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MANAGING DYNAMIC RELATIONSHIPS By JIE TIAN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2006 Copyright 2006 by Jie Tian ACKNOWLEDGMENTS I am deeply indebted to my advisor, Professor Joel S. Demski, for his guidance and support along my journey of learning in the Ph.D. program. His faith and passion for scholarship have been the greatest inspiration in the pursuit of my academic career. He taught me much more than knowledge and skills. He taught me about life. I wish to thank Professor Karl Hackenbrack and Professor Jonathan Hamilton for their help throughout my study at the University of Florida. I am grateful for their comments for my drafts and patience in reading and refining my work. I thank Professor Haijin Lin for her constant encouragement and s. 1i. ii I have also benefited from discussions with Professor John Fellingham, Professor David Sappington and Professor Nathan Stuart. I wish to express my deep appreciation to my fellow doctoral students, especially Monika Causholli, Liang Fu, Carlos Jimenez, Richard Lu and Adamos Vlittis, who have provided me with wonderful memories at the University of Florida. Finally, I am truly thankful for my husband, Yuanfang Lin, for his patience, understanding and encouragement in every step of my dissertation writing. TABLE OF CONTENTS ACKNOWLEDGMENTS ....... LIST OF TABLES ........... LIST OF FIGURES .......... ABSTRACT .............. CHAPTER 1 INTRODUCTION ........ 2 LITERATURE REVIEW .... 2.1 Delegating Decision Rights 3 THE ONEPERIOD MODEL . 3.1 The Role of Communication 3.1.1 The Model ...... 3.1.2 Contracting with Full 3.2 The Role of Auditing .... 3.3 Summary .......... 4 THE DYNAMIC MODEL .... page iii vi vii viii Commitment 4.1 Full revelation . . . . . . . . 4.1.1 Continuation Contract with Full Revelation ......... 4.1.2 ExAnte Contracts that are Consistent with Full Revelation 4.2 Partial Revelation . . . . . . . 4.2.1 Benchmark: No Audit Case P ............... 4.2.1.1 Continuation contracts with partial revelation . 4.2.1.2 Exante contracts that are consistent with partial revelation . . . . . . 4.2.2 The Original Problem PP . . ......... 4.3 The Optimal Information Flow .. ............... 4.4 Sum m ary . . . . . . . . 5 UNVERIFIABLE INFORMATION .. ................ 5.1 The Investment Problem .. ................... 5.2 The Effect of Renegotiation .................. ..... 52 5.3 Summary .................. ............. .. 55 6 CONCLUSION .................. ............. .. 57 APPENDIX: THE PROOF .................. ......... .. 61 REFERENCES .......... .. ............. ...... .. 77 BIOGRAPHICAL SKETCH .............. . .. 82 LIST OF TABLES Table page 31 Audit technology ............... ........... .. 26 41 Comparing the control cost ............. ... ..... 46 LIST OF FIGURES Figure page 21 The general timeline ............... .... 7 31 The timeline in a full commitment setting ............ .. 22 41 Timeline when renegotiation is present .............. .. .. 30 42 The indifference curve ............... ........ .. 41 51 Timeline when unverifiable information is observed . . 53 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy MANAGING DYNAMIC RELATIONSHIPS By Jie Tian August 2006 C'!h In': Joel S. Demski Major Department: Fisher School of Accounting This dissertation investigates the role of information in longterm managerial investment decisions. The regulatory environment of financial reporting and auditing dictates how information is communicated and thus has a significant effect on managerial behavior. Standard setters who believe that the goal of financial reporting and auditing is only to maintain accuracy simplify the analysis and overlook the fact that managers are rational economic agents. Enlarging the useful information set, we then investigate the role of unverifiable information in managerial investment decisions. Contract renegotiation is served as a mechanism to make use of newly discovered information, even if it is unverifiable. It is efficient to take timely information into consideration in a longterm contracting relationship. CHAPTER 1 INTRODUCTION Financial reports are communications between managers and investors. When investors delegate decision rights to managers, there is a demand for information about managers' action. At the same time, how information is reported affects managers' incentives to fulfill their responsibilities, which in turn affects the underlying resource allocation. For example, given the widespread concern for accuracy of financial reports in the postSarbanesOxley environment, managers respond by abandoning accounting treatment but resorting to real business decisions to manager earnings, as documented in a recent survey paper (Graham, Harvey and R i, pal [2005]). Managers may delay a profitable project because it requires an immediate injection of fund, which can lower the current earnings. Apparently, the rules on financial reporting and auditing change the preparers' behavior. Since most business activities in the United States are carried out in investorowned business enterprises, how the information is measured for financial reporting has a significant impact on the welfare of economy. Measurement itself changes the behavior of the subject that is being measured. Some issued and proposed FASB statements have been criticized for their dysfunctional effects on resource allocation. For example, critics of Statement No. 8 (replaced by SFAS No.52) contend that the inclusion of gains and losses from translation of foreign currency may force companies to engage in uneconomical hedging transactions. Among all the concerns, the most significant cause may be managers' incentive structure is preoccupied with shortterm financial results. The company's interim financial information is reviewed by auditors (See PCAOB Auditing Standard No.l). Some even argued that the time for continuous audit has come, which allows using financial information with audited report in real time (See Searcy and Woodroof [2003]). When investment outcome takes a long time to realize, however, periodic financial reporting and auditing change managers' incentives in making proper investment decisions. A1 iw: of the financial reporting rules or audit procedures seem to ignore the dynamic effect of managers' decisions. For example, auditors are instructed to make sure all amounts are correctly included (the completeness objective) and transactions are recorded in the period when they actually took place (the cutoff objective) (Arens, Elder, and Beasley 2005). While transactions reflect managers' longterm perspective in decision in, 1:;i the related reporting issues should also be carefully addressed. Otherwise, the misaligned managerial incentives will drive the firm to operate at an inefficient level. This dissertation highlights the economic substance in evaluating rules of financial reporting and auditing. Different accounting settings cannot be understood without considering the effect on managerial actions. Moreover, the unique role p1l iv. d by accruals forces us to understand accounting from a multiperiod perspective. The effect from dynamic planning adds more concerns to standardsetting, because the standardsetters are not regulating nature but are rational economic agents. This concern raises questions about the zealous pursuit in accuracy of financial reports, especially the concept of "neutrality". Neutrality is defined as "absence in reported information of bias intended to attain a predetermined result or to induce a particular mode of behavior." (FASB Concepts No. 2) In a setting with symmetric and perfect information, such a bias can be easily removed and each party's behavior can be costlessly monitored. In other times, reporting standards affect the parties' incentives to communicate the unobservable information, which in turns affects the parties' incentives to perform their duties. Reporting standards are bound to "induce a particular mode of b, !i i.,'. i A naive view of standardsetting will cause the economy to perform at an inefficient level. The plan of the study is in the following order. In C'!i lpter 2, I selectively review the historical and contemporary literature. Three lines of literature are explored: first, delegating investment decisions to managers; second, dynamic considerations for standardsetting; third, the audit function. In C'!i lpter 3, I introduce a singleperiod model that studies the role of communication and auditing. Even though the model is abstracted from any dynamic effect, it helps answering the following questions: First, why investment decision is delegated and what problems could this cause to investors? Second, what kind of information can investors obtain from financial reports and is communicating the information helpful to solve the problems? Third, for public companies, a related issue with financial reporting is that the reported information is audited, what is the value of auditing? In ('! Ilpter 4, a dynamic model is studied. When there are long lags between the manager's effort and the project's final outcome, reported information can be used for other purpose. For example, the manager's contract is subject to renegotiation. Renegotiation occurs as long as there are mutual gains from revising the contract. The disclosed information will be used in the future when parties start to discuss the manager's compensation package. Anticipating that, the manager changes his initial motivations. In ('! Ilpter 5, a related problem is how to implement optimal investment policy. Previously we focus on using revelation mechanisms (communication) to motivate the manager. Now we focuses on using observed information to design right incentive structures, even the information is not verifiable. In this chapter, we do not constrain our understanding of managerial investment behavior by reading 4 financial reports (we are dealing with unverifiable information). We investigate the large library of accounting information. In C'!i lpter 6, I summarize the main results of the dissertation and provide directions for future research. CHAPTER 2 LITERATURE REVIEW 2.1 Delegating Decision Rights Investors hire a manager to make various decisions. It is probably because the manager's expertise offers him a unique access to some information set. Upon observing and analyzing the acquired information, investors are updated about the state of nature, thus being able to adjust the production plan. Since the collected information is valuable to reduce the risk of future production, these information discovering activities, though costly, should be encouraged. It appears that the traditional agency theory would suffice to explain the problem, because it shares a similar feature when a conflict of interest exists in agency: the agent has incentive to shirk, because exerting higher effort in gathering information incurs higher disutility, and his effort is not observable to the principal. But the new problem is more delicate because there are two separate decisions need to be made: the decision for information acquisition and for production. Whether to delegate only the information acquisition decision or both to the agent generates a stream of related research questions, particularly when the collected new information is only observable to the agent. For example, the principal might want to delegate the production decision to the agent as well, if it is costly to communicate the agent's private information to the principal. It seems to be more efficient to hand over the decision right to the betterinformed. But being privately informed, the risk averse agent might seek a production level in his own interest other than the risk neutral principal's. Then there is some spillover effect between motivating information acquisition and motivating production decision. The spillover between the two activities could become so severe that the principal would find it optimal to explicitly allow some underinvestment or overinvestment in production, in order to motivate the agent more efficiently to acquire information. These concerns are termed induced moral hazard, which highlights the tension between the two control problems. That is why sometimes it is not worthwhile at all to motivate any information acquisition activities, even if the information is useful. I will explore various related settings in the literature. While some let the agent choose his effort in gathering information as mentioned above, others treat the information system as exogenously endowed to the agent. But they are all concerned with how the valuable information should be utilized in decision making. Before we proceed, let's introduce some common notations and assumptions in the literature: x = production outcome, with x E X, where X represents an interval of the real line or some discrete levels. T] = the agent's effort in gathering information, i.e., choosing among different information system. 7r(T) = the signal which the agent privately observes, based on the information system he selects. 7 e II, where II is a bounded interval on the real line or some discrete levels. m(7) = the agent's report given 7. m(7) E M, where M is the acceptable reports set. e(7) = the agent's production effort given r. I(.) = the agent's compensation where I(.) is piecewise continuous. U(I) = the agent's utility function with U'(I) > 0, U"(I) < 0. C() = the agent's cost functions from exerting effort in either gathering information or production. C'(.) > 0, C"(.) > 0. (The agent's utility function can be additively or multiplicatively separable in wage and effort) x I = the principal's utility function. f(x lT, e) = the posterior probability density of outcomes. f(T) = the prior probability density of the signals. H = the reservation utility of the agent. t=0 t = t=2 t=3 t=4 Contracting Agent's effort Agent Investing effort Output I(x, m(7)) in gathering observes in production is observed information, Tr signal 7r(q) e(7) x Figure 2 1. The general timeline Conroy and Hughes [1987] are among the first who address the problem of how to motivate the agent to acquire information. They include several important assumptions besides other classical assumptions in their moral hazard model: (1) the acquired information by the agent is publicly observable; (2) the principal retains the right to take the productive effort, upon observing the agent's collected information; and (3) higher effort in gathering information rI is preferred because it shifts the expected outcome x from production to the right in the sense of firstorder stochastic dominance. The first assumption puts the extra control problem due to ..i iii i I ic information to silence. So the only focus is the moral hazard concern in exerting effort to acquire information. Given that the acquired information is verifiable, it is more efficient to let the principal decide the production level. The second assumption eases the moral hazard concern with respect to productive effort. The third assumption implies that the focus effort Tr can be ranked in the same way as in conventional agency theory. The three assumptions make their results similar to the conventional agency theory. The conventional agency theory's focus on motivating the productive effort e has been shifted to motivating the information gathering effort TI only. Their model is distinct from other works in this area in that the agent cannot observe 7. His effort can only let him observe a sample outcome y, which is not a sufficient statistic of the underlying state 7. The main result is, if and only if the production outcome x is conditionally (on y) informative about the agent's effort l,] the principal is better off by contracting on both the sample outcome y and the production outcome x than on the sample outcome y alone. Since their analysis applies to some outsourcing contracts between the firm and an outsider, for example, market researchers, political pollsters, census takers, and so on, it is a useful extension of agency theory. Penno [1984] directly addressed the effect of the predecision .i1i:i:. 1i ic information inside the firm, when the agent is delegated to conduct a productive decision. Then the deeper question is whether the agent should be granted such an access to private information prior to action. His model assumes the agent's private information is exogenously endowed. Although the principal can design the information system only accessible to the agent, the agent is not endogenously motivated to acquire this information. That is, referring to our timeline, the step at t = 1 is omitted. The agent's information is his effort's marginal effect, indicating the random working environment. For example, the information could be the potential market demand: if the demand is rather sluggish, investing much in marketing activities is useless; the reliability of machinery, which is crucial in deciding the efficiency of any productive effort. Specifically, the effect of the information is perfect substitute for the agent's effort f(x 1, e) = f(x le): if the agent observes a signal indicating that high output will probably occur, it is not necessary for him to work hard in order to achieve the goal. For that exact reason, the principal might not be willing to let the agent have some superior information than herself. On the other hand, the information can also help the agent reduce 1 That is, f(x y, Tr) depends on Tr. effort when there is almost zero marginal effect for his effort, while increase effort when its marginal effect is high. The paper demonstrates that if the principal can costlessly provide partition on the information set to the agent, a strict Pareto improvement will occur. The main result is, assuming the optimal effort e* induced by the optimal contract under symmetric information (no private information is accessible to the agent), and the principal can costlessly design the partition on the agent's private information set, then there is a partition on II : [0, 7], such that a strict Pareto improvement will occur. The intuition is as follows. Consider this partition: {[0, e] (c, T)}. For an arbitrarily small e, the agent saves on his effort from e* to 0 if he knew [0, e] realizes; but his effort upon observing (e, T) increases, which increases the principal's expected utility. The net effect is to increase expected production. Thus, providing partition to the agent improves the total welfare, even it is only observable to the agent. A 1 i, i" assumption here is that the principal is able to design the information system, which is a little at odds with the issue that the information is only observable to the agent, not the principal. In another words, the principal can control how much the agent knows, but she cannot observe what the agent knows. It seems that the agent usually has much more broad channels than the principal in order to know the details of production environment. The control problem that the principal faces originates from the agent's superior knowledge. If the principal can control the agent's knowledge, the problem is alleviated. Therefore, whether some information .,i::i.:, I ry should be created intentionally in organizations deserves more attention. Lambert [1986] studied a more sensible setting where the agent needs to exert effort to acquire useful information. Based on observed information, the agent is motivated to make a proper investment decision. If the agent invests, the project returns (randomly) either a high cash flow 7 or a low cash flow x. Rejecting the project will keep the status quo, that is, a constant cash flow x will result, and x < x < T. The cash flow E {x, x,} is observed by both parties. Three cash flows are used to model the tradeoff between motivating the manager to make a proper investment decision and compensating the manager for the risk he bears. A distinct feature of this model from conventional agency theory is that the agent's effort cannot be ranked in the sense of firstorder stochastic dominance. If the contract imposes too little risk on the agent, the agent would not search for information but choose the risky project; if the contract imposes too much risk, the agent would not work either but p1 iv safe. The contract design is more delicate. The analysis shows that without communication, both underinvestment and overinvestment may occur. But with communication, the problem of underinvestment can be tamed. This result sheds some light on the role of financial reporting from the stewardship perspective. If financial reporting is to communicate information to investors, it helps adjusting risk level on managers so they would work more diligently. Lambert [1986] can be seen as an example of Demski and Sappington [1987]. Demski and Sappington [1987] formulated a general model to study the spillover effect between motivating the agent to acquire information and to make a proper decision: planning and implementation. They show that even if implementation creates no disutility to the agent, the implementation activity can be distorted in order to provide the agent with incentives to become informed. While communication can alleviate the induced moral hazard, sometimes communication offers no gain. The result depends on the specific information structures. Laux [2004] continued to investigate the spillover effects among multiple tasks. Specifically, three tasks are motivated: the agent is motivated to gather information; to make an investment decision based on the observed signal; and to exert an effort to implement the project. Whether the agent invests is contractible; the other two decisions are not observable. The agent's effort in gathering information to evaluate the project, Tr, is either 0 or 1, with cost c if he works. His implementation effort is e E (0, oo], with cost e. XT = X(eT) is the target chosen by the principal, i.e., eT is determined endogenously. If the project is undertaken, the outcome is a function of both the project quality and the agent's implementation effort x = OX(e), 0 E {0, 1}. The agent's effort T] = 1 allows him to observe two distinct signals 7, or 7b, which is informative about the project quality 0. It is assumed that the principal induces the agent to invest when 7, realizes, and reject the project when 7b realizes. The information 7r, or rb is not observable. The contract depends on the outcome and investment decision. Since there are only two signals, and a separating equilibrium is assumed. The agent's private information is fully revealed by his observable investment decision. For the same reason, there is no problem of underinvestment or overinvestment (in contrast with Lambert [1'1 ,]). So the only spillover effect in this model is between motivating information acquisition T] and project implementation e. The paper shows that if the concern of motivating information acquisition dominates the concern of motivating project implementation, the risk imposed on the agent for the purpose of motivating information acquisition is sufficient to motivate him to exert high effort in project implementation. Then any informative measure of the implementation effort is redundant. The study offers another view why firms often disregard some informative performance measures in evaluating their managers. Another interesting result is that motivating information acquisition is never gratuitous even when spillover between multiple tasks is present inside the firm. Imposing risk to motivate the agent to work diligently in project implementation will not automatically offer the agent enough incentive to acquire information beforehand. It is ah,v more efficient for the principal to explicitly monitor the agent's effort in information acquisition. In next chapter, I show an audit of financial reports provides such monitoring to motivate the agent to become informed. 2.2 Dynamic considerations for standardsetting Standard setters believe the primary role of financial reporting is to facilitate decision making. "Financial reporting should provide information that is useful to present and potential investors and creditors and other users in making rational investment, credit, and similar decisions." (FASB, Concepts Statement No. 1) Therefore, accurate financial reports may be more useful. Although it is true for a single decisionmakeran information system is preferred to its Blackwell garbling, it is generally not the case when there are multiple p l i rs and the game lasts more than one period.2 Kydland and Prescott [1977] investigated various occasions where a policymaker has to make a decision. A1 ii.: have argued that, at each point in time, the decision should be made optimal given the current and past situation. But the current actions of economic agents also depend in part on their expectations of future policy changes. A wellknown example is patent policy. Given that resources have already been spent on inventive activities, the efficient policy is not to offer patent protection in order to reduce monopoly rents. But we know this decision will ruin the incentives to engage in any inventive activities. This expectation affects agents' current actions, which in turn affect the policymaker's future choice. Convergence does not ah,v occur. Accounting poliivmakers, however, do not 2 In a trading game, for example, if all investors get the same information and make a decision on it, investors may well prefer that information not be provided. See Hirschleifer [1971], seem to care enough about the economic foundation for standardsetting such as the dynamic effect driven by rational expectation. Accounting policies seem to be shortterm oriented. Attentions have been focused on producing accurate and reliable financial reports at any snapshot of time, which is at odds with the goingconcern assumption. Among other early work on dynamic consideration for accounting policies, C'!i I. I i, Demski and Frimor [2002] studied accounting policies where contracts are subject to renegotiation. Renegotiation affects dynamic uses of information. The disclosed information will be used in the future when parties start to discuss the agent's compensation package. Anticipating that, the agent changes his initial motivations. In a twoperiod moral hazard setting, a perfect accounting system causes the agent's incentives to collapse as in Fudenberg and Tirole [1990]. The intuition is as follows. Once the agent has exerted effort, it is efficient to provide the agent with complete insurance. Foreseeing that his eventual p .ivment would be independent of the outcome, the agent would then prefer to choose the lowest feasible level of effort. However, other regimes that allow the agent to move output from the first to the second period provide him incentives to work in the first period because the agent's effort creates reserves that will be rewarded in the second period. The paper examines the effect of different accounting policies on the agent's firstperiod effort: perfect accounting, ..'regate accounting and conservative accounting. The result emphasizes that policymakers are not only concerned about making a good choice but also constrained by the fact that p1 ii rs are strategic in making their choices as well. Gigler and Hemmer [2004] compared two reporting regimes on the information about the agent's past action, when contract renegotiation is considered. Two performance measures are considered: earlyrevealed information (y) and laterevealed information (x). The late information is publicly observable. But the early information can either be made public by a transparent regime, or be kept private under an opaque regime. So the principal has to rely on the agent's selfreport on y under an opaque regime. If full commitment is achievable in coi i, iiir. transparency is certainly preferred, because it is usually extra costly to induce the agent to report truthfully. But renegotiation makes the problem more subtle. Renegotiation tends to make the contract rely more on the information revealed before renegotiation, because the information revealed after renegotiation becomes less credible. If the agent's high effort is motivated, the insurance opportunity from using the laterrevealed information is lost. The contract does not reference the late information. At the renegotiation stage, the agent's effort is sunk and the principal's only goal is to reduce compensation cost by lowering risk premium. She will then offer a fullinsurance contract given the information observed before renegotiation. That is, the agent's incentive can be provided only through a shortterm contract: on the earlyrevealed information y only. This opens a door to an opaque regime, where the agent's information is kept private before renegotiation and is only revealed at the renegotiation stage. Thus, the laterrevealed information can be used. It is used to induce the agent to report his private information truthfully at the renegotiation stage. Since no more renegotiation is allowed afterward, the Revelation Principal applies.3 Motivating truthful report on the early information y will in turn provide the agent incentive to exert high effort. Therefore, although the early information is kept private, it 3 There is a minor problem with the constraints listed in the opaque regime.The ex ante truthtelling constraints (TT,'i) should not be imposed, because full commitment is not maintained as required by revelation principal. The ex post truthtelling constraints (ITTH and ITT,) are valid because full commitment is achieved at the renegotiation stage. This might change some points stated in the paper. But since the ex post truthtelling constraints will automatically imply the ex ante truthtelling constraints, the equilibrium is not changed. offers the principal extra incentive to reference the late information. Thus both information can be used in the contract, lowering compensation cost. Two studies on renegotiation are included here to demonstrate the dynamic concerns. Renegotiation allows the principal to move again based on her observation at some interim stage. Anticipating the principal's move, the agent revises his current choices. Dynamic concerns are also present in other scenarios. For example, Baiman and R li in [1995] study a setting with incomplete contracts. 2.3 Auditing Auditing is an attestation service. To do an audit, there must be some information to be attested. Some communication problems must be present for the auditor to verify. Financial reports are communications. It implies we need to consider at least three parties in order to study auditing questions: investors, the manager and the auditor. The incentive interactions among the three parties give rise to the demand of auditing. On the one hand, it is important to recognize the area of auditing is closely related to the area of financial accounting and certainly cannot be isolated with managerial incentives. On the other hand, we find that in literature it is difficult to endogenize the three parties' behavior all together. Antle [1982, 1984] uses a multiagent model to study the role of communication and auditing. Investors hire a manager to perform duties that affect the outcome of the firm. Investors hire another agentthe auditorto engage in some investigative action about the manager. The contractible information 7r (e.g., earnings) is observable to the manager only. Therefore, without an auditor, the manager would not have incentives to perform his duties since he can report whatever is in his best interest. The auditor exerts effort to verify the manager's selfreport wr, observes some information A and issues a report A. The manager and the auditor choose their actions simultaneously. The principal's (investor's) goal is to design the contracts using both agents' reports to motivate each other. If the auditor works and truthfully reveals her observation, her report should be consistent with the manager's. Likewise, the p clientt to the manager should be set higher if the auditor's report confirms his report and the opposite holds if the two reports conflict. The threepl! i' r framework is useful to visualize the relation between investors, the manager and the auditor and is also widely used in practice. Nevertheless, the model is not tractable enough to incorporate that sidepl ivments can be transferred from the manager to the auditor. Auditor's independence is presumed in that the auditor is able to deny selfinterested behavior completely. Antle [1982] noted, "Modeling the auditor as a pl! i, r opens a Pandora's box of methodological problems." Again, the model is a good benchmark to embark on auditing issues, but more questions need to be answered. For example, law requires no contingent fees be paid to auditors; with the manager's report absent, what mechanism can provide the auditor with incentives to work? Baiman, Evans and Noel [1987] also set up a threepl li, r game but the sequence of events is different. The auditor attests to the manager's report after it is issued, so the auditor's report is conditional on the manager's report. One of the results is that there exists no equilibrium in which the manager reports fully. This is because if the auditor knows the manager's report is correct, she would not expend effort to audit it. The manager's misreporting behavior is tolerated only to provide the auditor with incentives to work. For tractability, the manager is modeled to take no productive action and his only job is to report his observation. The purpose of the model is to show the role of auditor as a "utilitymaximizing i,'' ni but the model seems to be too focused on the auditor while overly simplifies the manager's behavior. Many other works circumvent the modeling impediment by focusing on the interaction between two parties only, leaving the "unimportant" issues exogenous. Fellingham and Newman [1985] studied an auditormanager game, where the manager chooses the effort to reduce the probability of a material error and the auditor chooses whether to extend audit procedures. The two p!l li rs move simultaneously. The focus of the paper is to show the auditor should consider the audit risk model strategically. The manager's behavior is influenced by his conjecture of the auditor's action and vice versa. Relying on singleperson decision theory, the auditor ended up with incorrect evaluation of audit risk. The model is highly 1 i i. .1 but it is among the first to point out that a successful audit relies on a thorough understanding of managerial incentives. In addition, the paper shows that the auditor may frequently use a randomized strategy. That is, the manager cannot predict what the auditor will do and he can only guess the auditor's strategy probabilistically. Anecdotal evidence shows that many audit failures are due to predetermined analytical procedures, because it is easy for the manager to plan accordingly. Strategic considerations are indispensable to study auditing issues. Leaving financial reporting problems unmodeled, Antle and N I. 1buff [1991] focused on the negotiation process between the auditor and manager. Financial statements should be read as a joint output from the auditormanager negotiation. The users only see the final negotiated outcome. Whether conservatism reigns in the final outcome is unclear even when the auditor starts with a conservative gesture. The manager has superior information and he only protests understatements. The paper shows, with a costsharing contract designed to maximize joint auditormanager surplus, the expected ex post bias is alvi, upward. Cuccia, Hackenbrack and Nelson [1995] studied the ability of professional standards to mitigate .,.i'ressive reporting. Although the experiment was set in a tax setting, the issue seems to be more general to all reporting behavior. The paper shows that practitioners will interpret more liberally a vague professional standard in order to justify ,. ressive reporting while interpret the evidence more liberally when facing a more stringent standard. The results are intuitive to capture the practitioners' intentions to exploit discretion embedded in professional standards. But why the practitioners albv choose to report .,.ressively is not clear. The practitioners' incentives (for example, resulted from compensation package) are not explicitly studied. 2.4 Summary In this chapter, I selectively reviewed the literature in three areas: Delegating decision rights, Dynamic concerns for standardsetting and Auditing. We start with the role of financial reporting, approaching from a management stewardship perspective. (FASB, Concepts Statement No.l) When investors rely on a manager's expertise and delegate some decisions to the manger, there is a demand for information. Communication is valuable especially when the manager endogenously acquires the information and use it to make a production decision. Apparently, financial reporting and auditing standards that govern the communication process affect managerial decisionmaking and have profound consequences on underlying resource allocation. Pondering on managerial decision 11 i1:;i: we raise some concerns for periodic financial reporting and auditing. Do we pursue an accurate financial reporting system or a dynamic communication process? The value of auditing is directly related to the value of financial reporting. The literature reveals the difficulty to incorporate interested parties (investors, the manager and the auditor) endogenously. It also presents us the opportunity to practise the art of modeling. We emphasize on the firstorder effects: there must be some reporting problems that auditing can help alleviate (the endogenouslycreated demand for auditing) and there must be some strategic considerations in auditing. Then another tough choice has to be made. Do we focus on the manager's strategic considerations or the auditor's? CHAPTER 3 THE ONEPERIOD MODEL 3.1 The Role of Communication The manager commonly expends effort to investigate profitability before investing in a risky project. Periodic financial reporting allows the manager to communicate the acquired information to the investors so that the investment decision can be monitored.1 But the selfreported information may not reflect the true value based on the manager's observation. For example, R&D expenditures may carry some information about the firm's future investment opportunities. Although R&D expenditures are all expensed as incurred, classification of R&D expenditures can be problematic. The manager may want to include ordinary operating expenditures in R&D. R&D expenditures can also be classified as the followthrough in an early stage of commercial production so the amount can be capitalized. Due to lack of active markets, classification of R&D expenditure is difficult. Therefore, the auditor's report, as a reliable (but imperfect) source about the manager's private information, can be valuable in monitoring the manager's behavior. 3.1.1 The Model The riskneutral principal (investors) owns an option to invest in a risky project. She hires a riskaverse manager to make a decision on whether to invest in the project: v E {0, 1}. If the manager invests, v = 1, the project returns 1 Penno [1984], Lambert [1986], Demski and Sappington [1987] and Melumad and Reichelstein [1987] have shown that in many cases, communication is strictly valuable when the manager has superior predecision information. (randomly) either a high cash flow 7 or a low cash flow x. Rejecting the project (v = 0) will keep the status quo, i.e., a constant cash flow x will result, and x < x < T. The cash flow x E {x,x,7} is observed by both parties.2 The manager can understand more about the risky project by searching for additional information. Let the information be the posterior probability of the high outcome occurring: Pr(T ) = 7. The manager observes three such signal realizations: 1 > 7T > 72 > 73 > 0. The prior probabilities of these signals' occurring are P1, P2 and P3, respectively.3 Therefore, if the manager does not work, he can only 3 predict the project's profitability via the expectation of the signals: m  Piri. i=1 The manager's effort can be either high or low: r] {c]H, IL}. The personal cost of low effort is normalized to 0, but the manager incurs cost c > 0 if he exerts high effort, ]H. (That is, working hard allows the manager to observe a better information system UrH.) The manager is assumed to incur no extra cost to invest in the project. Hence, the only moral hazard concern is to motivate the manager to acquire information. As we shall see, the manager's investment decision affects his decision to acquire information when the two tasks are jointly motivated. Since risk aversion is a firstorder effect and the change in risk aversion is not, I assume constant absolute risk aversion for the manager's utility function: U(I, c) = exp(r(I c)). I is the manager's compensation and c is the monetary cost of exerting high effort. Without loss of generality, the manager's next best employment opportunity is assumed to carry a certainty equivalent of 0, that is, his 2 As in Lambert [1986], three cash flows are necessary to model the tradeoff between motivating the manager to make a proper investment decision and compensating the manager for the risk he bears. 3 As we shall see, at least three signals are required to characterize the interim communication problem when renegotiation is present. reservation utility level is eo = 1. Let '(U) be the inverse function, that is, the principal will 'p iv the amount of I = T(U) =  n(U) to the manager. The optimal investment policy deserves some explanations. I restrict the analysis to the cases where the principal prefers that the manager select the risky project only if 71 or 72 is observed. That is, if the principal can either observe the manager's effort or the manager's collected information (the firstbest scenario), this investment policy will return the largest expected cash flow.4 This assumption is stated as Condition 1. 722x + (1 7r2) > x > 7r3x + (1 7r3) The principal only wants to avoid the worst scenario 7s. Let 712 17r3 denote this investment policy. Obviously, this is the firstbest investment policy. The rest of this analysis examines how the contract is designed in order to implement the firstbest policy and whether the firstbest policy is still optimal in various secondbest settings. To capture the idea that the informationdiscovering activities are pervasive in practice, I further assume that acquiring information is ahv, preferred, that is, high effort UrH is ahbv motivated.5 Notice the principal can infer perfectly the investment choice from the final outcome (, x or x), because the choice renders (ii iiI outcomes. This does not, however, make our problem disappear. The principal does not know why the project was selected or rejected. Was it because the signal the manager received 4 Two manager types are induced to invest because there should be some pooling before renegotiation takes place. The details will be clear when renegotiationproof contracts are introduced. 5 This assumption can be satisfied when the project is very risky, i.e., 7ir + (1  7ri) >> x >> 7rT3 + (1 7T3), and the cost to acquire information (c) is not too large. indicated the project is not profitable, or did he simply make the decision without searching for information? The principal does not know, either, whether the manager followed the desired investment policy, because the principal cannot observe the information the manager acted upon. 3.1.2 Contracting with Full Commitment The direct output of the manager's effort is information. Auditors, whose stock in trade is their ability to process information, seem to be helpful here. This section shows why the principal is better off imposing an audit. As a benchmark, the principal is assumed to maintain the full commitment power in this section. (Full commitment means the principal can credibly promise not to alter the terms of a contract, even if it is common knowledge that mutual gains are available from revising the contract.) Principal Manager Manager Manager makes Manager Outcome offers CBM chooses observes investment reports i, realized effort Tr to signal decision auditor x, x or x, gather 7(q) based on 7 verifies Payment made information report, issues A Figure 31. The timeline in a full commitment setting The manager's effort is not publicly observable, nor is the collected information. The manager observes the signal and has the authority to make the investment decision.6 The Revelation Principle allows us to look for the optimal solution 6 This regime is equivalent to the one in which the principal retains the authority to make the investment decision, because the manager communicates his information and the investment decision is observed. A similar situation can be found in Melumad and Reichelstein [1987]. under a direct revelation mechanism only (\ yerson [1979], Harris and Townsend [1981]). The manager's compensation is contingent on the realized cash flow (e) and his report on the received signal (if). There are five p ivment levelsIl, I; 72, I2; I3 when the investment policy 7rFr2 173 is implemented. Correspondingly, the induced utility levels are U1,Ui; U2,U2; U3. Since the manager's investment decision is observable, all the other offequilibrium outcomes can be easily penalized. (For example, if the manager reported 73, but invested in the project, the principal would observe I or x, and the manager is then punished so severely that he would never make that choice.) At the end of this section, I will show that the implemented investment policy is indeed optimal. The manager is motivated to exert high effort, so his expected utility is EU = e[Pil17U1 + Pi(1 7Tl), + P272U72 + P2(1 72)2 + P3U3]. But if he shirks, his expected utility is based on the expectation of the project's profitability: 3 m >Pi7ri. The principal's constrained costminimization problem (PBM) is: i= 2 Min YNP*t[i(Ui) + (1 rTT)(UL)] + P3 (U3) U1,UI,U2,U,3i= 1 Subject to: EU > 1 (1) EU > nUi + (1 m)U (2) EU > mU2 + (1 rn)2 (3) EU > U3 (4) 7rU1 + (1 7Tl)i > 7rU72 + (1 27l)U (5) 7lU1 + (1 T)U1 > U3 (6) 72U2 + (1 72)L2 > 72U1 + (1 72)L (7) 72 + (1 72)2 > U3 (8) U3 > 7T3U1 + (1 7T3)1i (9) Us > TTU2 + (1 73)2 (10) Inequality (1) is the IR constraint; inequalities (2)(4) are the IC constraints for effort selection. If the manager decides to shirk, he can disguise his behavior by claiming he receives signal 71, 72 or 7r3, but he cannot really observe the signal so he has to rely on m to evaluate his expected utility. Inequalities (5)(10) are the IC constraints for each manager type to report his information truthfully after having exerted the effort to acquire that information. Notice that the problem of motivating the manager to invest properly has been replaced with the problem of motivating the manager to report truthfully. This is because the investment decision is observable and thus can be enforced based on the reported information. Lemma 1. Assume no audit is performed. If m > 72, the optimal contract imposes risk on type 7T only, that is, U1 > U, and U72 = V; if m < 72, the optimal contract may impose risk on types 7r and r2, that is, U1 > UU and U2 > UV2 The contract should not only motivate the manager to invest properly, but also motivate him to acquire information. Lemma 1 shows how the manager's incentives in the two tasks interact. The intuition is similar to Lambert [1986]. When the project is expected to be relatively more profitable, that is, m > 72, (the mean is above the median.) the manager would ahvl invest if he did not acquire any information. This is because the advocated investment policy 7r172 lT3 encourages investing at any signal realization better than r3 but now the expectation m is already above the cutoff investment level. Thus, the manager's offequilibrium behavior (i.e., when he shirks) is to claim he received signal Tr or 72, so that he is justified to invest. This means constraints (2) and (3) are binding. Therefore, the principal has to design a "less atti I li,1 contract to alleviate the manager's temptation to invest. She equates the contract for the investing type to the noninvesting type, that is, type 2T receives the same p client as type 7r3, U2 = V Us. Type 72 is then indifferent between investing and not investing. Equivalently, he is indifferent between reporting 72 and 7r3. The investment policy affects the manager's incentive to acquire information. The manager's incentive to invest is set weaker in order to provide him with a stronger incentive to search for information. The manager's incentives are different when the prior is opposite, that is, m < 72 (the mean is below the median.) In this case, if the manager decides to shirk, he is not clear about whether to invest or reject the project because m is between 72 and 73. Constraints (3) and (4) are binding. If the manager invests without collecting any information, there is a high probability he might be wrong because the project is not very attractive: m < 7r2. If the manager rejects the project without collecting any information, his chance of being correct is also slim because he may miss the investment opportunity in two possible events 7r and 7r2. Therefore, with less concern to motivate the manager to acquire information, the principal can impose risk on both type 7i and type 7r2. Finally, we need to confirm there is no better investment policy in the secondbest setting. The principal can choose to induce investing in the project only when the manager receives the best news and forgo the project otherwise, that is, policy 71127ra73. The contract to implement TrT1r27T3 consists of four 1p .vments {Ui, U1; U; U3 }, which can implement policy T17T2 ir3 because type 72 is offered a fixed p .iment and thus is indifferent between investing and not investing. Investing when signal 72 is realized not only increases the expected cash flow as indicated by Condition 1, but also expands the set of variables for contracting (U2 and U2, instead of a single p ivment U2). Thus it is never wise to deviate from policy 71TiTT2 73. 3.2 The Role of Auditing We now introduce the audit function by assuming the auditor is well motivated by professional standards, and follows the audit rules diligently. The model focuses on the procedure of auditing and its function to discipline the manager's possibly opportunistic (offequilibrium) behavior. The auditor samples and tests the transactions and so is prone to errors. The audit technology is summarized using the following conditional probabilities: Table 31. Audit technology Approve Disapprove The manager's report is true 1 a a The manager's report is false 3 1 3 The auditor's report is AT if she approves the manager's treatment and issues AF if she does not. a can be interpreted as a Type I error and 3 as a Type II error.8 I assume a E (0, ) and 3 E (0, {) so the auditor's report is informative about the true status of the manager's information.9 Proposition 1. Auditing is strictly valuable in a full commitment setting. 7 Remember I have assumed it is ah,v preferred to acquire information. Other investment policies 1TT273 or iTT127T31, i.e., abhv~ rejecting the project or ahv investing in the project, do not require the manager to collect any information to implement the policy. 8 For simplicity, I assume the audit technology does not vary with the manager's reporting strategies. For example, the sampling error is 3 whether the type 7r3 manager reports 7r or 72. This simplification only reduces the notation and does not qualitatively change the results. 9 It is common in the literature to model audit technology as a garbling of the manager's information. For example, Dye [1993] and Antle [1984]. Currently, it is mandatory to audit the annual financial statements for public companies. Without incurring extra costs, the principal cannot be worse off by referencing the contract to the auditor's report. It is simply because the principal maintains full commitment power, and she alvi has the option to ignore the auditor's report when offering the contract at the start of the game. Moreover, in the twotask setting, an audit has strict value. On the one hand, it verifies the manager's selfreport so the contract based thereon forces the manager to report truthfully. Based on the (truthful) information, the desired investment policy can be enforced. On the other hand, the contract that references the auditor's report provides the manager greater incentive to become informed: if the manager did not work hard to search for information, he possessed no information, so he had to lie all the time; but the auditor detects lying with a positive probability. An effective audit makes the two tasks become more complementary and thus the expected compensation cost is reduced. 3.3 Summary This chapter extends the line of literature where the agent is motivated to generate information before making a decision.10 In such situations, the contract has to provide incentives for the agent not only to make a proper decision based on the observed information but also to acquire that information. One of the interesting findings is that the principal at times has to distort the agent's decisionmaking incentives in order to provide sufficient incentives for the agent to acquire information. I show that an audit of the acquired information helps align the agent's incentives in both tasks and therefore is strictly valuable. 10 Other examples include finding out about the probability of winning before tendering the bid and researching the potential investments before choosing portfolios for clients. See Lambert [1986], Demski and Sappington [1987], Laux [2004] and Malcomson [2004]. CHAPTER 4 THE DYNAMIC MODEL An important issue is how to audit the manager's acquired information. It may not alv i be efficient to motivate the manager to report accurately what he knows because of the incentive issues that arise in dynamic employment relationships. When there are long lags between the manager's effort and the project's final outcome, the manager's contract is frequently subject to renegotiation. If the auditor motivates the manager to reveal his information accurately, in equilibrium, the investors would be able to infer perfectly that the manager has exerted effort to acquire information. At the following renegotiation encounter, the contract will be revised to provide more insurance to the risk averse manager, that is, the p .ivments will not vary with the outcome of the project. Foreseeing that the final contract will not depend on the project's outcome, ex ante, the manager would have less incentive to become informed. Since renegotiation occurs as long as there are mutual gains from reconl i ,l .iii this trade friction itself can limit the usefulness of accurate financial reports. Unless the auditor's report is highly informative about the manager's private information, it is not beneficial for the investors to know the manager's information fully. Arm's length relationships may be preferred in the dynamic investment game. As mentioned previously, full commitment may not be a realistic scenario. There may be several years before the project's outcome is realized. Throughout the intervening years, parties can ahv, choose to tear up the initial contract and open a new contract, as long as both parties agree to the revision. Renegotiation thus enters our longterm projectinvesting story naturally. Renegotiation implies interim optimization. From an ex ante perspective, the interim optimization problem may add constraints, because both parties' ex post incentives need to be considered at the renegotiation stage. The amount of information to be revealed before renegotiation affects the interim optimization problem. Recalling the full commitment case (C'! Ilpter 3), full information revelation is motivated because the principal offers a contract first and commits herself to the rules about how the information is used. With the extra optimization problem, we now reexamine whether information should also be fully revealed. The timeline is revised to include the renegotiation encounter: At the initial contracting stage, the principal offers a contract, C1, to the manager, who can either accept or reject the contract. If the manager rejects the contract, the game ends and both get their reservation utility. After the manager accepts the contract, he chooses effort Tr to collect information. Based on the subsequent signal, the manager makes the investment decision v. The interim reporting stage comes before renegotiation takes place, when the manager communicates his information to the public (Vi)1 and the auditor verifies the manager's report (A).2 At the renegotiation stage, the principal offers a new continuation contract, C2, to the manager. If C2 is rejected, C1 is the final contract and determines the manager's compensation. If C2 is accepted, it becomes the final contract. 1 It is common for the board of directors to observe some information before convening to evaluate the manager's performance. 2 To capture the feature of periodic auditing, the auditor issues the report at the interim reporting stage. 30 At the final reporting stage, if the manager has not communicated fully his private information at the interim reporting stage, he can elect to report it now (F T). The project outcome is realized and the manager is compensated based on whichever contract is in place.3 Principal Manager Manager Manager Manager Contract Manager Outcome offers chooses observes makes reports re reports realized, contract effort fr signal invest i, negotiated iF X, x C1 to 7T(r) ment auditor C2 or x. gather decision verifies Payment infor based report, made nation on 7T issues A Figure 41. Timeline when renegotiation is present At the renegotiation stage, the principal makes a takeitorleaveit offer to the manager.4 The manager can take the newly offered continuation contract C2 or reject it so the initial contract C1 remains in effect. I will show we can restrict 3 I allow two reporting stages to ensure there is no restriction on the timeline. Renegotiation can take place before or after information release. One may also consider another timeline where the investment decision is made after renegotiation, thus after the interim reporting stage. The alternative timeline does not change the results qualitively, however. Full information revelation before renegotiation will render a full insurance continuation contract whether the investment decision is made before or after renegotiation, because the investment decision is observable and no further incentive concerns are left at the renegotiation stage. (Details will be clearer after I introduce the renegotiationproof contract.) Moreover, the current timeline seems to be more plausible, since the investment decision is delegated to the manager but communication often occurs at yearend. 4 It is comparatively simple to let the principal (instead of the agent) propose a contract at the renegotiation stage. Since the manager possesses private information, the contract proposal itself can reveal information. More analyses can be found in Maskin and Tirole [1992]. attention to the contracts that are renegotiation proof. A contract is renegotiation proof if, at the renegotiation stage, it minimizes the expected compensation cost while leaving no manager type worse off relative to the initial contract. That is, the contract is optimal from the principal's perspective, conditional on her conjecture regarding the choices the manager has made. Thus, the principal will not choose to alter it at the renegotiation stage. The principal chooses a continuation contract based on what she knows: observing the manager's interim report V' and the auditor's report A, she updates her belief about the manager's private information through Pr(T ri A). Of course, the posterior probability distribution Pr(7rl A) also depends on the principal's conjecture regarding the manager's effort Tr and the disclosure level enforced by the auditor. Since the investment decision (v = 0 or 1) is sunk and the decision can be perfectly inferred, type 7v or 7r2 cannot be mixed with type r3.5 The continuation contract takes the following form {(UjkikiU i), (U3k)}Jje{,2},ke{T,F},ie{1,2}. Type 71 or 72a manager's utility levels are specified in the first parenthesis. The p clientt depends on the interim reports (f, Ak), the final report (rii) and the realized cash flow (7, x). Type 73 manager's utility level is specified in the second parenthesis. Since type 73 is not induced to invest and the investment decision is observable, type 7r3 can be identified with certainty after the interim reporting stage. The p livment only depends on the manager's report (V\) and the auditor's report (Ak). Definition. A contract C = {(Ujki, jkiJ, (U3k)}jE{1,2},kE{T,F},ie{1,2} is renegotiation proof, for distribution Pr(T ri A), if it minimizes the expected compensation cost given Pr(7rl A): 5 I will show the policy 7T12 i 3 is still optimal.in Sections 5 and 6. For type 7v or 7r2, who invested: 2 Pr(7i t, ,Ak)[7itI ) + (1 i)(k)l i 1 among all the contracts {(7., jkij)}je{1,2},ke{T,F},ie{1,2} that satisfy for any (wf, Ak): 7iUjki + (1 7i)Ljki > 7r 7 + (1 7r) Vi' e {1, 2} (IIC7w, 7rij, Ak) tr ijki + (1 ri)ujki > TU7iji + (1 i)LLjki (IIRti, trj, Ak) For type i73, who did not invest: among all the contracts {( )} that satisfy for any (i(, Ak): > U3k (IIR73, Ak) At the renegotiation stage, the principal chooses among the incentivecompatible contracts that will be accepted by each manager type. The interim incentive compatibility constraints (IIC) restrict the set of contracts to those that induce truthful reporting from the manager, that is, all the private information will be revealed at the final reporting stage. The Revelation Principle is invoked here because the timeline presumes no more renegotiation. Notice there are no IIC constraints for the manager who received signal 73, because no .iii. Ii ic information problem remains. (IIC constraints are imposed for type i71 or 7t2, because entering the renegotiation stage the principal may not be certain about these two types.) The interim individual rationality constraints (IIR) restrict the possible continuation contracts to the class in which each type is offered a (weak) improvement in expected utility relative to the existing contract C. IIR constraints are defined recursively. If none of the contracts lowers the expected compensation cost relative to the existing contract, C, the principal has no incentive to offer any renegotiation; hence, the contract C is renegotiation proof. Proposition 2. Suppose an equilibrium exists in which (1) the initial contract is C, (2) the final contract is C* and (3) the manager's strategy profile is B = (UIH, 71i2 1i3, i, F). There then exists an equilibrium in which C* is the initial as well as the final contract, and the manager's strategy profile is unaltered. Therefore, without loss of generality, we only consider renegotiationproof contracts. Exploiting this representation device, the rest of the analysis shows the optimal disclosure level enforced by an auditor. At the final reporting stage, any unreported information will be revealed, so the focus is how much information should be disclosed at the interim reporting stage. Since the investment decision is sunk, there are only two reporting rules: 1. The manager is motivated to report completely what he knows, {{7i}{7r2}{73}}. The auditor examines whether the manager's report is truthful. This partition is denoted as full revelation. 2. The type 73 manager is motivated to report truthfully as i4, but types ri and w2 are motivated to report the same as w{. Thus the principal will know the manager received signal 73 when he reports i, but will not know the manager's information for sure when he reports w{. In this case, the auditor only verifies whether the manager's investment decision is justified based on his acquired information. That is, the auditor only worries about the misstatements that affect the principal's perception about the firm's investment opportunities, and a minor misstatement between 1 and 2a is tolerable. Denote this partition, { {i "72}{1i3}, as partial revelation. 4.1 Full revelation If the manager's information is disclosed before the renegotiation stage, the principal will use the disclosed information to renegotiate the original contract. Foreseeing that, the manager has less incentive to give away his advantage. Consequently, if the principal continues to push for more information, the manager may have less incentive to acquire information. Intuitively, an audit enforcing full information revelation at the interim stage can be harmful. In fact, the manager never discloses all of his information before renegotiation if there is no auditor to attest to his report. Lemma 2. Without an auditor, information acquisition followed by full information revelation at the interim reporting stage cannot be sustained in equilibrium. The manager knows that if he reveals all of his information, the story ends there: he has acquired information and invested according to the instructed policy. There is no incentive problem left for the principal to solve at the renegotiation stage. The principal will offer a full insurance contract. But knowing the final contract is a full insurance contract, the manager would prefer the low effort instead." Notice this result is reminiscent of Fudenberg and Tirole [1990]. The difference is that in my scenario the reporting problem is intertwined with the effort problem. The pursuit of truthful reporting completely removes the manager's incentive to exert effort to acquire information. The reporting requirement pollutes the real production. 6 The only feasible equilibrium other than implementing the low effort TIL is in mixed strategies. This paper assumes high effort is ahv, preferred. I will show later, with the auditor's report or adequate information rationing, high effort (in pure strategies) is indeed implementable. Fortunately, we have an auditor. As we shall see next, the manager's incentive to acquire information is completely provided by contracting on the auditor's report. Given an auditor and using the renegotiationproof representation, we characterize the optimal full revelation contract. Since the manager reports all his information before renegotiation, no information is left for later reporting, and the contract only relies on the interim report (w'), the auditor's report (A) and the project outcome (e). 4.1.1 Continuation Contract with Full Revelation At the renegotiation stage, the principal offers CT {(Ujk, Ljk), (U3k)}jE{i,2},ke{T,F} that minimizes: 7T 7.,) + (1 7r)TLik) subject to: 7,/ ., + (1 iJ) jk > 7jUjk + (1 m)uLk (IIR7j, Ak) and: \ (, ,) subject to > U3k (IIR3,Ak) At the renegotiation stage, six possible events may be observed: ( (, AT), (w{,AF), (72,Ar), (72,AF), (V, Ar) and (i ,,AF). Note the only constraint in each information event is one IIR constraint, and there are no IIC constraints. The principal believes the manager has made the proper strategy choices BT = (lH, 7172 13, j rj), so no incentive problem remains at the renegotiation stage. In the next subsection, I will show that the principal's beliefs about the manager's choices are indeed correct. Proposition 3. When the auditor's report is used to enforce full revelation, p ,'ments to the manager do not vary with the final outcome of the project. 4.1.2 ExAnte Contracts that are Consistent with Full Revelation At the initial contracting stage, the principal offers a contract CT {(Ujk, Ujk), (U3k)}j{1,2},ke{T,F} that is renegotiation proof given the principal's beliefs and the contract induces the manager to choose strategies consistent with the principal's beliefs BT = (/H, 17172 1T3, v = Tj). The principal's overall problem 7T, therefore, is: 2 Min P I{(1 a) [ 4(UT) + (1 (t )w >(U )] Ujk,ULj,U3k j1 + a[j4,(Uj,) + (1 7T,)(U1)]} + P3{( a) 3T(U3T) + a(U3F)} Subject to: EU> 1 (11) EU > 3[mUnI + (1 nm),T] + (1 )[mU1F + (1 m)1F] (12) EU > 3[mU2T + (1 Tm)21 + (1 )[mU2 + (1 nm)2F (13) EU > U3T + (1 )U3F (14) (1 a)[7T1U71 + (1 TT1)1] + aTT1FI + (1 1TT)u1] > s3iUT2r + (1 7i)1 + (1 0)[717U2 + (1 7iL)1F (15) > U3T + ( )U3F (16) (1 a)[72U2T + (1 72)T2r] + a[72 2 + (1 72)L2Fl > 0[Kr1T + (1 1F2)u] + (1 )[i1F + (1 12)Lf] (17) > U3T + ( )U3F (18) (1 a)U3T + aU3F > 0[771T + (1 3)LmT] + (1 3)[31F + (1 73)LF] (19) > 0[u3 2T + (1 73)L2] + (1 3)[3U2F + (1 3)L2F] (20) U1T = UIT (21) U2T 2T (22) 7U1F = L (23) U2F 2F (24) where 2 EU e { P(1 a)[7UFjT r+ (1 TF)Uj] j=1 + PJa[7jUjp + (1 Tj)J]F + P3[(1 a)U3T + aU } The exante individual rationality constraint (AIR) is (11). Inequalities (12)(20) are the exante incentive compatibility constraints (AIC). Among them, (12)(14) are included to motivate the manager to collect information and (15)(20) are included to motivate him to report truthfully. Inequalities (21)(24) are the constraints resulting from renegotiation. Notice that problem PT differs from the full commitment case by adding four extra constraints (21)(24), i.e., the project outcome is not used. The presence of renegotiation makes the contract fail to reference another informative contracting variable. Hence, the principal loses the opportunity to insure the risk averse manager. Renegotiation reduces the efficiency of contracting with the agent.7 The auditor's report is issued before renegotiation; thus, the contract that references the report can provide some shortterm commitment. When the auditor's report is observed (AT or AF), the manager's utility level based on the auditor's report is in the bank. The principal cannot lower the manager's utility level at the following renegotiation stage. Recalling the full commitment setting, the auditor's report is useful to motivate information acquisition and truthtelling. In the same way, the auditor's report can be used to induce high effort, even in the presence of renegotiation. Renegotiation adds extra constraints; however, and consequently the expected compensation cost will be higher. Pursuing full revelation before renegotiation also makes the principal shortsighted: the contract puts all the weight on the auditor's report and ignores the potential information content of the investment outcome. The manager's incentives are provided completely from the auditor's report. But can the auditor live up to such an expectation? The next proposition shows it depends critically on the audit technology. Proposition 4. When a,3  0, the compensation cost is close to the firstbest case; but when a, 3  0.5, motivating high effort becomes infeasible. Proposition 4 implies that the audit technology determines whether it is beneficial to reveal the information fully. If the audit errors are close to 0, it is equivalent to allowing the principal to observe the manager's information directly. The control problem becomes trivial, the firstbest scenario. But if the audit errors 7 Notice that investment policy 71Tr217 is motivated here. Other policies are not optimal. Since the overall contract does not reference the project outcome, the contract is the same no matter what investment policy is motivated. are large, the auditor's report is not informative enough to motivate high effort. The decision about the project has to be made without information. If this is the case, the principal can switch to the other reporting rule to motivate the manager. 4.2 Partial Revelation Alternatively, the manager can be induced to reveal his information partially at the interim reporting stage {{i7, 72}{73}} and the remaining information is solicited after renegotiation. Accordingly, the auditor here only verifies whether the received signal falls into the investment region {71, 772} or the noninvestment region {13}. The essence of partial revelation can be best illustrated through a benchmark case where no audit is available. I will then show that the original problem 7P is simply an improved version of the benchmark case. Denote the benchmark case as PL. 4.2.1 Benchmark: No Audit Case PL 4.2.1.1 Continuation contracts with partial revelation At the renegotiation stage, the principal updates her beliefs about the manager's type based on his report iij. Given the manager's reporting strategy both type 71 and type 72 report 1{, but type 7r3 reports the principal has Pr(7 {l) = P Vi E {1, 2} and Pr(73 1r) = 1. The principal offers C = { (Ui,Ui), (U3)}iE{1,2} that minimizes if f{i is observed: 2 i= 1 subject to 7TTi + (1 7) j > 7TTi, + (1 )L,; Vi' e {1, 2} (IIC7it, 1) iTUi + (1 7i)L > 73Ui + (1 7i) iU (IIR7i, ,1) if wr is observed: vlf(n.) subject to U3 > U3 (IIR7T3) Notice the principal offers contract CL to induce a truthful report from type r1 and type w2i: IICri, {. This is the only incentive problem for the principal at the renegotiation stage. As we shall see, this incentive problem is essential. Without it, a full insurance contract will result and the manager would not exert high effort (see Lemma 3). But now the principal has to impose risk in order to induce truthful reporting. The risk, from letting p ',lments vary with the final outcome, can be sufficient to motivate the manager to exert high effort. Lemma 3. If C, is a renegotiationproof contract and induces investment policy 12TTliTT3, the following must hold: U1 > U1, U2 2 U2, 7"2U2 + (1 7"2)L2 72U1 + (1 7"2)1. The continuation contract insures the low type (72) but imposes risk on the high type (r1i). This is the main result from Stiglitz's [1977] insurancepolicyoffering problem. The key to this adverse selection problem is that a full insurance contract is not optimal. A pooling contract that involves complete insurance limits the principal's ability to extract rents from different agent types. Thus the contract (for the high type) alv,v involves risk and varies with the final project outcome. 41 Lemma 4. Let C = {(U(I Ui), (U3)}ji{1,2} be a feasible continuation contract satisfying 1 > U1 U2 =2 r72U2 + (1  2,  72)L2 2 771 + ( 1 72) . CL is then renegotiation proof if and only if P1 < 7Tl 7T2 _"(U2) P2 i (1 r (1) /(L1) The intuition can be grasped from the following figure. It l II 450 (,L1) Figure 42. The indifference curve The slope of the indifference curve for the type 71 manager is U and 2 U'( for the type 72 manager. Thus type 7Fi's indifference curve is alv steeper than type 72's, as type 7r2 with a higher probability of encountering the low outcome values insurance more. It is optimal for the principal to insure the low type (72) but impose some risk on the high type (71) in order to deter the low type from mimicking the high type. Naturally, if the low type's p clientt could be set higherfrom I2 to 2 he will have less incentive to mimic the high type. Thus the risk imposed on the high type can be reduced from (II,/,) to (II, 1). By doing so, the principal's compensation cost may be lowered because the risk premium paid to the high type is reduced, although the p clientt to the low type is increased. But this alteration leaves some room for the principal to improve the current contract. She keeps altering the p clients until the gain from reducing the risk imposed on the high type is balanced off by the loss from increasing the p liment to the low type. That is, the principal reduces T'(U1) ''(iU) while increasing T'(U2) until the inequality in Lemma 4 holds. If the inequality is satisfied, it means no gain remains to be reaped via renegotiation, and the principal has reached the optimum. That is, the contract is renegotiation proof. 4.2.1.2 Exante contracts that are consistent with partial revelation Foreseeing these effects of renegotiation, the principal solves the exante problem PL. 2 Min YPt[ (U) + (1 7)w(U)] + P3'(U3) UiLi,U3 i 1 subject to EU > 1 (25) EU > mU1 + (1 m)U1 (26) EU > mU2 + (1 m)UL (27) EU > U3 (28) 7iiU + (1 i)L, > U3 (29) 2a72 + (1 72)L2 > U3 (30) U3 > 1 T3 + (1 73)U1 (31) U3 > T37U2 + (1 73)U2 (32) 2 2 (33) 7T2 U2 + (1 7T2)2 w 1 + (1 12) (34) P1 11 w12 "(U2) < (35) P2 7 1(l 71) TWO (L) 2 Where EU ej{ZP[U, + (1 )U] + P3U3}. i= 1 Inequality (25) is the AIR constraint. Inequalities (26)(28) are the AIC constraints for effort selection. Inequalities (29)(32) are the AIC constraints for investment policy 712Tr 3. These ex ante constraints make sure that the principal's ex post beliefs at the renegotiation stage are consistent with the agent's strategies. Notice that the extra constraints resulting from renegotiation are (33)(35).8 Proposition 5. When motivating partial revelation without an audit, the optimal renegotiationproof contract CP takes the following form: when m > 72, 8 The policy 7rr2 173 is still optimal in the partial revelation case. Implementing policy 71 1T27r3 is not optimal. The investing type will be offered with a full insurance contract. The same contract has to be offered to the noninvesting types. With a full insurance contract, high effort cannot be motivated ex ante. SPI(1 i) + (P2 + P3)( ) 1 ( r)enr P3(72 73) P17 (P2 + P3)72 + m7e P1 P( 2 T3) U3  r +e^ U2 112 U3 2 (i7 2)e r P(2 2 2 3) when mn < 2a, S PI(1 1 i) + (P2 + P3)(1 7) (1 2)e6r PU( i =2) SP7 1 (P2 + P3)72 + 2rc P1I 72) U2 1L2 U3 _1, if the renegotiationproof condition m < (2 is satisfied. Taking into account the effect of renegotiation, the manager's ex ante incentives are as follows. Since no risk is imposed on type 72, type 72 and type 7i3 must receive the same p client U2 U3 in order to induce policy 71r2 73. From the effect of renegotiation, U2 = 7r2U1 + (1 r2)U1, the manager will implement policy 71ri2 T3. If the prior belief indicates the project is promising (m > 72); however, the manager might want to misreport as 7i in order to avoid searching for information. That is, constraint (26) is binding. Similarly, if the project is not that promising, (m _< 72), he might reject the project (by claiming 73) before ever searching for information. That is, constraint (28) is binding. If the contract specified in Proposition 5 does not satisfy the renegotiationproof condition, the principal will increase type 7r2's p .,ment and reduce the risk imposed on type 7rl (Refer to Figure 1). The reduced risk on type 7rl will not be sufficient to motivate the manager to exert high effort. If 7r is close enough to 1, however, the renegotiationproof condition can be satisfied. With r7 close to 1, Ui, Ul, U2 are all finite terms. Hence the ratio I,(U2) in the renegotiationproof condition is also finite, but the ratio 11r2 can go unbounded. Thus, contract CP will be able to motivate the high effort. To illustrate the feasibility of this contract, consider the following numerical example. Let vi = .9, 7r2 .5, 73 .1, P1 .4, P2 .4, P3 = .2, c = 200 and r = .0001. The optimal contract is 7I 1097.67, 1 = 1341.46, 2 3 = 196.08, and the contract does satisfy the renegotiationproof condition: P = 1, and 71w2 J(U2) 18.6. P2( ) 4"(Ui)4"(U1) The total expected compensation is 223.86. (In the remainder of the analysis, I consider the contract C, only when the renegotiationproof condition can be satisfied.) 4.2.2 The Original Problem PP Now return to the original problem where an audit is available. The audit function at the interim reporting stage is to discern whether the manager's information is consistent with the reporting rule {{T7r, 72}{T3}}. The auditor does not distinguish whether the manager received good news (72) or great news (Tr). Thus the audit function is in effect designed to monitor the manager's investment decisions. Lemma 5. An audit is weakly efficient in the partial revelation case. The principal cannot be hurt by the auditor's report, although it is issued before renegotiation. This is because the auditor's report is only a garbling of the manager's reported information, and the principal cannot obtain more information from observing the auditor's report. Releasing the auditor's report does not create an incentive for the principal to further renegotiate the contract. But its release helps the principal monitor the manager's investment decisions and provides shortterm commitment before renegotiation takes place, so the auditor's report is valuable to motivate the manager to acquire information. (Recall the value of auditing in the full commitment setting. The auditor's report is informative about the manager's effort. If the manager did not acquire any information, he has to lie and the auditor can detect lying with a positive probability.) 4.3 The Optimal Information Flow Compared with the full revelation case, partial revelation limits the principal's incentive to renegotiate the contract. Restraining information flow, as a substitute for commitment, can make it easier for the principal to manage the longterm relationship with the manager. Recall that the manager's incentive to reveal his information fully at the interim reporting stage depends solely on the auditor's report. The audit technology determines whether to pursue full revelation. Specifically, if the audit accuracy is high, i.e., a,/3  0, when to reveal the manager's information is trivial. However, if the audit accuracy is low, i.e., a,/3  0.5, when to reveal the manager's information is crucial. Inducing partial revelation can successfully motivate the manager to exert high effort, even if no auditor is present. In this way, the adverse consequence of low audit accuracy can be avoided. Proposition 6. If a,3 i 0, full revelation can be preferred; if a,3 i 0.5, partial revelation is preferred. Using the same parameter values of the numerical example as in Section 6.1.2, the table below compares the total expected compensation between the two reporting rules. Table 41. Comparing the control cost ( ) (.01, .01) (.2, .2) (.3, .1) (.4, .2) (.4, .4) full revelation 200.02 200.89 201.08 203.04 212.09 partial revelation 204.46 206.38 206.93 209.75 215.86 ((o,3) (.4, .45) (.45, .45) (.45, .47) (.47, .47) (.49, .49) full revelation 221.43 250.08 278.21 341.28 1647.66 partial revelation 218.28 220.94 221.86 222.68 223.69 The table shows that full revelation dominates partial revelation when a and 3 are small, but the compensation cost increases dramatically when a and 3 are close to 0.5. The compensation cost from inducing full revelation is sensitive to the audit technology. When audit accuracy is high, it is wise to use the auditor's report fully, i.e., the auditor is instructed to check all details of the manager's information. But if the audit accuracy is too low, the compensation cost becomes extremely large; ultimately the auditor's report becomes useless to provide the manager incentive to choose high effort. The proof follows directly from Propositions 4 and 5 and Lemma 5. 4.4 Summary Partial revelation can be useful. The acquired information is forward looking and communicating it requires estimation. Daily involvement with the firm's operations and the expertise to search for information put the manager in a better position to interpret the acquired information than the auditor. The auditor will commonly have difficulty reaching agreements with the manager on the reporting issues. Realizing that the audit accuracy can be low in handling this type of information, the auditor should be motivated to allow the manager to withhold some information. The audit is still useful because it verifies whether the manager's investment decision is justified by his acquired information. But leaving some information unverified can benefit the longterm contracting relationship in that it allows investors to learn gradually about the manager throughout the project and matches better with the manager's longterm perspective. Of course, some accounts are easier to verify than others. If the auditor is confident with her audit technology, it is reasonable to enforce full revelation. Again, the auditor's judgment is required. Paralleling the auditor's decision, this result also speaks subtly to the value of earnings management. Auditors are less likely to require adjustment of earnings 48 management attempts when some information is subject to more discretion. (See Nelson, Elliott, and Tarpley [2002].) Perhaps this is because allowing some information to be kept private can avoid disrupting the manager's longterm objective. Withholding information arises due to the joint effect of longterm investment plans and audit errors. CHAPTER 5 UNVERIFIABLE INFORMATION In this chapter, we consider a larger set of available information for investment decisions. Useful information is not limited to financial reports. Information that comes to help can vary from a formal managerial accounting system to a walk around the factory. One problem is, some of the information is unverifiable. For instance, in the development of a project, both the principal and the manager commonly observe information before making the next move. But evaluation of the project based on the observed information may be subjective. It is not easy to present such information to a third party without causing ambiguity, so this type of information cannot be used in contracting with the manager. Under some carefullydesigned mechanisms, this type of information can still be useful for decisions even if it is not directly contractible. Demski and Sappington [1991] provide an interesting analysis in which both the principal and agent exert productive effort. The principal observes the agent's effort (the unverifiable information) and has the option to require the agent to purchase the business at a prenegotiated price. For example, a retailer usually can discern the quality of a product manufactured by a corporation before supplies effort to market the product, and the corporation has sufficient fund to buy out the retailer. The problem can be solved costlessly by letting the manufacturer buy out the business whenever the product quality is not satisfactory. Baiman and R li in [1995] study a setting where only the principal can observe the unverifiable information so she is subject to moral hazard concerns when she p .]i the agent based on the unverifiable information. One clever way to use the unverifiable information with multiple agents is to allow the principal to allocate discretionary bonus among the agents but the total bonus pool is based on some contractible information. 5.1 The Investment Problem Returning to our investment problem, we know some times underinvestment or overinvestment may occur. One of the reasons may be the decisionfacilitating information is unverifiable. The received signals 71, 72T or 73 are difficult to articulate so the contract cannot take each contingency into consideration. With the contract going incomplete, some efficiency is lost when the investment decision is delegated to the manager. (For simplicity, I assume both the principal and manager can observe the information, even it is unverifiable. A more general situation would be, the principal and manager observe different information since they may have their own information sources and may interpret the information differently even when they are reading the report from the same consultant.) Since the acquired information is not contractible, the principal offers contract {U,U, U}. The p ,iment depends on x {7,x, x} only. To minimize the expected compensation cost, the following program (P2FB) is set up to implement the firstbest investment policy 1r2 173s. Min [Pii + P27 2]T(U7) + [P1(1 T1) + P2l 2t)] ) + P'V3) u,u_,u Subject to: EU > 1 (36) EU> mU + (1 m)U (37) EU > U (38) 727U+(1 7r2)> U (39) U > 3U+ ( 3)U (40) where EU ec"{[P171 + P27T2]+ [P1(1 ) + P2( 2)U+ P3U}. Proposition 7. When m > 72, implementing 1172713 is strictly less costly than implementing the firstbest policy 121a 73. If the firstbest policy is implemented, the manager has more incentives to avoid searching information because the expected profitability m is already above the induced investment level r2. The project, "on av I', is profitable. The manager's incentives to search for information are different when implementing the policy 11 7273. The manager cannot tell whether the project is worth investing based only on the expected profitability m. "On av( I ;, the project may or may not be worth investing. Therefore, the riskaverse manager would search for more information to settle the uncertainty. It becomes less costly to motivate the manager to acquire information. If the investment gain is not too large to sacrifice when 2a is observed,1 the principal can be better off implementing the "secondb. policy 7rr27r3. In order to motivate the manager to acquire information, it is generally beneficial to impose maximal uncertainty so the riskaverse manager is more willing to reduce the risk by acquiring information. Inducing the manager to make an efficient investment decision, however, has to rely on the acquired information. The amount of risk has to match up with the manager's type, i.e., his information. The risky type (the manager type who observes relatively bad signal 72) should be provided more insurance relative to the safe type (7r). Therefore, it is difficult to 1 That is, P2 [2r2 + (1 72)x x] is not too large. reconcile the conflict in designing the contract. That is, the contract may not be able to provide incentives to acquire information and invest efficiently at the same time.2 5.2 The Effect of Renegotiation In order to avoid the "underinvI ii,, problem, one approach is to set up some revelation mechanism, where the principal and agent report their observation to the judge simultaneously. The judge will then penalize the two if their reports conflict. There exists a Nash equilibrium in which the parties can credibly reveal their private information and based on the report, the optimal investment policy can be implemented.3 Nevertheless, presenting evidence to a court seems to be different from sending messages inside a firm. Accounting reports only admits some type of information and is restricted in certain formats. In addition, it is difficult to proceed under the revelation mechanism when parties have different private information. In this section, we resort to ex post contract renegotiation to implement optimal investment policy, without invoking any report of the unverifiable information. The principal offers to renegotiate the manager's existing contract after the acquired information is observed but before the manager makes any investment decision. Now the new continuation contract can take into account the 2 Proposition 7 characterizes the problem of underinvestment. Similarly, an overinvestment problem may happen when m < 7r2. In that case, implementing 7iTTi2 T3 may be less costly when 71r27r3 is the firstbest policy. The reason is the same: create maximal uncertainty to induce information acquiring activities. But implementing overinvestment policy has to compensate the riskaverse manager for the additional risk. A random cash flow results if investing when 72 is observed. So the benefit of inducing overinvestment is relatively smaller. 3 Cremer and McLean [1988] study an auction setting where the seller wants to induce buyers to reveal their imperfectly correlated valuation. realized information implicitly. The risk level based on the information can be set properly so that the manager's investment incentives can be straightened out. The following timeline reflects the change in the order of events. Principal Manager Unverifiable Contract Investment Outcome offers chooses information renegotiated decision realized, contract effort r 7() C2 made x, x C1 to observed or x. gather Payment infor made nation Figure 51. Timeline when unverifiable information is observed At the renegotiation stage, the principal offers a new continuation contract to minimize the expected compensation cost given the observed information. Of course, the initial contract provides the manager with the default utility level. The result is similar to the full revelation case in Chapter 4. Since I assume there is no extra cost to implement any investment policy, the principal's optimal choice is to offer a full insurance contract based on the observed information. Suppose the initial contract {Uss, Uss, USB} induces the secondbest investment policy 7 r27r3. At the renegotiation stage, the principal offers a new contract {UI, U2}, where the new offer is U1 when the principal observes 71, and is U2 when the principal observes 72 or 73. Manager types 72 and r3 are offered the same contract because the initial contract induces both types not to invest thus providing the same utility level. If the principal does not observe any new information at the renegotiation stage, she offers U2 to the manager. Then we have 71u7SB + (1 70i)USB U1 (41) USB = U2 (42) Proposition 8. The renegotiated contract {UI, U2} implements the firstbest investment policy and induces the manager to acquire information at a lower cost compared with the secondbest contract {Us0B, USB USB} where no renegotiation takes place. The effect of renegotiation is to reduce risk premium. In this case, when there is no more incentive problem for the principal to handle, the risk premium is reduced to zero. With a fixed p ,ment, the manager is completely shielded from any risk resulting from his investment decision. He will implement the firstbest investment policy. In order to motivate the manager to acquire information, the following constraints are binding for the initial contract {S UiSB, USB}: {P cSB + Pi(1 7l) B (2 + )SB} > 1 {P SBpi7 + P( ) (2 + P)USB} > USB + (1 r)SB e" {PilS + Pi(1 w)U + (p2 + P3)US} > USB Since the renegotiated contract offers the manager the same utility level, the manager's ex ante incentives to acquire information are not altered. (These constraints are satisfied when we substitute the renegotiated contract {UI, U2} with (41), (42) and mUns + (1 mn)USB U2. The last equation is implied by the binding constraints.) Based on the newly observed information, however, the principal is able to reduce the risk premium by insuring the manager types who are invited to invest. Therefore, the expected compensation cost is strictly lower. The benefit of renegotiation is, it isolates the spillover effect between acquiring information and making an investment decision. After the manager's effort is sunk, the contract is revised to reflect the current situation. The current situation is to induce the manager to make a proper investment decision, so the ex post efficient contract will provide the manager with the right incentives. The incentives are reshuffled to accommodate the current need. This result can be seen as an application of Hermalin and Katz [1991] in a multitask setting. Renegotiation occurs and takes advantage of the unverifiable information. In contrast, the compensation cost cannot be reduced to the firstbest level as in a conventional moral hazard model. The same as their model, the principal can observe the manager's effort directly: if the manager works, 71, 72 or 7i3 can be observed, but if he shirks, no information is observed. But the initial contract sets different default utility levels based on the observed information. Hence, the renegotiation process cannot lower the manager's default utility directly to the firstbest level. Endogenously created information changes the manager's preference entering the renegotiation stage. We have studied contract renegotiation in ('!i lpter 4 and 5, but the effects are distinct. ('!i lpter 4 studies a setting where renegotiation is purely a trade friction. When the manager holds private information, how the information is reported affects the following renegotiation process which affects the manager's incentive in productive actions: acquiring information and making a proper investment decision. ('!C Ipter 5 deals with unverifiable but observable information. There are no reporting problems. Renegotiation serves as a mechanism to use the unverifiable information indirectly, thus can be beneficial. 5.3 Summary There are longstanding concerns about efficient investments. Underinvestment in research and development will slow down the longterm growth of the economy. Failure to pull the plug when the project runs on a losing course can cost the ("onI ii hugely. These problems occur partially because the manager's incentives are not adjusted properly along the project's duration. Newly discovered information calls for a reevaluation of the project's profitability. How to make use of the discovered information is the focus of this chapter, even if the discovered information is unverifiable and thus cannot be used directly in contracting with the manager. Instead of relying on some revelation mechanisms, the principal can renegotiate the existing contract based on the newly discovered information. The ex post efficient contract provides the manager with uptodate incentives to make a proper investment decision. One caveat of our model is that the investment cost is simplified to be zero. Therefore, a full insurance contract is resulted to take care of the investment incentives. If the project needs an unobservable fund injection after the contract is renegotiated, then a risky contract will be offered. Maybe it is not beneficial to isolate the two tasks by inserting contract renegotiation in between. Sometimes, the spillover effect may be beneficial. For example, the risk imposed to motivate the manager to acquire information may coincide with the risk to motivate the manager to make a proper investment decision, so it is trivial to consider implementing the investment decision. Sometimes, inducing an efficient investment policy may also automatically motivate the manager to acquire information. The nature of multitasking determines the usefulness of contract renegotiation. CHAPTER 6 CONCLUSION Acquiring information for a risk averse manager is never a trivial task. One might think the imposed risk from motivating another task would naturally force the manager to collect more information. But the contract design is subtle. If the imposed risk on the manager is too small, he will not acquire information, but just invest in the project; if the imposed risk is too high, the manager will not do the work either, but just forgo the project.1 This paper shows that .mdlll i when conducted properly, can help create efficient incentives for the manager to acquire information. An audit of the manager's acquired information is beneficial because it aligns the manager's incentives in acquiring useful information and in making a proper investment decision. But if the board of directors cannot commit not to use the disclosed information to renegotiate the initial contract, an extensive audit may exacerbate the control problem. Therefore, if the audit technology is not highly effective in identifying misstatements, the auditor may only want to verify whether the manager's report is consistent with his investment decision, but allow the manager to keep the finer details private. This arrangement is beneficial because it also reins in the selfinterested behavior coming from the owner's side. Together with the manager's behavior, it depicts an interesting balance in equilibrium. 1 Laux [2004] pointed out that motivating the manager to implement another task cannot automatically provide the manager the right incentive to collect information. It is ahv i necessary to motivate information acquisition explicitly. Financial reports contain information that is useful for future decisionmaking. The consequences of past decisions are also recorded in financial reports. The auditor verifies the reported information thus serves as a monitoring device of managers' decisions. It is important for the auditor to understand the manager's dynamic decisions making. The manager's decision in financial reporting is correlated with his decision in productive actions, which in turn affects the underlying resource allocation. Ex post uses of reported information influence the manager's ex ante incentives to acquire information and make a proper investment decision. It is also important to recognize the economic consequences of standard setting. The rules on financial reporting and auditing change the preparers' behavior. Standardsetters are not regulating nature but rational economic agents. The results echo the line of literature that provides explanations for earnings management based on the effect of renegotiation (a violation of the Revelation Principle's assumptions).2 My analysis focuses on how renegotiation affects the manager's investment behavior when the audited information is endogenously acquired. Audit technology determines how much information is to be disclosed. In contrast, a perfect audit in my model results in a firstbest scenario and the manager's information should be disclosed. The intuition is that the manager's shirking means no useful information is produced and thus will be detected in the audit. The adverse effect of renegotiation is amplified only when the audit technology is relatively ineffective so using the auditor's report alone is not informative enough to provide incentives for the agent to work. My analysis emphasizes the subi 1. i, of the audit function and therefore the solution is 2 See Demski and Frimor [1999], C'!1 i1. i , i, Demski and Frimor [2002], C'!i i. 1I, i, Feltham and Sabac [2004] and Gigler and Hemmer [2004]. "interior" motivating accurate financial reports may or may not be efficient. Auditors' judgments are the centerpiece. Some argue that we impose too much responsibility on the auditor. The auditor's job is to "check whether a reported number is correct". The auditor does not ask why and how the number is generated. As the auditor assesses audit risk and materiality before performing substantive tests of transactions, however, she is concerned about management. SAB 99 advises the auditor to investigate the manager's incentives carefully as opposed to setting some mechanic materiality threshold. Accounting firms hire experts to audit R&D contracts because they have superior knowledge to evaluate the manager's performance. Auditing is not a simple task in that it requires the auditor formulate judgments. The deeper the auditor understands managerial decisions, the easier the auditor reaches a correct conclusion. Some worry about the auditor's incentives if she is provided more discretion. That is a valid concern. There is another round of incentive problems. One problem is how the PCAOB evaluates the auditor's work when their opinion is at odds with the auditor's judgments. Auditor's exposure to legal liability forces standard setters to consider simple, rulesbased standards that permits less discretion. The audit fees, market competition, etc., all influence the auditor's behavior. A model with multiple pl.i , rs would be more appropriate to address these questions. But our model provides a salient structure of the audit function. More importantly, we point out the gap in the understanding of financial reporting and auditing. If financial reporting is a sophisticated communication process, auditing should help to serve this goal. We first provide a benchmark where an ideal auditor should perform, then we search for feasible mechanisms to induce to the auditor to perform as we hope. After all, the questions boil down to the trade off between revealing information enforced by an auditor and the resulting concerns for efficiency. The main message from my study is well reflected here: the optimal auditor's choice depends on the context that creates the incentive nexus and there is no panacea for all the reporting issues. Auditors are expected to rely on judgments to deliver highquality work. Besides revelation mechanisms, there are other mechanisms make the discovered information useful. Contract renegotiation takes into consideration newly discovered information. Thus the manager's investment incentives are better aligned with the current situation. In this way, the spillover effect between information acquisition and investment decisions can be isolated. Efficiency is strictly improved. However, the result hinges on the assumption that there is no additional cost to invest in the project. An extension would drop this assumption and examine more about the spillover effect between the two tasks. We might find that interim contract renegotiation can disrupt the synergy between the two tasks. APPENDIX THE PROOF Proof of Lemma 1. First we identify the binding constraints for each of the two situations: m > 7r2 or m < 72. A. when m > 2. In a less restricted problem, where only constraints (1) (2) (3) (8) (10) are present, all the constraints are binding. Then I show the less restricted program is feasible to the original problem. Let A, p11, 2 3, 14 represent the Lagrangian multipliers for each constraint. The FOCs provide Z'(U1) = Ae" + 1l [ere 1 + 12rc 4i'(gL) Ae + pl [ c 1 r + /rc '(U2) = erc + rc + 2(rc 2) +4 [4p7 r 1 1 m 1 3 4"'(g2) AeC + Ple + 2(ec P2(1 2)] + 3 4p2(1T2) I'(U3) Aer + 1eerc + /2rc [33 + P41 Remember T(.) is the inverse function of U(.). Since U'(.) > 0 and U"(.) < 0, '() = y > 0 and "'(.) [u 2U"(.) > 0. So the RHS increases in U. Suppose P3 = 4 = 0. With U3 > U2, 2, it implies type 7r2 manager alv,i reports 7F3. Suppose p3 = 0, /4 > 0, again we have U3 > U2,U2. Suppose p3 > 0, p4 = 0, two possibilities: ap2 > 0 and b2 = 0. a implies U2 < L2, because r > 2 71272 + (1 72)2 < 7132 + (1 73)2, since 72 > 13. Either constraint (8) or (10) must be violated. b implies U2,U > U3. The type 73 manager will ah,v report 7r2. Only 13 > 0, p4 > 0 is valid. Constraints (8) and (10) are binding: w2U2 + (1  7r2)U2 T3U2 + (1 7T3)U2 U3. Since 72 i 73, the only solution is U2 2= U3. Suppose p = P2 = 0, then we have U2 / U2, contradict to the result above. Suppose i = 0, /2 > 0, then we have U1 = U1. With U2 U2 U3, truthful reporting requires all the p ivments are equal. Then the manager will not work. Suppose p > 0, P2 = 0, then we have U2 / U2, which contradicts to the derived result U2 = U. It is easy to check that the rest of constraints are satisfied with the established binding constraints. Hence, constraints (1) (2) (3) (8) (10) are binding for the original program. The FOCs and K < Pl1m imply UI > U1. B. when m < r2a. Similarly, we can find the binding constraints are (1) (3) (4) (7). Reassign A, /M1, [2, 3 to represent the Lagrangian multipliers for these four constraints. The FOCs from the relaxed problem are: 'I(U1) Aer + I l rc + [26erc 3 7 (i) Ae rc 2rc 7r I'(U2a) Aerc + rc 7 2) + rc P + L3 I'(L2 ) Arc + p l(erc 7) + e rc + /3 1 P2(I 2) P2 W'I(U3) Xerc + 1e rc + 2(erc ) It is also easy to check that the rest of the constraints are satisfied with the established binding constraints. The FOCs and 2 < 1 2 imply U1 > Ui; P171 P1(17W) P2 < P1n implies U2 > UL. QED. PiT P2(12)  Proof of Proposition 1 Auditing expands the set of contracting variables. The problem with no audit is a restricted version of the problem where an audit is available, so the noaudit problem can be written as follows: 2 Min P{(1 a) )[Ti (77iT) + (1 7i) (UiT)]+ UiT,UiT,UiF,UiF,U3T,U3F aL[7Tw(U7F) + (1 7Ti)4(rF)l]} + P3[(1 a)I(U3T) + a4((U3F)1 Subject to: EU > 1 (Al) EU > 3[mnU1r + (1 m)U,1 + (1 3)TnUIF + (1 m),]FI (A2) EU > 3[mU2T + (1 Tm)U21 + (1 3)[mnU2F + (1 m)L2F] (A3) EU > fU3T + (1 )U3F (A4) (1 a) [71UIT + (1 1T1)lIT + aw[7lUF + (1 7T1)LF] > P/[71U2T + 1 ] 1 + (1 /0)[7T1U2F + (1 T1)2F] (A5) > U3T + (1 3)U3F (A6) (1 a)[7272T2 + (1 72)L2T] + a[72U2F + (1 72)2F] > P0[72U1T + (1 712)LT] + (1 3)[722U1F + (1 712)lF] (A7) > _U3T + (1 /O)U3F (A8) (1 a)U3T + aU3F > 0[7"3U1T + (1 73)UTI + (1 3) [73U1F + (1 73)LF] (A9) > /3 [73U2T + (1 73)r2T] + (1 /)[T3U2F + (1 7F3)L] (A10) UiT = U7F (All) LiT = UiF (A12) U3T U3F (A13) Where 2 EU e= e{ Pi[(1 a)(FiT + (1 ri)LT)+ i 1 aQ(wUiF + (1 mi)iF)] + P3[(l a)U3T + aU3F} It is clear that auditing cannot increase the expected compensation cost by relaxing constraints (All)(A13). To show that auditing can strictly reduce the expected compensation cost, consider an audit that is conducted only when r3 is reported. That is, given UiT = U iand UT = ULiF, I show that the constraint U3T U3F is binding. A. when m > 72 I have shown that in the proof of Lemma 1, constraints (Al) (A2) (A3) (A8) (A10) are binding. Let A i,p1 P2, P3, P4 represent the Lagrangian multipliers for these constraints so they are all positive. Let p5 represent the Lagrangian multiplier for the extra constraint (A13). The FOCs for U3T and U3F are 'I"(U3T) Aerc + ierc + p12r 13P (l + 4 + P5 ) 3(1a) 3 P3(1a) (U3F) rc 1lrc 2rc 3 R 5 I"(U3F) AeC + [eT +pe12 /13 K 1 [15 p Since A, p1,p2, 33, 4 > 0, in order for U3T U3F to hold, p5 must be negative because 1 < K Therefore, constraint U3T = U imposes extra costs to the problem. The proof for m < 72 is similar. Since adding more audits will not increase the compensation cost when 71 and 72 are reported, auditing is strictly valuable to the principal. QED. Proof of Proposition 2. Suppose the principal offers Ci = C* at the initial contracting stage and that the manager accepts and chooses strategy profile B = (T]H, 7172 73, I3 jiF). If C* is not renegotiation proof, there must be another contract, C, which offers every type of the manager at least the same expected utility as C* but leads to a lower compensation cost for the principal. Yet such a contract cannot exist, because C* is the final contract and hence optimal at the renegotiation stage. Thus C* is renegotiation proof given the manager's strategy profile. The manager's strategies remain the same, because his compensation depends only on the final contract. If in equilibrium, the manager chooses B when C is the initial contract and C* is the final contract, then he makes the same choices when C* is offered initially. QED. Proof of Lemma 2 Suppose without an auditor, the manager reports truthfully 71, 2a or 7r3 before entering the renegotiation stage. Since the low effort produces no information, the principal realizes the manager has already exerted effort to acquire information. Given the principal's belief that the manager has worked, made a proper investment decision 7Tr172 r3, and reported his private information truthfully, a contract C = {(U71, ), (U2,)2), U3} is renegotiation proof if Uj, Lgj arg min 7j T ((Uj) + (1 7j) (Uj) subject to FUTT, + (1 7F,) > > U7 + (1 F,)U,; Vi C {1, 2}, (IIR7w) and U3 E argmin l (u3) u3 subject to U3 > U3. (IIR7T3) With a single IIR constraint in each information event, the principal's best strategy is to offer a fixed p .,iment: Uj = U = Uj. Then the p clientss should be equal for all the three events in order to induce the manager to report truthfully. We have U = U2 U3, i.e., a full insurance contract. But a full insurance contract cannot induce the manager to work, which contradicts the principal's belief that the manager has worked. QED. Proof of Proposition 3. The result can be derived directly from the interim optimization program. For 1 type v7 or 72, at each information event (wf, Ak), the principal solves a costminimization problem with only one IIR constraint. The principal's optimal strategy is to offer a fixed p .ivment conditional on each information event, i.e., U1T = UT U2T L2T; U1F LF; U2F U2F. For 2 type 73, there is no room to gain via renegotiation. Since there is only one fixed p ,iment for each information event ((,, Ak), U3T and U3F are renegotiation proof. Given each information event, the principal offers a full insurance contract: CT {(UIT, U1F), (U2T, U2F), (U3T, U3F)}. QED. Proof of Proposition 4. Considering the following contract: {IjT = c + C, IjF = 0}, where c > 0. For this contract to be feasible for the program, the inequalities (11)(14) should be satisfied: ',,[(1 a)(er(c+c)) + a(e)] > 1 erc[(1 a)(er(c+c)) + a(e0)] > per(c+c) (1 3)eo Notice that other constraints are satisfied using this contract, since 1 a > 3. Rewriting the two inequalities, we have _6rc > _a _r 1 _r > a rc 3 C rc 13  a 1a3 1a3 Thus, c should be large enough to satisfy the two inequalities. When c, 0, the RHS of the two inequalities is close to 1 so e can be reduced close to 0. e 0 means the compensation cost becomes c as a,3 i 0, i.e., the firstbest solution becomes feasible in the limit. When a,j i 0.5. First multiply P1, P2, P3 to the inequalities (12)(14), respectively. Then add the three inequalities together. This rearrangement returns er{P[(1 a)UT + aU1F] + P2[(1 o)U2T + aU2F + [(1 a)U3T + aU3F]} > P [/UlT + (1 I)Ul] + P2[3U2T + (1 )U2F] + PU3T + (1 U3F] Substituting the negative exponential utility and rewriting the inequality, we have erI1T [ePi (1 a) P1/] er2T [ercP2(1 a) P2 1 er3T [eCP3(1 a) P3 > _erhIF [P(1 ) erc ] rI2F 2(1 ) ec2] erI3F [P3( 13) ecp3a] The inequality must hold for the program to be feasible. er > 1 and 1 a > P imply ercPi(1 a) > Pi3. Thus the LHS is less than 0. The inequality requires the RHS must be less than 0, too. This implies at least one Pj(1 3) ercPja from the RHS must be greater than 0, i.e., 1 3 > erca. But when a, 3 i 0.5, this inequality will be violated. QED. Proof of Lemma 3 The proof is similar to Fudenberg and Tirole [1990], Lemma 2.1. There are four situations concerning the two IIC constraints. Three of them will be eliminated. 1Suppose both constraints are binding. IIC7T, 1{' is binding implies 71 12 f (~l 2) (2 1), and IIC72, f{ is binding implies 1g2 (1 u2) (u2 12u). Since 711 / 712, it must be l = "u2 and u2 = u. That is, the two types receive the same p clients 7, u, a pooling contract. There are three possibilities: a u > u, b 7 < u, or c = u. a Suppose 7 > u is offered to both types. Consider the following contract for type 72: a single p client to the manager who claims 72 and U2 = 72u + (1 7a2), while keeping the contract unchanged for type 71. Then all the constraints are still satisfied, but the compensation cost for type 72 is reduced, because 4(U2) < 72T(7U) + (1 72)1(.). Since the compensation cost for type 7T is unchanged, the above alteration reduces the total compensation cost. b is similar to a, except a change for type 71: a single p clientt ul = 7u + (1 7rl), while keeping the contract unchanged for type 7r2. The expected compensation cost is lowered. c Suppose 7 = u is offered to both types. That is, a full insurance contract is offered and each manager type receives the same utility U = U = U. The problem becomes 1 {U} c argmin {[Pi7r + P2121 T(u) + [Pi(1 Ti) + P2(1 12)11u)} u,u PI + P2 Subject to: 7T2u + (1 wT2)U > U The first inequality is the IIR constraint for type 7r2. Since vi > 72, iT1 + (1  7))u > Tr2u + (1 72)u, the IIR constraint for type 71 is satisfied. Denote A and p as the Lagrangian multipliers for the two constraints. I will show p : 0 and thus the extra constraint u= u is costly. The FOCs with respect to u and u are '() 1+P (PI + P2) and (') (1 (pl + p2). Pl7Fl+P27F2  PI (1 71) +P2 (1 72)" We know A > 0, because the principal can alvi., reduce the expected compensation cost by offering (u u E), where E is a small positive number, and the IIR constraint will still hold. Suppose p = 0. In order to satisfy u = u, 72 must be equal to P5( 1w72 But simple algebra returns the former P1 7s +P2x 2 Pl(11)+P2(172) ratio is larger than the latter because of the assumption 71 > 72. Hence, p / 0, the constraint u = u adds more costs to the principal. Offering a full insurance contract is not optimal. 2Suppose neither constraint is binding. Cost minimization implies a fixedamount p client to type 7v and 72, respectively. In order to induce a truthful report, the p clients should be equal: u1 = u2. But a full insurance contract is not optimal. 3Suppose IIC71 is binding, but IIC72S is nonbinding. Then the cost minimization subject to the rest of constraints yields 7u = = u1. Rewriting the two IIC constraints, we have 72a2a + (1 72)u2 > u1 2= 712 + (1 7rl)2. This implies ~2 < u2. For the contract to be incentive compatible to induce the investment strategy 7r172 173, the following inequalities must hold: 7r2u2+(17r2) 2 > u3 > 7T3U2 + (1 73)U2. But with u2 > 72, and 72 > 73, the inequality cannot hold. 4If IIC72 is binding, but IIC71 is nonbinding. Then the cost minimization subject to the rest of constraints yields T72 = 2 = 2. Rewriting the two IIC constraints, we have 177ru + (1 7i)tt > u2 = u271 + (1 72)u1. This implies TT > u1. QED. Proof of Lemma 4 It is similar to Fudenberg and Tirole [1990], Lemma 2.2. From Lemma 3, we know the optimal renegotiationproof contract insures the low type (72), but imposes some risk on the high type (71). But this condition may not be sufficient for the contract to be renegotiation proof. The principal might be able to offer the high type more insurance by increasing the low type's expected utility. She keeps doing this until the gain from more insurance for the high type is balanced off by the loss from higher p liment to the low type. Notice it is not beneficial to increase the high type's expected utility. Keeping the low type's utility unchanged and maintaining the incentive constraint IIC72, the principal has to impose more risk on the high type in order to prevent the low type from mimicking (See Figure 1). The principal has to p ,li the high type more for the increased expected utility level and the increased risk premium. There is no gain for the principal. Thus, the principal's only strategy is to increase the low type's utility while keeping the high type's expected utility constant. Let V2 U2 + c, where c is a small positive number. Keeping the contract incentive compatible and the high type's expected utility constant, we have 2V1+ (1 72)VI V2 U2 + TIV1 + (1 7ri)I 17U1 + (1 Ti)Li Then we can solve the new contract for the high type as a function of the existing contract and e: V1 =U 1 7rl 71 7i2 V, = +  7T1 7T2 Notice the risk on the high type is indeed reduced. Substitute the new contract (V1, V, V2) into the objective function at the renegotiation stage and take the derivative with respect to c. For the contract to be renegotiation proof, this derivative must be nonnegative, i.e., P 1 (1 7)7 P2 1[71 '(U1) + 1'(l)] + '(U2) > 0 PI + P2 1 72 7i 2 1 P+ 2 Rearranging it, we have the inequality < l72 I'(U2) QED. P2  7(17) qJ'(U1I)4J(U1) Proof of Proposition 5 Substituting U2 2= U2 into the AIC constraints (30) and (32), we have U2 U3. Then the overall problem ,Pa reduces to Min Pi[7rlI(U1) + (1 7r1)T()]) + (P2 + P3) (U3) Ul,U1,U3 subject to EU > 1 (25) EU > mU1 + (1 m),U (26) EU > U3 (28) 7rl1 + (1 7rl) > U3 (29) U3 > i3Ul + (1 i73)U1 (31) U3 72U1+ (1 7T2)1 (34) P!, 7TI 7T2 /(U2) (35) P2 1 7i(1) 0/(U71) 1 /1)(l) Where EU = er{Pl [7FU + (1 7l)L] + (P2 + P3)U3}. Since 7r > 7r2 > 7r3, with constraint (34), constraint (29) and (31) are nonbinding. We have two situations: If m > 72, mU1 + (1 m)U1 > U3, constraint (28) is nonbinding. I show the only effort selection constraint (26) must be binding. Let A, 1, p2 represent the Lagrangian multipliers for the constraint (25) (26) and (34). (For the current analysis, I only consider when the contract is renegotiation proof, i.e., when constraint (35) is satisfied.) The FOCs are 'I(Ui) AXe + pi [ec j F1\ /p1 i c L c P17) P11(1t1) iP'J) Ae + pi[e a p,(i)1 P2pj(iW) 'I'(U3) Aec" + p1C+ rc 2 p2+p3 Suppose pi = 0. There are three cases. a 2 = 0 b 2 > 0 c P2 < 0. a p/ = 0 and P2 = 0 imply a full insurance contract. b and c imply either U1, LU < U3 or UI, VU > U3. Thus constraint (26) must be binding. I now show the AIR constraint (25) is also binding. The proof is similar to Fudenberg and Tirole [1990]. Currently, we have two binding constraints, (26) and (34). Obviously, offering rent does not relax the qualities. The only possible benefit of offering rent is to relax the renegotiationproof constraint: P1 < 71r2 ''(U2) A rent can only influence the inequality through the P2 7F11(1'1) q '(U1)T/'(Lz) ratio ,() If the rent increases the ratio, then the principal might want to offer the manager some rent. Let erR be the rent with R > 0. A contract offering rent is V1 = e'(I1+R) = e'R]1, V, = e'(I1+R) = erRU, and V3 er(I3+R) = erU, where U1,U U3 belong to the contract without rent. I have assumed the negative exponential utility, V'(U) = Substitute the i i i function into the ratio, V2 1 = Thus offering rent rV ++ + I V1 1 rU1 rU 1 U does not relax the renegotiationproof condition. The AIR constraint (25) must be binding. Therefore, we can solve three equations (25), (26) and (34) for three unknowns. This completes the proof for the first part of Proposition 5. If m < 72, mU1 + (1 m)LV < U3, constraint (26) is nonbinding. Similarly, we have three equations (25), (28) and (34) for three unknowns. This completes the proof for the second part. QED. Proof of Lemma 5. The problem with an audit can be solved in a similar way to the benchmark case, except that the dimension of contracting variables is enlarged. At the renegotiation stage, the principal offers CP {(Ulki,Liki), (U3k)}ke{T,F},ie{1,2} to minimize: (1) If 1f and A' are observed: 2 p 1 [7Pi (Fi ) + (1 qi(i1J>1 i= 1 subject to i (1k i + (i 7i' IkiF + (1 7i)tlki,; Vi' {1, 2} riU1ki + (1 7i)u1ki > 7riUlki + (1 (2) If i and A' are observed: subject to S,, > U3k From Lemmas 3 and 4, contract CP takes the following form: Ulk1 > .ilkl Ul7k2 r lk2 7"2U1k2 + (1 Ulk2 712)Ulk2 1 2U1kl + (1 712)lk1l, 7i)llki (IIC7, i, A') (IIR7Ti, A ) (IIR7T3, A ) 74 and CP is renegotiation proof if and only if the following inequality is satisfied: P < 7I 72 '(Ul2) Vk c {T, F}. P2 7i(17I) (Ulkl) '()Ulkl) The overall problem PP is: 2 i(i 1 )[7r (7T)+(17i)W(L i)]+Pia[i^(Ul^)+(1 i)W(lF)] il + P3[(1 a) (U3T) + aT(U3F)1 Subject to: EU > 1 EU > 3[mTnUT + (1 EU > 3[mnUT2 + (1 m)UTI] + (1 m)L2}1 + (1 3)[TmUI1 + (1 3)[mTnUF2 + ( EU > 3U3T + (1 )U3F (1 a)[7U (1 ] + + (1 l)r17T1 + Qa[TTl7F1 + (t1 ] LiFII > 3U3T + (1 /3)U3F (1 a)[U2U1T2 + (1 12)LlT2 + aW2TTF2 + (1 12)lF2I > 3U3T + (1 /3)U3F (1 a)U3T+ aU3F > P3[U31T + (1  > 3[73TIT2 + (1  73)LiTi] + (1 73)LIT2] + (1 3)[73U1F1 + (1 0) K3U1F2 + (1 Ulk2 1 lk2 712U1k2 + (1 7r2)lk2 = 2U1kl + (1  Pi l 7T2 1 "(rlk2) P2 71(t 71) (1k1)1 Lk1) Where Min Ul1ki,llki,U3k m)ULF ,l mn)LIUF2 F3) 1F1] 73)lLF2I 72)L kl 2 EU er { P(1i a) [7UtMT + (1 7T,)L,]l + Pia[7wUIFi + (1 i)tlF]i i= + P3[(1 a)U3T + aU3Fp} Thus the benchmark case Pp differs from the original problem 7P by adding four constraints: UIT1 = UIFI, IT = UIF1, UIT2 U1F2, and U3T U3F. The expected compensation cost of problem PP is weakly lower than that of problem PL. QED. Proof of Proposition 7. Let A, P1, P2 represent the Lagrangian multipliers for each constraint (36) (37) and (39). I show A, l, p2 > 0. The FOCs for this problem are I"'(U) = Aee + i[e P P\ll PP + 72p p22 P17 Vrl +P27r2 P1i+P2 r2 {i/TT\) rc i rc I _2__1 'I(U) AeTe e pg(1w_)j+p2(l_2)l 2p1(i( 9)+p2(1_2) 'I(U) AeC + Ie 1 2 Suppose p1 = P2 0. A constant p ,iment is then offered. The manager would not work. Suppose 1 = 0, L2 > 0, we have U < U, U. The manager will ahiv invest. Suppose /i > 0, 2 = 0, U,U < U3. The manager never invests. Therefore, 11 > 0 and P2 > 0. The IR constraint is alir binding, thus A > 0. When m > 72, tt is easy to check that the rest of constraints are satisfied with the established binding constraints. Similarly, if implementing the investment policy T1 17273, we can find the binding constraints are erc{P SB Pi(l )U + (s + P3)US} > 1 erc {Pii + Pi(1 T)USB+2 3)USB} > mU + (1 )SB rc {PiiSB + Pi(1 i)SB + (p2 + P3)USB} > USB crcPTU Pit TO It turns out the contract that implements the firstbest policy 1r2 1 r3 is feasible to induce the policy 7r11i2 3, since 727U+ (1 2)U U, mU+(1m)U > U and then er'c{P7l1U + Pi(1 7i)U + (P2 + P3)U} > U. The expected compensation cost to implement the firstbest policy is [P1711 + Pr272](U) + [P1(1 711) + P2( 72)](UL) + P3J(U3), which is higher than P1TrlI(U) + PI(1 7l)(U) + (P2 + P3)4(U3), because 72(U7) + (1 7r2)(U) > '(U) from Jensen's Inequality. Since the contract that implements the firstbest policy is only feasible but may not be optimal to implement policy Tr7l27 3, the expected compensation cost to implement policy 7Ti 27r3 is strictly lower than the one that implements the firstbest policy. QED. Proof of Proposition 8. 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BIOGRAPHICAL SKETCH Jie Tian, nicknamed Jc.v, was born on May 21, 1976, in Beijing, Cliii i Her parents, Shilin Tian and Xulin Cao, were both engineers. After graduating from the Experimental Middle School of Beijing, she entered Renmin University of China to study international economics. She earned her bachelor's degree in economics in August, 1998. Soon after the graduation ceremony, she came to the United States to study statistics at University of Nevada, Reno. She received her Master of Science degree in August, 2000. She joined the Ph.D. program of Fisher School of Accounting at the University of Florida and she is expected to receive a PhD degree in 2006. 