Managerial reporting discretion and the truthfulness of disclosures

Economics Letters North-Holland

39 (1992) 163-168

163

Managerial reporting discretion and the truthfulness of disclosures Anil Arya and Richard

A. Young

The Ohio State Unil,ersity, Columbus OH, USA

Peter Woodlock (‘ase Western Resewe Unirersity, Clec>eland OH, USA Received Accepted

31 January 1992 24 March 1992

In a single period agency model in which the agent has some discretion regarding how to report his performance, conditions on the type of discretion and production technology under which reporting can be useful in contracting agent is permitted to misstate his performance.

we provide only if the

1. Introduction Principal-agent models in which the agent’s communication is costless often fall into the class of revelation games [Myerson (198211. In order for misreporting of performance to be equilibrium behavior in an agency model, communication must be limited or costly [Dye (1988)l. In a general setting, Green and Laffont (1986) provide a necessary and sufficient condition under which all equilibria can be produced with truthful disclosures. The condition is termed the nested range condition (NRC). While violations of NRC imply the existence of equilibria that cannot be produced in truth, it does not imply that the optimal contract in an agency setting will involve misreporting. Even when there are NRC violations, there exist equilibria in which the agent reports truthfully. In this note, we focus on a narrower setting than Green and Laffont (19861, allowing us to identify conditions under which equilibrium behavior necessarily requires misreporting. The setting is similar to that in Dye and Magee (1991), but we depart from their work in two ways. First, the type of reporting discretion we assume is different than theirs. They assume conservative monotone reporting, while we do not require conservatism. Second, we address misreporting, while their focus is on contract form. The type of reporting discretion we permit the agent to have is consistent with external auditors who guarantee honest disclosure only up to a materiality threshold, and with internal control Correspondence State University, 01651765/92/$05.00

to: Richard Young, Department Columbus, OH 43235, USA. 0 1992 - Elsevier

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of Accounting

Publishers

and MIS, College

B.V. All rights reserved

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164

Events

A. Atya et ul. / Managerial

1

Agent offered contract

2

3

4

I

I

I

Random variable i occurs; its probability distribution depends on act selected

Agent selects act

reporting

discretion

5

Agent makes report r, confined to the report set R(z)

Agent compensated based on report

Fig. 1.

systems that detect gross exaggerations of performance. We provide conditions under which the agent must be permitted to misreport his performance if his report is to be valuable in contracting.

2. The model The time line of the model is a depicted in fig. 1. Events 1-3 comprise the basic principal-agent problem. A principal offers a contract which induces the manager to select an unobservable action a which affects the realization of a random variable f. If the variable f were available for contracting, the optimal contract would be characterized by, for example, Harris and Raviv (1979) Holmstriim (1979), or Grossman and Hart (1983). We assume, however, that 2” is not available for contracting. Further, the manager’s reporting discretion is limited, in that his report Y must belong to a set R(Z), which depends on the realization z of 2. One interpretation of the model is that Z denotes economic earnings, which are self-reported by the agent. This is representative of financial reporting in publicly traded firms, where managers often carry out two activities under moral hazard: (1) choosing productive actions, and (2) choosing an accounting system and constructing financial statements. We assume the objective of the principal is to minimize the expected cost of inducing the agent to choose a particular act, taking into account his self-interested behavior with respect to his act selection and his reporting. The following program summarizes the contracting problem:

Program R

min E[s(r(z’))

1al,

SC.),p

subject

to

(1) r(z) E arg

max

s(r)

for

all z,

r~R(z)

(2) E[U(s(r(Z))) Inl - b’(a)2 (3) a E arg yt;{E]U(s(r(i)))

I!?, /a^]- V(a^>).

In this program, E[ .] denotes the expectation operator, A is an action set, A = [a,, a]; R(z) is the set of feasible reports, conditional on the realization z of the random variable f. U and V represent the agent’s preferences over compensation and action. Constraints (1) and (3) state that the manager’s report and action by utility-maximizing, respectively: (1) states that, for each z, the agent’s report maximizes his compensation s(r), within the corresponding report set. Constraint (3) takes the agent’s reporting behavior as given, and states that the manager’s action maximizes his expected utility among all available actions. Constraint (2) imposes a lower bound on the agent’s expected utility from the contracting setting.

A. Arya et al. / Managerial reporting discretion

165

As in Dye and Magee (1991) it is important that the principal not be able to observe the agent’s feasible report set R(z), since if R varies with z, its observation is equivalent to observation of z itself. Thus, the restrictions on the agent’s report set that r E R(z) must be enforced by some outside party, e.g., an external auditor. It is, in fact, typical for an external auditor to disclose only an attestation as to the manager’s report, and not to disclose supplemental information that he obtained during the audit. The report sets are assumed to have the following structure: (1) Z E (z,, ZZ’.. (3) R(z,>={Z;-~,~

,z,l, z,-,,+I ,...,

2,-l,

z,, Li+l,...,

z,+k,J, where

Z,_j,Lzr

and z;+~,IzN.

This notation reflects two assumptions. First, report sets have no gaps. Defining L, = ziPi, 5 zi between L, and M, is a credible and M, =zitk 2 zl, no gaps means that any income realization report. We further assume that Li+l 2 L, and M.,+, 2 M;; that is, the maximum and minimum credible reports are increasing in the realization of z. ’ These restrictions on the agent’s reporting discretion have a natural interpretation. Managers propose to external auditors a set of financial statements, and work with auditors until they agree that the statements ‘fairly represent’ the firm’s financial condition. Very infrequently are financial statements issued along with a qualified opinion from the auditor. The external auditors attempt to detect misrepresentations, but only claim that the financial statements are representative up to some materiality threshold. We now introduce definitions which describe characteristics of report sets. Definition 1. Report sets satisfy ouer-reporting if M, > zi for some i 3.

if R(zl)=

{z,, z,,},

R(z,)

= (z,+,,

full ouer-reporting

zN}

and

if

R(z;)=

Uniform report sets have the intuitive interpretation that the precision of the report is independent of actual income. The Financial Accounting Standards Board has suggested six qualitative characteristics of useful accounting information: (1) relevance to decisions, (2) reliability, (3) consistency and comparability, literature it is (4) efficiency, (5) materiality, and (6) understandability. ’ Often in the accounting asserted that there is a tradeoff among these objectives of reporting. This paper demonstrates conditions under which the objectives of reliability and relevance must be traded off. Formal definitions of reliability and relevance are now introduced. Definition

3.

Reporting

Definition contract.

4.

Reporting

is relevant is reliable

if an optimal if an optimal

contract contract

cannot

satisfy s(r) = s for all i.

can be reproduced

by a truth-telling

A necessary condition for the agent’s reporting to be relevant is that the optimal act be interior. Otherwise there would be no reason to impose risk on the agent by choosing s(.) to be a non-trivial ’ Our assumption of ‘no gaps’ and monotonicity of M(i) is similar to the conservative monotone assumption in Dye and Magee (1991). Our report sets differ in that we assume z E R(z) for all z, which allows a misreporting interpretation. ’ Financial Accounting Standards Board, Statement of Financial Accounting Concepts No. 2 (1980).

A. Arya et al. / Managerial reporting discretim

166

function of r. Since the agent’s compensation would then be independent of his report, his reporting would be reliable, but not relevant. Denote the cumulative distribution of 2 by F(zi 1a), and assume F( .) is differentiable in a. The following proposition demonstrates conditions under which there exist contracts which are incentive compatible with respect to both the agent’s act selection and his reporting behavior at an interior act. Proposition

1.

A sufficient

condition for (1) and (3) to be consistent

at a > a,_ is either:

report sets exhibit partial or:er-reporting and the probability distribution satisfies: aF(z, 1a>/aa < 0, for all 2, < zN, or (ii) report sets are uniform and the probability distribution satisfies: aF(z, 1a>/aa I 0, for all z, < zn, with strict inequality for at least one z,. (i)

Proof. (i) By definition of partial over-reporting, there exists at least one i such that M(i) < m(i + 1). Without loss of generality, choose any such i, and let k be the index of M(i), i.e., zk = M(i). Define sL as the agent’s pay for any report less than or equal to zk, i.e., set sL = s(z,) = . . . = s(zk). ... =s(z,,,), where sH>sL. Under the restriction on F and because Similarly, set s H=~(~k+l)= U’ > 0, the principal can ensure that (1) and (3) are satisfied by choosing s” to be sufficiently larger than SL. (ii) Under uniform report sets, M(i) < M(i + 1) for all i < N - 1. The principal may choose an i < N - 1 such that aF(z, / a),& < 0, offer the same type of contract as in the proof of part (i), and a > aL is implementable. As long as it is not true that aF(z, I a)aa = 0 for all i uL is feasible. 0 Under the conditions in Proposition 1, the agent’s reporting would be relevant provided that there exists an interior act such that the risk premium paid by the principal to the agent does not exceed the extra benefit achieved by inducing that act. Condition (i) imposes stronger conditions on the production technology than does (ii), but weaker conditions on the report sets than does (ii). Note that the conditions on F are weaker than the monotone likelihood ratio condition [Mirlees (1975)]. Further note that conditions (i) and (ii) can be weakened. The important feature making (1) and (3) consistent is that the agent’s action non-trivially affects the probability distribution at a realization z which can be usefully distinguished from an adjacent realization due to the constraints on the report sets. ’ In a very general setting, Green and Laffont (1986) show that all equilibria can be implemented in truth if and only if the nested range condition (NRC) holds. We consider a narrower model, enabling us to address whether reporting will be reliable, i.e., whether the optimal contract can be achieved via truthful disclosure. The structure we impose on report sets means that only two types of violations of NRC exist. This is formalized in Lemma 1 below [see Woodlock and Young (1991) for a proof]. Lemma 1. Assume L( .) and M( > are monotonically only two types of ciolations of NRC are possible:

increasing with no gaps and zi < z, < zk. Then

Type I: zi E r(i) and zk E r(j) but zk is not in r(i), or Type 2: z, E r(j) and z, E r(k) but zi is not in r(k). and i Suppose V(a,)= 0 and V(a,)= 1. Let the probability of z,, z? and z3 given uL be 0.5, 0.25, and 0.25, respectively, R(z,)=lz,, z3), and R(z,)={z,l. let the corresponding probabilities given at, be 0.25, 0.5, and 0.25. Let R(z,)=(z,l, Then (I) and (3) are consistent if one sets U, = U, = I/, +4, even though neither condition 6) nor (ii) holds.

167

A. Arya et al. / Managerial reporting discretwn

Proposition

2 addresses

whether

Proposition 2. Assume the monotone likelihood

the agent’s

reporting

is reliable.

the agent’s reporting is relet’ant and the probability ratio condition (MLRC). Then:

distribution

off

satisfies

(i) a Type I t:iolation implies reporting is unreliable; (ii) if all 1%iolations are qf Type 2, reporting is reliable. C’orollary I.

Assume

report sets are uniform.

Proof of Proposition 2. (i> Assume report sets are as follows: R(z,)={z,,

zz},

without

R(zz)=(zz7

Then, if reporting is relerlant it is unreliable. loss of generality

z3),

R(zJ={z,}

that

and

z E (z,, z2, z3, ZJ

and

the

R&)={z&

Truth-telling implies the contract satisfies s(z,) 2 s(zz) 2 s(z3). It can be shown that MLRC further implies the best contract which motivates truth-telling satisfies s(z,) = s(z2) = ~(2~). Now on his report of let Yr = 121, 22, z,}, yz = (z,), and let s( y,) denote the agent’s pay conditional z, E y;. Incentive compatibility on the act and a > a,_ implies that s( y,) < s( y2). Denote the best truth-telling contract and corresponding best act by s*(y,) and a*. The probability of report belonging to y , or yr is q(y, I a*) =p,(a*) +pz(a*> +p&a*) and q(yz I a*) =p&a*), respect ively. We construct a new contract by making an adjustment to s*(y,>; set s(z,) < s(z?) < s(z~) < s(z4). The agent’s optimal reporting behavior is as follows: I I-uesignal i

Agent’s report r(z)

Let q(r 1a*) denote the probability of a report r, i.e. q(z, I a”) = 0, q(z, I a*) =p,(a*), d-z3 I a*) =pz(a*) +p&a*), and q(z, /a*) =pJa*). Furthermore, set s(z,) = 0, dzl) = s*(Y,) - 6, .dzj) = s*(y,)+6, and s(z4)=s*(yZ)where E>O and 6 satisfy: [s*(Y,>

-E]p,(a*) + [s*(yO +6l[PAa*)

+Pda*)l

Satisfaction of this relation implies that the agent’s expected pay is unchanged by the adjustment. Solving for 6 provides 6 = l p,(a*)/[ p,(a*> +p,(a*>l > 0. Now apply the proof of Proposition 3 in Holmstrom (1979). The Corollary follows from the fact that uniform reporting exhibits Type 1 violations. (ii) Assume without loss of generality that z E {z,, z2, zJ and the report sets are as follows: R(z,)

= {z,l>

R(z,)

= {z,> zJ>

RGJ

= Izz> 4.

The set of possible lying contracts is as follows: (i> s, > s2 and s2 > So, (ii) s, = s2 and s2 > So, or (iii> s, > s2 and s2 = sj. MLRC implies that a contract that sets s, = s2 = si is truth-telling and Pareto dominates any of these lying contracts. q

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reporting discretion

References Dye, R., 1988, Earnings management in an overlapping generations model, Journal of Accounting Research 21, Autumn, 195-235. Dye R. and R. Magee, 1991, Discretion in reporting managerial performance, Economics Letters 35, 4477456. Financial Accounting Standards Board, 1980, Qualitative characteristics of accounting information, Statement of Financial Accounting Concepts no. 2 (McGraw-Hill, New York). Green, J. and J. Laffont, 1986, Partially verifiable information and mechanism design, Review of Economic Studies 53, 359-363. Grossman, S. and 0. Hart, 1983, An analysis of the principal-agent problem, Econometrica, Jan,, 7-45. Harris, M. and A. Raviv. 1979, Optimal incentive contracts with imperfect information, Journal of Economic Theory 20, 231-259. Holmstrom, B., 1979, Moral hazard and observability, Bell Journal of Economics 10, Spring, 74-91. Mirlees, J., 1975, The theory of moral hazard and unobservable behavior, Part I, Working paper (Nuffield College, Oxford). Myerson, R., 1982, Optimal coordination mechanisms in generalized principal-agent problems, Journal of Mathematical Economics, 67-81. Verrecchia, R., 1986, Managerial discretion in the choice among financial reporting alternatives, Journal of Accounting and Economics 8, 175-195. Woodlock, P. and R. Young, 1991, The effect of internal controls on the relevance and reliability of financial disclosures, Working paper (Ohio State University, Columbus, OH).