goal of the Sarbanes–Oxley Act of 2002 was to enhance theresponsibility of chief executives with respect to the truthfulness and relevance of compulsory financial statements.1 At thesame time, changes in the federal sentencing guidelines in 2001 and 2003 significantly raised penalties for financial fraud,economically damaging frauds being placed at the same level as armed robberies.One implicit assumption behind such a regulatory twist is that ‘‘honesty is the best policy’’ or, in the economists’ jargon,

that more information is always better than less. However, we all know from every-day life experience that, depending onthe situation, telling the naked truth might not be the most efficient strategy. Sometimes, lies help avoiding a useless andexpensive conflict. To take an example provided by Fletcher (1966), a Britishmoral philosopher, it may bewise to keep fromtelling your wife that you do not like her new green dress, even if this is your true opinion. This common sense principledoes apply to the world of businesses too. As emphasized by Lev (2003, p. 36), ‘‘the more common reason for earningsmanipulation is that managers, forever the optimists, are trying to ‘weather out the storm’—that is, to continue operationswith adequate funding and customer/supplier support until better times come’’. The literature on corporate financial distress

∗ Corresponding author. Tel.: +33 134433183.E-mail addresses: besancenot.damien@univ-paris13.fr (D. Besancenot), vranceanu@essec.fr (R. Vranceanu).

1 Other important goals were to tighten up supervision of the practices of the accounting profession, strengthen auditor independence rules, enhancethe timelines and quality of financial reports of publicly listed companies, and protect employees’ retirement plans from insider trading (Coates, 2007).

1090-9443/$ – see front matter© 2008 University of Venice. Published by Elsevier Ltd. All rights reserved.doi:10.1016/j.rie.2008.12.002

12 D. Besancenot, R. Vranceanu / Research in Economics 63 (2009) 11–21

has emphasized that the image clients and suppliers have about a company plays an important role in determining its actualfinancial health. More precisely, if creditors start having doubts about the financial soundness of a company, they can ask fora higher default premium, which represents an indirect bankruptcy cost for the firm (e.g., Altman (1984), Wruck (1990) andAndrade and Kaplan (1998)). So, in difficult times themanagermight well communicate on better than actual performancesonly to get more favorable contracting terms and push down these indirect costs. On the other hand, if the manager cannotuse the communication weapon freely, his company will be submitted to additional strain. Reduced flexibility in choosingthe most appropriate communication strategy might therefore entail an indirect cost of doing business in a decentralizedeconomy.2The main goals of this paper are twofold. Firstly, it aims at developing a simple decision model of a top executive who

must choose between an honest and a dishonest communication policy. Secondly, this model will be used to analyze theimpact of a tougher sanction for fraudulent disclosure on the indirect cost of bankruptcy. The basic framework is a one-shot game between the manager – who chooses his communication policy – and the supplier of an essential input, undersupplier’s asymmetric information about the type of firm. Both agents are risk-neutral. The supplier grants a commercialcredit to the firm. As a residual claimant, he prices the firm such as to break even. Hence, the indirect bankruptcy cost is wellcaptured as the economy-wide default premium. There are two types of firms, the high and the low expected return firm.The manager must announce the type of the firm before the time when the supplier posts the input price. He may eitherdeclare honestly the true type of the firm or lie. The end-of-period revenue of the firm is random. Depending on whetherthe firm may reimburse the trade credit to the supplier, it survives or it is pulled out of the market. In general, firms thatbecome bankrupt come under close public scrutiny. We thus assume that when a firm files for bankruptcy, managers whohave disclosed false information are fined. Our analysis focuses on the Hybrid Bayesian Equilibrium, where at least some ofthe managers at the head of fragile, low expected return firms choose to disclose false information. When the penalty forfraudulent disclosure goes up, several effects come into operation. As expected, more managers at the head of low-returnfirms will truthfully state that their firm is fragile. They thus have to pay a higher input price and are subject to a largerprobability of default. On the other hand, the default premium for managers who claim that their firm is solid goes down,the input price diminishes, and the probability of default of these firms declines. The overall frequency of default and theaverage default premium depend thus on the cost of the sanction.The model can be solved analytically in the special case where the firm income follows a uniform distribution and direct

bankruptcy costs are zero. In this context, it can be shown that in the hybrid equilibrium an increase in the penalty fordishonest managers entails a net positive variation in the overall default premium. It also can be shown that the frequencyof defaulting firms is increasing with the sanction. If there are some kind of direct bankruptcy costs that are not included inthe firm’s books, this analysis would suggest that both indirect and these direct bankruptcy costs rise if managers are subjectto a tougher sanction for fraudulent disclosure. This conclusion would probably hold even if we include an undifferentiateddirect bankruptcy cost.3 Indeed, since both fragile and solid firms can default, such a cost would only push up the defaultpremium for both types of firms.4However, itmay be sensible to assume that direct bankruptcy costs are larger if themanager hasmanipulated information

prior to bankruptcy than if he was honest. As pointed out by Bris et al. (2006), in the case of fraudulent disclosure thelength of the litigation trial should be longer, administrative costs would go up and the value of the assets to be liquidatedwould decline. In order to analyze the impact of a tougher sanction on both direct and indirect costs under this additionalassumption, we resort to a numerical simulation. As in the simple analytical model, indirect costs edge up if the sanctiongets tougher. For a positive gap between honest and dishonest manager bankruptcy costs, a stronger sanction helps reducethe overall direct cost. Hence, the design of a socially optimal sanction should aim at striking the right balance betweendirect and indirect bankruptcy costs.Morris and Shin (2004) have also put forward that increasing the quality of public information might exacerbate the

coordination problem among creditors, and thus foster the bankruptcy rate in a decentralized economy. In their analysis,if a creditor believes other creditors will call their loans, it becomes individually rational to call his loan. Hence creditors’actions are strategic complements. Creditors try to infer what other creditors believe, as well as the intrinsic quality of theborrower from a publicly available information. This ‘higher-order beliefs problem’ results in each creditor overweightingpublic signals relative to their own private information when making inferences. Consequently, more transparent publicinformation can result in more frequent default, for a given intrinsic quality of the borrower. This model shares with Morrisand Shin (2004) the idea according to which lenders’ perceptions of default risk have a real economic impact in that theyinfluence the reality of default. However, in our paper, the main result is obtained in a more straightforward way, sincethere is no coordination problem. The mechanism at work is simple: if the creditor perceives the borrower as being of thelow intrinsic quality with a high probability of default, he will offer less favorable terms of credit, which in turn increase theprobability of default. This paper can also be connected to studies that analyze the two-person game between an auditee

2 Assessing costs and benefits of the Sarbanes–Oxley Act is a difficult endeavour (Coates, 2007). Zhang (2005) argued that this regulation might havebrought about value losses for US public companies as high as 1400 billion dollars.3 Empirical estimates set direct bankruptcy cost into the range of 5% to 10% of a firm’s value. See Bris et al. (2006).4 We notice that the scope of manipulation is enhanced in a repeated game with fixed decision horizon. In such a framework, the bigger the reputationcapital of a formerly honest manager, the larger his incentive to lie if he is subject to difficult times at the last period.

D. Besancenot, R. Vranceanu / Research in Economics 63 (2009) 11–21 13

who can commit fraud and an auditor who can cover this fraud; they emphasize the necessary conditions for fraudulentoverstating to be an equilibrium.5 We would also emphasize that, in order to focus on the trade-off between managerialdishonesty and the probability of default, the model is built on a highly stylized theory of corporate investment that leavesaside other important issues such as the conflict of interests between shareholders and bondholders that might push themanager to undertake negative NPV projects.Themethodology for analyzingmanagerial communication policies and financial distress developed in this paper fits the

bestworld of classicalmanufacturing and productive service companies. Further researchmight apply themodel to financialinstitutions. Indeed, during the recent financial crisis of 2007–2008, several bank top executives issued false, overoptimisticsignals just before their company went into deep trouble.6 Such a behavior can be easily interpreted in the framework ofour model.7The paper is organized as follows. The next section introduces the basic assumptions. Section 3 presents the equilibrium

of the game. The relationships between the level of the sanction, the economy-wide default premium and the frequencyof defaulting firms is analyzed in Section 4. Section 5 presents a numerical simulation with positive bankruptcy costs and(log)normally distributed firm incomes. The last section concludes the paper.

2. The model

There is a continuum of firms that each lives one-period. The income of the firm i is a random variable y, following acumulative distribution F i() on the support [0, τ i].We assume that there are only two types of firms, the (H)igh and the (L)ow expected return firm. Denoting the expected

income by yi =∫ τ i0 ydF

i(y), with i ∈ H, L, the two types of firms are thus characterized by yH > yL. In the particular casewhere the income y is uniformly distributed on [0, τ i], the assumption yH > yL is tantamount to τH > τ L (τ i is the upperbound of the income distribution).The total number of firms is normalized to one; the frequency of H-type firms in total population of firms is denoted by

q, with q ∈]0, 1[; this frequency is common knowledge.In order to produce the final good, themanager of the public companymust buy one unit of an essential commodity from

an external supplier. We assume perfect competition between suppliers. Information is asymmetric: the manager does notknow the future value of y, but knows the type of the firm (i.e., he knows whether the income distribution is F L() or FH()).The supplier knows neither the future value of y, nor the type of the firm he trades with. All he knows is a statement aboutthe type of the firm, made by the manager prior to contracting the input. The message is represented by a, with a ∈ h, l,where h is the statement that the firm is of the H-type, and l is the statement that the firm is of the L-type. Hence, themanager’s announcement strategy can be represented as a function s(i) : L,H → l, h that defines for all types of firmsthe manager’s statement. The manager of an L-type firm may honestly announce that the firm is of the L-type (play l), ormay lie and announce that the firm is of the H-type (play h). In this model, the manager of the H-type firmwould never lie.8Therefore, the irrelevant action l = s(H)will be omitted in the following developments.Let Ω denote the supplier’s beliefs about the manager’s degree of honesty contingent upon the type of firm. As H-firm

managers never lie, suppliers assign a unit probability to the fact that a manager at the head of a high-return firm is honest.The subjective probability that themanager of a low-return firm is honest (announces that the firm is of type L) is denoted byµ. For instance, if µ = 1, the supplier believes that the manager is honest, if µ = 0, the supplier believes that the manageris dishonest and if µ ∈ ]0, 1[, the supplier believes that the manager randomizes between the two pure strategies withprobability µ (alternatively, µ can be interpreted as the perceived frequency of honest managers in the total population ofmanagers running L-type firms).

Ω =

Pr[l|L] = µ, where µ ∈ [0, 1]Pr[h|H] = 1. (1)

Given his beliefs and the observed signal, the supplier determines the offer price of the commodity unit according to astandard zero-profit condition. This price is posted immediately after the manager’s announcement about the type of thefirm, and depends on this announcement. Hence the unit cost of the input is denoted by ca with a ∈ l, h. Then the tradetakes place: the supplier delivers the input, but agrees on cashing the promised price at a later time, once that the firmrealizes the output. In other words, the supplier grants the firm a trade credit.

5 See e.g. Antle (1982), Anderson and Young (1988), Newman and Noel (1989), Yoon (1990), Patterson and Reed (2003), Besancenot and Vranceanu(2007) and Arya and Mittendorf (2007).6 For instance, on September 10, 2008, the executive of the now bankrupt investment bank Lehman Brothers calculated that the firm needed at least 3billions US dollars in fresh capital, one day after they assured investors on a conference call that the bank needed no capital at all (Private optimism maskedprivate scramble for Lehman, Wall Street Journal, 07.10.2008).7 See Besancenot and Vranceanu (2008) for a variant of the model as applied to the banking sector.8 The formal proof can be obtained by comparing the H-type firmmanager’s payoffs in the two cases. Intuitively, the manager who declares that a goodfirm is bad would lose twice, since indirect costs go up and he may be fined for false statement.

14 D. Besancenot, R. Vranceanu / Research in Economics 63 (2009) 11–21

Fig. 1. Decision tree.

In this first part of the paper, we assume that there are no direct bankruptcy costs. Now, at the end of the period,depending on the realized value of the income (which is a random variable), the manager might not be able to fully complywith his liabilities, i.e. might not reimburse the full amount of the credit; therefore, ca must include a premium related tothe risk of payment default. The supplier is the residual claimant, hence, in the worst of cases (if the income is lower thanthe price agreed ex ante), he gets the firm’s income.9If the firm makes a positive profit (y − ca > 0), the manager obtains a reward from work proportional to this profit

(in order to keep the model as simple as possible, the manager’s gain is set equal to the profit).10 If the firm defaults on itsliabilities (y < ca), the firm’s profit and the manager’s reward becomes zero.According to regulations in force the developed countries, managers who disclose false information are subject to heavy

sanctions (if caught). However, in practice, it is highly probable that if a fragile firm does not file for bankruptcy (because itbenefits from a favorable income shock), inspectors cannot prove ex post that the manager has lied. On the contrary, whena firm gets bankrupt, it will fall under close public scrutiny. Hence, we assume in the following that an external inspectionboard checks files of all the bankrupt firms, and imposes a fine z (with z > 0) on managers who have delivered falsestatements.Fig. 1 represents the basic sequence of decisions:At the outset of the game, Nature chooses the type i of the firm; next, depending on the type of the firm, the manager

makes his optimal statement, a. Then, given the signal issued by the manager, the supplier upgrades his prior beliefs andposts a price ca for the input. The dotted line linking the upper grey dots indicates that the supplier who observes the signalh does not know whether he trades with an H or an L-type firm. Next step, Nature decides on the income of the firm, y.Depending on whether the firm’s resources suffice (or not) to pay the contracted price, the firm is either solvent or notsolvent; in this latter case, the firm is pulled out of the market and the residual revenue is transferred to the supplier.Remark that both H and L-type firms may be subject to default. The manager’s payoff at the end of the game depends on

the type of the firm, his announcement and Nature’s choice of output.

3. Equilibrium

A Bayesian Equilibrium of this game is defined as a pair (s,Ω) such that amanager’s announcement strategy smaximizeshis expected payoff given the supplier’s beliefsΩ , and the supplier’s beliefs are correct given s. A separating configurationimplies that the manager’s announcement unambiguously reveals the firm’s type (s(H) = h and s(L) = l). A poolingconfiguration appears when all managers deliver the same signal whatever the type of the firm; in this model, s(i) = h,∀i.The game presents a Hybrid Bayesian Equilibrium (HBE), where some managers running low expected return firms willcommunicate truthfully, and some will lie; in this case, the equilibrium frequency of honest L-type firms’ managers (µ)belongs to the interval ]0, 1[. Pure strategy equilibria can then be interpreted as special cases of this hybrid equilibrium,which obtain for µ→ 0 (the pooling case) and µ→ 1 (the separating case).

9 In Section 5 we perform a numerical simulation allowing for positive direct bankruptcy costs k. In this case, when the firm gets bankrupt, the supplier’sincome is maxy− k, 0.10 Several studies put forward a strong relationship betweenmanager compensation and a firm’s share value, probably explained by the dramatic increasein the share of option-based pay in total compensation over the nineties (Murphy, 1999; Hall, 2005).

D. Besancenot, R. Vranceanu / Research in Economics 63 (2009) 11–21 15

To determine the equilibrium of the game, we first have to define the input price depending on the announcement. Thisprice is needed in order to determine the objective probability of default which, in turn, has a bearing on the manager’sexpected payoff. The objective probability of payment default of the firm whose manager has announced a is defined asPr[y < ca].

3.1. The input price defined

As already mentioned, the input market is perfectly competitive, with free entry.Let us now consider a supplier who observes the signal issued by the manager. Given his beliefs Eq. (1), the probabilities

he assigns to the type of the borrower contingent upon the signal issued by the manger, that is Pr[i|a], are:Pr[L|l] = 1Pr[H|h] =Pr[h|H] Pr[H]

Pr[h|H] Pr[H] + Pr[h|L] Pr[L]=

q1− µ(1− q)

.(2)

We have denoted by ca the price charged by the supplier, depending on the signal a issued by the manager. If the firm’sincome is large enough (y > ca), the supplier will receive the full price ca. If the firm’s income is lower than the contractedprice (y < ca), the supplier, who is the residual claimant, will get yi. We denote by c the cost for the supplier to produce theessential commodity unit (this cost is common knowledge).11 To focus on the default premium, in the following we assumethat suppliers, who act as trade lenders, are risk-neutral individuals.(a) If the supplier receives the signal l, he can unambiguously infer that he deals with a low-return firm (type L). Under

the zero-profit condition, the price c l is implicitly defined by:

c =∫ c l

0ydF L(y)+

∫ τ L

c lc ldF L(y). (3)

Considering a uniform distribution for the income of the L-type firm, c l is the solution of:

c = c l −(c l)2

2τ L, (4)

where c l > c . It can be checked that a price c l exists if τ L > 2c . Remark also that the solution c l is independent of z.(b) If the supplier gets the signal h, he must take into account the possibility that the good signal might have been issued

by a low-return firm. Hence, the posted price ch is implicitly defined by:

c = Pr[H|h]

(∫ ch

0ydFH(y)+

∫ τH

chchdFH(y)

)+ Pr[L|h]

(∫ ch

0ydF L(y)+

∫ τ L

chchdF L(y)

)(5)

or, given the uniform distribution of the firm’s income, by:

c = Pr[H|h](−(ch)2

2τH+ ch

)+ (1− Pr[H|h])

(−(ch)2

2τ L+ ch

). (6)

In the next section, Pr[H|h] appears to be a function of z; hence the solution ch depends on this variable.Eqs. (4) and (6) could be solved to obtain explicit forms for c l and ch. Yet calculationswith roots of seconddegree equations

are neither very aesthetic nor easily tractable. Such difficulties can be overcome if we use for further developments thedifference between c l and ch. The difference must be positive, given the uncertainty related to dealing with a manager whoannounces h (there is no uncertainty related to announcing l). By subtracting Eq. (6) from Eq. (4), we get:

c l − ch =(ch)2 Pr[H|h]

(1− τ L

τH

)2τ L −

(c l + ch

) > 0. (7)

In order to focus on a nontrivial case, we admit that τ L > c l. If this condition does not hold, no supplier will accept tolend to a manager who declares that the firm is of the L-type.

3.2. Conditions of existence of an HBE

Let us denote by W [a|L] the expected payoff of the manager at the head of the L-type firm who issues a signal a. Thispayoff is related to the manager’s reward for profits (identical to profits if these are positive, zero if else), less the fine for

11 Alternatively, c might be seen as a certain price that the supplier might get in a risk-less trade.

16 D. Besancenot, R. Vranceanu / Research in Economics 63 (2009) 11–21

fraudulent statements, to be charged only in the case of default. Formally, the expected payoff of the manager of an L-typefirm who announces l is:

W [l|L] =∫ τ L

c l

(y− c l

)dF L(y) (8)

=

[12τ L − c l

]+12(c l)2

τ L(9)

and the expected payoff of the manager who announces h is:

W [h|L] =∫ τ L

ch

(y− ch

)dF L(y)− z

∫ ch

0dF L(y) (10)

=

[12τ L − ch

]+

(ch

τ L

)[12ch − z

]. (11)

A hybrid equilibrium exists if the L-type firm’s manager is indifferent between announcing l or h:

W [h|L] = W [l|L]∫ τ L

ch

(y− ch

)dF L(y)− z

∫ ch

0dF L(y) =

∫ τ L

c l

(y− c l

)dF L(y). (12)

In the uniform distribution case, the former equation simplifies to:(c l − ch

) [2τ L −

(ch + c l

)]= 2zch. (13)

After replacing the term(c l − ch

)as defined by Eq. (7) into Eq. (13), the necessary condition for an HBE becomes:

Pr[H|h] =2zτH

(τH − τ L)ch. (14)

We can now be more specific about the nature of the equilibrium. Recall the definition of Pr[H|h] building on supplier’sbeliefs Eq. (2):

Pr[H|h] =q

1− µ(1− q)∈ [q, 1]. (15)

Writing the equality between Eqs. (14) and (15), the equilibrium frequencyµ of honest L-type firms’managers can bewritten:

µ =2zτH − q

(τH − τ L

)ch

2zτH(1− q)= G(z). (16)

The hybrid equilibrium exists for µ ∈ ]0, 1[: this can happen if z ∈]z1, z2[, with the two bounds implicitly defined byG(z1) = 0 and G(z2) = 1.12If z ∈ [0, z1], the strategy of honesty cannot be optimal for the manager of the L-type firm. The pooling equilibrium –

where all managers announce that their firm is a high-return one – occurs (µ = 0). Hence, the antifraud policy wouldbecome effective only if the sanction exceeds a critical threshold, z > z1.If z ∈ [z2,∞[, the separating equilibrium emerges: all managers announce the true type of their firm, honesty is

generalized (µ = 1).We focus hereafter on the hybrid equilibrium, which encompasses as special cases the pooling and separating situations.

Explicit solutions are provided for the uniform distribution case.

4. Consequences of a tougher sanction

Consequences of a tougher sanction can be analyzed by studying the impact of dz > 0 on the main variables. Both theinput price ch and the proportion of honest managers running L-type firms depend on the sanction. It turns out that:

Proposition 1. In the hybrid equilibrium, the input price for managers who announce that their firm is of the H-type is decreasingwith the sanction level.

12 In next subsection we will show that, in the hybrid equilibrium, the frequency of honest managers is an increasing function in the sanction level,dµ/dz > 0 (Proposition 2). We also notice that since ch is solution to a second degree equation (6), the explicit forms of z1 and z2 are not very aesthetic.They need not be displayed here.

D. Besancenot, R. Vranceanu / Research in Economics 63 (2009) 11–21 17

Proof. We replace Pr[H|h] such as defined by Eq. (14) in Eq. (6):

ch = c +(ch)2

2τH

(2zch

)τH

(τH − τ L)+(ch)2

2τ L

[1−

2zch

τH

(τH − τ L)

]= c −

zch

τ L+(ch)2

2τ L. (17)

Differentiating the former expression, we get:

dch

dz= −

ch

z + τ L − ch< 0. (18)

Proposition 2. In the hybrid equilibrium, the frequency of honest L-type firms’ managers (µ) is increasingwith the sanction level.

Proof. From Eq. (16), we obtain:

dµdz=

(q1− q

)(τH − τ L

2τH

)(ch

z2

)(2z + τ L − ch

z + τ L − ch

)> 0. (19)

These first two propositions are rather trivial. A tougher sanction helps reducing dishonest disclosure by managersrunning L-type firms and, since the quality of the signal H improves, the risk of doing business with amanager who declaresthat he runs a good company declines, hence the supplier may reduce the input price.We use now the model in order to analyze the impact of a tougher sanction on the default premium – defined as the cost

in excess over c that firms have to pay for the input – and the frequency of defaulting firms. The default premium is aninteresting variable since it measures the economic cost of expected default. Indeed, in this model, risk-neutral and perfectlycompetitive suppliers price the firm as residual claimants who break even. This default premium has a real economic effectbecause requiring a higher default premium results in higher input prices, which in turn can bring about a self-fulfillingincrease in the frequency of bankruptcy.We can state:

Proposition 3. In the hybrid equilibrium, the overall default premium is increasing with the sanction level.

Proof. We denote by Γ the overall price of the input as posted by suppliers at the beginning of the period. This pricecorresponds to the total amount of resources borrowed by firms from their input providers. We can define:

Γ = qch + (1− q)[µc l + (1− µ)ch

]. (20)

The excess borrowing cost (as compared to the perfect information set-up) isΓ−c . Its derivativewith respect to the sanctioncan be written:

d(Γ − c)dz

=dΓdz= [q+ (1− q)(1− µ)]

dch

dz+ (1− q)

(c l − ch

) dµdz. (21)

Replacing dch

dz anddµdz by their expressions in Eqs. (18) and (19), and (1− µ) by its equilibrium value Eq. (16), we obtain:

dΓdz=

qch(τH − τ L)2z2τH

[z + τ L − ch

] [−zch + (c l − ch) (2z + τ L − ch)] . (22)

The sign of dΓdz is the same as the sign of the expression between braces. We show that:

LHS(z) ≡(c l − ch

) (2z + τ L − ch

)> zch ≡ RHS(z). (23)

Indeed, this is true for z = 0. Since

dLHS(z)dz

−dRHS(z)dz

=

(2τ L − ch

) (c l − ch

)+ 2zc l

z + τ L − ch> 0, (24)

the inequality will be true whatever z > 0. Hence, dΓ /dz > 0.

When the sanction level increases, more managers will honestly announce the type of the firm (µ goes up), the value ofthe signal h increases leading to a lower price ch. But the number of managers who benefit of this better offer declines (thereare less dishonest managers at the head of low-return firms). At the same time, the number of managers that have to paythe bigger price c l increases. In this model, the average input price that managers have to pay, a proxy for financial distress,is increasing with the sanction level.

18 D. Besancenot, R. Vranceanu / Research in Economics 63 (2009) 11–21

Wecan also analyze the impact of the sanction on the frequency of defaulting firms. This simple analyticalmodelwas builtunder the assumption of zero direct bankruptcy costs. Hence, the number of failures can be of interest only if bankruptciescome with substantial private losses that do not appear in a firm’s book value. For instance, such a cost can be imposed onworkers that must search for another job. We can show that:

Proposition 4. In the hybrid equilibrium, the frequency of firms that default on the loans from their input suppliers is increasingwith the sanction level.

Proof. Let ν denote the frequency of defaulting firms in this economy. It depends on the distribution of firms between high-and low-return firms (q and 1− q), on the frequency of dishonest managers (1− µ) in the population of L-type firms, andon the default rate recorded in each population of firms:

ν = qFH(ch)+ (1− q)

[µF L

(c l)+ (1− µ)F L

(ch)]

=qτHch +

(1− q)τ L

[µ(c l − ch

)+ ch

]. (25)

Given that dc l/dz = 0,

dνdz=dch

dz

[qτH+(1− q)(1− µ)

τ L

]+dµdz(1− q)τ L

(c l − ch

). (26)

Replacing dch

dz anddµdz by their expressions in Eqs. (18) and (19), and (1− µ) by its equilibrium value Eq. (16), we obtain:

dνdz=qch(τH − τ L)

[(2z + τ L − ch

) (c l − ch

)− z

(ch − 2z

)]2z2τ LτH

(z + τ L − ch

) . (27)

This derivative is positive if the expression between braces is positive, that is if:(2z + τ L − ch

) (c l − ch

)> z

(ch − 2z

). (28)

This is true, given that inequality (23), which is true, implies (28).

The rationale behind this less intuitive result follows the same logic as before (Proposition 3). Firstly, when the sanctionincreases, a higher proportion of L-type firms announce their type honestly. As a result, the pool of firms declaring to beH-type has a smaller proportion of firms that are actually L-type, and thus must pay a lower input price; in turn, this leadsto a lower default rate on this price. However, the above effect is more than offset by the fact that a higher proportion offirms which are L-type now pays a promised input price that correctly reflects their risk of defaulting on it, and this leads toa higher default rate for these firms.

5. A variant with direct bankruptcy costs

In order to narrow the gap between the model and reality, we bring into this section two important changes. Firstly, weallow for positive direct bankruptcy costs. These costs are assumed to differ depending on whether prior to bankruptcy, themanager was honest or dishonest. Let us denote by k1 (and k2) bankruptcy costs if themanager was honest (and respectivelydishonest). A nontrivial result is expected in the plausible case wheremanagerial dishonesty entails larger bankruptcy coststhan managerial honesty (the length of the trial increases and the value of the existing assets declines), i.e.: k1 < k2.When including direct bankruptcy costs, it becomes impossible to get an analytical solution. Hence, in this section, the

model is solved numerically.13 The advantage of this less general method is that it can be implemented for a more realisticincomedistribution function than the uniformdistribution. The lognormal distribution iswell suited to this problembecausethe income can take only positive values and extreme values have a smaller density than the average. At difference withthe uniform distribution, the lognormal one has no superior bound (τ i → ∞). Hence, the assumption of a higher incomeaverage for good firms than for bad ones (yH > yL) can be transposed in terms of c.d.f. into: FH(y) > F L(y),∀y.If the firm income is lower than the contracted input price, y < ca with a ∈ l, h, the firm gets bankrupt and lenders get

the residual value, maxy− kj, 0with j ∈ 1, 2. If the income is lower than the direct cost, lenders get nothing. With thesechanges, Eqs. (3) and (5) become respectively:

c =∫ c l

k1(y− k1) dF L(y)+

∫∞

c lc ldF L(y), (29)

c = Pr[H|h]

(∫ ch

k1(y− k1) dFH(y)+

∫∞

chchdFH(y)

)+ Pr[L|h]

(∫ ch

k2(y− k2) dF L(y)+

∫∞

chchdF L(y)

). (30)

13 The Maple programme that allows us to perform this simulation can be provided on request.

D. Besancenot, R. Vranceanu / Research in Economics 63 (2009) 11–21 19

Fig. 2. The frequency of defaults.

Fig. 3. The average indirect cost of default.

We choose F L() such that the average income yL = 1.60 with a standard deviation σ L = 0.85 and FH() such that yH = 2.65with standard deviation σH = 1.41. We set the frequency of H-type firms to q = 0.8 and the cost of producing the essentialcommodity unit to c = 1. The bankruptcy costs for the honest and respectively dishonest manager are k1 = 0.025 andk2 = 0.05.The price charged by supplier for the input when the manager announces that the firm is of the L-type, i.e., c l is obtained

as the solution to Eq. (29). In this example, c l = 1.088.The problem is then solved iteratively for various values of the sanction z. We allow z to vary with a step of 0.001 in

the closed interval from 0.185 to 0.225 so that µ is increasing from zero to one, covering the full range of hybrid equilibria.The hybrid equilibrium condition Eq. (12) allows us to determine ch (this equation does not change if including positivebankruptcy costs).Finally, we solve Eq. (30) for Pr[H|h], then obtain the equilibrium frequency of honestmangers at the head of L-type firms

(µ) from Eq. (2). More precisely, µ = Pr[H|h]−qPr[H|h](1−q) with µ ∈ [0, 1] in the hybrid equilibrium.

When z goes up, the cost ch declines from 1.022 to 1.012 (managers who announce that their firm is solid have to payless and less for the input). The frequency of defaults ν increases from 9.0% to 9.5% (Fig. 2), and the average cost of the inputΓ increases slightly, from 1.023 to 1.025 (Fig. 3). Hence the numerical solution corroborates the outcome emphasized inPropositions 3 and 4 of the simple analytical model.

20 D. Besancenot, R. Vranceanu / Research in Economics 63 (2009) 11–21

Fig. 4. The average direct cost of default.

The numerical version also allows us to study the impact on the sanction on the average direct cost of default A, such asdefined by:

A = qFH(ch)k1 + (1− q)

[µF L

(c l)k1 + (1− µ)F L

(ch)k2]. (31)

In this expression, the two bankruptcy costs are weighted by the frequency of various types of firms (solid firms, fragilefirms run by honest mangers and fragile firms run by dishonest managers). As shown in Fig. 4, the average direct cost isdecreasing in z.When the sanction z increases, less managers running bad firms will be dishonest, and the frequency of default of those

who still are dishonest declines. The overall frequency of firms exposed to the high direct cost k2 goes down. The nowhonestmanagers are subject to a bigger frequency of default, but the cost of default of a company run by an honest manager (k1)is less expensive than the default of a company run by a dishonest manager. If k2 is large enough as compared to k1, theaverage cost should decline. If the two costs were identical, the A(z) curve would have the same positive slope shape as thefrequency of defaults.

6. Conclusion

According to conventional wisdom in economics, more transparency is always better than less. This paper challenges tosome extent this conjecture as applied to corporate communication policy.Themodel features two players: the supplier of an essential input – who acts as a commercial lender, and themanager of

the company that produces the final good –whomust communicate about his firm’s financial health prior to contracting theinput. Suppliers have only imperfect information about the intrinsic quality of the firm. They update their beliefs accordingto the signal issued by the manager. A honest manager will tell the truth about the type of the firm, a dishonest one willstate that a fragile firm is actually solid. Managers running fragile firms would resort to dishonest communication in orderto benefit from better contracting terms, and contain the financial distress of their firm.This framework allows us to analyze themanager’s decisionwhether to lie or not about the true situation of his company.

In the aggregate, we measure the indirect cost of bankruptcy by the average default premium charged by risk-neutralsuppliers for their commercial credit. In the aftermath of the US corporate scandals of the late nineties, many governmentsrose the sanctions for managers who resort to fraudulent window-dressing. Our model can be used to analyze the impactof such a reform on several key indicators.In a model without direct bankruptcy costs and given a uniform distribution of the firm income, we can put forward in

an analytical way that both the economy-wide default premium and the overall frequency of defaulting firms rise whenthe sanction for fraudulent disclosure is pushed up. In general, when more managers running fragile firms declare honestlythe type of their company, these firms will be submitted to additional financial pressure, which will in turn exacerbatethe original difficulties. This phenomenon should not be underestimated by policymakers called to regulate the corporateinformation market.The model was also solved numerically with positive direct bankruptcy costs and a more realistic income distribution.

While the former results still hold, if direct bankruptcy costs of firms run by dishonest managers are large enough ascompared to direct bankruptcy costs of firms run by honest managers, the average direct cost of default is decreasing withthe sanction, mainly because there are less dishonest mangers in the economy. In this context, finding the optimal sanctionlevel becomes a matter of right balance between direct and indirect bankruptcy costs.

D. Besancenot, R. Vranceanu / Research in Economics 63 (2009) 11–21 21

Acknowledgements

The authorswould like to thank one anonymous referee and Philippe Frouté for their suggestions and remarks that helpedthem to improve the quality of the paper, and Raluca Vranceanu for helping them to remove one programming difficulty.

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