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.lournal of Accounting ResearchVol. 26 No. 2 Autumn 1988Printed in U.S.A.

Earnings Management in anOverlapping Generat ions ModelRONALD A. DYE*

1. IntroductionIn this paper, I propose and analyze two reasons shareholders mightnot be inclined to eliminate the tendency for managers to engage inearnings management. The first motive is related to the stewardshipvalue of accounting information. Once shareholders have determinedwhich productive act they seek their management to implement, theymust design a contract to encourage management to select that action.If shareholders' sole objective in designing the contract is to minimizethe expected cost of inducing managers to select their preferred action,and the expected cost-minimizing contract encourages earnings manage-ment, then an "internal demand for earnings management" exists.In contrast, shareholders are said to have an "external demand forearnings management" if, holding managers' compensation and produc-tive action fixed, they can improve their firm's contractual terms withoutsiders by managing earnings. Though there are obviously severalpotential sources of such external demand (because of, e.g., accounting-

based contracts with suppliers, debt-covenant restrictions, rate-of-returnregulations), I analyze the external demand for earnings managementinduced by current shareh olders' attem pts to alter prospective investors'perceptions of the firm's value.

* Northwestern University. I wish to than k Joel Demski, workshop participan ts at theUniversity of California at Los Angeles, Northwestern University, the University ofPennsylvania, and two anonymous referees for helpful comments on previous drafts.Research support was provided by the Accounting Research Center at NorthwesternUniversity and the Institute of Professional Accounting at the University of Chicago.[Accepted for publication July 1988.] 195

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19f) JOURNAL OF ACCOUNTING RESEARCH, AUTUMN 19 88To assert that shareholders might have a demand for earnings man-agement might seem perverse, since unmanaged earnings are typicallyconsidered preferred to managed earnings, ceteris parihus. But the as-sumptions implicit in the ceteris paribus qualification are frequently noltenable. For example, to give a manager no incentive to engage in earningsmanagement may necessitate altering his compensation scheme by mak-ing it independent of accounting data. Such alterations may change themanager's preferred action choice. So it may be impossible to eliminateearnings management while holding the manager's action choice cori'stant.The purpose of this theory is to describe necessary and sufficientconditions for earnings manag ement to occur, to identify how the internaland external demands for earnings management differentially alfect the

firm's optimal earnings announcement policies, and to indicate thebenefits and costs to shareholders of earnings manipulation. The twoprincipal factors which generate earnings management in these modelsare the inability of managers to communicate all dimensions of theirprivate information to shareholders and the inability of investors toreveal completely all facets of their managers' compensation schedulesto prospective investors. These considerations play a prominent rolebecause they affect the applicability of the Revelation Principle (Harrisand Townsend [1981], Holmstrom [1978], and Myerson 11979]) to thismodel of earnings management. Although the Revelation Principlewhich, loosely speaking, states that a contract can be designed so as togive each of the parties to it an incentive to reveal his/her privateinformation truthfully^was originally designed simply as a technicaldevice to help characterize resource allocations in asymmetric informa-tion environments, it is in fact central to any explanation of earningsmanagement: when the Revelation Principle applies to a model whichdepicts earnings management, there exists another equilibrium of themodel in which earnings management does not occur.

The theory also provides implications about the magnitude and direc-tion of stock price reactions to earnings announcements and identifieswhen shareholders are better off if their managers issue two distinctearnings announcements (one private, for purposes of appraising man-agement's performance and influencing management's compensation,and another public, for purposes of influencing prospective investors"opinions of the value of the firm).

The study of the internal demand for earnings management requiresappraising the stewardship value of earnings announcements. A single-period agency model, modified hy assuming that the firm's economicearnings are not publicly observable, is suitable for its study. Studyinj;the external demand for earnings management necessitates differentiat-ing between a firm's current shareholders and its prospective investors.We accomplish this by employing an "overlapping generations" model

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EARNINGS MANAGEMENT 197(Samuelson [1958]), in which one generation of shareholders transfersthe ownership of the firm to the next generation through a stock market.The demand for earnings management derives from one shareholdergeneration's attempt to impress the next generation with the firm's pastperformance. The analysis is affected by the length of time the firm'smanager stays in office. If a manager stays in office for only onegeneration, his opportunities for earnings management are limited to theone time while he is in office that the firm goes up for sale. In this casethe manager's incentives to engage in earnings management are deter-mined by how his earnings report affects his immediate compensation.Observability of his compensation contract is therefore critical to futuregeneration's interpretation of his earnings report. When the manager isin office for longer periods (during which time the firm's ownershippasses through multiple generations of shareholders), the manager'sincentive to engage in income-sm oothing is affected by the impact it hason his attempt to engage in intertemporal consumption-smoothing. Al-though most of the analysis of this latter situation is conducted underthe assumption that the manager consumes what he earns each period,we show in an example th at giving the manage r access to capital m arketsneed not eliminate his incentives to income-smooth. The reason is thatengaging in intertemporal transfers via capital markets or, alternatively,via income-smoothing, is not a perfect substitute, and so the managermay find it advantageous to use both devices to transfer consumptionintertemporally.

The principal intellectual antecedents of this paper are Demski andSapping ton [1987] and S amuelson [1958]. Demski and Sappington [1987]provide the modeling insight used here to investigate the feasibility ofearnings management. Their idea that restricted communication chan-nels can be an effective modeling device to vitiate the Revelation Prin-ciple is central to what follows. Overlapping generations models origi-nated with Samuelson [1958] and have been used extensively to studymonetary phenomena (see, e.g., Karaken and Wallace [1980]), but I amunaware of their previous use in an accounting context. Trueman andTitman [forthcoming] and Verrecchia [1986] contain alternative theoriesof earnings management.In section 2, I consider extensions of the single-period principal-agentmodel to illustrate pure forms of the internal and external demands forearnings management. In section 3, I merge the models introduced insection 2. Since the earnings announcement policies generated by theinternal and external demands for earnings management may not coin-cide, I also exam ine share holde rs' incentives to have managem ent providedistinct public and private earnings announcements in section 3. Insection 4, I present a multi-period principal-agent model to illustratesome income-smoothing phenomena. Section 5 concludes the paper andoutlines an agenda for future research.

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198 RONALD A. DYE2. Models of Pure D emand for Earnings M anagement2.1 INTERNAL DEMAND

The model in this section focuses on the sequence of events illustratedin the time line in figure 1. This time line chronicles a standa rd p rinci pal-agent problem, apart from the principal's inability to observe the man-ager's "output," the firm's actual earnings x. Instead of contracting onactual earnings, the principal must compensate the manager on the basisof his reported earnings. Absent restrictions on the relation betweenactual and reported earnin gs, the m anager will exert no effort and simplyannounce that report which maximizes his compensation. But in factthere are restrictions on the relation between actual and reported earn-ings: internal and external auditors, audit committees, GAAP, and thelaw all serve to impose a relation between a manager's report and thetruth. We summarize the web of restrictions on the manager's reportimposed by these (and related) institutio ns via a "feasible reporting set,"y(x; (). This set delimits the range of earnings reports y the managercan make, given that actual earnings are x and the manager's otherpriva te information (the purpose of which is described below) take s onthe value e. The manager makes his report y after observing both x ande. As long as the manager's reported earnings y falls in the set Yix; t),the firm's owners cannot detect that the manager has misstated earnings;if y is outside Y{x; f), the owners learn that the manager's earningsreport is false, although they do no learn anything else about actualearnings in that event.In addition to positing the existence of this auditing technology toconstrain the manager's earnings management, I allow for the possibilitythat the manager incurs personal costs if he produces an inaccurateearnings report. These costs might include a distaste for lying, theeducational costs of learning the firm's accounting system sufficientlywell so as to be able to modify a component of earnings without havingthe modification be detected (or criticized) by the firm's auditor or therelated costs involved in discovering how large e is (i.e., how large anerror will not be detectable), or the costs involved in bribing an auditornot to report a discrepancy in the earnings report. Let c{x, y, e) indicatethe cost to the manager of reporting that earnings are y when actualearnings are x and his other private information is e. I assume c{x, y, t)

ContractissignedManagerchooses bisunobaervableaction (a)

Managerprivatelylearns actualearnings (x)and some otherinformation (f)

ManagermakesreportManageris compensatedbased on bisreport

Fie;. 1

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EARNINGS MANAGEMENT 199> 0 (i.e., the manager does not get utility from lying), and c{x, x, e) = 0(truth-telling is costless).To complete the specification of the model, let U{d) - g(a) denote themanager's utility from consuming d and exerting effort level a E A = Ig,a]; let f{x\a) denote the density describing the stochastic relation be-tween the manager's effort and earnings; let U be the manager's utilityfrom alternative employment opportunities; and assume the owners ofthe firm are risk-neutral.We can study the internal demand for earnings management afterestablishing some definitions.

D E F I N I T I O N 1. An earnings a nnou ncem ent policy is a function >'(, )specifying, for every realization x and (, an announcement y{x, t) .Throughout the subsequent discussion, announcement policies will be

set with an underbar, whereas particular announcements will have thesuperscript ' . Thusy is an announcement consistent with the policy yi,) if there exists (x, t) w ith>' = >'(x, () . (Also, " denotes a random variable,whereas a variable without a ~ denotes the realization of the variable.Thus, X is a realization of x.)D E F I N I T I O N 2. An earnings announcement policy ^(, ) induces

earnings management if, with positive probability, y{x, 1} does not equalX. This definition of earnings management is quite general and is likelyto encompass any other definition of earnings management one mightpropose. In particular it should be noted that this definition, which canbe applied in a multi-period context on a period-by-period basis, imposesno intertemporal restrictions on the relation between the time series ofactual earnings and the tim e series of earnings announ ceme nts.'

D E F I N I T I O N 3. Suppose current shareholders wish the manager toimplem ent action a G A, and the only report the m anager can ma ke toshareholders is an earnings announcement. Then there is said to be aninternal demand for earnings management provided every contract s(")which solves the program:Min ^ [ s (^ ( i , t))\a](), .y( ')

subject to:( 0 fo r a l l X, e, y{x, e ) E a r g m a x s{y) c{x, y, e ) , y E Y{x, t )

( u ) a E a r g m a x E[Uis{yix, ()) - c{x, yix, t ) , I)) \ d ] - g{d), d E A{Hi) E[U(siy(x, ()) - c{x, y{x, t ) , e)) \ a] - g{a) > U

induces the manager to engage in earnings managem ent.' Income-smoothing, which is typically considered to involve understatements of incomefollowed hy overstatements (or vice versa), in contrast, does impose intertemporal restric-

tions on earnings. Income-smoothing is discussed in detail in section 4 helow.

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200 RONALD A. DYEThis definition simply recasts the description of an internal demandfor earnings management given in the introduction; such demand existsif inducing earnings manag ement is the expected cost-minimizing way to

motivate the manager to select a particular action. (The counterpart tothis definition when the manager can make an announcement t aboutthe realization of his private information t, in addition to x, simplyinvolves replacing y{x, c) by a joint reporting policy (yix, t), t(.x, t)) inthe above program, with e{x, t) = e being interpreted as the man ager'sreport of f.) In the sequel, the value of the objective function of thisprogram when evaluated at its optimum is denoted by w{a).As previously noted, th e Revelation Principle is a nemesis to the studyof earnings m anagem ent: when it applies, any con tract w hich encouragesearnings manipulation can be viewed as arbitrary, since another contractcan be constructed which does not induce earnings management andwhich provides the sam e utilities to all contracting parties as th e originalcontract. When the manager can communicate all dimensions of hisprivate information (i.e., x and t) to shareholders, the Revelation Prin-ciple does indeed apply, and so no internal demand for earnings manage-ment exists. Thus, a necessary condition for the existence of an internaldema nd for ma nageme nt is th at some dimension of managem ent's privateinformation cannot be costlessly communicated. This point has beenmade in various contexts by Demski and Sappington [1987], Green [1984],and G reen and Laffont [1983]. Proposition 1 below shows tha t, apartfrom some mild regularity conditions, blocked communication of man-agement's private information e is also a sufficient condition to generateearnings management.

P R O P O S I T I O N 1. If (i) for every realization (x, t) of {x, t), the set y(x;e) contains a neighborhood of x; (ii) c(x, y, e) is differentiable in y insome ne ighborhood of j) = x, for every (x, t); (iii) it is prohibitively costlyfor the manager to report t, and so the manager's compensation dependsonly on his earnings announcement; (iv) the manager's optimal contract.s(") is differentiable in the e arnings an nounce me nt; then there exists aninternal demand for earnings management unless shareholders requestthe manager to select the lowest possible action a in A.Proposition 1 is based on the idea that if c{x, x, () is identically zeroand dx, y, t) is differentiable in y at y = x, then the marginal cost ofearnings management is zero in the vicinity of the true earnings x, i.e.,very low levels of earnings management are essentially costless to themanager. Therefore, in order for the manager's contract not to inducesome earnings management, the manager's compensation must be inde-pendent of his earnings announcement. But constant contracts areoptimal only when the manager's optimal action is the lowest possibleaction. Thus, if shareholders wish managers to exert some nontrivialeffort level, they must tolerate some earnings management.Note also that Proposition 1 is valid whether or not t is degenerate.This might appear to be inconsistent with the Revelation Principle

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EARNINGS MANAGEMENT 20 1

because, when ( is degenerate and the manager announces a claimedvalue for i's realization, he is clearly reporting on all dimensions of hisprivate information (there is only one dimension). To see what liesbehind this claim, suppose Y(x; f) = (=, x + 1] for all x and f and siy)is strictly inc reasing in y. Then, the m anager's optimal reporting strategyis 3'(x) = X + 1. But the contract six) = ,s(.y(x)), which usually correctsthe reporting bias of a non-truth-telling contract, does not produce atruth-telling contract: since s(*) is increasing, so is ('), and hence themanager's optimal reporting strategy when compensated with () is alsoyi'). The Revelation Principle does not apply here even though themanager can report on every dimension of his private information,because the reporting set Yix; e) varies with the realization of x, i.e., hismessage space is partially blocked.'

In addition, while the proposition states that earnings managementmust be tolerated to get nontrivial effort from the agent, it does notguarantee that any nontrivial effort level can be implemented by meansof some contract which does result in earnings management.' However,obvious sufficient conditions for this latter result exist, e.g., suppose A isfinite, x and e are discrete, Y(x; t) = (-co, x + e], and cond itional on a EA, X + t's distribution possesses the concavity of distribution functioncondition and the monotone likelihood ratio property, and that there isno pair of distinct actions for which x + e's distribution is the same foreach action. Then, for any action, a contract can be constructed toimplement that action.^2.2 EXTERNAL DEMAND

I now consider factors affecting the external demand for earningsmanagement, while ignoring the moral hazard problem between currentshareholders and management which gives rise to an internal demandfor earnings management. That is, I assume that, upon being paid a wagew to cover his opportunity cost of employment, the manager will imple-ment any earnings management policy requested by his employers, thefirm's current shareholders. (To make this passive behavior rational for-1 wish to thank Bruce Miller tor belpful conversations on this point. Also, anotber

variation on this example is of some interest: suppose the manager's reporting set Y{x; t)consists of all real numbers regardless of tbe realization of x or f, and tbat he nowexperiences personal costs in m anipulating earnings, as represented by c{x, y) = 'My - x)'-.If s(y) = y is the manager's contract and x = x occurs, tben the manager solves Max y -V2{y - x)'^. Tbis bas solution y(x) = x H- 1. It is easy to check that s(x) = s{y{x)) will notproduce truth-telling, nor will tbe alternative "Revelation Principle" style contract s(x) s{y{x}) - c{x, y(x)). Tbe Revelation Principle fails here, not because of blockage of anymessage space (there is no sucb blockage), but rather because tbere are noncontractablecosts of earnings manipulation.' I.e., the proposition says tbat earnings n:ianagement is a necessary condition for effortexertion , but it does not identify sufficient conditions for effort ex ertion. I wisb to tbankMilt Harris for this observation.'' Tbe proof is available on request.

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20 2 RONALD A. DYEthe manager to adopt, I assume in this section that c{x, y, t) = 0 andthat the action set A is the singleton [a].)This is an "overlapping generations" model (as in Samuelson [1958]);that is, two generations of shareholders, "young" and "old," coexist ateach date, and the old transfer ownership of a firm to the young on asecurities market. This overlapping generations framework highlightsthe distinction between curren t and prospective investorsan d thereforegenerates an "external" demand for earnings management. In addition,this framework, together with the assumption that all old investors arerisk-neutral in consumption, eliminates unanimity problems which typ-ically arise when firms confront dynamic decision problems.In any period t of this model there are equal numbers of "young" and"old" investors. Each generation of investors lives for two periods. Aninvestor born in period t gets utility c, -I- c,+]/(l -I- r) from consuming c,in period r, 7 = t, t + 1. Trade in a firm's shares, which transfersownership from the old to the young, occurs after earnings are disclosedby period t incumbent m anagement. Earnings announcem ents may influ-ence the price the old receive (and the young pay) for the firm.Each generation contracts to have the firm run by new management,and each manager must be given a contract ,s() so that his utility fromworking for this firm is at least U, the (exogenous) utility obtainablethrough alternative employment. In this section, since the manager isassumed not to be subject to moral hazard, the contract ^s() is a wage w,where U{u!) g{a) = U. The (successive) managers' preferences andemployment opportunities are assumed not to vary over time, and to becommon knowledge to all investors.The time line in figure 2 provides more detail on the chronology ofevents in this model. The time line does not indicate the effects ofpassage of ownership of the firm to the young. Ownership of the firmentitles new sha reholders (in period t, say) to two property rights: (1) theright to obtain proceeds in the next period from the sale of the firm tothe next period's new generation {t + 1) of investors in proportion to thefraction of the firm purchased, and (2) the ownership of this period'sactual economic earnings also proportionate to purchases.The second property right merits further explanation. Earnings gen-erated by a manager hired in period t are assumed not to be transformedinto consumables until after investors born in generation t have died,i.e., these earnings are consumed by investors born in generation t + I.This ass ump tion accords with the idea tha t earnings may not be availablefor consumption purposes for substantial periods of time, and it intro-duces some intertemporal considerations even if earnings follow anindependent and identically distributed {iid) time-series process. If theold generation sold the young generation the firm exclusive of current-period economic earnings, thenin an iid worldthe new generation ofinvestors would be indifferent toward all earnings ann ounce me nts, sincethe earnings annou ncem ents would contain no information regarding the

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204 RONALD A. DYEeconomic value of the firm to them . Of course, when period t real earningsdo become their property, they will be concerned with previous manage-ment's announcement of earnings, in which case earnings announce-ments will serve an allocative role, even in an iid model.One other note on the time line: even though members of the newgeneration observe only the previous management's announced value ofearnings at the time shares are purchased, I assume th at they (as well asthe subsequently installed new management and all other future gener-ations of investors) learn the actual value of economic earnings by thetime they make their consumption/investment/contracting decisions.This assumption means that people ultimately learn the value of whatthey buy and that records of earnings are kept.'

I also assume that the firm's actual earnings are distributed to share-holders and not reinvested in the firm. (Section 4 below introduces amodel in which earnings may be retained at the manager's discretion.)To complete the specification of the model, I now describe the firm'sstochastic production technology and the consequences of and the man-ager's opportunities for earnings management. f{x \ a) denotes the prob-ability density (or mass) that next period's economic earnings will be x,given that the manager takes action a this period. That is, the earningsprocess in this paper is iid, conditional on the manager's action, althoughthe results generalize to general Markovian processes (see Dye [1987J).The support X = \x\ f{x\ a) > 0\ of/is assumed independent of a. Let l{x,y, f) denote the corporate costs of earnings management, i.e., of reportingtha t earnings are y when actual earnings are x and the manager's privateinformation is t, with l{x, x, t) = 0 an d iix, y, f) 5: 0. Th e in tent is tocapture phenomena, like bond defeasance or intentionally stocking oulto dip into LIFO layers, which enhance reported earnings while poten-tially reducing firm value. Finally, as in the model of the internal demandfor earnings management, I postulate that shareholders have access toan imprecise monitoring technology which allows them to discernwhether earnings have been excessively overstated. All shareholders aliveat a given date are assumed to be capable of discerning whether an-nounced earnings fall into some set Y{x; t) (which contains a neighbor-hood of %).

The central point concerning the external demand for earnings man-agement made below is that the existence of this demand depends on theobservability of current shareholders' instructions to their manager (re-garding the firm's earnings management policy) to the next generationof investors. If these instructions are not (are) observable to the next'This difference hetween announced and actual earnings is assumed to he correcltdretrospectively in the firm's records. Also, the analysis would change somewhat if con-sumption/investment decisions were made hefore economic earnings were known. In thatcase, earnings announcements would have an additional economic effect, and "truthful"earnings announcements would become more valuahlehy aiding in the early resolutionof uncertaintv.

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EARNINGS MANAGEMENT 20 5generation of shareholders, there is (is not) an external demand forearnings management, irrespective of the manager's ability to commu-nicate all dimensions of his private information to shareholders.

These results are easy to explain. First, observe that if P(y) denotesthe market-clearing price of the firm when the manager announces y,andy{, ) denotes his earnings announcement policy (e.g., if y{x, t) -y, the m anager announces y upon learning x = x, ( = f), and s(y) denotesthe manager's compensation upon announcing y (under the presentassumptions, siy) = w), then current shareholders (whose preferencesare by assumption linear in second-period consumption) unanimouslyseek the manager to adopt the policy y(*) which maximizes:

subject to the c onstrain ts yix, t) G Yix, t) for all (x , e).*'Suppose current shareholders instruc t their m anager to adopt a "truth -ful" earnings announcement policy, i.e., y{x, f) = x. Then, the market-clearing price of the firm is:

P{y) = y + i^/(i + r)for some constant v representing the value of the firm (exclusive ofcurrent-period earnings) to the next generation of shareholders (v isconstant only in the case where earnings follow an iid process). Currentshareholders' expected utilities from second-period consumption underthis policy are given by:E[P{i) - six) I a] - E[x \ a] -h v/H + r) - w.

Now suppose that the current generation alters its earnings announce-ment policy to, say, y{x, e), and that this alteration is observable tofuture generation s of investors. The n th e equilibrium pricing rule changesto , say, P("), satisfying:

P ( y ) = E [ x - l i x , y , e ) \ a , y = y i x , ()] -\- v/{l - h r ) .' To see that all shareholders desire to maximize E\l^ .s], consider a shareholder born

in period t who has initial wealth W, purchases fraction 6 of the firm (in period () whosemarket price is P, , and learns that the firm's "net" economic earnings in period ; are:Xi" ^ X, l{xi, i'l, t , ) .

If he invests / dollars in a riskless asset which returns (/ + r)/in period ( + 1, and consumescv in period T = t,t + I, then his consumption/investment opportunities are given by:c, + I ^ W+ 0{xr - P,)

where .s,+ i is tbe contract his generation offers to tbe firm's manager. It is clear that,regardless of the choice of c, or /, the investor wishes s,,, to be chosen to maximize E[ P, + ,- s,+ t], as long as his position f) in the firm is not negative.

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2 ( ) f i R O N A L D A . D Y E(v does not change because it is determined by the next generation'sbehavior.) Current shareholders' expected utilities from this revisedpolicy are equal to:E[P iyix, t)) - siyii, e)) | a] = E[i - Hi, yjx, e), f) | a]

+ u /d 4- r) - w < E[x I a] -I- v/il + r) - w.(The inequality follows from / > 0.) Hence, when current shareholders'earnings announcement instructions are observable to future generationsof investors, current investors do not profit by deviating from a truthfulearnings announcement policy. This result has been demonstrated forthe case where the manager does not communicate t; exactly the sameargument applies when the manager does announce e.

The intuition for th is result is clear: deviating from a truthful earningspolicy is not beneficial because (1) prospective shareholders revise theirdemands for the firm's shares (thereby altering the equilibrium pricingpolicy) as current shareholders publicly change their earnings announce-m ent policy (i.e., prospe ctive sh areho lders do not exhibit functionalfixation) and (2) earnings management may be costly (/(x, y, 0 > 0),whereas truthful earnings announcements are free {l{x, x, t) = ()). If.however, prospective shareholders cannot observe current shareholders'earnings announcement instructions to their management, a truthfulearnings announcement policy is not consistent with equilibrium hehav-ior by current shareholders. Before proceeding with the proof of thisclaim, I define formally the notion of an equilibrium for this case.D E F I N I T I O N 4. A stationary equilibrium associated with unobservableearnings announcement instructions in the absence of managerial moralhazard consists of a pricing function Pi*), an earnings announcementpolicy y ( ) , and a constant v such that:

i i ) F o r e a c h . y , P{y) = E{x - H x, y , t) \a, y = y ( i , f ) | + v/il + r)H i ) E j P i y i x , e)) - w\

ri i i i ) F o r e a c h ix , t ) , yix, 0 G a r g m a x P ( y , (), y E Yix; t ) .

Conditions (0 and iii) assure that the market-clearing price of the firmequals the sum of expected current and discounted cash flows, conditionalon the manager's actual announcements y and the announcement policyyl', ) future shareholders believe current shareholders requested to heimplemented. Condition iiii) distinguishes this case from the case above:since future shareholders cannot observe current shareholders' instruc-tions to their management presently, current shareholders attempt loexploit this informational asymmetry by selecting their earnings an-nouncement policy optimally, taking future shareholders' beliefs--and

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EARNINGS MANAGEMENT 207hence, the functional form of the equilibrium pricing function P(*)asgiven. Of course, in equilibrium, future shareholders are not fooled, as(iii) indicates: their beliefs turn out to be correct.

It is now clear why the truthful earnings announcement policy y{x, t)= X cannot be part of an equilibrium, as long as Y{x; t) contains aneighborhood of points around x, for each (x, t) . If prospective investorsbelieved that current shareholders adopted a truthful earnings policy,then the market-clearing price would be given by:Piy) -y + f^/(i + ^)-

Since current shareholders can implement any earnings announcementpolicy y{', ) which satisfies y(x, 0 E Y{x; e) for all (x, 0 withoutprospective shareholders detecting their deviation from a truthful earn-ings announcement policy, current shareholders will maximize theirutility by having management select y(x, t) = Sup Y{x; e). Thus, atruthful earnings announcement policy cannot be part of any equilib-riumand this is true independent of the corporate costs of earningsmanagement.The intuition here is also straightforward: since modifications inearnings announcement policies are unobservable to potential investors,earnings management is irresistible to current shareholders interested inmaximizing the firm's current market value. Although this argument waspresented assuming tha t the manager announces only y, exactly the sameargument applies when announcements of e are allowed.In summary, we observe that the internal demand for earnings man-agement is driven by the inability of managers to report all dimensionsof their private information, whereas the external demand for earningsmanagement is driven by the inability of current shareholders to reportthe earnings announcement policy they instruct their management toadopt to future shareholders.3. An Integrated Model of Earnings Management

In practice, it is probably rare to find pure forms of either internal orexternal demands for earnings management. Shareholders may be con-cerned about both the cost of getting managers to adopt their preferredactions as well as the external effects of the earnings announcementpolicies induced by mana gem ent's com pensation schemes. In this section,I illustrate what happens when these dem ands for earnings m anagementare merged.The time line for the merged model is identical to the time line infigure 2 above, which depicts the sequence of events for the modelillustrating an external demand for earnings management. The featuredistinguishing the merged model from the "external demand" model isthat the manager is now subject to moral hazard, and so must be

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20 8 RONALD A. DYEmotivated to choose the appropriate action and earnings managementpolicy by judicious design of his compensation scheme. Also, just as theobservability of the manager's earnings announcement instructions in-fluenced the external demand for earnings management, so does theobservability of the manager's contract affect the demand for earningsmanagement in the merged model.In the following definition of equilibrium, "unobservable managementcontracts" is shorthand for "the contracts offered by one generation ofshareholders to their manager are not observable to the next generationof shareholders." The interpretation of "observable management con-tracts" is analogous. (These two notions of equilibrium are sometimesreferred to as OCK and NCE, short for observable and nonobservablecontract equilibrium, respectively.)

DEFI NI TI ON 5. A stationary equilibrium associated with unobservablemanagement contracts (NCE) cons ists of a pricing function P(), anearnings announcement policy 3'(, ), an action a*, a contract s*(), anda constant v such that:( 0 F o r each y, P{y) = E[i - l{i, y , 0 \a*,y = y(x, ()\ + v/i\ + r)

Ul) E[P{yii, 0 ) - s*(y{i, -,))]u =

(iii) Taking P(-) as given, >'(), -s*(), and a* maximize E[P{y(x, 0 )- siyix, t))\ a] among all y(), .s(), and a satisfying:

(a) for all x, e, yix, e) arg max U(s{y) - eix, y, t)), y Yix; ,)

ib ) a m a x i m iz e s [ ( / ( s ( y ( i , e ) ) - dx, yix, t))\d] - gid)a m o n g a l l din A

ic) E[U (siyii, ()) -cix,yii, f) , t ) ) i a ] - ^ ( a ) > U.This equilibrium is similar to the one defined in section 2.2 above: {i)an d iii) state that the value of the firm is the discounted sum ol' its

expected actual earnings; (iii) states that the old investors of any gen-eration seek to maximize the expected value of the firm net of theexpected cost of management compensation, subject to the manager'swillingness to work for the firm (condition iiii)ic)) and implement theproposed earnings announcement policy (condition iiii){a)) and action(condition iiii)(b)), while taking as given prospective investors' percep-tions of the current manager's contract/action/earnings announcementpolicy (and therefore the functional form of the pricing function Pi')).The formal definition of an OCE differs from the definition of an NCEpresented above in the specification of the market-clearing pricing func-tion. In an NCE, this function can depend at most on the current

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EARNINGS MANAGEMENT 209manag er's earnings announcem ent. In an OCE, this function also dependson the current manager's contract. Consequently, in an OCE investorsknow (rather than conjecture) what earnings announcement policy theprevious generation's manager adopted, and so the market-clearing pricefunction will change as the manager's earnings announcement policychanges. This is modeled by substituting:

P(y I y(*)) = E[i - lix, y ( i , I), I) I a, y = y^d, e)] + u/(l + r)for P{y) in the definition of equilibrium, where y is to be interpreted asthe earnings announcement policy induced by whatever contract theprevious generation gave their manager.

Proposition 2. (a ) If:(/) f(x\a) and w{a) (the minimum expected cost of getting themanager to take action a) are continuous in a, for each a E A =[a, d], and the set X of possible realizations of x is finite;(ii) c"= 0; / = 0 and Y{x; e) ^ (-oo, x + t]

then there exists an equilibrium associated with observable managementcontracts, with the earnings announ cem ent policy y{x, e) = x + e.(b ) If, in addition to (0 and (ii):

(iii) f's density defines a scale parameter family with the monotonelikelihood ratio property;"(iv) Fix I a) is convex in a, where F( - | a) is the cum ulative d istributionfunction associated with /( | a);"(v ) u;(a) is convex in a;

then there exists an equilibrium associated with unobservable manage-ment contracts, also with the earnings announcement policy y(x, f) =X -H e .Three remarks about this proposition follow.(1) Under the assumptions of Proposition 2 and both notions ofequilibrium, managers make the largest earnings announcement possiblewhich is not discernibly false.'' This result occurs for two reasons. First,

A family of density functions \fix\ll}\e ^ il\ indexed hy some ordered set Si possessesthe monotome l ikel ihood rat io properly i f fix \ O)/f{x \6') is increasing in x for 0 greatert h a n e'. This family of densi ty funct ions is a "scale parameter" family if/(A:| d) = f{x - 0)for each 6 and x. (See Lehmann [1959].) Milgrom [1981] shows that, if appropriatedifferentiability conditions hold, a family possesses MLRP if/(x [ fl)/f(x \ 0) is increasing inX (subscrip ts d enote p art ial derivat ives here). C onsequently , i f i (*) is e 's densi ty , then I'U)/lU ) is decreasing in e when /() defines a scale parameter MLRP family. This fact is usedin the proof of Proposition 2.

" Condit ion (iv) is also referred to as the concavily of distribution function condition;see, e.g . , Grossman and Hart [1983].

" Unfo rtunately , I do not know of sufficient c ondit ions which gu arante e tha t theseannouncement pol icies are unique.

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21 0 RONALD A. DYEit is easy to show when c = 0 = / and Y(x; e) = (-00, x -- e], tha t amongthe contracts which induce the manager to adopt any particular action aat lowest expected cost, there e xists a contract which is increasing in themanager's reported earnings.'" Given such a contract, the manager isobviously motivated to make the largest possible earnings report. B ecausethe next generation can observe this contract in the case of an OCE, thisfact is itself sufficient to guarantee that an OCE equilibrium exists withthe announcement policy y{x, () ^ x -\- t. For an NCE, one must alsoobserve th at, since there are posited to be no corporate costs of earningsmanagement ( = 0), the ma rket-clearing price of the firm is an increasingfunction of E[x \ a, yix, e) = y], i.e., of current expected earnings, condi-tional on the manager's earnings announcement policy, action choice,and actual earnings report. When future investors believe the manageralways makes the largest earnings announcement possible (y{x, t) = x +0, it can be shown that the current-period expected earnings are anincreasing function of reported earnings, when I's density defines a scaleparameter MLRP family. C onsequently, the mark et-clearing price of thefirm is an increasing function of the earnings ann ouncem ent, so currentshareholders prefer the highest possible earnings announcement.

In brief, given the assumptions of Proposition 2, the earnings an-nouncement policy which maximizes the market value of the firm coin-cides with the policy which minimizes the expected cost of getting themanager to adopt current shareholders' preferred action. This commonpolicy consists of having the manager always make the largest possibleearnings announcement (i.e., adopt the least conservative reporting pol-icy) under both equilibrium constructs.(2) More hypotheses are employed to establish the existence of anequilibrium associated w ith unobservable co ntracts (those in Proposition2.2) than for observable contracts (those in Proposition 2.1) because, inthe former case, the prospective investors have to make conjectures aboutwhat contract current shareholders have offered their manager which, inequilibrium, turn out to be correct. No such conjecturing is necessarywhen contracts are observable to prospective investors, and so an equi-librium exists under fewer restrictions in that case.(3) Though the earnings announcement policies for both equilibriumconstructs are the same, other aspects of the two equilibria differ.Explicitly, if we add to the list of hypotheses in (6) that \f{x\a)\a t A\is an MLRP family and that f{x \ a) is differentiab le in a, we can showthat the equilibrium action associated with the observable contractequilibrium (which maximizes E[x \ a] - w{a)) is greater than the equi-librium action associated with the unobservable contract equilibrium,and, hence, the expected marke t-clearing price of the firm is higher with

" T h is resul t holds even for some cos t funct ions (( ) which are not ident ical ly zero.Specifically, as long as c(x, y, i) is nondecreasing in y, the result follows.

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EARNINGS MANAGEMENT 211the OCE than with the NCE. The reason for this ordering is clear: underan NCE, any modification in a manager's contract which induces him toincrease his action generates a positive externa lity for future shareholdersfor which current shareholders are not compensated, because the market-clearing price canno t depend on the con tract offered in an NCE. Clearly,no corresponding externality exists under an OCE. In tbat case, futureinvestors pay for any change current investors make in their manager'scontract which increases the manager's preferred action.In both equilibrium constructs, the next generation of shareholderscorrectly assesses in equilibrium the contract the prior generation ofshareholders gave to their management, so it might seem that thereshould be no differences in the social welfare obtainable from thesealternative equilibrium notions. In fact, it can be shown that the alloca-tions associated with an OCE generally strictly Pareto dominate thoseassociated witb an NCE. This ca n be explained by viewing the thre e setsof economic actors (tbe "next" generation of shareholders, the "current"generation of shareholders, the "current" manager) as all being membersof a hierarchically organized firm, with the "next" generation at the topof the hierarchy, the "c urrent" generation in the middle, and the currentmanager at t he bottom . From this perspective, the current generation ofinvestors is an agent of the next generation, and the action they takeconsists of the selection of their manager's contract. Now, as is true inany agency relationship, the principal is (typically strictly) better off ifhe can observe his agen t's action. In particula r, future investors are bette roff here if they can see the ac tion (i.e., the contrac t) the ir agents (currentinvestors) select.

The strict Pareto superiority of observable management contracts overunobservable con tracts is puzzling in view of the relatively s parse infor-mation contained about management contracts in proxy statements.What could account for this? One answer is technological; it may beinfeasible to describe all details which determine the (present value ofthe) manager's compensation, since the evolution of his contract fromone period to the n ext is affected by myriad, often unan ticipated, factors.An alternative explanation for the absence of observable managementcon tracts comes from consideration of strategic interac tions am ong firms.Fershtman, Judd, and Kalai [1987] show that the ability of firms toengage in collusive behavior increases when their firms' managers con-tra cts are observable to other firms. (Katz [1987] studies a related model.)When collusive behavior is socially undesirable, prohibitions againstproducing publicly observable contracts may be welfare-enhancing.Whether these desirable effects of unobservable management contractspersist when the strategic context of Fershtman, Judd, and Kalai [1987]is combined w ith the setting of this paper^where contrac t observabilityproduces a positive externalityremains an open question.

Finally, given the differences in welfare attainable between NCE and

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212 RONALD A. DYEOCB equilibria, one might expect that future-period investors would haveincentives to expend resources to discover the (functional form of the)contract between current-period investors and their manager. Surpris-ingly, if any future investor cannot sell what he learns about the contractto other future investors (and hence, can use what he learns only tomodify his own investment decisions), then no investor will pay anypositive amount to determine the contractual relation between currentinvestors and their manager. The reason is that, in equilibrium, theinvestor can infer what contract is offered. Hence, by incurring costs toobserve the contract, the investor only confirms what he previouslyinferredand so observation of the contract does not improve theinvestor's knowledge of the relation between the firm's report and theunderlying value (x) of the firm. Consequently, no utility-maximizingfuture-period investor would every pay these costs of confirming thecurrent-period manager's contract. Thus, there may be a role for man-dated disclosure of the details of management (and related) contracts, arole which is examined in Dye, Balach andran , an d Magee [1987].

We should not expect the earnings announcement policies generatedby the internal and external demands for earnings management to bealways as closely aligned as they are under Proposition 2's hypotheses,or to be independent of the observability of management's contract tosubsequent generations of investors. In Proposition 3 below, we explorethe potential for differences in earnings announcement policies arisingfrom these distinct sources of demand for earnings management, bygiving managers the opportunity to issue two earnings announcements,one private (to current shareholders) for purposes of performance eval-uation a nd com pensation, and one public, designed to influence prospec-tive investors' perceptions of the value of the firm.The results presented in Proposition 3 below depend on how themanager's personal cost of earnings management c(x, y, e) and thecorporation's cost of earnings management l{x, y, t) vary with themanager's private and public earnings announcements. In this proposi-tion, we posit that the managers' personal cost of earnings managementdepends on their private rep orts, since they can be expected to bear somepersonal costs whenever they alter their private earnings announcementsto influence their compensation. Whether these private announcementsalso generate corporate costs of earnings management is case-specific,e.g., altering the timing of the recognition of revenues and expenses toaffect the private earnings figures may be costless to the corporation(excluding the effect on management compensation), whereas alteringthe firm's inventory policy for the same purposes may be costly. Conse-quently, we analyze separately the cases in which the corporate costs ofearnings management are affected by the manager's private announce-ments or his public announcements.

PRO PO SITIO N 3.1. When manag ement contrac ts are publicly observa-

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EARNINGS MANAGEMENT 213ble (the OCE case), and when both the corporate (/) and managementic ) costs of earnings manipulation are a function of the earnings an-nouncements made in private, then no generation of investors obtainsany advantage by having managers issue distinct public and privateearnings announcements.

P R O P O S I T O N 3.2. When management contracts are publicly observable(the OCE case), and w hen the corporate costs il) of earnings manipulationare a function of earnings announcements made in public, whereas theman agem ent costs (c) of earnings mana gem ent are a function of earningsannouncements made in private, investors may seek to have distinctpublic and private earnings announcements. In particular, under theadditional hy potheses of Proposition 1 above, earnings m anagem ent inprivate will occur, although there will never be any manipulation ofpublic earnings announcements when [(x, y, t) 9^0 for y ? x.P R O P O S I T I O N 3.3. Suppose th at, as in Propo sition 3.1, both th e cor-porate and management costs of earnings management depend on themanager's private earnings announcements. If C2(x, x + t, e) = oo, thenfor any stationary NCE whose current-period market-clearing price isstrictly increasing in the current-period earnings announcement, thecurrent generation of investors will have their manager issue distinctpublic and private earnings reports.Proposition 3's conclusions follow directly from the rationality offuture generations of investors. When management contracts are observ-able, current investors do not fool future investors by having distinct

public and private earnings announcements when all costs of earningsmanagement derive from earnings announcements which future investorsdo not see. In this case, future investors use the public earnings an-nouncement solely to update their knowledge of both the realized valueof X and the actual corporate costs of earnings management; on average,their expectations will be correct and the amount they will pay for thefirm will be independent of whether the public earnings announcementpolicy is distinct from the private earnings announcement policy. In thiscase, public earnings announcements are known to be purely "windowdressing" subject to the informational constraint y t Y{x'; e).In contrast, when the corporate costs of earnings management arise

from public earnings statements (though management costs of earningsmanipulation remain a function of earnings statements made in private),current investors can profit by proposing distinct public and privateearnings announcement policies. In view of the rationality of futuregenerations of investors, current investors can do no better than offertheir manager incentives to reduce the corporate costs of earnings man-agement to zero (e.g., by ado pting a policy of no public earnings manage-ment), regardless of what private earnings announcement policy theyseek to implement. Since we know from Proposition 1 that, for earningsanno unce me nt policies which affect th e man ager's com pensation, a policy

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214 RONALD A. DYEof no earnings management is typically not feasible, it follows (in thiscase) that public and private earnings announcement policies generallywill not coincide.

Comparing Proposition 3.1 and3.3, we conclude that the observabilityof management's contract to subsequent generations of investors alsoaffects the desirability of issuing public and private earnings announce-ments. This is not surprising. When current management's contractcannot be observed by potential investors, current shareholders willdisregard the effects of their choice of compensation schemes on thecorporate costs of earnings management (and hence, on the market-clearing price of the firm) induced by the management's private earningsannouncements. Instead, investors' optimal private earnings announce-ment policy will be chosen to minimize only the costs (which they bear)of getting their manager to select their preferred action. The publicanno uncem ents will be chosen solely for their impact on the firm's price,i.e., for any fixed x, t, the public announcem ent y will satisfy:P(y) = Max P ( y ) , y < x + t. (i)

The policy which attains (1) will not coincide typically with the privateearnings announcement policy which minimizes the expected cost ofgetting the manager to adopt current investors' preferred action. Al-though not presented here, a result similar to Proposition 3.2 holds forNCE. These and related results are summarized in figure 3.4. Income-Smoothing4.1 MODEL DESCRIPTION

In this section, I present a model in which m anagers have two periodsof tenu re in order to study earnings m anagem ent w hich involves shiftingreported income across periods. This model is significantly more complexthan the one studied earlier for two reasons. First, successive time periodsare no longer symmetric in that periods differ depending on how long amanager has been inoffice. Second, the number of decisions the managermust make increases geometrically w ith the length of his tenure in office.W hat insight does this ad ditional complexity reveal? The principal resulthere is tha t, un der very mild assum ptions, income-smoothing (i.e., over-stated earnings are followed by understatements, or vice versa) is inevi-table when investors are incapable of determining the firm's periodiceconomic earning s.We begin with an explicit definition of income-smoothing for a man-ager whose first earnings announcement occurs in period fl.

DEFINITION 6. A two-period announ cem ent policy y,-,( I, y,( ) in-duces income-smoothing if, with positive proba bility:y , _ i ( % , _ ] , t ,- i) < x,-y a n d y , ( x , - i , x, , t , . . , ) > x, or

y , _ . , ( x , - , . t ,- i) > .x,-i a n d y , ( x , ,, x,, e,..,) < x,.

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EARNINGS MANAGEMENT 21 5

c, / both based on privateearnings announcementsOCF

No advantage to distinctreports;Common report (for cho-sen action) minimizesE[s + I] (x' ^ y ^ x' +t'}

Advantage to distinct re-ports;Public report is truthful;Private report (for cho-sen action) minimizesE [ s \ {y = x - )

NC EAdvantage to distinct re-ports;Public report maximizesmarket-price;Private report (for cho-sen action) minimizesE [ s ] { y ^ x ' + * ' )Same as abovebased on private an-

n o u n c e m e n t ;/ based on public an-n o u n c e m e n t

F I G . 3 .Factors contribut ing to current investors ' des ire to have management issuedis t inct public and private earnings announcements . The las t express ion in each box is theoptimal public earnings announcement in the case where c(*) and / () are both increasingin y when the market-clearing price of the f i rm is increasing in the earnings announcement ,for a given realization {x', t'} of {x,, f , ) . For the resul ts in the NCE boxes , cjx, x + f, i) =cc is assumed.

Earnings management as defined in Definition 2 is a necessary butnot sufficient condition for income-smoothing as defined here. Earningsmanagement involves misstatements of income, whereas income-smooth-ing requires understatements (or overstatements) of earnings to befollowed by overstatements (understatem ents).The model setup is as follows. We assume, initially, that the managerconsu mes wha t he earn s in each of the two period s he is in office (thislatter simplifying assum ption is used in much of the m ulti-period agencyliteraturesee, e.g., Lambert [19831 or Rogerson [1985]). New ma nagersare installed in even-numbered periods. If t is even, Xt+, denotes arealization of the firm's economic earnings in period t -\- 1 arising fromthe new manager's first action choice a, (in period t) . As in previoussections, the manager's period t -\- 1 earnings announcement yt+i isconstrained by yt+i < i + i + e^+i, where e,+i is the realization of somerandom variable privately observed by the manager.F or income-sm oothing to be viable, investors born in period t + 1mustnot learn the actual value of x,+i subsequent to hearing the manager'sreport and purchasing shares in the firm. This poses a serious problem:what utility do these investors get from owning the firm, apart from itsexit value? One could assume these investors have (loosely speaking)rational expectations and that they get utility from the expected valueof the firm's actual earnings of period t + 1. But this is not methodolog-ically acceptable because all investors' utilities from ownership shouldbe derived from their utilities over consumption. Instead, I shall assumethat the manager in period t + 1 actually distributes earnings in period t-I- 1 to the young investors of that period in an amount equal to his

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216 RONALD A. DYEearnings announcement for that period. Therefore, I assume that inves-tors of generation ^ -I- 1 get utility from this explicit d istributio n of thefirm's earnings as well as from selling the firm to the next generation ofinvestors. Thu s, the period t + 1 earnings annou ncem ent is, for all inten tsand purposes, a declaration of dividends.The manager takes another action a,.n in period t + 1 (which willdepend typically on the realization x,+, and the announcement v,+ ;) ,thereby generating a distribution for x,+^, the firm's period t + 2 earnings.In period / + 2, the manager makes another earnings announcement y,+:!-Clearly, the range of feasible announcements y,+. should depend on theactual period t + 2 earnings x,+2 as well as any undistributed (or, ifnegative, overstated) earnings x,+, - 3), + , of period t + 1. There are avariety of ways to combine these constraints. I shall assume y,.-j< x,^,+ x,-t2 yi+i. That is, I assume (cumulatively) conservative earningsannouncements are undetectable, whereas overly liberal announcementsare found out.''

Subsequent to purchasing the firm, investors born in generation t + 2learn the actual value of the sum of period t + 2 earnings and previouslyundistributed earnings x, ,2 + x,+ i - 3}^,, and th en they h ire a newmanager and the cycle repeats itself In every even-numbered period t(when a new manager is hired), the investors born in that period learnX,, whereas in every odd-numhered period, investors born in that periodlearn about that period's actual earnings only by gleaning informationfrom the manager's reported earnings. This artificial cyclical asymmetryin investors' knowledge of the firm's actual earnings is just a simple wayof approximating the more typical situation in which investors' knowl-edge of the firm's financial condition varies over time (due, say, to thetime elapsed from the firm's last audit).

A (new) manager hired in period t has time-separable preferencessumm arized by U(c,+ i) ~ gia>) + fi[iUic,+2) - gia,+i)], when he takesaction o, and consumes c,+i, tor T = t, t + 1. fi is his personal discountrate.Most of the rest of the model's description is contained in figure 4 andpoints (l)-(6) below. These six points explain the equilibrium in a"hackward dynamic programming" format: the last thing the managerdoes in his second period in office is described in point (1), next to lastin point (2), etc.

" Notice that, in contrast to tbe assumption made for period ( + 1,1 assume no privateerror term, f,,,,, exists. One story for tbis runs as follows: while a manager is m office, hemay have the option of shifting income across periods. In the manager's last period inoffice, however, the m anager may have to "pu t his house in order": unjustified accrualscould be detected by the newly installed management and result in tbe previous managerbeing punisbed. Alternatively, tbis could be considered as tbe defining condition of aconservative "income recognition" rule, in which cumulative income recognized does notexceed cumulative casb flows over long enough time horizons. See also Antle and Demski[forthcoming].

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S 6I Sfi I-- C O

T301t >.>- '^

(D- 9 -

I-:u +^r- --2 >

?) 03

G =" .2 ^:? s cbO n iS 03 U

c (B _ c g >O be +j

O ? 0) - I - WJ fi i I-

I S

t I HI

_ ! li f i

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21 8 RONALD A. DYEPeriod t + 2 earnings management policy. (1) Taking the previousperiod's actual earnings x,+ i and reported earnings y,,, as given, uponlearning period t + 2's actual ea rning s :c,+2, the incum bent managerchooses his utility-maximizing last period report y,+,, subject to theconstraint y,+ , +y,+. < x,-+, + x,+2.Period t + 1 action policy. (2) Taking the reporting strategy describedin (1) as given, the incumbent manager chooses his last-period actiona,-M optimally, conditioned on the previous period's actual earnings andreported earnings.Period t -\- 1 earnings management policy. (3) Taking his last-periodaction and earnings management policies as given, upon learning theperiods + 1 values of %,+i ande,+ i, the manager chooses reported earningsyt+i to maximize the sum of his current period and discounted expectednext-period utilities, while also considering the dependence of his periodt + 2 contract on his period t-\-l earnings report, subject to the cons traint

yi+t < x,+i + ( ,+] .Period t action policy. (4) Taking the policies described by (l)-(3) asgiven, the ma nager's in itial action choice maximizes the discounted sumof the expected utilities over the two periods he is in office.Contract choice. (5) Taking the manager's behavior (as described by(l)-( 4)) as given, each generation of investors selects the contract for themanager which maximizes the expected proceeds they receive from thesale of the firm to the next generation of investors net of the manager'scompensation, while taking the contracts of all other generations as

given, subject to the contraint that, regardless of the realizations of anyrandom variables, the manager's periodic expected utility is at least 0.Consistent expectations. (6) The behavior of each generation of inves-tors and managers coincides with the behavior other generations ofinvestors and managers perceived that generation would adopt, and thepricing rules are correct (i.e., they satisfy recursions analogous to thosein the definition of an unobservable con tract equilibrium in the previoussection).4.2 ANALYSIS

Proposition 4 provides sufficient conditions for income-smoothing tooccur.PRO POS ITION 4. If:

( i ) c=l = O;iii) no generation of investors ever seeks to have their firm's m anagerexert the minimum possible effort level;(iii) every optimal earnings announcement-contingent contract is dif-ferentiable in the earnings announcement;iiv) no generation of shareholde rs can commit subsequent generationsof shareholders to adopt previously defined management con-tracts;

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EARNINGS MANAGEMENT 21 9(v) the earnings process \x,\ satisfies:

x,+i = ax , + /32,+i + i+i, w h e r e

Zf-,-1 ~ q{zt+i\a), \t\ i s iid, a > 0 , and\q{zt+i I a) I a ( A j is an MLRP family;

then income-smoothing occurs in every NCE and every OCE wheremanagers have two periods of tenure, even if {I, \ is degenerate, providedthe manager's discount rate ii is sufficiently close to one.Th e proposition illustrates tha t income-smoothing may be expected tooccur for several time-series processes. The essential idea of the proofcan be conveyed by considering the case where Xi is iid. It can be shownthat, for income-smoothing not to occur in this case, the manager mustdistribute all of the firm's earnings to shareholders at the end of his firstperiod in office. If he does so, the optima l one-period con tract th e "next"generation of shareholders will offer th e m anager is the same as the one-period contract his first employers offered. The reason is that themanager is endowed at the st art of both periods with the same productiontechnology and the same (zero) initial level of undistributed earnings.Bu t, if the m anager is offered a sequence of identical one-period con tracts,he will be tempted to engage in income-smoothing to achieve (personal)consumption-smoothing, so the assum ption th at income-smoothing doesnot occur leads to a contradiction.Insight into the causes of income-smoothing in Proposition 4 can beobtained by considering the "internal" and "external" demands forsmoothing when the time-series process is iid. If the m anager's discretionin action choice is eliminated , an externa l deman d for income-smoo thingderives solely from shareholders' attempts to increase the price of thefirm by distorting the earnings re ports . For even integers t, the constrainty(+i + yt+2 ^ Xi+\ + ^1+2 prevents the manager from overstating the sumof period t-l- 2 earnings (x,+:!) and previously und istrib uted earn ings {x,+i- y^+i)- Con sequently, in the iid case, the period t + 2 market-clearingprice of the firm will be strictly increasing in the report yt+2, so the old

investors of generation t + 2 will want their manager to announce thelargest report possible. It then follows that income-smoothing occursover the time interval t + 1 to f -t- 2 if and only if earnings man agem ento c c u r s int + 1, s i n c e yt+2 = Xi+i + x,+2 y,+ i i m p l i e s yt+2 ^ Xt+2 as y,+ , ^x,+i. But, the question of when the old investors in t -I- 1 wish theirmanager to engage in earnings management is the one-period problemanalyzed in section 2, so we have the following result.

COROLLARY 1. If, in the model of this section, the manager has nodiscretion in action choice, the earnings process is iid, and for each t, Xt,and ,, Yixr, t,) contains a neighborhood of x,, there is an external

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22 0 RONALD A. DYEdemand for income-smoothing if and only if the earnings announcementpolicy investors instruct their manager to adopt during his first periodin office is not observable to subsequent generations of investors.'"

The existence of an external demand for income-smoothing does notprovide a complete explana tion of Proposition 4, because Proposition 4'sconclusions are not predicated on the observability of the manager'sannou ncem ent policy (more generally, con tract). So we now consider theinfluence of the existence of an "internal demand" for income-smoothing.The re are two principal differences between the definition of an interna ldemand for income-smoothing and the definition of an internal demandfor earnings management introduced in section 2: first, it is defined withreference to the manager's implementation of a two-period action policy;second, to be consistent with the assumption maintained here that onegeneration of investors cannot precommit subsequent generations tocontracts with their manager, we assume that the two-period contractswhich induce the manager to adopt a particular action policy are chosensequentially, each subject to the restriction that the manager's periodicutility exceeds U.To study the internal demand for income-smoothing, we make use ofthe following lemma.Lemma. Given any two-period contract S/+i(y,>i), s,+^ (>',+ >) which getsa manager to adopt the action policy (a,, a,+ i), there exists anothersecond-period contr ac t ,9,"+2 such tha t th e con tract pair ,s,+ i, s',+-> (1)provides both shareholders and the manager the same utilities as they

obtained under the original contract pair, (2) implements the actionpolicy (a,, a,+]), and (3) sl^-, is increasing in y,+2.The lemma states that, by evaluating contracts only in terms of theirexpected costs of compensation, no generation of shareholders is madeworse off by giving the manager a contract which is increasing in hisreport for his last period in office. Consequently, no generation ofshareho lders' cost of com pensating th e m anager is increased by assumingthat the manager implements the second-period announcement policyy, , ^ x,+ i -I- x,+v yi-n. But, from the preceding discussion, we alreadyknow that the exit value of the firm to the old shareholders in period t-F 2 obtained by using this announcement policy yi.f.2 is strictly higherthan with any other policy. These two results establish the uniqueoptim ality of the policy y,., 2 = x,+ i + Xi+.> - y,+ i in the original problemregardless of the observability of the manager's contract.

As was noted above, if the period t -h 2 contract takes the form y^ j (asjust defined), income-smoothing does not occur over the interv al t + I tot -\- 2 if earnings management does not occur in t 4- 1. In that case, themanager start s his contract with investors born in / -I- 1 without any'- Co rollaries 1 and 2 and the following lemma are proved by using arguments similar tothose used to prove Proposition 4 and are not reproduced here.

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EARNINGS MANAGEMENT 22 1undistributed earnings, just as at the start of t. Hence, whatever actionwas optimal for the generation born in t to induce the manager toimplement must similarly be optimal for the generation born in t + 1,and both generations offer the manager the same contract. However,offering such a pair of identical con tracts produces incom e-smoothing bythe manager. Specifically:

COROLLARY 2. If a manager is given the same nonconstant contract ineach of two successive periods t + I, t + 2 and Yix,+u ft-n) contains aneighborhood of x,+ , for each X,M, then he will engage in income-smoo thing provided his discount rate is sufficiently close to one.This corollary depends on the separability and time-stationarity of themanager's preferences. If the manager's second-period utility from con-sumption depends on his first period's consumption, or deviated in someother significant way from his utility for consumption in the first period(as would be true if his discount rate were significantly different fromone), then the corollary might not hold.In summ ary, we see tha t "ex ternal dem and" concerns preclude income-smoothing only if no earnings management occurs at the end of thema nage r's first period in office. Th is, in conjunction with the station arityof the environment, makes each generation of investors request themanager to adopt the same action choice. Finally, we note that anyefficient contract pair which induces the manager to select this constantaction policy and the second-period earnings anno unce me nt policy ,+^;generates an internal demand for income-smoothing. So the income-smoothing documented in Proposition 4 rests on the interaction ofinternal and external demands for income smoothing.Proposition 4 is explicit in not requiring the manager to experienceblocked communication of either t, or his compensation scheme forincome-smoothing behavior to emerge. Blocked communication is notcrucial here, although it was in previous sections, because no generationof shareholders is presumed to be able to precommit other generationsof shareholders to multi-period management contracts. If they couldenforce such contracts, then the conditions under which the RevelationPrinciple would not apply (i.e., income-smoothing would prevail) wouldconsist of the same blocked communication conditions discussed inprevious sections. Without the protection obtainable from multi-periodcontracts, the manager may not be willing to reveal earnings truthfully,even if no communication channels are blocked because the managercould anticipate that earnings disclosures might affect the design ofsubsequent management contracts and thereby adversely affect his ex-pected utility.4.3 EXAMPLETh e demonstration in Proposition 4 that income-smoothing must occurdoes not provide much indication of what form the income-smoothing

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222 RONALD A. DYEwill take. The following example i l lustrates a two-per iod manager ' sop t imal income-smoo th ing behav io r . ' '

L et a two-per iod manager born in period t have t ime-separable uti l i tyfunction (./(c,+ i) g(a,+,-t) = a:c,+ i 57+1 fcaf+,-i,forposi t ive constan ts , ,

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EARNINGS MANAGEMENT 22 3This example also illustrates what modifications must be made to the"reporting set" Yix,+,; 6,+,) to get alternative forms of income-smoothingbehavior. For example, if we define:

i t is easy to show, when the hypotheses of this example continue to hold,th a t the o pt imal earn ing s man age me nt pol icy y ,+i ( ) takes the form:

fx,+i + c,-n, if Xi+i + (,+i < y= y .

When th ere are two-sided con straints on the manager's earnings reports,he overreports when realized earnings are low and underreports whenrealized earnings are high, consistent with conventional notions of in-come-smoothing.4.4 INCOME-SMOOTHING AND CAPITAL MARKETS

The preceding analysis was conducted under the assumption that theman ager had no access to capital ma rkets . Although this is a conventionalassumption in the multi-period agency literature, it is obviously notrealistic. Since income-smoothing was shown to be a device to facilitateconsumption-smoothing in the preceding section, one might suspect thatif the manager is capable of borrowing and lending on his own account,then income-smoothing would no longer occur. The purpose of thissubsection is to present an example which demonstrates that this con-jecture is not correct.In this example, the manager's preferences for consumption and effortare posited to take the form:

, a/) + fiUic,+-2, a,+,) (2)where:

i, a,) = -exp[-r(c,+, -The manager's utility function is time-separable with constant absoluterisk-aversion and multiplicative (rather than additive) disutility fromeffort. The purpose of this specification of preferences is (1) to ensurethat the manager's second-period effort choice is unaffected by anysavings left over from his first period in office (the constant absoluterisk-averse utility function assures the absence of such wealth effects)and (2) to make the manager's second-period individual rationalityconstraint "sensible" in the presence of borrowing and lending fromprevious periods. In the second period, the manager's willingness toaccept the firm's contract should not be influenced by how much he hassaved from the first period, but rather by the utility the contract itselfprovides. Thus , for exam ple, if the m anager saved $ VV (with interest) for

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22 4 RONALD A. DYEconsumption in period t + 2 and was offered the second-period contracts{x,.t-i}, it is inappropriate to write the second individual rationalityconstraint as:

E[Uis(xn2) + W, a,+,)] > U. r.])Instead, this constraint should be written:

i>,-j), a,.,d] ^ U,even though the manager's total expected utility in period / + 2 is givenby the left-hand side of (3). The negative exponential utility functionmakes feasible the decomposition of the manager's expected utility intothat derived from his employment contract and that derived from hisprevious savings. (Unfortunately, most risk-averse utility functions donot have this property.) W ith these specifications, and assum ing that themanager can borrow and lend any amount on the capital market atinterest rate I) 1, we have the following result.

PROPOSITION 5. (a) If the manager's preferences and second-periodindividual rationality constraint respectively take the forms given in (2)and (3) above, and assumptions (i) - (v) of Proposition 4 hold, then anecessary condition for the manager not to engage in income-smoothingwhen he has access to capital m arkets is tha t his compensation functionbe a linear function of earnings, whether or not {e,| is degenerate, ib ) If,further, the manager's first-period consumption sometimes exceeds hisfirst period's compensation, then the manager will engage in income-smoothing whether or not his compensation function is linear.This result demonstrates that access to capital markets will noteliminate income-smoothing in general. The reason is that when themanager has access to both capital markets and income-smoothing tofacilitate consumption-smoothing, he will typically use both to takeadvantage of any differences in their rates of return. Investing $1 in thecapital m arket today will yield the m anager $h tomorrow. If the managerwere to income-smooth when his first period's earnings realization isx,+ i, he can reduce his consumption today by $1 and get back tomorrowthe uncertain return s,+2ix,+-2 + co), where s,+i(x,+ ,) - .s,-n(x/-, i - w) = $1 .For the manager never to seek to engage in income-srroothing when hehas access to capital markets, the rate of return 3 must be identical tothe rate of return s,^-,ixM2 + < ) (appropriately adjusted for the latter'sincreased riskiness) for every x,+ i; if the latter return were even greater(less) than 3, the manager would be inclined to save (borrow) more thanhe would if he only had access to capital markets. When the manager'scompensation scheme is nonlinear, it is possible to show that there arealways some profitable intertemporal transfers to engage in via income-smoothing. When the manager's compensation scheme is linear in hisperiodic earnings report, the rate of return on income-smoothing isconstant, just as the rate of return in the capital market is constant, and

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EARNINGS MANAGEMENT 22 5SO, in this linear case, it is possible th at augm enting the m anager's abilityto transfer consumption intertemporally via income-smoothing may notincrease his utility beyond that achievable by his participation in thecapital market. But, even in this linear case, if we knew that themanager's first-period consumption sometimes exceeds his first period'scompensation, we can conclude that the manager must income-smooth:the discount rate on income-smoothing is zero (a $1 reduction in com-pensation today is offset by a $1 increase in compensation tomorrow ifthe sam e linear com pensation schedule is in effect both periods), whereasthe discount rate in the capital market is positive. Hence, the managerwill borrow via income-smoothing (transferring the firm's earningsandhence consumptionforward, when the compensation function is in-creasing) and save via the capital market.5. Conclusions

This paper identifies two distinct sources of shareholders' demand forearnings management: an "internal" source, intended to minimize theexpected cost of getting a manager to adopt shareholders' preferredaction, and an "external" source, based on current shareholders' desireto influence prospective investors' perceptions of their firm's value. Theexistence of the internal source of earnings management was shown tovary systematically with the ability of managers to communicate alldimensions of their private information. In contrast, the existence of theexternal source of earnings management was shown to vary systemati-cally with the ability of prospective investors to observe the contractualrelationship between current shareholders and their management. Inaddition, both sources of earnings management are affected by thedependence of both the corporation's and the management's (personal)cost of earnings managem ent on the manager's earnings announcem ents.In addition, the model of section 4 illustrates circumstances under whichincome-smoothing is sustainable as equilibrium behavior.Several economic forces which could impinge on income-smoothinghave not been considered here. There is no labor market on whichmanagers could develop reputations for not managing earnings, nor hasconsideration been given to explanations of earnings management basedon the bounded rationality (see, e.g., Simon [1955]) of either current orprospective investors. Limits on the rationality of either group of inves-tors could generate earnings management, of course. The analysis hasbeen undertaken within the "mechanism design" paradigm (see, e.g.,Hurwicz [1972]). In the present context, this implies that current andprospective owners rationally anticipate the earnings management in-duced by management compensation schemes and adjust their actionsaccordingly. Whether the "mechanism design" approach taken here issuperior to this "bounded rationality" alternative remains an open ques-

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226 RONALD A. DYEtion, since a formal, operational theory of the latter has yet to bedeveloped.There are several earnings-related questions which this paper leavesunanswered. No explanation of large write-offs to earnings is provided,nor is the reluctance of firms to divulge all details of their manager'scompensation rationalized. The latter phenomenon is particularly puz-zling, because it can be shown in the context of this paper tha t the re arestrict welfare gains for current shareholders to disclose the details ofmanagement compensation arrangements. There must be powerfulforces, such as the possible proprietary losses arising from compensation-related disclosures, opposing these gains from disclosures, which are notmodeled here. This paper also has not explored the relation between theinterest rate investors use to discount a firm's cash flows and the firm'searnings management policy. Such an exploration would be helfpul inexamining claims that investors employ a higher interest rate to discountthe cash flows of firms whose time series of earnings are volatile." Andno analysis of the earnings management policies adopted by very long-lived managers (to reflect the typical case in which the tenure of managersexceeds the tenure of a typical stock in an investor's portfolio) has beenundertaken.

Extensions of the model developed in section 4 may he useful inimproving empirical studies which attempt to document income-smooth-ing behavior. Conventional studies merely establish whether the timeseries of earnings exhibits certain statistical properties, such as negativeautocorrelation (see, e.g., Ronen and Sadan [1981]). But such studiesignore the usefulness of market reactions to earnings announcements inobtaining estimates of the magnitude of earnings management. Modelsof income-smoothing may help create estimates of the market's assess-ment of the am ount of earnings m anagem ent as a function of the observedstock price reactions to earnings announcements. The time-series prop-erties of these estimates (rather than total earnings) may then provideevidence about managers tendencies to smooth income.

Finally, it should be noted tha t th e "financial" overlapping generationsmodel developed here may be useful for studying a variety of phenomenaother than earnings management, such as determining the factors whichcontribute to managers' alleged emphasis on short-run performance, orevaluating the relative merits of alternative earnings measures. Thisoverlapping genera tions framework is well suited for such studies, becauseit embeds the principal-agent contracting problem into a capital marketsetting.

'' See Trueman and Titman [fortbcoming] for an analysis of tbis effect.

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EARNINGS MANAGEMENT 227APPENDIX A

Earnings ManagementProof of Proposition 1

O bs erv e , f i r s t , t h a t s inc e c (x , , y , , e,) > 0 fo r a l l y, and c(Xf, Xt, (,) = 0:- c{x,, y, e,) ! v=r = 0.^y

Cons equent ly , i f s ( ' ) i s the contr ac t offered to the m anager , to obta in noearnings management , i . e . :X, E arg ma x s( y) c(xj, y, t , ) (with prob abil i ty one)

y e Y{x,,i,)we would require that the following first-order condition be satisfied:

But this implies:TT [s{y) - c( x, y , e,)] | :=.,, = 0.dy

,s(y ) | ,_ , , = 0dyfor every possible realization of X/. This can only happen if s(y) is a wagecontract, which will fail to get any action other than a implemented.Proof of Proposition 2

(i) The proof for OCE is trivial: let a* attain Max\E[x | a] - w{a)\ and11, Adefine u hy v = {E[x | a*] ;(a*))/r. Set y(x, t) = x + ( and P{y) =

E[x \a*, y = i + U + 1^/(1 + r) . Given this specification of P{'), it isclear that a* is the "right" action for current shareholders to adopt, sincethey wish to choose a to maximize E[P{y{x, e)) | a] w(a). Theseremarks, in conjunction with {iib) below, which shows that the policyy(x, () = X -h ( is a cost-minimizing announcement policy regardless ofwhat action a the manager is directed to take, complete the proof of (i).

{ii) The proof for NCE runs as follows: if future investors believecurrent investors induce their manager to adopt the earnings announce-me nt policy y(x, t) = x + t, then current investors will in fact adopt thatannouncement policy because:{iia) that policy maximizes the price of the firm for every realization(x, i) of (x, t) , as E[x \ X + e = y, a] and therefore P{y) ^ E[x \x + i y, a] + v/il + r) is easily shown to be increasing in y for any realization{x , e) of (x, e) (no matter what action a t A future investors believe the

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22 8 RONALD A. DYEmanager adopted) andy(x, () = Sup Yix; t);

iiib) that policy minimizes the expected cost of whatever action, saya* G A, current investors seek to have their manager adopt: this claimfollows by observing that, given any contract s( ). there exists an increas-ing contract .s*(') which induces the manager to take the same action ashe took under ,s(*) and generates the same expected costs to the currentinvestors.(The contract s*iz) = Sup .s(y) does the job, since, for any ix .

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EARNINGS MANAGEMENT 229maximand in this program is (jointly) continuous in (a, ), so we canapply Berge's theorem to conclude that its set of maximizers, r(a), isupper-semicontinuous. In fact, this set Tia) is convex: let h{y \ a) denotethe density ofy = x+t, given a. h inherits the concavity of distributionfunction condition from x, so, since E[x\x + (= y, a] is increasing in y,the integral part of the maximand is concave in a for any fixed a. Sincewia) is, by assumption, convex in , this implies that the (whole)maximand is concave in a for every o. Hence, the set of mazimizers Via)is convex, i.e., r(') is convex-valued.

Since the agent's action set A is a closed interval, we can now applyKakutani's theorem to establish the existence of a fixed point a* ofr ( - ) - Notice that this fixed point does not vary with u, the hypothe-sized value of the firm to the next generation of shareholders (exclu-sive of current-period earnings). Hence, there is no circular reasoninginvolved in setting u = iE[x \ a*] - wia*))/r. With these specifications,the proof is complete.Proof of Proposition 3

Proof of 3.1. Let v/il + r) denote the present value of the firm to thenext generation exclusive of next period's economic earnings. C onditionalon the realization of x, this value is independent of any policies adoptedby prior generations of investors or managers. If the next generationbelieves that the private (public) earnings management policy adoptedby the prior period management is y(x, f) (y(x, ()), then the market-clearing price of the firm contingent upon the announcement of y is :

E\x - lix, y(x, f), e) -I- t)/(l + r) I a, y = y(x, e)],where a is the action which the next generation of investors can inferfrom observation of the management's contract. Investors of the priorgeneration seek to maximize:E[E[x -lix, y(x, f), 6) + v/il 4- r) I a, y = yji, i)]

subject to:ii) for all (x, (), y(x, t) E arg m ax siy) c{x, y, e)

Hi) oG arg max E[U is{yix, ()) - cix, yix, 0 , 0 I d]iiii) E[Uisiyii, e)) - c(x, y(x , I), i)) \ a] - gia) > Uiiv) for all (x, e), y(x, e) E Yix, t) .

(Since y(x, () does not enter into the manager's contract, he will adoptany earnings announcement policy which the investors who hired himprefer, subject to the public informational constraints iiv).)Since the unconditional expectation of a conditional expectation is the

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