Optimal Internal Control Regulation

Transcription

1 Optimal Internal ontrol Regulation Stean F. Schantl University o Melbourne and lred Wagenhoer University o Graz bstract: Regulators increasingly rely on regulation o irms internal controls (I) to prevent accounting raud. This paper considers a welare-maximizing regulator s task to set the optimal tightness o an I standard. We study an economy with strategic and compliant owners who sell their irms to investors who then make investment decisions based on the inancial report. We show that I standard tightness and the cost o non-compliance are complements i the cost is below a threshold and are substitutes i the cost becomes higher. The complementarity arises because a minimum non-compliance cost is necessary to induce strategic owners to invest in I eectiveness. Once the non-compliance cost grows urther, the optimal standard declines to avoid inducing too much costly investment in the I system. The greater the proportion o strategic owners, the more eective is I regulation and the higher is the welare-maximizing I standard. Keywords: Internal controls, internal control standards, compliance, enorcement, regulation, inancial reporting quality. JEL: D60, M4, M48 9 ugust 07

2 . Introduction Securities regulators, such as the United States Securities Exchange ommission (SE), increasingly rely on regulation o irms internal controls over inancial reporting to prevent raud and increase investment eiciency. For example, in its inancial report 05 the SE emphasizes insuicient internal controls as one area o particular attention in pursuing its goal o enhancing accounting standard compliance (SE 05, p. 35). The Securities Exchange ct 934 requires the management o listed irms to maintain internal controls over inancial reporting to prevent misstatements in inancial reports. The Sarbanes-Oxley ct (SOX), as amended by the Dodd-Frank ct, mandates that a irm s management assesses the eectiveness o internal controls and discloses signiicant deiciencies and material weaknesses. In addition, the auditor is required to veriy management s disclosures. Regulations in many other countries mandate similar requirements or implementing eective internal controls over inancial reporting. However, internal control (I) regulation imposes signiicant implementation and maintenance costs on all irms subject to the regulation, even on irms with a low accounting raud risk. For example, ater the enactment o SOX many irms decided to go dark (Leuz, Triantis, and Wang 008) or go private (Engel, Hayes, and Wang 007) indicating that SOX imposed signiicant compliance costs on irms. Further Krishnan, Rama, and Zhang (008) provide evidence showing that a large part o compliance costs caused by SOX is attributable to the establishment o sophisticated internal control processes. This paper studies (i) under which conditions I regulation is welare-enhancing and (ii) how tight an I standard should be set given a compliance mechanism to enorce such a standard. We consider a regulator whose objective is to maximize social welare, which comprises the economic wealth created by irms less the direct costs o implementing and maintaining I systems. onsidering both the beneits and costs o I regulation is important Substantial compliance costs were the main reason that smaller irms were later exempt rom SOX.

3 to assess how particular regulation aects inancial reporting quality and investment behavior and to provide guidance on how I standards should be set. We consider an economy with irms that dier in their productivity ollowing, among others, Schwartz (997), Dye (00), and Lu and Sapra (009). Firms are sold or generational reasons to new investors in the capital market. Investors use the inancial reports to update their belies about irm productivity, which is important or their investment decision in a growth opportunity the irm oers. nticipating their investment, they determine the price they oer to acquire a irm. Financial reporting thereore has a direct eect on investment and welare, which implies that inancial reporting quality is an important actor in this economy. There are two types o irm owners, owners that are compliant with standards and regulations and others that are strategic and choose whether to comply or to deviate in order to maximize their expected wealth. The strategic owners may engage in costly manipulation o the inancial report to achieve a higher price or their irm. The likelihood o success o manipulation decreases in the eectiveness o the I system they have previously implemented. Strategic owners can also choose not to comply with I regulation. We establish that strategic owners always underinvest in I eectiveness relative to a given I standard. This result is reminiscent o a shadow standard in the sense o Dye (00). I underinvestment by strategic owners is driven by two actors: (i) compliance costs and (ii) the beneit rom the increased success probability o uture manipulation. The latter actor can be so strong that strategic owners do not implement an I system at all. Once the costs o non-compliance with I regulation (reputation or I enorcement costs) exceed a certain threshold, strategic owners will invest in the eectiveness o the I system. Through its eect on the implemented I system, a higher I standard increases equilibrium reporting quality, the transaction price, and investment eiciency. Surprisingly, it does not necessarily reduce owners manipulation eort because owners trade o the cost o manipulation with the beneits that arise rom greater sensitivity o the price and the reduced cost o direct enorcement that ollows rom the greater reporting quality. We also ind that direct public

4 enorcement has a reinorcing eect on I eectiveness through mitigating I underinvestment incentives, which in turn alleviates the necessity or stringent I regulation. We then determine the welare-maximizing tightness o the I standard. We emphasize that I standards and the non-compliance costs imposed by I enorcement are inherently linked. When strategic owners I underinvestment incentives are stronger than the non-compliance costs rom enorcement o the I standard, I regulation is strictly welare ineicient because strategic owners do not implement an I system, while it (unnecessarily) imposes compliance costs on compliant irms. Given that the proportion o compliant to strategic owners is suiciently small and when I non-compliance costs lie beyond a certain threshold, the optimal I standard prescribes the maximal eectiveness; and i they increase urther, there is another threshold beyond which it becomes optimal to lower the I standard since the induced compliance costs become very large. Intuitively, setting the highest I standard complements the eect o intermediate costs o non-compliance rom I enorcement to induce strategic owners to invest in an I system. In contrast, i the proportion o compliant to strategic owners is small either no I regulation or an I standard that is not too high is welare-optimal. The reason is that compliant owners compliance costs represent costs o I regulation without a corresponding beneit and too tight an I standard would lead to excess costs that are socially ineicient. Our paper has important implications or regulators. For example, the SE s current strategy is to enorce I regulation through external auditors and reporting o I weaknesses and deiciencies (han 06) and relies, to a large extent, on irms reputation to comply with the regulation. The combined evidence provided by shbaugh-skaie, ollins, Kinney, and LaFond (008), Beneish, Billings, and Hodder (008), and Doyle, Ge, and McVay (007a) is in line with the argument that irms with reported I weaknesses publish lower quality inancial reports and ace a higher cost o capital. However, the reporting o I weaknesses by managers and auditors as required under SOX Sections 30 and 404 reduce irms incentives to underinvest in Is, but does not ully eliminate these incentives. One implication o our 3

5 model thereore is that without proper I enorcement that contributes to outweighing strategic owners I underinvestment incentives by imposing suiciently large noncompliance costs, any I regulation is strictly welare ineicient as it imposes excessive compliance costs on irms with low manipulation risk. second implication o our paper is that the optimal tightness o I standards crucially depends on the composition o irms in an economy: when irms corporate governance and culture is generally law abiding, too tight I standards lead to excess compliance costs on the large proportion o compliant irms, thus reducing social welare. Our paper has also implications on the relation between I standard tightness and I enorcement. onventional wisdom suggests that a tighter I standard requires a stronger I enorcement implying that stronger enorcement allows the regulator to set a tighter standard. Our analysis shows that this intuition is incomplete: the optimal tightness o an I standard and the strength o I enorcement are complements i non-compliance costs are low, but substitutes i they are large. Low enorcement does not provide suicient incentives to implement an eective I system; hence, it is only costly to compliant owners and not eicient. Increasing enorcement induces strategic owners to implement an eective I system, but the cost to compliant owners is still so strong that the optimal I standard is set not too high at irst, but then increases in enorcement. Finally, i enorcement becomes suiciently strong, the regulator optimally reduces the standard to trade o greater investment eiciency with higher I implementation costs. With these results, our paper contributes to a better understanding o the actors that determine the desirable tightness o I standards.. Related literature This paper is related to the literature in auditing and corporate governance which studies the eectiveness o internal controls to mitigate manipulation o inancial reports. The literature on the endogenous choice o I systems typically assumes that the manager or the Models with exogenous internal control eectiveness include, e.g., Smith, Tiras, and Vichitlekarn (000) and Marinovic (03). 4

6 owner o a irm invests into the eectiveness o an I system beore the manager observes private inormation and chooses a level o manipulation o a inancial report. Then an auditor perorms I and substantial testing beore releasing the inancial report to outside investors who base their pricing and investment decisions on that inormation. Pae and Yoo (00) identiy conditions under which an increase in auditor liability can exacerbate an owner s I underinvestment incentives and lower audit quality. Patterson and Smith (007) study the eect o an auditor s report o I weaknesses and ind that when managers are penalized or non-compliance with I regulation, they implement more eective Is and manipulate less, although it can reduce the auditor s eort to testing the I system, which ex ante increases audit risk. han (06) studies the eects o the disclosure o I weaknesses i the accounting inormation is used not only or valuation but also to incentivize the manager. He assumes that the owner implements the I system and shows that the disclosure o I weaknesses increases investment in Is and can strictly increase his expected payo. These papers model a strategic auditor as an enorcement mechanism, but take I regulation as given, whereas the present paper investigates whether it is welare-optimal to impose I regulation on irms in the irst place. Other literature investigates additional orces that aect investment in I systems in the absence o auditing. Ewert and Wagenhoer (07) ind that a more conservative accounting system enhances the incentives o managers to invest in more eective I systems, thus curbing their own beneit o manipulation. Gao and Zhang (06) show that a manager s observable investment in an I system creates a positive externality or peer irms because managers manipulate more i they expect other irms to manipulate more. Since irms do not internalize this eect, they ex ante choose a less eective I system. Gao and Zhang use this insight to argue that regulation o I system choice can strictly improve social welare. In contrast, we show that I regulation can be strictly welare decreasing. Our paper is also related to the literature on optimal regulation to ensure compliance with accounting standards. For example, Friedman and Heinle (06) study a cash diversion problem in which an insider diverts cash, which is harmul to outsiders and overall impairs 5

7 social welare. social planner chooses the strictness and uniormity o a regulation, where the regulation resembles exogenously given I regulation that detects cash diversion with some probability. They also assume that irms ully implement the regulation. The main ocus o Friedman and Heinle (06) is costly lobbying by irms to inluence the social planner when choosing the regulation and they show that uniorm regulation gives rise to a ree-rider problem, which overall reduces distortions rom lobbying. In contrast, in our paper irm owners strategically decide whether to comply with the I regulation, and this decision is important or the assessment o I regulation s welare-eectiveness. Other papers speciically study the setting and enorcement o accounting standards directly, whereas the present paper studies I regulation as a compliance mechanism to enorce existing accounting standards. Dye (00) studies the setting o an accounting standard that requires classiying events into binary categories, where the manager can manipulate the outcome o the classiication at a cost. He inds that irms apply a shadow standard, that is dierent to the oicially stated standard and considers how sophisticated or naïve standard setters set the classiication threshold. Laux and Stocken (07) study two instruments that jointly inluence inancial reporting, a classiication standard and ex post enorcement. In their model, the manager engages in costly research and development and discovers a project and the classiication accounting system provides inormation about the project to investors who decide whether to inance it. The standard and its enorcement aect manipulation attempts and investment in R&D. Schantl (07) establishes that the penalties incurred by irms rom regulatory enorcement can yield an inversely U-shaped association between the tightness o the accounting standard and irm value as assessed by outside investors. He urther shows that more inormative inancial reporting can coexist with a lower irm value. Gao and Zhang (07) ind that tightening auditing standards can reduce incentives o auditors to acquire proessional expertise. 6

8 3. Model Production technology and reporting system The economy consists o two types o irms, which dier in their level o productivity. Productivity is a result o the availability o special core competences, such as technical expertise, know-how and organizational and process knowledge, and it determines a comparative advantage (or disadvantage) o the irm in undertaking projects. With equal probability, productivity can be high ( = ) or low ( = 0). Productivity aects the value o existing assets and that o a growth option. The growth option consists o the opportunity to realize an investment project that yields an expected project return o I rom an investment volume I. The production technology is similar to that used in Schwartz (997), Dye (00), and Lu and Sapra (009). The irm s shares are held by a representative owner who also acts as the top manager o the irm (the owner or previous owner ). The owner must sell the irm to investors or lie-cycle reasons beore being able to realize the investment opportunity. For example, investing requires an amount o capital the owner is unable to raise due to a short time horizon. Beore selling the irm, the owner issues a mandatory inancial report that is inormative about the irm s productivity. The inancial report is denoted by r {r L, r H }, where r L indicates a low and r H a high productivity type, respectively. Investors determine the price o the irm s shares based on the inancial report r and also use the report to decide on the investment volume I. 3 The capital market is perectly competitive and investors hold rational expectations about the irm s productivity. They consequently price the irm s shares conditional on report r at the value o the investment project. The share price is denoted by P(r), where P L P(r L ) and P H P(r H ). 3 We thus assume that the new investors do not immediately learn the productivity ater acquiring control o the irm. reason may be that productivity is multidimensional and hidden in the organization, such that an in-depth understanding o productivity only develops over time. 7

9 To ocus on manipulation o inancial reports, we assume that the preexisting accounting system generates a signal that perectly inorms the current owner about the irm s productivity. This assumption implies that the applicable accounting standards are perect in the sense that they allow and require dierent accounting or dierent productivity. I owners were to report productivity truthully, they would issue a inancial report r H i = and r L i = 0. However, owners can manipulate the inancial report and report some r at a personal cost. For example, an owner may not impair existing assets i productivity turns out to be low. We assume two types o owners, compliant or non-compliant ( strategic ) owners to capture the act that some irms are more prone to deviating rom legal requirements than others. 4 Possible reasons are individual dierences o decision makers and corporate culture. The portion o strategic owner types is q and o compliant types q, where q (0, ], and the type is unrelated to the irm s productivity. Each owner in the economy privately learns her actual type ex ante, but is unable to credibly communicate this act. ompliant types obey regulations and standards as mandated in the regulatory regime and always report the irm s productivity truthully. Strategic owners decide whether to report truthully or to deviate to maximize their expected utility. ny enorcement mechanism is thereore concerned about the decisions made by strategic owners. Owners are risk neutral and their utility equals the expected selling price P less potential enorcement penalties (see below). Because P H > P L (this will be shown to hold in equilibrium), strategic owners have an incentive to manipulate r only i the irm has low productivity ( = 0). We model manipulation as the probability b (0, ] with which strategic owners bias the report so as to report r H ater observing = 0; the success o manipulation depends on the eectiveness o an internal control system as will be discussed below. I =, the accounting system already reports r H and there is no beneit o manipulation. To 4 This assumption allows us to assess the costs o uniorm regulation on dierent types o irms. See also Patterson and Smith (007) or a similar assumption. 8

10 manipulate with success probability b, owners incur a private and unobservable disutility o kb /, where k > 0 parameterizes the disutility. Internal control system Regulation can require irms to establish, operate, and maintain an I system, which assures the quality o inancial reporting. The main unction o the I system is to correct errors and to detect manipulation in the inancial report and, by doing so, to assist in ensuring compliance with the accounting standard. We assume a regulator sets or adopts I regulation which prescribes a certain level o I eectiveness which we shall reer to as I standard and which is denoted by S [0, ]. S = 0 is equivalent to no I regulation. Our regulator can be a single securities regulator who is also in charge o setting and enorcement o the I standard, or it can adopt or delegate these activities to another public or private institution. To comply with I regulation, irms should implement an I system with eectiveness s S. irm is non-compliant with S i s < S; in this case an I weakness arises. Because we assume the underlying accounting system is perect, errors only arise i owners manipulate the report. The eectiveness o the I system is a probability s [0, ] with which the system detects and corrects manipulation beore the inancial report is published. ter observing their types, owners choose the eectiveness s o the I system beore observing productivity. manipulation attempt b o the owner leads to a manipulated report r H with probability Pr(r H = 0) = ( s)b; manipulation is unsuccessul with probability Pr(r L = 0) = ( b) + sb. Implementing an I system with eectiveness s entails a private cost o cs /4 to the owner, where c > 0. osts o complying with mandatory I regulation can be high in practice, as evidenced in studies such as, e.g., Engel, Hayes, and Wang (007), Leuz, Triantis, and Wang (008), and Krishnan, Rama, and Zhang (008). ompliant owners do not manipulate the inancial report and the optimal s = 0 because the I system generates no beneit but is costly. However, because these owners are compliant, they implement the standard s = S. Strategic owners choose s by trading o costs and beneits o implementing s. In line with prior literature on I systems (e.g., Smith, Tiras, and Vichitlekarn 000, Patterson and Smith 9

11 007, han 06), we assume that the implemented I eectiveness s and the cost cs /4 are unobservable to the public, so that the investors directly iner neither s nor the owner s type i strategic owners choose s S. 5 The regulator is benevolent and maximizes social welare by choosing I standard S. 6 Social welare comprises the expected wealth generated by undertaking the new investment project and the cost cs /4 o implementing an I system with eectiveness s. We do not include the owner s disutility o manipulation kb / in the social welare measure because it is socially undesirable. ny non-compliance costs such as penalties are direct wealth transers and do not aect social welare. ompliance mechanisms Enorcement o the accounting standard relies on a direct regulatory enorcement mechanism and the I regulation. These mechanisms can be in the responsibility o a securities regulator or other public or private enorcement bodies, or they can be let to market orces, e.g., by prompting a reputation loss o the owner. The SE is an archetypal example o a regulatory institution that is in charge o the quality o inancial reporting and has the power to set standards and enorce them. It can perorm certain tasks by itsel, but can also delegate them to other institutions that it oversees. It has also the power to inlict penalties or non-compliance with accounting standards and or inadequate I systems. Regulatory enorcement o the accounting standard detects successul manipulation o a inancial report with some probability that is determined by both the probability o (random) investigation and the probability o identiying manipulation. I a violation is detected, the 5 I the eectiveness or the cost o implementing the I system were observable, investors would be able to discern compliant and strategic owners. To avoid that, we assume the cost is a private cost; alternatively, strategic owners who wish to deviate rom S but remain undetected, can pay out the cost cs /4 or some unproductive purpose. 6 related objective o a regulator is the (general) quality o inancial reporting that is induced by regulation and enorcement. This objective is implicit in our analysis as the inormation content o the inancial report is monotonic in the investment eiciency that determines social welare. 0

12 enorcer inlicts a penalty on the irm. Both the detection probability and the penalty size determine the expected penalty > 0, which we assume to be common knowledge. We reer to also as the strength o direct public enorcement o accounting standards. Detected manipulation can also lead to a restatement, but this inormation comes only ater investors acted based on the original inancial report. Thereore, such enorcement lowers the owner s utility o manipulation in expectation. We assume that even though regulatory enorcement ensues ater the sale o the irm to new investors, the penalty is borne by the original owner. 7 That is, i some penalties are inlicted onto the irm ater acquisition, the new owners can reclaim the penalty rom the original owner who was responsible or any non-compliance with the accounting standard. cquisition contracts oten contain contractual clauses with warranty or penalties or any wrong-doings by the previous management. In order to provide owners with incentives to consider the implementation o an I system we assume the existence o non-compliance costs that are privately incurred by an owner whenever s < S. The cost o non-compliance can either be direct penalties imposed by a regulatory enorcer or indirect costs either rom contract provisions or a loss o reputation. 8 We model the cost o non-compliance as a unction o the deviation rom the standard, S s /4, where > 0 captures the strength o the I enorcement mechanism. There is no non-compliance cost i s S. Much o our analysis is cast on the non-compliance cost parameter, which or simplicity we also reer to as non-compliance cost or I enorcement cost. 7 Otherwise, rational investors would reduce the acquisition price by the conjectured penalties, which are a constant in the owner s expected utility that determines the manipulation eort in the irst place. This would lead to more complicated strategies without oering more economic insights. See Schantl (07) or the valuation implications o irm-incurred enorcement penalties. 8 In the current institutional setting in the U.S., a criminal oence is i the owner does not report I weaknesses as required under SOX Section 30 (civil provision) and Section 906 (criminal provision).

13 Sequence o events Regulator chooses I regulation with tightness S. Nature determines the owner s type (compliant, strategic) and owners learn their type. Owners implement an I system with eectiveness s. Nature determines the irm s productivity. Owners observe a perect accounting signal about productivity Strategic owners engage in manipulation b = b() o the accounting signal. Financial report r is publicly disclosed. Firm is sold to new investors at market price P(r). New investors invest I(r) in the growth project. Enorcement o the accounting standard and the I standard occur and non-compliance costs are inlicted on the previous owner. Payo rom investment project realizes and the irm is liquidated. We discuss the signiicance o the model assumptions on our results and alternative assumptions in Section Results 4.. Internal controls and manipulation equilibrium Given the sequential nature o the game, we initially take the tightness S o the I standard as ixed and examine the current owner s I eectiveness and manipulation decisions and the inerence o productivity by the investors (who then choose the acquisition price and investment volume o the growth project). We derive the equilibrium conditions by backward induction and begin with the inal stage in the game, the investors investment and pricing decisions ater they observe the inancial report r. Proos are in the appendix. Investors conjecture that compliant owners do not manipulate the inancial report and strategic owners attempt manipulation only i they observe low productivity, = 0, with

14 probability ˆb, which is successul with probability ˆ 9 b( sˆ ). high report r H is indicative o high productivity, whereas a low report r L is indicative o low productivity, so that P H > P L. onjecturing P ˆ H P ˆ, strategic owners have an incentive to report r H regardless o the actual L. I =, the report r H ollows directly (and the owners have no incentive to underreport) and i = 0 the owners have an incentive to engage in manipulation. This results in the ollowing belies by investors: ˆ Pr( r ;, ˆ H b s) () qbˆ ( sˆ ) and Pr( r sˆ ) 0. report r L perectly inorms that = 0, whereas the probability that = ater r H is observed equals [/( + q), ]. Given these belies, investors choose the investment volume in the growth project, I(r), to maximize the value o the irm by maximizing Pr( r, bˆ ( r), sˆ ) I( r) I( r). () L ; or each report r = r L, r H. This implies I(r L ) = 0 and I( r ) Pr( r, bˆ ( r ), sˆ ) H H H. Note that the probability that the investment pays o, Pr( r, bˆ ( r), sˆ ), ully determines the price because in our payo unction the best the investors can do is to match the investment to the conjectured probability that the project yields a positive return. In a competitive market, the price o the irm relects the expected return rom the uture investment opportunity, which implies P L = 0 and P H ˆ qb( sˆ ) > 0. (3) This conirms the owners conjecture P ˆ P ˆ 0 or all bs, [0,] and the induced incentive H L to manipulate only i productivity is = 0, which underlies the investors ormation o belies. 9 hat indicates the rational conjecture o the respective variable. 3

15 To choose the manipulation eort, strategic owners, upon observing = 0 maximize their conditional expected utility based on the conjectured price P ˆ H, Pr( 0)( ˆ b rh PH ) k = ( ) ˆ b s by k (4) where we use Y (P H ) and Y ˆ ( P ˆ ) or the conjecture o Y. The expected incremental beneit o manipulation is H ( sy ) ˆ, which consists o the price dierential Pˆ Pˆ Pˆ less the expected penalty rom detected manipulation, weighted by the H L H probability ( s) that the I system does not correct manipulation. Manipulation overall pays o only i ( sy ) ˆ > 0, which requires that the enorcement o accounting standards is not so strong as to deter manipulation directly. Hence, owners choose b = 0 i Y ˆ 0. I Yˆ 0, then the b that maximizes (4) equals ˆ b min k ( s) Y,. (5) Inserting b, owners conditional expected utility or = 0 becomes or b < and b =, respectively. ˆ k ( s) Y i 0 ( s) Yˆ k ( 0, ˆ EU Y) ( ) ˆ k s Y i ( s) Yˆ k The owners determine I eectiveness s beore observing the accounting signal over the irm s productivity. Recall that the prior probability o = is /. ompliant owners always comply with the standard, s = S. Strategic owners choose s to maximize the ex ante expected utility, ˆ b s ( S s) Pr( rh ) PH Pr( 0, rh ) Pr( 0) k c (6) 4 4 Due o the act that b is bound rom above by, this expected utility is ( ) ˆ ˆ k s Y s ( S s) P i 0 ( ) ˆ H c s Y k ˆ EU ( PH ) ˆ ˆ ( s) Y s ( S s) P i ( ) ˆ H k c s Y k, 4 4 4

16 which yields ˆ S k Y max 0, i 0 ( s) Yˆ k ˆ c k Y s ˆ S Y ma x 0, i ( s) Yˆ k. c B (7) n equilibrium in this game between the current owner and new investors is deined as ollows. Deinition: For a given S, a perect Bayesian equilibrium (PBE) consists o the investors investment I(r) and pricing rule P(r), the owner s manipulation strategy b, and I eectiveness s such that: (i) Investment volume I(r) maximizes Pr( r, bˆ ( r), sˆ ) I I or r = r L, r H ; (ii) Price P(r) satisies P( r) Pr( r, bˆ ( r), sˆ ) I( r) I( r) or r = r L, r H ; (iii) Manipulation b by the owners is as ollows: ompliant owners always choose b = 0; Strategic owners choose b = 0 i = and chooses b ater observing = 0 to maximize where Y ˆ ( P ˆ ); H Pr( 0) ˆ b rh Y k, (iv) Implementation o I eectiveness s by the owners is as ollows, where b is determined according to (iii): ompliant owners always choose s = S; Strategic owners choose s to maximize ˆ b s ( S s) Pr( rh ) PH Pr( 0, rh ) Pr( 0) k c

17 In equilibrium, all conjectures equal the actual values, i.e., I ˆ( r) I( r), P ˆ( r) P( r), bˆ b, and ŝ s. It is apparent rom (5) that whether ( sy ) is greater or less than k, is important because it directly aects the equilibrium manipulation b. I ( sy ) > k, then the incremental beneit o manipulation exceeds its incremental cost actor, and strategic owners always attempt to report r H (i.e., b = ). On the other hand, i Y < 0, the expected costs rom direct public enorcement o accounting standards, outweighs the expected beneit so that strategic owners never manipulate (b = 0). To ocus on the more interesting cases or our analysis, we restrict the strength o direct public enorcement as ollows: ( q), (8) which ensures Y > 0 and b > 0 or any combination o manipulation and I eectiveness strategies. Notice that there is no similar natural boundary or because as long as < strategic owners will always set s < S (as we discuss later). Thereore, we state our results in relation to k and to capture the level o compliance with the accounting standard and I regulation, respectively. 0 The ollowing proposition establishes existence o a unique equilibrium. Proposition : For a given S, there exists a unique PBE with investors investment choice and price determination P L = I(r L ) = 0 and P H I( rh), (9) qb( s) and strategic owners manipulation and I eectiveness strategies {b, s} set out in Table, where k 0 and 0. 0 lternatively, the boundary or k can also be restated as a boundary on because the threshold is k = P H. 6

18 Table : Equilibrium manipulation and I eectiveness (Proposition ) k k k k ase (a) ase (b) ase (c) k Y c ( S b k Y b ) c k Y s 0 S k Y s c k Y ase (d) b b s 0 S Y s c Proposition establishes the existence o two (unique) thresholds distinguishing the our cases, k and. s shown in Table, the our cases, (a) to (d), are characterized by whether the strategic owners strategies b and s assume interior or boundary values because both b and s are bound to be within [0, ]. I condition (8) holds, the owners always manipulate with some intensity (b > 0). The cost o manipulation captured by the disutility scaling actor k can be so low that the owners always exert maximal manipulation eort (b = ) (cases (b) and (d)). In contrast, when the owners disutility rom manipulation is suiciently large, they choose an interior level o manipulation eort (cases (a) and (c)). The second threshold relates to I enorcement cost. I this cost is low, i.e.,, then the strategic owners do not implement an I system (s = 0) (cases (a) and (b)); otherwise the equilibrium I eectiveness is interior (0 < s < ) (cases (c) and (d)). The cases (c) and (d) are those cases in which setting an I standard has a positive eect on the inormation content o the inancial report and on irm value. We reer to these cases (and subcases thereo) in subsequent analyses. Figure provides an example o the our cases that arise in the equilibrium. First note that when { k k, }, the thresholds separating case (b) rom the adjacent cases (a) and (d) are constants. I either k k or holds, both thresholds are endogenously determined as they both include endogenous variable, which depends on the induced b and 7

19 s, ( ) and k k k ( ). The inormation content o the inancial report increases in s and decreases in b; hence, increases towards the north-east in Figure. Figure : haracteristics o the equilibrium or dierent costs o manipulation k and I enorcement costs (Parameters: c = 3, = /6, q =, S = ) 4.. Properties o the equilibrium In the ollowing, we discuss main properties o the equilibrium. We start with an observation on the implementation o I regulation. Lemma : Strategic owners always underinvest into the I system as compared to the prescribed I standard S as long as S > 0, i.e., s < S. Lemma ollows immediately rom considering the equilibrium s in cases (c) and (d) o Proposition. It is straightorward to see that the incentive to implement an I system or strategic owners arises rom the I non-compliance cost S s /4. Strategic owners would never overinvest (s > S) because it is only the I enorcement cost that induces an s > 0. Thereore, i S = 0, the owners choose s = 0 and need not ear any cost because they 8

20 comply with S. I S > 0, the equilibrium s is strictly less than S in case (d) where k (c), where k k, we have s < S as long as c > 0 (which we assume throughout). Lemma holds or any, and s approaches S i. k ; in case Two actors drive the underinvestment in the I system by a strategic owner. First, the investment is directly costly to the owner. The costs comprise the direct cost o implementing eectiveness s, cs /4. These costs increase in and S, so setting S * = provides the strongest incentive to implement an s > 0. Second, underinvesting in the I system increases the option value o subsequent manipulation attempts. I strategic owners do not implement any I system (s = 0)., this option is so valuable that In the ollowing, we state comparative statics analyses o the equilibrium or variations o the main determining economic and enorcement actors. We begin with a variation o the I standard S, which is important to understand the eects o the optimal choice o the I standard, which we examine in the next subsection. Proposition : Increasing the I standard S induces (i) an increase in the price P H ; the increase is strict i s > 0; (ii) an increase in I eectiveness s; the increase is strict i s > 0; (iii) a decrease or an increase in manipulation b; a necessary condition or an increase is b < and s > 0. Proposition conirms the intuition that a tighter I standard (higher S) induces owners to choose a more eective I system s because higher S increases the cost o non-compliance. This enhances the inormation content o the inancial report and consequently improves investors investment decision and the price they are willing to pay or the irm. However, the induced higher price P H makes manipulation b incrementally more proitable, which again dampens P H and works against the direct eect. Recall that the inormation content is equivalent to the probability that a report r H indicates high productivity, which is. The optimal investment volume is, and this is also the equilibrium price P H. 9

21 Proposition (i) and (ii) state that an increase o S unambiguously increases the price P H and I eectiveness s. I s = 0 in equilibrium (cases (a) and (b) o Proposition ), then a variation o S has no eect, so s and P H are unchanged, which implies the increase is weak in this case. I s > 0 in equilibrium (cases (c) and (d) o Proposition ), s strictly increases in S, which changes investors belies and results in higher investment volume and price P H. However, the tension between the direct and indirect eects is apparent when it comes to the equilibrium manipulation b. In case (d), the owners choose the maximal b = ; hence, b cannot be increased and there is no indirect eect. In contrast, in case (c), where b and s are interior and react continuously to slight changes in the parameters, Proposition (iii) establishes that an increase o S can induce either less or more manipulation b. The latter eect is counter-intuitive and occurs i ( q), given that 3 and k are suiciently low (see the proo). However, even i ( q) manipulation increases the probability that it is successul, the success o manipulation b( s) unambiguously decreases because the eect o the increase in s outweighs an increase in b on price. This implies that owners are less likely to incur the enorcement penalty rom direct public enorcement, which again creates a higher incremental beneit o manipulation. This beneit, together with that rom higher sensitivity o P H, can induce strategic owners to increase b or higher S. The next results provide more insights into the eects o the exogenous variables that determine the economy and the compliance mechanisms in place. orollary : n increase in the proportion o strategic owners q induces (i) a decrease in the price P H ; the decrease is strict i b < and/or s > 0; (ii) an increase in I eectiveness s; the increase is strict i b < and/or s > 0; (iii) a decrease in manipulation b; the decrease is strict i b <. orollary states that the existence o more strategic owners decreases the investment volume and reduces the price, which induces strategic owners to improve their Is and reduce their level o manipulation. The underlying reason is that investors anticipate a lower inormation content o a avorable report r H the more strategic owners are present in the 0

22 economy. Because the price reaction becomes smaller, strategic owners beneit o manipulation declines and mitigates manipulation incentives. It also leads to more compliance with I regulation because the option value rom manipulation declines, so a higher s reduces the I enorcement cost in equilibrium. lthough these eects on b and s again increase the price P H, orollary (i) shows that the inormation content o a report r H and the consequential price are still lower because the direct eect outweighs the indirect eects. The next two results provide insights into the eects o a variation o the strength o the compliance mechanisms. orollary : n increase in I enorcement cost induces (i) an increase in the price P H ; the increase is strict i s > 0; (ii) an increase in I eectiveness s; the increase is strict i s > 0; (iii) a decrease or an increase in manipulation b; a necessary condition or an increase is b < and s > 0. The results in orollary are similar to those in Proposition because the economic trade-os are the same. This suggests a substitutive relationship between the tightness o the I standard S and I enorcement. Overall, stricter I regulation induces implementation o a more eective I standard s, induces more eicient investing, a higher price P H, although manipulation incentives can be higher or lower. orollary 3: n increase in the direct public enorcement strength induces (i) an increase in the price P H ; the decrease is strict i b < and/or s > 0; (ii) an increase in I eectiveness s; the increase is strict i s > 0; (iii) a decrease in manipulation b; the decrease is strict i b <. orollary 3 shows that stronger enorcement increases price P H and I eectiveness s, and it decreases manipulation eort b. The reason is that directly reduces the incremental beneit o manipulation Y = (P H ) and, because o that, owners incentive to engage in manipulation. onsequently, given an I eectiveness s, they reduce b i b < (cases (a) and (c) o Proposition ). It is interesting to observe that increasing has a positive indirect eect on I eectiveness s i s > 0 due to the act that underinvesting in the I system becomes less

23 beneicial i the beneit rom manipulation declines. higher s decreases the expected beneit o manipulation and mitigates manipulation urther. The two eects o a higher S on b and s reinorce each other, which induces an increase o P H. Taken together, Proposition and orollaries and 3 establish that stricter I regulation and stronger direct public enorcement (at least weakly) improve the inormation content o inancial reports (as measured by ), which induces more eicient investment and results in a higher price P H. t the same time, the results point towards a non-trivial interaction o S,, and or determining manipulation, implementation o the I system and on the resulting price o the irm. In particular, direct public enorcement improves the eectiveness o I regulation by mitigating the I underinvestment incentives o the owner, which in turn reduces the necessity or stringent I regulation. Thereore, public direct enorcement partly substitutes or I regulation Optimal internal control regulation So ar, we have taken the I standard S as given. We now turn to optimal I regulation, that is the optimal tightness S o the I standard or a given eectiveness o I enorcement. The benevolent regulator sets the standard S to maximize social welare W ( q) S qs Pr( ) I( rh ) Pr( rh ) I( rh ) c. (0) 4 Social welare comprises the expected wealth generated by the investors through investing I(r) into the growth project, less the costs o establishing and maintaining the I system with eectiveness s, noting that with probability q owners are strategic and choose s and with probability ( q) owners are compliant and implement the standard, s = S. s mentioned earlier, we exclude strategic owners disutility o manipulation because it is not monetary and Even though we assume these costs are private to avoid separation o the types, inherently these costs are considered by the I regulator as they aect all irms.

24 a socially undesirable activity. The non-compliance cost captured by a wealth transer rom owners to the enorcer and is irrelevant or social welare. To simpliy the analysis, we set = 0. 3 Using the equilibrium investment, Ir ( H ), and Pr(r H ) = =, equation (0) is equal to qb( s) c W qs q S S s /4 is simply ( ). () We begin with a setting in which all owners are strategic (q = ), in which mandating an I standard S does not generate externalities to compliant owners, who would bear the ull cost cs /4 without any beneit. For q =, social welare equals W cs. () I the equilibrium s = 0 because the strength o the I compliance mechanism is low (cases (a) and (b) rom Proposition ), then S has no eect on social welare regardless o the amount. I is suiciently high and c is suiciently low (cases (c) and (d)), it is always optimal or the regulator to set S = to induce a greater s. However, the cost o implementing a high s can be so high that it can be welare maximizing to reduce S. The next proposition states the optimal I standard S or the case when I regulation is most eective; that is, when all owners are strategic (q = ). Proposition 3: ssume c > and q =. The optimal I standard S * and the induced I eectiveness s are as ollows, where 0 and the welare-maximizing I eectiveness s * (0, S * ); (i) i (cases (a) and (b)), then S * is arbitrary and s = 0; (ii) i (cases (c.) and (d.)), then S * = and s (0, s * ]; (iii) i (cases (c.) and (d.)), then * S (0,) and s = s * ; 3 We expect the main insights we derive rom this constrained setting extend to 0 < < /( + q). 3

25 The proposition characterizes the optimal choice o S * and the induced s, and particularly emphasizes how the equilibrium strategies depend on the non-compliance costs captured by parameter. Similar to Proposition, the disutility o manipulation k distinguishes cases b = and b <. The assumption c > is a suicient condition that the optimal S * can be less than. Proposition 3 (i) states that the results rom Proposition (cases (a) and (b)) carry over immediately. For I regulation to generally be beneicial and thus improve investment eiciency, it must be suiciently tight to induce strategic owners to implement an I system with eectiveness s > 0. I, then even the tightest I standard S = cannot induce s > 0. Thereore, any I standard S * [0, ] is optimal. The other statements o Proposition 3 reer to the cases (c) and (d) rom Proposition and distinguish two subcases in each case, (c.) and (d.), in which S * =, and (c.) and (d.), in which 0 < S * <. The proo establishes the existence o a unique threshold that separates these cases, and Proposition 3 (iii) and (iv) state the optimal interior S *. When exceeds threshold, then strategic owners invest in the I system (s > 0) enhancing reporting quality and thus investment eiciency. That is, to induce s > 0 i is not very high, the dierence between the standard S * and s is set as large as possible. For intermediate ( ) the optimal tightness is S * = and I regulation induces an I eectiveness s which is weakly welare-suboptimal, i.e., s s *. I I enorcement exceeds the threshold, the regulator can and will induce 4 strategic owners to implement the welare-optimal I eectiveness s *. Keeping S * = beyond would incentivize owners to invest too much in the I system because there is an optimal level o I eiciency due to the cost o implementing the I system (captured by c). Thereore, the regulator optimally sets S * <. The optimal standard S * decreases as * increases to keep the total non-compliance costs owners always choose s = s * or any particular. S s /4 constant such that strategic Figure illustrates the proposition or the case k < /4, which induces strategic owners to always attempt to manipulate (b = ). It depicts the behavior o optimal tightness S * and the

26 I standard S and induced s induced I eectiveness s that the strategic owners implement as a unction o S * and. S * starts with an arbitrary level depicted by the shaded area, then jumps to S * = (case (d.)) and later declines (case (d.)). The induced I eectiveness s strictly increases i and then remains constant at its optimal level s * i. Figure : Optimal I standard S * and induced I eectiveness s or only strategic owners (Parameters: q =, c = 3, k < /4) S * s I enorcement cost Next, we consider the optimal I standard or the more general case in which the proportion q o compliant owners in the economy is less than 00 percent. In the limit, when there are only compliant owners (q 0), then the optimal I standard S * = 0 because the only purpose o I regulation in our model is to detect accounting manipulation beore investors make their investment decision. Since compliant owners do not manipulate, the I system has no value. Proposition 4 generalizes the results o Proposition 3 or b = when q (0,]. Proposition 4: ssume c >, k < /4, and q. The I standard S * that maximizes social welare as deined under () is as ollows, where 0 q q and 0 : (i) q q: i (case (b)), then S * = 0; i (case (d.)), then S * = ; and i (case (d.)), then * S (0,) ; 5

27 (ii) q q q : i (case (b)), then S * = 0; i (case (d.)), then * S (0,) ; i (case (d.)), then S * = ; and i (case (d.3)), then * S (0,) ; (iii) q q: i (case (b)), then S * = 0; and i (case (d)), then * S (0,). The results in Proposition 4 are structurally similar to those in Proposition 3, but somewhat more nuanced. The reason is that i q <, the regulator must also take into account the cost o implementing S by the compliant owners, cs /4. By deinition, compliant owners not only implement the standard S, but do not manipulate, so these costs are a direct welare loss. The total costs o mandating an S are c qs 4 ( q ) S, which increases in ( q) because s < S. The regulator trades o these costs against the welare increase rom inducing strategic owners to implement an s > 0. Gross welare or b = is, and the beneit o q ( s ) increasing s declines the lower the proportion o strategic owners q are in the economy. s was already established earlier, there exists a lower threshold 0 that or it is optimal to orego any I regulation (S * = 0). This result contrasts with Proposition 3 (i) that stated multiple equilibria, because only the equilibrium with S * = 0 survives due to the strictly positive cost o mandating any S > 0 or q <. Except or this act, the unctional orm o the I standard S * described under Proposition 3 is similar as long as the proportion o strategic owners is high ( q q). The larger the proportion o strategic owners, the more beneicial is I regulation and, hence, it becomes useul already or relatively low enorcement levels. I exceeds the threshold, I regulation becomes eective to induce an s > 0. Proposition 4 describes the optimal S * or dierent combinations o q and. I q is suiciently small ( q q), setting S = is always too costly, so the regulator starts with setting S * < (Proposition 4 (iii)). For intermediate q ( q q q) there is a more subtle trade-o between costs and beneits o I regulation: Proposition 4 (ii) states that there is a 6