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AN ECONOMIC INQUIRY INTO ACCOUNTING RECOGNITION By JINGHONG LIANG 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 1998 Copyright 1998 by Jinghong Liang To my mother Shi Zeng Chun and the memories of my father, Liang Guo Cheng ACKNOWLEDGMENTS My greatest intellectual debt is owed to my principal advisor, Professor Joel S. Demski, who has guided my journey towards a PhD degree with patience and care. His pursuit of scholarship and professional craftsmanship have been and will continue to be my greatest inspirations. I wish to thank Professor David E. M. Sappington, Professor Bipin B. Ajinkya, and Professor Karl Hackenbrack, who served on my dissertation committee and patiently read and commented on my drafts. I also benefitted from discussions with Professor Anwer Ahmed, Professor Chunrong Ai, Professor Hadley P. Schaefer, and Professor John K. Simmons. I wish to express my deep appreciation to my fellow doctoral students, especially Sanjeev Bhojraj, Donna Bobek, Rick Hatfield, and Hui Yang, who have provided me with good memories of the rewarding years at the University of Florida. Finally, I gratefully acknowledge the financial support from the Arthur Andersen Foundation for my last year in the doctoral program. TABLE OF CONTENT ACKNOWLEDGMENTS ........................ ............. iv ABSTRACT ................................................ ................ vii CHAPTERS 1 INTRO D U CTIO N ............................ .............................. ............... 1 Accounting Recognition ............................... .. .. ............ 1 Research Objectives and Themes ................................................ 2 Plan of the Study ........................ ........................ .............. 3 2 RECOGNITION: A LITERATURE REVIEW ........................................ 6 M easurement Perspective .......................................... ............. 6 Information Content Perspective ............................................... 14 Econom ic Foundations ............................................ .............. 19 C conclusions ........................................................ ................ 25 3 ACCOUNTING RECOGNITION, MORAL HAZARD, AND COMMUNICATION .............................................................. 28 Introduction ........................... ............................ ............... 28 Organization Setting ............................................... ............... 29 Statement of the Principal's Problem ......................................... 32 Accounting Recognition and Moral Hazard .................................. 33 Accounting Recognition and Veracity Check ................................. 37 C conclusions ........................................................ ................ 43 4 ACCOUNTING RECOGNITION AND PERFORMANCE MANAGEMENT .... 47 Introduction ........................................................... ............... 47 Performance Management Literature ........................................... 48 M odified M odel ................................................ .... ........... 50 Information Regimes and Analysis of the Model ............................. 52 Empirical Considerations ................... .................. 58 Empirical Sim ulations ............................................ ............... 62 C conclusions ..................................................... .... ............... 66 5 CONCLUSIONS ........................................................................ 71 APPENDICES I PROOFS FOR CHAPTER 3 ............................................................. 75 II PROOFS FOR CHAPTER 4 ............................................................. 87 REFERENCES ..................................................................................... 92 BIOGRAPHICAL SKETCH ....................................................................... 99 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 AN ECONOMIC INQUIRY INTO ACCOUNTING RECOGNITION By Jinghong Liang December 1998 Chairman: Joel S. Demski Major Department: Fisher School of Accounting We begin our inquiry with a careful review of the historical and contemporary literature on the recognition issue. The foundation of the inquiry rests on the academic literature of information content and accounting structure. The analysis is set in a multiperiod agency model where accounting is a source of information for contracting purposes. In chapter 3, we focus on two complementary sources of information: one is an accounting source which partially but credibly conveys the agent's private information through accounting recognition and the other is an unverified communication by the agent (i.e., a selfreport). In a simple setting with no communication, alternative labor market frictions lead to alternative recognition policies. When the agent is allowed to communicate his private information, accounting signals serve as a veracity check on the agent's selfreport. Finally, such communication sometimes makes delaying the recognition desirable. In chapter 4, we study performance manipulation incentives where we allow the manager to shift a portion of the reported performance measures (e.g., accruals) across periods through early or late recognition rules. Under the conditions of limited communication and linear contracts, performance management may turn out to be equilibrium behavior that is encouraged by the principal. From the predictions of the model, we drive empirical implications for the empirical investigation of performance management (e.g., detecting income smoothing) and suggest new statistical procedures. Simulation results are provided regarding the effectiveness of the proposed procedures. From our analysis, we see contracting and confirmatory roles of accounting as its comparative advantage. As a source of information, accounting is valuable because accounting reports are credible, comprehensive, and subject to careful and professional judgment. In addition, tolerating performance management is an equilibrium response to the contracting and communication limitations. CHAPTER 1 INTRODUCTION Accounting Recognition All information systems manage their sources. The U.S. Labor Department uses elaborate rules and procedures to determine whether the price of a particular consumer good should be included in calculating the consumer price index (CPI). Judges use legal codes and their professional opinions to decide whether a piece of evidence should be heard by a jury. Likewise, accountants are selective about what can be recorded in an entity's financial records. The primary means to achieve this selectivity in accounting is through recognition rules. By recognition, we refer to the broad accounting issue of determining when and how particular events (e.g., transactions) enter the accounting records of an entity. These records are the basis of the entity's financial statements. By specifying what to include, recognition rules also exclude all other events from the accounting records during some time frame. For example, according to GAAP, internally generated goodwill and some types of holding gains are not recognized in the accounting records until the corresponding assets are sold. Therefore, accounting recognition, manifested in accounting standards, conventions, and in professional judgements by the accountants, prescribes the boundaries of accounting records and governs the content of the accounting products (e.g., financial statements). Thus it is no wonder the debates over recognition issues have had a rich and lengthy history. In the accounting policy arena, rhetoric about recognition is abundant. In its conceptual framework, the FASB prescribes four fundamental recognition criteria: definition, measurability, relevance, and reliability.' The conceptual statements further emphasize the tension between relevance and reliability. For instance, recording revenue before cash is received may sacrifice some information reliability. However, if "enough" uncertainty has been resolved, recognition is justified because relevant information may be conveyed in time to help users make various decisions. Research Objectives and Themes The objective of this dissertation is to examine the economic forces that underlie the accounting recognition issue in order to better understand the comparative advantages of accounting as a source of information. Numerous studies have addressed the recognition issue. In the first half of this century, accounting writers stressed an economic measurement perspective (e.g., Paton [1922], Canning [1929], and Alexander [1948]). The recognition debate was part of the larger income debate.2 Contemporary authors have adopted an information content approach (e.g., Beaver [1968], Butterworth [1972], Demski [1972], and Feltham [1972]). They view accounting as a source of information as opposed to a measure of some underlying stock or flow of value. Under this approach, recognition has been studied in terms of consumption planning (e.g., Antle and Demski [1989]) and security price behavior (e.g., Antle, Demski, and Ryan [1994] and Beaver and Ryan [1995]). FASB Statement of Financial Accounting Concepts No. 5, Recognition and Measurement in Financial Statements of Business Enterprises, paragraph 63. Essentially, accounting recognition may occur when the economic item in question has met the definition of an accounting element and is measurable, relevant, and reliable. All four criteria are subject to the pervasive costbenefit constraint and a materiality threshold. 2 See AAA Committee Report [1965], Horngren [1965], and Sprouse [1965]. The broader accounting vs. economic income debate is illustrated by Paton [1922], Canning [1929], Edwards and Bell [1961], and Lee [1974]. In this dissertation, we add three themes to the recognition debate. First, we focus on the incentive use of accounting information (i.e., to evaluate and compensate managers). Prior research has stressed valuation use (i.e., to predict the future payoff of an entity). However, accounting measures are widely used in managerial evaluation and compensation schemes (e.g., Antle and Smith [1985], Lambert and Larcker [1987], and Sloan [1993]). In general, the information system best suited for valuation purposes may not be best suited for incentive (or stewardship) purposes (e.g., Gjesdal [1981] and Feltham and Xie [1994]). By implication, one would expect that the best recognition rule for valuation purposes may not be the best rule for stewardship purposes. Second, we consider the interaction between accounting and nonaccounting information sources. There are many nonaccounting information sources concerning a typical corporate entity, such as voluntary disclosures by its managers and news stories from the financial press. Casual observation suggests information from these nonaccounting sources is often more timely than the typical accounting source. When determining the optimal recognition rule, it is critical to consider other information users may already have. Third, we explore the issue of performance management. Managers have, within the boundaries of the GAAP, partial control over recognition rules. Through discretionary accounting recognition, managers may be able to strategically "tamper" with the accounting report for some selfserving purposes (e.g., to affect their compensations). This possibility naturally will affect the equilibrium incentive design. Plan of the Study In Chapter 2, we review the historical and contemporary literature on the recognition issue. First, in a historical perspective, two debates stand out: historical cost as the basis for asset valuation and realization as the basic test for income determination. These debates are related to the recognition issue. Second, the economic foundations of the information content perspective are reviewed where decisionmaking orientation (both singleperson and strategic) is the focus. Applications of information economics to the study of accounting structure are also reviewed. A careful, economic inquiry into accounting recognition builds on the scholarly research on information content and on accounting structure. In Chapter 3, we study two complementary sources of information in a multiperiod agency model. One is an accounting source which partially but credibly conveys the agent's private information through accounting recognition. The other is an unverified communication by the agent (i.e., a selfreport). In a simple setting with no communication, alternative labor market frictions lead to alternative optimal recognition policies. When the agent is allowed to communicate his private information, accounting signals serve as a veracity check on the agent's selfreport. Finally, such communication sometimes makes delaying the recognition optimal. We see contracting and confirmatory roles of accounting as its comparative advantage. As a source of information, accounting is valuable because accounting reports are credible, comprehensive, and subject to careful and professional judgment. While other information sources may be more timely in providing valuation information about an entity, audited accounting information, when used in explicit or implicit contracts, ensures the accuracy of the reports from nonaccounting sources. In Chapter 4, we extend the model in Chapter 3 to include performance manipulation incentives. Through early or late recognition rules, the manager can, at the margin, shift a portion of the reported performance measures (e.g., accruals) across periods. Under the conditions of limited communication and linear contracts, performance management may turn out to be an equilibrium behavior that is encouraged by the principal. From the predictions of 5 the model, we drive empirical implications for the empirical investigation of performance management (e.g., detecting income smoothing). To resolve the truncation problem in cross section estimation, a Maximum Likelihood Estimator (MLE) and a classification procedure are presented. Further, we conduct empirical simulations of suggested statistical procedures to evaluate the effectiveness of the suggested procedures. In Chapter 5, we summarize the main results of the dissertation and provide directions for further research in this area. Finally, we reflect on our inquiry into accounting recognition by sharing some concluding thoughts on social science theories, accounting theory included, from a philosophical perspective. CHAPTER 2 RECOGNITION: A LITERATURE REVIEW "To seek the truth, seek the history first." an anonymous ancient Chinese scholar. Our inquiry begins with the long and varied standing of accounting recognition in the history of accounting thought. First, searching the historical discussions on recognition reveals a measurement approach with emphases on asset evaluation and income determination. Second, we review the recent rise of information school of accounting and its influences. Finally, the foundations necessary for a "modem" economic analysis of the recognition issue are reviewed. A careful, economic inquiry into accounting recognition builds on the research on information content and on accounting structure. Measurement Perspective Although not explicitly articulated, there seems to be an agreement among mainstream accounting scholars earlier this century that accounting serves a measurement function. In particular, income determination and asset valuation are viewed as the main functions of accounting. In his masterful book Accounting Theory, Paton [1922] wrote: "the essence of the accountant's task consists of the periodic determination of the net revenue and the financial status of the business enterprise." (p. 6) Alexander [1948] wrote: "[t]he determination of income is the principal task of the business accountants." (p. 131) The approach, mainly analytic, was to derive a measurement basis from some "selfevident" postulates (e.g., entity, continuity, periodicy. Thus, the disagreements arise mainly from different definitions of assets and income and different postulates about accounting's environment. Naturally, the disagreements produced different procedures to measure the underlying stocks and flows. A number of extensive debates over these issues took place with participants from all interested groups: scholars, practitioners, and regulators. Asset Valuation Debate Before the income statement became the dominant financial statement, asset valuation was the main topic of discussion in accounting debates. The most important part of the debate in asset valuation has been over historical costs. Theoretically, one can derive historical cost as the valuation basis for some accounting items from the continuity assumption. Since legally a corporation has an infinite life span, a going concern is assumed. Therefore, fixed assets should be valued at adjusted historical cost because they are not intended for sale, while current assets should be valued at current price because the eventual fate of current assets is for sale. Intended uses of the assets were emphasized as the driving force behind valuation procedures. This logic was shared by Lawrence R. Dicksee and Henry R. Hatfield, both prominent accounting theorists in the early 1900s. (See Chatfield [1974], p. 235) However, in accounting practice, conservatism was the dominant accounting principle at the time. Items like inventory, a current asset, were not valued at market value (lowerof costormarket was most popular). Reed Storey [1959] called this "an incomplete application of the going concern convention tempered by conservatism." (p. 236237) The dominance of conservatism may be influenced by bankers, who at the time were the main readers of financial statements and aggressively demanded conservative accounting rule. With the emphasis of accounting shifting to the income statement, other accounting principles like objectivity and matching were used to support historical cost accounting. American Accounting Association [1936] supported the view that "accounting is thus not essentially a process of valuation, but the allocation of historical costs and revenues to current and succeeding fiscal periods." (p. 188) Attaching historical cost to assets is thus a residual consequence. In fact, Paton and Littleton [1940] viewed assets as unallocated costs awaiting their destiny. Accountants were essentially "costers," not valuers. On the other hand, criticisms of historicalcost accounting have also been prevalent. Canning [1929] sees assets as expected future services and the only logical measurement is properly discounted future receipts from their uses. Changes in the asset value during the entity's ownership must be recognized in the accounts accordingly. This conclusion was shared by Paton [1922] and Alexander [1948]. In the preface of his Accounting Theory, Paton wrote: "[t]he liberal view that, ideally, all bona fide value changes in either direction, from whatever cause, should be reflected in the accounts has been adopted without argument. ... this logical position is the proper one for the professional accountant, at least as a starting point." (p. vii) After the two World Wars, historicalcost accounting was also under attack by the public due to the fact that inflation had become common. During a period with relatively high inflation, historicalcostbased financial statements were becoming more and more meaningless, or so it was argued. Edwards and Bell [1961] suggested using replacement costs (or buyer's price) as substitutes for historical prices in valuing assets. Chambers [1966] proposed the "continuously contemporary accounting" system, which relies on realizable market value (or seller's price) as the valuation basis. Based on a singletrader's decision model, Sterling [1970] uses information criteria (e.g., verity and relevance) and the quantitative theory of communication to support present market value as the proper valuation basis. Income Determination Debate Regarding income determination, heavy influence from legal decisions (e.g., corporate law and tax codes) and economic theories (e.g., economic theory of income) has been pervasive in the income debates. The adoption of the realization principle, as the main tool to deal with accounting income recognition (i.e., income may be booked only when it is realized), was strongly influenced by income tax legislation and court decisions (e.g., the Supreme Court's 1920 Eisner v. Macomber decision3). As a result, (taxable) income was directly associated with the separation from capital (i.e., realization), which usually requires an exchange transaction such as the sale of an asset. The realization principle also received wide acceptance by accountants. Paton and Littleton [1940] wrote that "[a]s a basis for revenue recognition in accounts, realization is in general more important than the process of earning." (p. 49) The matching principle, an intuitive and companion concept that essentially determines the expenses to be deducted from realized (therefore recognized) revenue, has also gained more acceptance for its expediency and convenience. Income does not have an intrinsic definition and was operationally defined as the result of applying the realization and matching principles. They offered the accounting profession the muchneeded protection against potential liabilities from the law or public 3 The high court ruled that receipt of common stock dividends did not constitute effective realization of income for tax purposes. It is the court opinion that income could not arise without (1) an effective addition to the wealth of the recipient, and (2) a "severance" of the gain from capital. perception. In short, the realization test had become one of the most important and durable concepts in income determination.4 Economists, on the other hand, were critical of this income debate. The lack of intrinsic definition of income in accounting literature frustrated economists like Canning, who wrote: "[a] diligent search of the literature of accounting discloses an astonishing lack of discussion of the nature of income." (Canning [1929], p. 93) In addition, he observed that "what is set out as a measure of net income can never be supposed to be a fact in any sense at all except that it is the figure that results when the accountant has finished applying the procedure which he adopts." (p. 9899) He suggested adopting economic income, defined by Irving Fisher [1930] as the starting point for analysis. Alexander [1948] began his monograph with a definition of income (influenced by Hicks [1941]): "a year's income is, fundamentally, the amount of wealth that a person, real or corporate, can dispose of over the course of a year and remain as well off at the end of the year as at the beginning." (p. 127) Additionally, the theory of the cost function of a multiperiod firm suggests that income at the firm level is nothing but the return to a factor of production: the capital. Under these economic approaches, all changes in asset value, realized or unrealized, must be included as income. However, literal application of economic definitions of income implies consideration of any changes in present value of future net receipts, including those caused by revision of expectation of future events like discount rates. This allencompassing concept of income 4 Chatfield [1974] noted on its wide acceptance: "Income finding depended on a series of interlocking assumptions which included historical costs, continuity, conservatism, and periodicity as well as matching and realization. These were made compatible by the ascendancy which income measurement had attained over asset valuation, and by the fairly stable prewar price structure. If not exactly elegant, they generally corresponded to the perceived reality as reflected in the periodical literature. It would prove very difficult to alter any one of them without changing their conglomerate effect. Those who accepted these assumptions confronted a closed and selfjustifying system which, like the laws of Newtonian physics at the turn of the century, seemed to leave little to be discovered." (p. 260) turned out to be too subjective for accountants to accept as a whole. Comparisons of the two income concepts (i.e., operational accounting income and intrinsic economic income) have been a major line of theoretical research in accounting. For example, Edwards and Bell [1961] introduce the notion of "entry" (i.e., buyer) and "exit" (i.e., seller) prices and build a system of income reporting that emphasizes the distinctions between operating and holding gains, between realized and unrealized gains. (Also see Lee [1974], and Parker, Harcourt, and Whittington [1986].) Challenges to the realization principle also came from accounting theorists who believed that the realization principle is too arbitrary and narrow. In the Accounting and Reporting Standards Underlying Corporate Financial Statements, AAA [1957] states that "[t]he essential meaning of realization is that a change in an asset or liability has become sufficiently definite and objective to warrant recognition in the accounts," (p. 3) which caused Sprouse [1965] to argue that this definition had made realization "merely a synonym for recognition." (p. 522). The 1964 AAA committee on the Realization Concept recommended a shift from liquidity to measurability as the test of recognition, further lessening the importance of realization. Horngren [1965] offered a compromise proposition which has a liberal recognition rule (for change in asset value) coupled with a strict realization rule (for earnings purposes). Myers [1959] proposed a criticalevent notion as an alternative guide to recognition,' that is still used in the policy and practical arenas (Johnson and Storey [1982]). Finally, the FASB abandoned realization as a major accounting concept in favor of a more 5 Myers [1959] proposed a critical event principle "which is both (1) as clear and uniform in its applicability as that of matching cost and revenue and (2) sound from an economics standpoint." (p. 528) general recognition concept (Concepts Statement No. 5) while realization is installed as one of two tests for recognition of revenue. Although some practitioners at the time had proposed some alternative, marketbased valuation models,' the primary concerns of the majority of practicing accountants were client relationships and legal liability. Departures from ideal measures were allowed to accommodate objectivity and conservatism. Alexander [1948] noted thishs desire to avoid responsibility has led accountants to set up two requirements for sound accounting that somewhat limit the choice of methods. These are the requirements of objectivity and conservatism. To the extent that accountants have achieved objectivity and conservatism they have made the measurement of income safer but they have also made it yield a result that only partially achieves the end sought." (p. 128) Devine [1985] made a similar observation that the accounting profession yielded to demands from liquidityminded bankers more than the calls from economic theories.7 The changing business environment has been the major force in changing accounting practices, not the evolution of normative accounting theories. Recognition in the Asset and Income Debates The two themes concern, in one way or another, what we now term "accounting recognition." They specifically deal with the questions of what economic event to include as part of the asset valuation process or the income determination formula. For example, the 6 See, for example, the selected speeches by then Arthur Andersen Chairmen, Spacek [1969] and Kapnick [1974]. Devine [1985] wrote, in the essay titled "Recognition Requirements  Income Earned and Realized," that "the accounting profession has been subjected to conflicting forces and demands. Economists have tended to assume that income is management's chief concern with only minor financial problems and have long been enemies of the realization concepts.... Lenders, on the other hand, have insisted on realization tests and have had little interest in measures of income not supported by current assets. The latter group has been so convincing that many accountants still are reluctant to show acknowledged increase in value even as footnotes." 13 historical cost debate can be rephrased as the choice between past transactions (e.g., historical costs) or current (or potential) transactions (e.g., holding gains) to present on the balance sheet. The realization debate can be thought of as when should accountants include a prospective sale event into the accounting records: at the time of the sale, the time of collection or some other point. Given that accounting serves as a measurement function, what to include depends upon what is the "right" measure. In Chapter XIX of Accounting Theory, entitled "Criteria of Revenue," Paton wrote: "the determination of a satisfactory evidence or test of revenue is essentially one aspect of the problem of valuation." (p. 468) Then he laid out the measurement consequences of various revenue recognition rules. For example, "if sale is to be used as the exclusive criterion, this means that all stock on hand must be priced at cost" (because they are not sold yet). Measurement is the focus in the analysis. In turn, the recognition and accounting procedures in general are evaluated on the merit of measurement. Again, Paton [1922] noted that "accounting procedure or principle is best which most nearly preserves the integrity of the statements for each fiscal period. .... with respect to the allocation of gross revenue to each year (or other accounting period), and the amount of the periodic net revenue, each method varies. And these are important matters." (p. 469) The main arguments in the challenges to the realization principle were also based upon the "right" measure of assets and net income. For instance, on the issue of unrealized changes in assets, the AAA Concepts and Standards Research Committee [1965] recommends that "unrealized" changes in the value of assets should not be included in the computation of reported net income, but should be shown on the income statement below the net income line. Therefore, these changes are recognized on the balance sheet (i.e., part of the right measure of asset), but not recognized on the income statement (i.e., not part of the right measure of income). Summary The majority of the early accounting writers adopted a measurement perspective. They treat accounting notions (e.g., assets and income) as measures of some underlying economic stock or flow. There have been attempts to establish foundations of accounting using this measurement perspective (e.g., Mattessich [1964], Mock [1976], and Ijiri [1978]). Ijiri [1965] constructed axioms upon which a conventional, historicalcostbased measurement system can be derived. Vickrey [1970] and Mock [1976] also tried to apply formal measure theory (e.g., Krantz et al. [1971]) to accounting. Under such an approach, an empirical relation system (ERS) is hypothesized to exist and a measure is nothing but a numerical relation system (NRS) that assign numerals to objects that preserve the distinctions in the ERS. The properties of a measure (e.g., homomorphism or isomorphism) are examined through representation theorems. Other attributes of the measure (e.g., uniqueness, and meaningfulness) are also discussed. However, the literature on accounting measurement exhibits a lack of concerns for the demand for accounting measures. Most of the discussions concern the measures themselves (e.g., asset and income), as opposed to the nature of empirical relation system that is being represented by such measures. Therefore, the measurement function of accounting is assumed, rather than derived. Information Content Perspective With the rise of an economic theory of information, the information perspective appears in mainstream accounting conceptual approaches. It sets foot in both empirical 15 research (e.g., Ball and Brown [1968] and Beaver [1968]) and analytic research (e.g., Demski [1972], Butterworth [1972] and Feltham [1972]). This information paradigm acknowledges information as a scarce resource, just like other resources that are used in production and exchange in the economy. It recognizes that demand for (and thus the value of) information is derived from improved decisionmaking. Accounting, in turn, is treated as one of many information sources, each with its unique characteristics and comparative advantages. The shift in perspective is best articulated by Beaver and Demski [1979]. They argued that income measurement loses its economic foundation in a world with imperfect and incomplete markets. They "offer a reinterpretation of income reporting and accrual notions in terms of a 'costeffective' communication procedure." (p. 38) Therefore, under this information content approach, the logical function for accounting to serve in such a world is to carry information. Accounting notions like assets, liability, and earnings are treated as information signals carrying information. The usual connotations attached to these accounting labels are of less importance. In turn, different uses of accounting information and the existence of other information sources besides the accounting source become important in understanding accounting.8 We defer the review of technical development of the information content approach to the next section. The rest of this section concerns the influence of this perspective on policy and practical discussions. a The idea of multiple uses is, of course, not new. Alexander [1948] recognized that there may be a number of uses of income measures and that the best for one purpose might not be the best for other purposes. He wrote: "Because different interpretations are possible, and because any concept of income can be justified only by reference to the use to which it is put, the only criterion by which a choice may be made among various methods of measuring income is the relative effectiveness of the different methods in serving the purposes for which the concept of income is to be used. But the concept is in fact used for many different purposes, so it is only natural that the measure of income best for one purpose should not be well suited to another." (p. 127) Influence of Information Content in Policy Discussions In the policy and practice arena, the influence of information concepts also emerges. The 1957 Accounting and Reporting Standards Underlying Corporate Financial Statements begins its introduction with the following statement: "The primary function of accounting is to accumulate and communicate information essential to an understanding of the activities of an enterprise[.]" (p. 1) It also considers the two important uses of accounting information: valuation and stewardship. "The use by investors of published financial statements in making investment decisions and in exercising control over management should be considered of primary importance." (p. 7) The importance of other information also received specific mention. "Therefore, accounting data ordinarily are most useful if supplemented by other types of statistical data and by relevant nonquantitative information." (p. 1) These important observations have been reiterated in other documents such as the AAA's A Statement of the Basic Accounting Theory (ASOBAT) and the Financial Accounting Standard Board's concept statements. As to the accounting recognition issue, the discussions are carried out with the same information content theme. During the FASB Conceptual Framework project, recognition issues received extensive investigation (see Ijiri [1980], Jaenicke [1981], Johnson and Storey [1982], and FASB Concept Statement No. 5). In its Concept Statement No. 5, Recognition and Measurement in Financial Statements of Business Enterprises, the FASB first defines recognition as the process of formally recording an economic item onto the financial statements. Then it establishes four fundamental criteria for accounting recognition (subject to the materiality threshold and the costbenefit constraint): (1) definition; (2) measurability; (3) relevance; and (4) reliability. As a throwback, two specific guidelines are prescribed for the recognition of the revenue item: revenue may be recognized when it is (1) realized or realizable; and (2) earned. In FASB's related studies (e.g., Johnson and Storey [1982]) and related concept statements (e.g., Concept Statement Nos. 2, 4, 6), information emphases were also prevalent. Uncertainty is explicitly acknowledged as part of the business environment that accrual accounting must deal with. In fact, uncertainty is claimed to be the "enemy of accrual accounting" (Johnson and Storey [1982], p. 19). Two kinds of uncertainty were cataloged: element uncertainty and measurement uncertainty,9 which are the origins of the first two fundamental criteria for accounting recognition. Furthermore, the consumers of accounting information are given explicit attention (e.g., relevance) while the integrity of the accounting product (e.g., reliability) is also to be maintained. In fact, reliability is claimed to be especially important in recognition issues. Johnson and Storey [1982] wrote that uncertaintyny is the primary source of reliability problems and that is why accounting recognition concepts focus on the reliability (representational faithfulness and verifiability) of the accounting information." (p.4) Further, the discussions of recognition issues seem to revolve around the reliability/relevance tradeoff"' (Concept Statement No. 5 par. 77). They may require the accountant to choose among alternative recognition policies, which, according to Johnson and Storey [1982], include (1) nonrecognition; (2) use of conventions; and (3) use of estimates and 9 It needs to be pointed out that these discussions of uncertainty are not completely consistent with the way economists typically speak of (or model) uncertainty. o0 This notion is not new either. It can be traced back to Canning [1929]: [t]he two tests of convenience, reliability and timeliness, are, of course, opposed to one anther. In any given set of circumstances the further back into the operating cycle one goes, the more difficult it becomes to make reliable estimates of what future final gross income will prove ultimately to be a fact. Just how far timeliness should be sacrificed to reliability is necessarily a matter to be left to that elusive and intangible thing called judgement." (p. 108) approximations. In choosing among these alternatives, they warned accountants to use "care and attention to the circumstances at hand. Otherwise, their application may result in a reduction in the reliability (and sometimes the relevance) of financial statement information. Accountants must be continually mindful of whether what is gained by using those alternatives more than offsets what may be lost by their application." (p. 8) This typical costbenefit rhetoric on recognition issue reflects a fundamental influence of the information perspective on contemporary accounting development. However, implied in these rhetorical policy discussions is the notion that there exists a set of abstract criteria (e.g., relevance, reliability) which one can use to select desirable methods as accounting standards. The general impossibility theorem in Demski [1973] refutes such a notion. The universal comparisons among accounting alternatives are not possible without details of the decisionmaking context and/or preferences of the economic agents involved. Summary Accounting recognition, as the fundamental accounting device that governs inclusion and exclusion, has been under intense scrutiny over this century. Participants in the debates came from academics, practitioners, and standardsetting bodies. Diverse approaches are taken because of the different fundamental concerns of the parties involved. To the academics, logical cohesion and internal consistency have been important, as professional protection and client relationships have been to the practitioners. To standardsetters, other economic (e.g., inflation) and political factors have played major roles. The language of the debates has transformed from the proper measurement of accounting stocks and flows into an explicit consideration of the information content and the 19 demand from its users. Contemporary discussion of the recognition issue has been carried out in the platform of the tradeoff between the relevance and reliability of accounting information. Somewhat curiously, few contemporary scholarly studies have been done on the subject." To better understand the issue, one must examine accounting recognition, part of the rich accounting structure, in a meaningful economic setting (especially a decisionmaking context), where demand for information is endogenous. In such a setting, one may start to compare the usefulness of alternative recognition rules and to study the interactions between accounting and nonaccounting information sources. Economic Foundations Now we turn to the economic foundations of information content and related studies on accounting structure. These studies provide the framework to study accounting recognition questions in economic settings and to assess the comparative advantages of accounting over other sources of information. Information Content and Value of Information In modem economic theory, information systems are treated as factors of production'2 at the very general level (Kihlstrom [1974]). Economists are interested in the private or social value of information. Just as any other scarce resource, information (system) has private (resp. social) value if a person (resp. society) is willing to pay something for it. However, information and conventional goods are somewhat different. Specifically, the value of Antle and Demski [1989] attribute this to "the increasing social science perspective of the scholarly literature," among other reasons. (p. 424) 12 Here we use the term "production" rather broadly. Information systems may help economic agents to "produce" better risksharing arrangements, etc. information is derived from the use of the information, in an uncertain world, to improve the decision made by an individual or society (to allocate productive resources). Decisionmaking under uncertainty and the value of information are intimately linked. There has been a long line of economic research on the value of information systems. The Blackwell Theorem (Blackwell [1951]) in decision theory establishes the necessary and sufficient conditions for one information system to be more valuable than another system regardless of the decisionmaking context. This important result has widespread influence in many fields of economics including information economics (Marschak and Miyasawa [1968]) and accounting (Demski [1973], Butterworth [1972] and Feltham [1972]). Empirically, Ball and Brown [1968] documented the famous "fan diagram" indicating that accounting numbers do provide information content, on an ex post basis, about the value of the entities. All the information content studies in this early literature are within a singleperson (nonstrategic) decisionmaking setting. In strategic settings, the decisionmaker operates in a stochastic environment with other rational decisionmakers (e.g., the opponents) whose decisions may affect his welfare. The nature of the value of information systems is somewhat different from that in singleperson settings. For example, in nonstrategic settings one can always choose not to use the information and be as welloff as without the information since no reactive behavior exists. Therefore, the value of a information system is at least zero. However, in a strategic setting, this "free disposal of information" is not always possible. The opponents may act differently depending upon whether the decisionmaker has access to a particular information system. This reactive behavior by the opponents may change the prospects the decisionmaker is facing. Therefore, it is possible, for example, that a particular source of information has negative value." The roles of information in nonstrategic and strategic settings are different. Demski and Feltham [1976] called these decisioninfluencing and decisionfacilitating roles. While the use of information can be different across strategic and nonstrategic settings, demand for information can also arise for different and distinct reasons or motivations. In general, economic agents may have information demands for production purposes (e.g., choosing which project to pursue), for consumption/investment purposes (e.g., choosing how much to save) and for contracting purposes (e.g., choosing the best sharing rules). Agency models have been used extensively to study the use of information in contracts between the shareholders (or owners) and the managers of a representative firm. Gjesdal [1978,81] considers a general agency setting in which the demand for stewardship information (e.g., how hard the manager has being working) and the demand for standard decisionmaking information (e.g., what are the prospects of the firm) coexist. Following these two demands, he distinguished two types of informativeness: stewardship informativeness and valuation informativeness". He then ranks the alternative information systems under the two different types of demands. It turns out that the ranking of information systems for valuation purposes is different from that for stewardship purposes. The reason for this difference is roughly the following. In valuation (nonstrategic) settings, the value of the information system depends on how well the signal updates the prior beliefs of the decisionmaker. As a result, the value of the information system depends upon the properties of the joint probability structure. In 13 A takehome exam is a good example. Some students may not like a takehome exam (i.e., have access to additional information sources) because the exam may be harder. 14 Gjesdal [1978] called this decisionmaking purposes. We believe the word decisionmaking should be reserved for general uses that include decisionmaking in both strategic and nonstrategic settings. So we use valuation instead of decisionmaking here. 22 incentive settings,"5 stochastic properties associated with the other party's behavior both on and off equilibrium paths are important. Consequently, the value of information hinges on the properties of the likelihood ratios of equilibrium versus offequilibrium behavior." Feltham and Xie [1994] expand this idea into multitask agency settings, where the agent has more than one productive, but personally costly, act. One important insight is that while an information source (e.g., the stock price of a firm) may efficiently aggregate publicly available information for valuation purposes, it is not likely to be an efficient aggregation for incentive purposes. This justifies the use of additional performance measures (e.g., an accounting signal) to evaluate employees even though some other aggregate information (e.g., the stock prices) has already been used in the labor contract. The driving force behind the result is, again, the difference between the valuation and the stewardship uses of information. Similar results are obtained in variant models in Bushman and Indjejikian [1993] and Baiman and Verrecchia [1995]. Accounting Structure From centuries of accounting practice, accountants have accumulated a large collection of measurement procedures and techniques to collect and process the recording of economic events regarding the accounting entity. This has lead to recognizable patterns in the practice of accounting. Examples are the fundamental accounting equation, the use of lowerofcostor s1 In this dissertation, incentive and stewardship are used interchangeably. 16 In Holmstr6m [1979], inclusive information systems (information system A includes information system B if B provides a signal x and A provides the same signal x and an additional signal y) are compared in an principalagent setting. He developed the informativeness criterion for an additional signal to have marginal value. His results were further augmented by Kim's [1995] meanpreserving spread (MPS) criterion. Also, see Shavell [1979] market valuation, and conservatism more generally. Collectively, we call these common procedures and practices accounting structure. Looking at a specific accounting structure, Brief and Owen [1970,73] phrase the accounting depreciation problem in a statistical estimation setting. Optimal depreciation schedules are derived under the assumption that users of the accounting information want to estimate the economic rate of return. Statistical estimations (e.g., leastsquare methods) are employed as the theoretical framework. The work of Edwards and Bell [1961], with further development by Peasnell [1982] and Feltham and Ohison [1995], gives valuation meaning to the clean surplus accounting relationship. This line of work theoretically links the economic variables (e.g., expected present value of future cash flows) and the accounting variables (e.g., book value and abnormal accounting earnings). Under mild assumptions, the clean surplus relation preserves the valuation equivalence of the two. Implicitly, valuing the firm using accounting numbers is the objective of the users, although this demand is exogenous to the models. Demski and Sappington [1990] construct an accounting model with explicit accounting features such as accruals and valuation language.'7 They identify the conditions under which the accounting income measurement fully reveals the underlying information about the firm. They suggest that accounting accrual notion may not interfere with (and better yet, may be essential for) providing underlying information to the audience. The works of Ryan [1995] and Beaver and Ryan [1995] feature accounting structures such as delayed recognition and conservatism. For example, Beaver and Ryan [1995] study the effect of these features on the BooktoMarket ratio and the predictability of security prices. 17 In their paper, these two features are called tidiness and consistency, respectively. 24 Although the study has the appeal of accounting structure, demand for information with such a structure was not the focus of the attention, nor was it the purpose of their study. Antle, Demski, and Ryan [1995] consider the interaction between accounting and nonaccounting sources of information in a valuation setting. Summary The field of information economics has provided a framework to ask interesting questions regarding the use of information. It emphasizes the decisionmaking context, which renders the demand for information endogenous. Studies on accounting structure have made specific accounting apparatuses (e.g., depreciation, clean surplus, and accruals) the focus of attention. The logical next step is to combine these two literature in order to ask accounting questions in an explicit decisionmaking context. One such study is Antle and Demski [1989]. They explicitly model the revenue recognition rules within a particular decisionmaking context. In their model, revenue recognition is framed as an early production of information about the prospect of the future cash flow. The recognition problem is the tradeoff between the quality and the timing of the information. The value of this early information production (or early resolution of uncertainty) is derived from better consumption planning. The financial market is highlighted, although labor market frictions (e.g., moral hazard and asymmetry of information) are also present. In order to give theoretical meanings to practical terms like the "earnings cycle" and "critical event," a particular production technology described by a Markov process is adopted, which simplifies the labor input space.'" The main result of their paper is that straightforward characterization of optimal revenue recognition rules (e.g., early or late recognition) are not 18 Specifically, the labor input is only required in the first period of a threeperiod model, which starts a particular Markov chain, so the number of incentive compatibility constraints is reduced. apparent even in elementary settings. Further, the characterization is greatly confounded if other concerns (e.g., truthtelling) are considered simultaneously. Their model is a useful benchmark setting to ask accounting recognition questions in agency settings. Conclusions The traditional measurement perspective in accounting stresses connotations of accounting items like assets and income. Without modem analytic methods, earlier writers "skipped" the step of developing an explicit demand for accounting measurements; so they focused on the specific aspects of accounting measurement structure (e.g., the nature, the definition and the procedure). Today, ways to explicitly model information are available and the information content theme stresses the use of accounting numbers in decision under uncertainty. Issues like alternative uses and sources of information are carefully studied. Accounting structure has been, unfortunately, neglected to some extent. The famous "fan diagram" in Ball and Brown [1968], in a sense, challenges accounting researchers to think deeper about the comparative advantage of accounting as a source of information. One important observation of the diagram, confirmed by subsequent studies with refined research methods and by studies in security markets outside the United States, suggests that most of the security price adjustments are made prior to the announcement of accounting numbers. Other information sources appear to be more timely in conveying information to the security market than the typical accounting source. To be able to examine the comparative advantage of accounting as a source of information, we believe one must bring the two literatures (i.e., information content and accounting structure) together. Without the explicit consideration of the structure of accounting measurement, no conclusions can be drawn about accounting specifically. Without 26 the decisionmaking paradigm, one cannot assess the usefulness of accounting information, let alone its comparative advantage over other sources. Figure 21: Selected History of American Accounting Thoughts and Practices Outside Influence Theory of Accounting Preclassical 1920's Classical economics 1930's Inflation acc. Sweeney 1933 AAA Statements Keynesian "Tentative 1936 1940's Economics 1950's Game Theory Nash Decision Blackwell 195 Info. Economic Marschak Entity Theory Paton 1921 Proprietary Canning 1929 HistoricalCost Acc. "Acc Prin. 1941 Paton & Littleton 1940 "Acc Con. 1948 Fund Theory Vatter 1947 "Acc Con. 1951 Accounting Structure "Acc and Axiomatics Rep. Std. 1957 Mattessich 1957 Ijiri 1965 Cont Comp. Acc ASOBAT 1966 Chambers 1966 Information Content Econ. Measurement Butterworth 1972 Edwards and Bell Demski 1972 1961 Feltham 1972 Transaction & Event Modern Financ Ball & Brown 1970's CAPM Beaver 1968 Empirical Fama Use of ac. Info. Rational Exp empirical analyti Lucas' sec. price exch. Sorter 1969 Deprecations Brief & Owens 1970, 71 Critique literature models Econ. Of Agency 1980's Ross, Jensen Holmstrom Strategic Accounting 1979 compensation Revenue Recog. Gjesdal 1978 income smoothing Antle & Demski 1989 Accrual Accounting Demski & Sapp. 1990's 1990 Clean Surplus Feltham & Ohison 1995 Practice of Accounting Balance Sheet Emphasis flexibility, mgt. Service Nopar Stock problem Outside Influence Industrial Revolution Bankers Demands Free Economy Pragmatic Theory Depression Sanders, Hatfield, & Moore SEC Income Statement Emphasis Investors earnings power Demands Committee on Accounting PostWWII Procedures (CAP) inflation Replacement Cost Controversy Accounting Principles Board (APB) Financial Accounting Standard Board (FASB) LIFO, FIFO issues Current cost (FAS 33) Gen vs. Spe. Inflation Adj. FASB Concept Statements relevance & reliability Market value Back to Balance Sheet Dirty Surplus Acc. Public Control SEC, FTC, GAO, CASB OSHA, IRS ICC, FCC, HUD ERISA, DOD Oil Crisis Inflation Deregulation S&L crisis Fin. market innovations Info Tech Explosion International CHAPTER 3 ACCOUNTING RECOGNITION, MORAL HAZARD, AND COMMUNICATION Introduction We begin our analysis by constructing a multiperiod agency setting where the principal's major concern is motivating a privately informed agent. Alternative recognition rules partially convey the agent's private information at different points in time. We then analyze the usefulness of these recognition rules. Next, a manager's selfreport is introduced, playing the role of a nonaccounting information source. We use this expanded setting to study how other information sources affect the use of accounting information and the choice of the optimal recognition rule. By adopting an agency perspective, the results of this chapter add new insights to the recognition debate. First, we provide a setting where it is best to have recognition occur in the period when the moral hazard problem is most critical rather than the period when the most uncertain event in the earning process takes place. Second, and more importantly, we show that when other information sources are present, accounting serves the role of a veracity check. Specifically, contracting on an audited accounting signal helps encourage a truthful selfreport by the manager. While the selfreport is, in equilibrium, useful in predicting future cash flows, we show it is the pending accounting signal that ensures the selfreport is reliable. Third, the existence of an earlier selfreport, coupled with this veracity check role of accounting, suggests that delaying accounting recognition may be optimal at times. While feeding timely information to the security market is not the comparative advantage of accounting, the veracity check role makes accounting uniquely valuable among competing information sources."9 Organizational Setting A stochastic technology is operated by a manager (the agent) who is hired by the owner (the principal) of the technology. This agency relationship lasts for three periods. The agent supplies two unobservable labor inputs, denoted a, e A (t = 1, 2), at a pecuniary personal cost of c(a,).2" To use the simplest model to convey our main ideas, we employ binary structures wherever possible. Each labor input can be either high or low: A= {H, L} with c(H) > c(L), and c(L) set to 0. After supplying the labor input in period t, the agent privately observes a signal, denoted z, e Z (t= 1, 2). Each signal can be either good or bad news: Z={G, B). A single output, denoted x e X, is realized and observed publicly at the end of the third period. The output can be zero or one: X = {0, 1}. The monetary value of output x is given by qx with q > 0. The principal pays I, to the agent at the end of period t based upon the publicly available information at that time. Figure 1 summarizes the sequence of events. We neutralize the principal's risksharing desire and consumption timing by assuming the principal is riskneutral and only cares about the endofthegame net cash flow. The principal's utility is given by qx I, I2 13. The agent is riskaverse, with the utility function U(I,, 12, 13; a, a2) = exp(r(I,+I2+I3c(a,)c(a2))). The utility function exhibits constant absolute risk aversion '9 Sundem, Dukes, and Elliott [1997] make a similar point in their monograph on the value of accounting and auditing. Auditing plays a very important role here. To be able to serve as a veracity check on other sources of information, the integrity of accounting information must be sustained. 2 In the third period, there is no explicit productive input provided by the agent. The model yields the same results if an unobservable and productive a3 is admitted. Sidestepping an explicit a3 merely simplifies the analysis. 30 (CARA) with the ArrowPratt measure r (> 0). It is also multiplicatively separable over time periods. This means the agent has no incomesmoothing desires and only cares about total income less total personal cost, with a zero discount rate.21 If the agent chooses not to participate in the agency, his opportunity utility is U. Let P(x, z,, z21 a, a2) denote the joint probability of (x, z, z2) given the agent's input sequence (a,, az). In this section and Section III, we assume: [Al] P(x, z,, z2 a, a2) = P(xI a, a2) P(z,ia,) P(z21az) [Al] entails certain separability about the stochastic environment. In particular, given any input sequence, x, z,, and z2 are conditionally independent. [Al] also implies the agent's choice of a, does not affect the probability of z2 and his choice of a2 does not affect the probability of z,. The latter is natural since z, is realized before a2 is chosen. We label the agent's effort and the output such that high effort in either period produces a higher chance of success, i.e., P(x= I HH) > P(x= 1 I HL) > P(x= 1 LL) and P(x=l IHH)> P(x=l ILH) > P(x=l LL).22 Following the agency literature, we assume there is decreasing return to effort such that the Concavity of Distribution Function Condition (CDFC) is satisfied:' [A2] P(x= IHL) > 6 P(x=l LL) + (16) P(x=l HH) P(x=l ILH) > 0 P(x= ILL) + (16) P(x= IHH) 21 Presumably, one can assume banking opportunities exist and explicitly model the consumption plans for the agent. However, it would create unnecessary distractions for the model (e.g., the information set available to the banker, how the banking market works, etc.). This assumption on the agent's intertemporal tastes is a simple way of sidestepping the distractions. See Malcomson and Spinnewyn [1988] and Fudenberg et al. [1990]. 22 We adopt the mnemonic notation HH to represent (H, H), and similarly for HL, LH, LL. 3 As shown in the proof of proposition 1, with CDFC, input sequence (L, L) is so unproductive that in designing the optimal labor contract, the principal can ignore the incentive compatibility constraint involving (L, L) once other constraints are satisfied. See Grossman and Hart [1983] for more on the CDFC assumption. where 6 = 1/(1 + exp(r(c(H)))) Similarly, we label the news such that high effort produces a higher chance of good news, i.e., P(z,=Gla,=H) > P(z,=G a,=L) and P(z2=Gla2=H) > P(z2=Gla2=L). Given [Al], one can "learn more about act a," from output x and signal z, than from output x alone. Formally, we say z, is incentive informative about a, conditional on x. Following Gjesdal [1978], we adopt the following definition of incentive informativeness: [DI] The information source giving signal z is said to be incentive informative about act a e {H, L} conditional on x if P(zlx, H) P(zlx, L) for some z, and some x. Intuitively, an information source is incentive informative about a, if different choices of a, produce different conditional (on x) probability specifications of z. [Al] implies z, is informative about a, conditional on x (t= 1, 2). Effectively, z, is an independent monitor of a, that is privately known by the agent. Since the agent observes some signal before choosing a,, his secondperiod policy can be thought of as mapping a: {all possible signals available to the agent before a2 is chosen}  {H, L). Along with his firstperiod act, the agent's strategy for the entire game can be represented by (a,, a). We assume q is large enough that the principal always prefers the agent to provide high effort in both periods regardless of what information might become available to either party. Thus, the preferred strategy is (H, a"), where a" denotes the second period policy where high effort is provided for all possible prea2 signals.' 24 In general, the optimal labor input is endogenous to the principal's problem. In this dissertation, we neutralize the production decision in order to focus on the incentive use of accounting information. Statement of the Principal's Problem We formulate the principal's problem in our basic model where only output x is contractible. The principal can collapse the three periodic payments into a single payment I(.) at the end of the game because both parties only care about total compensation. Let E[U(I(x);)  a2, a] denote the agent's expected utility if he adopts strategy (a,, a) under the payment scheme I(x). To induce (H, a"), the principal faces the following mechanism design problem: C' = minimum E[I(x)  H, a"] = Ex P(x  HH)I(x) (1) I(x) Subject to E[U(I(x); )  H, a"] U (2) E[U(I(x); ) I H, a"] E[U(I(x); )  a, a] V a,, a (3) The principal chooses the best payment plan I(x) to minimize the expected compensation to the agent (expression (1)), subject to the individual rationality (IR) constraint (inequality (2)) and incentive compatibility (IC) constraints (inequalities in (3)).` We assume a solution to the optimization problem exists.27, 28 2 The agent's induced decision tree in the basic model is the following: aa(aaG 1(x) aE{H,L) z,E{G,B} a2c{H,L} z2e(G,B) xe{0,1} 26 To avoid uninteresting cases, we assume the set of possible payment schemes satisfying constraints (2) and (3) is nonempty. 27 See Grossman and Hart [1983] for details on existence. 28 [Al] and [A2] imply that when solving the optimization problem, the only IC constraints that can bind are those involving strategies (L, a") and (H, aL) where a' denotes the secondperiod policy in which low effort is provided for all possible prea, signals. (See the proof of proposition 1.) The IR constraint always binds due to the assumptions on the preferences of the principal and the agent (Holmstr6m and Milgrom [1987]). Accounting Recognition and Moral Hazard We now introduce accounting recognition. We show that alternative labor market frictions affect the usefulness of the accounting recognition rules. Accounting Recognition In our setting the recognition issue centers upon when to produce information that can help the principal control the agent's actions. We consider two recognition rules: one calls for early and the other for late recognition. The early recognition rule, called R,, produces an accounting signal denoted y, e Y = {1, 2} at the end of the first period. We model y, as a noisy signal of z,. The late recognition rule R2 produces accounting signal y2 e Y at the end of the second period. Similarly we treat y2 as a noisy signal of both z, and z.29 Essentially, y, (resp. Y2) is a garbling of z, (resp. (z, z2)).* The choice between R, and R2 is a choice between early (but incomplete) and late (but comprehensive) information.3' Since accounting signals are publicly reported and subject to audit, we assume y, and y, are contractible. Principal's Problem with Accounting Recognition The principal's contracting problem under R, can be written as the following program: C(R,) = minimum E[I(x, y,) I H, a"] (4) I(x, y, 29 In the third period, an "adjusting accrual" y3 can be created to make sure y,+y3=qx (t= 1, 2). Knowing x and y,, y3 is clearly redundant in our setting. 30 Here, accounting merely transmits, with some noise, the agent's private information. In reality, accounting systems may require some new information to be created in addition to conveying what the agent privately knows. Due to tractability concerns, we assume there is no new information generated by accounting. 31 We elaborate on how aggregation occurs in the way we model accounting recognition. It can occur over time. An accounting system does not always produce information every time some private information is available. Under R, (resp. R2), accounting is silent when z2 (resp. z,) is known to exist. On the other hand, the aggregation can occur over the realizations of the underlying private signals. Due to the noise in y,, not all possible realizations of the underlying signals z, can be uniquely conveyed through the accounting apparatus. Subject to E[U(I(x, y,); ) H, a"] a 1! (5) E[U(I(x, y,); )I H, a"] a E[U(I(x, y,); )l a, a] V a,, a (6) Notice under R, that the strategy set of the agent expands because he can base his secondperiod input a2 on the realizations of accounting signal y, as well as his private signal z, (i.e., the agent's secondperiod policy is a mapping a: ZxY A).32 Usefulness of Accounting Recognition The principal weakly prefers accounting recognition R, to no recognition, i.e., C(R,) s C' (t= 1, 2). Clearly, the principal can always choose (and commit) not to use the additional information generated by the accounting system and resort to the optimal contract in the basic model. (The original optimal contract is feasible in the expanded program.) Proposition 3.1: Assume y, and Y2 are not independent of z,, and y, is not independent of z2, then: (i) P(x = 1 LH) > P(x = 1 HL) implies early and late recognition are useful; and (ii) P(x= 11 LH) < P(x = 1 HL) implies late but not early recognition is useful. When P(x = 1 LH) > P(x= 1 I HL), shirking in the first period (i.e., (L, a")) is "less likely to be detected" than shirking in the second period (i.e., (H, aL)). In turn, the principal is more concerned with the agent supplying low effort in the first period than in the second period. In this case, both early and late recognition rules are useful because both y, and y2 are generally incentive informative about a, conditional on output x." When P(x= 11 LH) < P(x=I 1 HL), the principal is more concerned with the agent supplying low effort in the second 32 The agent's induced decision trees under R, and R2 are: R,: % I(x, y,) ae{H,L) ze{G,B} y,E(l,2} a2E(H,L} z2e{G,B} xe(0,1} R2: 'A  % a a ax, 2y) a,e{H,LJ z,E{G,B) a2e{H,L} z,e{G,B}) y,(1,2} xe{0,1} 33 Under the restrictive condition that y,2 is independent of z,, we have the stronger result that only early recognition is useful. period. Here only late recognition is useful because y2 is incentive informative about a2 conditional on x while y, is not. In short, the principal's preference over R, and R2 depends upon which moral hazard problem (a, or a2) is more critical." Delayed output realization, among other features, contributes to the above result. In the basic model, output x is used to control the agent's labor inputs in both periods. Technically, this implies that, in the basic model, the two relevant IC constraints involving (H, aL) and (L, a") are nested. With our binary structure, each constraint essentially imposes a "steepness requirement" on the incentive scheme. As a result, only the steeper of the two requirements is in effect, leaving the other IC constraint inactive.35 Naturally, if the IC constraint involving (L, a") is inactive, information about a, is useless. This is in contrast to repeated moral hazard models (e.g., Lambert [1983], Rogerson [1985], Radner [1985], Malcomson and Spinnewyn [1988], and Fudenberg et al. [1990]) where periodic output is observed between the agent's labor inputs, and longterm effects are typically neutralized. Therefore, the issue of nested IC constraints is not present. Discussion The key idea in this section is that the optimal recognition rule is affected by the nature of contracting frictions. "When to recognize" depends upon which of the two labor inputs poses a more critical incentive problem. Earlier studies of informativeness criterion in agency settings (e.g., Holmstr6m [1979]) and Kim [1995]) replace global IC constraints with a single local constraint. Here, there are two IC constraints that may bind. A signal's informativeness about the agent's act may not guarantee its usefulness in contracting because the IC constraint with respect to that act may not bind. 35 There is an issue of redundant constraints here. IfP(x=l HL)=P(x=l LH),thetwoIC constraints are identical and one is clearly redundant. Technically, it causes an indeterminancy of the Lagrange multipliers associated with the two IC constraints. If this is the case, the rank condition in the ArrowHurwiczUzawa theorem is not satisfied (Takayama [1974]). This rank condition is a sufficient condition for the validity of characterizing the solution using the KuhnTucker conditions. To avoid complicating the matter, we simply assume P(x= I LH) P(x=l IHL) to satisfy the rank condition. The notion of critical event has played an important role in recognition debates since Myers [1959] first introduced such a concept. Take revenue recognition as an example. Usually, some critical event, such as a transfer of merchandise, must occur to trigger revenue recognition. Most of the literature treats uncertainties associated with the major events in the earning process as the focus of the recognition issue (e.g., Johnson and Storey [1983]); the control aspect of these events is not at center stage. This chapter stresses moral hazard concerns in the recognition debate. When control is a viable concern, the optimal time to produce information about managerial actions is not when the most uncertain event in the earning process has occurred, but when the critical labor input appears. To illustrate, when P(x= 1 LH) < P(x = 1 HL), we can infer that firstperiod labor input a, is marginally more productive than secondperiod input a2. If we treat labor inputs as purely random events (i.e., no control problem is present), the critical event in this earning process occurs in the first period in the sense that knowing a, leaves less uncertainty about future cash flow x. However, in the presence of moral hazard, Proposition 1 tells us that information about a, is useless while information about a2 is valuable. Therefore, the critical event occurs in the second period. In short, the critical event in valuation settings can be different from that in agency settings.31 3 We use a numerical example to elaborate. Let P(x= iHH), P(x= 11HL), P(x= 1LH), and P(x=l ILL) be 0.8, 0.7, 0.6, and 0.3 respectively. Suppose the labor inputs are purely random (1/4 probability for all four combinations). The prior probability P(S) is .6 (=(.8+.7+.6+.3)/4). If a, =H, the posterior P(x=l la=H) = (.8+.7)/2 =.75; and similarly if a,=L, P(x=la,=L)=.45. Changes from prior are 15. On the other hand, knowing az only changes the prior by 10. Therefore, a, can be thought of as "the most uncertain event" in the earning process because knowing the realization of a, changes the posterior probability the most. However, if the agent's acts are not random but subject to moral hazard, by Proposition 1 we know (since P(x= 11 LH) < P(x= 1 HL),) the useful information is about a,, not a,. Accounting Recognition and Veracity Check In this section, we consider a setting where the agent's private signals are informative about the realization of output x. Communicating such information (e.g., a selfreport on z, by the agent) can reduce agency costs (Christensen [1981] and Melumad and Reichelstein [1987]). We study the role of accounting recognition in such a communication regime. In the previous section, accounting signals were used to control the agent's labor inputs. In this section, they are used to control the agent's selfreport as well. Valuation Information When signal z, is informative about the output x, we say it is valuation informative. Following Gjesdal [1978], we adopt the following definition: [D2] The information source giving signal z is said to be valuation informative about future cash flow x conditional on signal to in the presence of input sequence (a,, a2) if P(zlx', t, a,, a2) P(zlx", o, a,, a2) for some x's x", some z, and some w. In our context, the conditioning information source to may refer to other z, or the accounting signal y,. Intuitively, z is valuation informative about x if z is not independent of (x, w) for a given input sequence. [Al] clearly precludes z, from being valuation informative about x because it assumes independence among x, z,, and z2 for all input sequences. We replace [Al] with two assumptions. First, we assume: [A3] P(z, a, a2) = P(z,) for all (a,. a2), t=l, 2; and P(z1, z2 x, aa, a2) = P(z, Ix, a1, a2) P(z2 x, a,, a2) The agent's labor input choice does not affect the probability of z,." The private signals z, and z2 are conditionally independent. In addition to [A3], we assume for all z,: 7 This assumption isolates the veracity check role of accounting information. If z, is also incentive informative about a,, then accounting signal y, is also incentive informative about x when z, is not known. It will be hard to tell whether the usefulness of y, is attributed to its veracity check role or its incentive informativeness. [A4] P(xz,=G, a,, a2) P(xlz,=B, ai, a2) when (a1, a2) = (H, H); P(xlz,, a,, a2) = P(xja,, a2) when (a,, az) = (H, L), (L, H), (L, L) Under [A4], z, and zz are valuation informative about x only when the agent provides high effort in both periods. When the agent supplies low effort in either period, x, z,, and z. are mutually independent (in fact z, and z2 reduce to pure noise).38 One can interpret [A4] as a complementarity effect among the two factors of production (i.e., the agent's efforts and the information content of the signals). If the agent works hard, he is likely to receive forward looking information. If he shirks, his information may not be useful to him.39 Principal's Problem Turning to the contracting problem with communication, we focus on a setting where a single message is reported by the agent immediately after he privately observes z, Therefore, the agent's selfreporting strategy is a mapping m: Z Z, with m(z,) denoting the message reported when z, is observed. Relying on the Revelation Principle, we restrict our attention to truthtelling mechanisms.4 Let mn denote the truthtelling reporting strategy and let E[U(I(x, y,, m()); )la, m, a] denote the agent's expected utility if he supplies input sequence (a,, a) 38 [A4] simplifies the derivation of the sufficient conditions for communication to be strictly preferred (Proposition 2). However, Proposition 3, the more important result, does not rely on [A4]. 39 We give a numerical example of such a probability structure. Consider the following: (a,, a,)=(H, H) (a, a2)=(H, L) (a,, a2)=(L, H) (a,, a,)=(L, L) x= 1 0 1 0 1 0 1 0 z,=G .51 .09 .36 .24 .42 .18 .18 .42 z,=B .29 .11 .24 .16 .28 .12 .12 .28 Consistent with [A3], P(z, =G a,, a2) = P(z, =G) = .6. [A4] is also readily verified. The joint probability structure of x and z2 can be constructed similarly. 0 Two conditions are assumed: (1) full communication is costless; (2) the principal has commitment power. See Myerson [1979] and Harris and Townsend 11981] for more on the Revelation Principle. and adopts reporting strategy m under payment scheme I(x, y,, m(.)). The mechanism design program for the principal can be written as: C(R,, m) = minimum E[I(x, y, m(z,)) I H, m', a"] (7) I(.) Subject to E[U(I(); )  H, m', a"] 2 U (8) E[U(I(); *)IH, mT, a"] E[U(I(); *)Ia,, m, a] V a,, m, a (9) The incentive scheme I(*) is now a collection of contingent payment schemes indexed by the agent's message m(z,). Effectively, the payment schedule depends upon m(zi), as well as the public information x and y,. Notice the set of IC constraints (inequalities in (9)) also includes the truthtelling constraints.4' Demand For Veracity Check We begin with the case where no recognition rule is used. In this case, the agent issues a selfreport on z, but the two parties can only contract on x.42 Proposition 3.2: When only x and the agent's message are contractible, communication of z, is strictly valuable if (i) P(x = 1 ILH) > P(x = 1 IHL); and P(x= IIHH) P(x= OILH) P(x= liz, = G,HH)P(x= 0[z, = B,HH) (ii) P(x= ILH) P(x= 0OHH) < P(x= 1 z, = B,HH)P(x= 0z, = G,HH) 41 With communication, the agent's induced decision trees under R, and R, are: RI:  a  Iat I(x, m, y,) a,e{H,L} z,E{G,B) m(z,)e{G,B} ye{l,2} ac{H,L} z,e{G,B) xe{0,1} R,: Ua %.. %,a,(at I(x, m, y,) a,e(H,L} ze(G,B} m(z,)e{G,B} ase(H,L) z2e{G,B) yze{l,2} xe{0,1} 42 The agent's decision tree in this special case is: a,aa ze(GB} m(z IGB)(x, m){HL z a,e(H,L} zE{G,B} m(z,)e{G,B) a2e{H,L) ze{G,B} x{0,1} Intuitively, the two conditions appeal to mutual gains through communication. Under condition (i), the only binding IC constraint involves (L, a"), absent communication. This gives the principal more flexibility in designing the optimal contract. Condition (ii) requires that the probability revision caused by z, is large enough to make the communication worthwhile.43 We give the following numerical example to illustrate Proposition 2. Suppose, P(z =G)=.6, P(x= 1z,=G, HH)=.85, P(x=1 I z =B, HH)=.725, P(x=l LH)=.7, P(x= lIHL)=.6, P(x=l LL)=.3, c(L)=0, c(H)=2,000, r=.0001, and V = exp(rl5,000). Without communication, the expected payment to the agent is 21,640. With a selfreport on zi, the expected payment is 21,542. Notice condition (i) and (ii) in the proposition can be verified: (i)P(x= ILH) = .7 > P(x= 1HL) =.6; and (ii) (.8) (.3)/((.7)(.2)) = 1.714 < (.85) (.275)/((.725)(.15) = 2.149. When communication is strictly valuable, accounting recognition is useful as long as y, reveals something about the realization of z,. In other words, there exists a strict demand for a veracity check for the earlier selfreport. Proposition 3.3: Assuming communication is strictly valuable, recognition rule R, is useful ify, is not independent of z1. Recall that accounting signal y, (resp. Y2) is at best a garbling of the agent's private signal z, (resp. (z,, zz)). Normally when y, is a garbling of zi, contracting on y, is not useful when z, is already used in the contract. In our setting, however, z, is selfreported through m(z,), and the selfreporting is subject to additional (induced) moral hazard." In turn, 4 This is similar to the notion of information gap in Christensen [1981]. The moral hazard on reporting is induced because any misreporting per se does not factor into the agent's utility. The agent has no incentive to lie just for the sake of lying. However, the agent is also asked to provide unobservable, and personally costly, labor inputs, as well as the report. contracting on accounting signal y, helps the principal combat the moral hazard associated with the selfreporting. Should he choose to lie in his report (i.e., m(zi)*z,), the agent runs the risk of being "punished" by the upcoming accounting report. This disciplining role is what makes y, valuable for the principal. Discussion In general, an entity's accounting report and the voluntary disclosure by its managers are both useful to its stakeholders. In our setting, both the accounting signal (y,) and the self report (m(z,)) help the principal mitigate his contracting problem. More importantly, the two sources of information are complementing each other as well. The selfreport has the comparative advantage of being early and having the ability to predict x. However, it lacks trustworthiness because, if not controlled, the agent has the incentive to lie to his advantage. On the other hand, the accounting signal may not be valuation informative about x conditional on a truthfully reported z, by the agent. But it has the advantage of being a veracity check on the agent's earlier selfreport because the typical accounting report is subject to audit and there is no (or considerably less) incentive problem associated with this source.45 This is the key to understanding the usefulness of accounting information in our context. This result has implications for the different functions served by accounting. In empirical research, especially event studies, earnings announcements fail to explain a large part of security price movement, and this is interpreted as suggesting, if not implying, accounting 45 The auditing process and reputation management by the accounting professionals are outside of this model. We take the easy route of assuming they result in no incentive problems associated with these professionals. But it is by no means implied the process and behavior are unimportant. The growing literature on earnings management has indicated that managers have, on the margin, some control over the accounting reports. This possibility is absent in this chapter and is explored in Chapter 4. Our current focus is the interaction between audited accounting reports and other, unaudited sources of information. reports lack usefulness (e.g., Lev [1989]). In this chapter, however, accounting is useful not for its expediency in providing timely valuation information to the security market, but for its ability to provide a veracity check on other, unaudited sources of information. These other sources (e.g., the manager's selfreport) are more readily controlled because there is a pending, undisputable accounting report. Therefore, the noted empirical regularity does not necessarily imply the lack of usefulness of accounting information. In fact, limited reaction to the accounting report is expected in equilibrium. The important insight is that the usefulness of accounting comes from its disciplining function through labor contracting." Communication and Optimal Recognition Finally, we examine how the presence of the earlier communication changes the usefulness of alternative recognition rules. We use a series of numerical examples to illustrate how the presence of communication may prompt the principal to favor the late recognition rule (R2). We continue with the numerical specifications from the last numerical example; in addition, suppose z2 is such that P(z2=G)=0.5 and P(x= 11 z2=G, HH)=0.82. Under R,, y, is a garbling ofz, with P(y,=2z,=G) =.8 and P(y,=2z,=B) =.05. Under R2, P(y2=2z2=G) = .55 and P(y2=2I z2=G) = .45. In Figure 2, we plot the four expected payments C(R), C(R2), C(R,, m), and C(R2, m) for different values of conditional probability r  P(y2=21z,=G) with rT e [.5, .8]. Intuitively, higher ri means y2 conveys "more information" about z,. Absent communication C(R2) decreases in Ti as "more information" about z, is available with higher ir. Naturally, C(R,) is a constant as the stochastic property ofy, does not 6 Here the disciplining function is through formal contracting, which is a modeling convenience. In practice, the disciplining may be achieved through managerial reputation and retention, etc. The focus of this study is on the disciplining function, not the form of the disciplining function. change with T. With communication, C(R2, m) and C(R], m) display a similar pattern. Examination of Figure 2 shows that in the parameter region where ii ranges from approximately .505 to .763, communication makes delaying accounting recognition optimal (i.e., R, is preferred absent communication and R2 is preferred with communication).47 The key idea shown in these numerical examples is that other information sources (e.g., the manager's selfreport) interact with the accounting source. Therefore, when evaluating alternative recognition rules, one must keep in mind this interactive effect among the proposed recognition rule and other sources of information. In this instance, the presence of other information makes delaying the accounting recognition optimal. Conclusions In accounting theory and practice, recognition issues have been controversial. We seek to enrich the debate by acknowledging the incentive use of accounting information and the interaction between accounting and other information sources. We cast a recognition choice problem in a stewardship framework and allow other information sources into the picture. We see that the optimal recognition choice depends on whether the moral hazard at the proposed recognition time is critical, not whether the most uncertainty about the earning process has been resolved. When we allow other information sources into the model, the veracity check role of accounting surfaces in our analysis. Finally, the presence of other information may call for later recognition. In our model, the contracting and the confirmatory roles of accounting are highlighted. We see these two roles as the comparative advantage of accounting as a source of information. 47 Analytic isolation of this timing delicacy remains an open question. 44 Accounting is valuable to the extent it is credible, comprehensive, and subject to careful and professional judgment. Naturally, this makes accounting information a perfect candidate for contracting and confirmatory uses. While other information sources may be more timely in providing valuation information about an entity, audited accounting information, when used in explicit or implicit contracts, helps ensure the accuracy of the reports from other sources. Tractability concerns clearly limit the analysis. As an interesting extension of the study, we can allow the agent to have partial control over the accounting apparatus. This will enable us to examine the accounting structure in the more realistic setting where performance manipulations may exist. Figure 31: Event Sequence of Models in Chapter 3 t=1 t=2 t=3 agent's inputs a, e {H, L) a2 E {H, L} agent's private information z, E {G, B} z2 e {G, B} output x e {0, 1} accounting recognition rules: early: R, y, e {1, 2} n/a late: R2 n/a Y2 E {1, 2} agent's net compensation lic(a,) 12c(a2) 3 principal's net cash flow I, 12 qx 13 Figure 32: Expected Payments under Alternative Recognition Rules and Communication Regimes 21800 21600 21400 21200 a 21000 20800oo 20600. 0.5 0.52 0.54 0.56 0.58 0.6 0.62 0.64 0.66 0.68 0.7 0.72 0.74 0.76 0.78 0.8 P(y2=21z,=G) C(R2) C(R1) ""_1C(,, m) C(R2, m) m CHAPTER 4 ACCOUNTING RECOGNITION AND PERFORMANCE MANAGEMENT Introduction We continue our analysis by extending the agency setting of the previous chapter. In Chapter 3, the agent was assumed unable to select the prevailing recognition rule. In this section, we examine the more realistic setting where the agent has partial control over the recognition rule. We modify the model in Chapter 3 so the manager can, at the margin, shift a portion of the "reported" output across periods without being detected. We study the resulting performance management incentives. We discover that with limited communication and linear contracts, performance management can appear as equilibrium behavior, and even be encouraged by the principal. The predictions of the model provide new theoretical and empirical insights into performance management phenomena. As a prelude to our analysis, performance management studies in accounting literature are reviewed. Next, we provide the details of the model modification. Then we analyze efficient contracting under different information regimes (e.g., recognition rules) and derive the main results, followed by a discussion of recognition and performance management. Finally, we discuss some important econometric issues regarding the empirical investigation of performance management. Performance Management Literature Managers generally have some discretion or influence over reported performance measures. One such discretion is selective use of accounting recognition. Schipper [1989] defines earnings management4 as "a purposeful intervention in the external financial reporting process, with the intent of obtaining some private gain." (p. 92). There have been numerous academic studies regarding the causes and consequences of such discretion. The most important question in this literature has been under what conditions these performance management practices are possible. In most analytic studies, researchers provide explanations by identifying economic settings (e.g., consumption planning and incentive design) where performance management is equilibrium behavior. Arya et al. [1998] organize the possible explanations according to possible violations of the Revelation Principle. The Revelation Principle states that any equilibrium outcome can be replicated by a truthtelling equilibrium outcome in which the agent reports all of his private information. However, the Revelation Principle relies on the assumptions of full commitment power, costless communication and unlimited contracting forms. Looking at potential violations of these assumptions is a natural way to explore endogenous performance management. For example, if there is blocked communication (as opposed to costless communication), performance management may convey information about managerial inputs (Demski [1998] and Dye [1988]) or it may be used to balance other incentives (e.g., crossgenerational share sales in Dye [1988]). Alternatively, if longterm contractual commitment is not possible (as opposed to full commitment power), performance management arises as a way to cope with the limited 4 Schipper also used the term "disclosure management." We use the term performance management. We treat these three terms interchangeably to the extent earnings and disclosure are performance measures of the firm or its managers. commitment ability (Fudenberg and Tirole [1995] and Arya et al. [1998]). Schipper also mentioned other factors such as limited human ability to process information (bounded rationality) and prohibitively high contracting costs as potential reasons. To a certain extent, these factors are also violations of Revelation Principle assumptions. On the other hand, most empirical researchers assume performance management is ongoing and focus on documenting instances of such management. They recognize that certain components of performance measures are not subject to manipulation as accounting institutions (GAAP and auditors) place limits that constrain reporting. This portion of the measure is nondiscretionary. The difference between the total performance measure (e.g., total accruals) and its nondiscretionary portion is deemed discretionary and subject to managerial manipulation. Researchers have spent a great deal of intellectual effort to identify the discretionary component of total accruals. Then they relate the discretionary component to some conjectured motivation for managers to exercise their accounting discretion. These motivations include (1) to seek bonus compensations (Healy [1985]), (2) to avoid debt covenant violations (Bartov [1993]), (3) in anticipation of future expected growth (DeFond and Park [1997]), and (4) to win a proxy contest (Collins and DeAngelo [1990]). Methodological issues regarding estimating discretionary accruals also receive much attention (Dechow et al. [1995] and Kang and Sivaramakrishnan [1995]). One of the unresolved issues between the analytic and empirical approaches to performance management issue is the (un)observability issue. When empirical researchers devise statistical procedures to estimate the "managed earnings," the implicit assumption is such a measure is observable, as least in a statistical sense. Analytic researchers stress that if managing earnings is easily detected, the users of the accounting information, who have more at stake financially than academic researchers, can "undo" the managerial discretion and obtain the "truthful," unmanaged performance measure. Then one is not sure why performance management can exist as equilibrium behavior to begin with. In this chapter, we attempt to add insights to both literature as we construct the theoretical model with empirical implications that are mutually compatible. Modified Model The labor input setup is identical to that of chapter 3. The agent provides a sequence of two unobservable labor inputs, a, e A (t= 1, 2), at a personal cost of c(a,)+c(a2). Each input can be high or low: A={H, L} with c(H) > c(L) = 0. The output setup is different. At the end of period t (t= 1, 2), an output is realized and privately observed by the agent, denoted x, E R (t= 1,2). However, total output x (= x, + x2) is publicly observed at the end of the agency relationship. At the end of the first period, the agent also privately observes a signal z e Z {d, d) where d>0. (We suppress the second period private signal z2.) The monetary value of output x is given by qx with q > 0. Figure 41 summarizes the sequence of events. The periodic outputs are generated by the following random processes: [A5] x, = a, + El x, = k, a, + k2 a2 + z + E2 where H > L and L is set to 0. We further assume 1 > k, > 0 and 1/k,+k,> k2.49 The two random variables e, and e2 are mutually independent and drawn from a normal distribution with mean zero and standard deviation a, i.e., et N(0, 02), t=l, 2. Therefore, the first period output is a normally distributed random variable with mean a, and standard deviation a. 49 These assumptions on the productivity parameters rule out situations where compensation might be negatively related to one of the measures. 51 The second period output has a mean equal to k, a, + k2 a2 and two random shocks (i.e., z and e2). Notice that z provides the agent foreknowledge about whether there will be an increase (i.e., z =d) or a decrease (i.e., z= d) in output in the second period. For simplicity, we assume the probability of either case is .5 so the expected shock is zero and z is independent of the other two random variables (i.e., E, and E2).5 The preferences of the two parties are the same as before. We neutralize the principal's risksharing desire and consumption timing by assuming that the principal is risk neutral and only cares about the endofthegame net cash flow. The principal's utility is given by qx I. Similarly, the agent is riskaverse, with the utility function U(I; a,, a2) = exp(r(Ic(a,)c(a2))), with I denoting the total compensation. The agent has no consumptionsmoothing desires and only cares about the total amount available for consumption (I c(as) c(a,)), with a zero discount rate. If the agent chooses not to participate in the agency, his opportunity utility is U. We restrict the contract form to be linear.5" The total compensation to the agent consists of a fixed salary (6,) and a payforperformance bonus scheme where 6 is an N x 1 vector representing the bonus coefficients and r is an N x 1 vector representing the potential performance measures. [A6] I = 6o + 6' F 50 Similar results obtain otherwise. s1 This restriction is important because Mirrlees [1974] shows that firstbest solutions can be approximated arbitrarily closely by using a nonlinear twotiered contract. See Holmstr6m and Milgrom [1987] for a discussion. 52 Depending on the availability of contracting information, N can be one or more than one. As in Chapter 3, we assume q is so large that the principal always prefers high labor input in both periods. Information Regimes and Analysis of the Model We consider three information regimes: full output observation, aggregate output observation, and accounting reports. Full Output Observation This is a benchmark case where both output measures (xi and x2) are publicly observed. In this case, 6' = [61, 62] and r' = [x1, x2]. The agent's second period policy a is a mapping a: RxZ A.52 Let aH (resp. a L) denote the particular policy where the agent provides high (resp. low) effort regardless of the realizations of x, and z. The principal's problem can be represented by the following optimization program. C1" = minimum E[I(x,, x2 ) H, a"] (10) 60 6, 62 Subject to E[U(I(.); ) H, a"] i U (11) E[U(I(.); )IH, a"] E[U(I(.); *)a, a] Va,, a (12) Lemma 4.1: The optimal linear contract in the full output observation case has: t1* = (1 k,/k2) 6, and 62' = 6/k2, where 6 c(H)/H. In this benchmark case, the two IC constraints associated with the {L, a"} and {H, a')} policies are binding, and this determines the two payforperformance coefficients (i.e., 6, and 62). Given these two coefficients, 60 is chosen so the IR constraint binds. (The preference 52 The agent's induced decision tree under the full output observation regime is: a ed a{ a I (x) aE{H,L} x,e R ze{d,d} a2e{H,L} x2 e R x = xJ+X2 structure of the two parties allows us to deal with IR and IC constraints independently. See Holmstr6m and Milgrom [1987].) We provide a numerical example. Let H = 100, c(H) = 2,000, d = 100, o2 = 5, r=.0001, _U=exp(r 15,000), k, = .5, k2=2. (Notice 1/kl+k, = 2.5 > k2 = 2.) The optimal contract is I'(x,, x2) = 16,256 + 15 x, + 10 x2, and the expected compensation E[I'(x,, x2)] = 20,256. When k2 > k, + 1, the first period labor input (a,) is less productive than the second period labor input (a2). However, since 6'* > 62' in this case, the bonus on the first period output (i.e., $15 per unit of output) is higher than the second period output ($10 per unit of output). This is because a less productive but unobservable act (e.g., a, in this case) is "harder for the principal to infer from the output." Therefore, the principal must place a steeper incentive on the first period output to induce the same labor input level (i.e., H). Given this bonus structure, the agent has a natural incentive to move output, if he can, from the second period to the first period. On the other hand, if we set k2 = 1 so k2 < k, + 1 and keep everything else the same, the solution yields I'(x, x2) = 17,951 + 10 x, + 20 x2, and the expected compensation is E[I*(x,, x2)] = 21,951. Notice in this case, 6,' < 82', and second period output commands a higher bonus than first period output (i.e., $20 vs. $15). The agent's natural incentive is to move output from first period to the second period. Aggregate Output Observation Now consider the case where only aggregate output x (= x, + x2) is publicly observed. In this case, 6 = [6] and r = [x]. This is equivalent to the full output observation case with the added constraint 8, = 62 = 6. 54 Lemma 4.2: The optimal linear contract in the aggregate output observation case has: 6S* = 62' = d' = max {(/(1 +k,), 6/k2, where 6 H c(H)/H. In this case, one payforperformance coefficient is chosen to satisfy two IC constraints. When k2 > kI +1, the first period IC constraint is binding (i.e., 6' = 6/(1 +k1)). On the other hand, if k2 Again, the fixed salary figure (60) is chosen such that the IR constraint binds. Continuing with our numerical examples, when k2 = 2, the optimal contract under aggregate observation is I'(x)= 16,002 + 13.33 x and the expected compensation is E[I'(x)] = 20,668. When k2 = 1, the optimal contract is l'(x)= 17,701 + 20 x and the expected compensation is E[I'(x)] = 22,701. Comparing the two benchmarks, we see, naturally, full observation is preferred regardless of kI. Accounting Report As a third information regime, we introduce accounting reports prepared by the agent. At the end of each period, the agent is to report a single dimensional accounting report y, e R (t=l1,2). The accounting structure requires articulation, i.e., y,+y2=x. Essentially, once y, is declared by the agent, he does not have any discretion over the y2 report. The agent observes the realizations of x, and z before issuing y,, so, in general, a reporting strategy can be any mapping 1I: R X Z R. However, we assume an unmodeled auditor restricts the set of possible mappings from which the agent may choose. Specifically the agent may choose from a set of three reporting options. Any other mapping will be detected and disallowed by the auditors.5 This set is denoted by T {r, 4rT, fL}, and the individual options are as follows: 53 The auditor is exogenous to the model and therefore plays a passive role. See Demski [1998] for more on the role of auditors. In that paper, there are two types of auditors, strong and weak, and the audit environment interacts with other endogenous variables in the model. (1) "Truthtelling" option (*r) specifies: y, = x,, and subsequently, y2=x2; (2) "Borrowing" option (i1): y, =x, +d if z =d > 0; yi =x, otherwise, and subsequently, y2= x, + x2 y,; and (3) "Lending" option (IL): y, =x, if z =d > 0; y, =x d otherwise, and subsequently, y2= x, + X2 y. The recognition theme is clear from this setup. When z=d > 0, the agent knows there will be an increase in next period's output and can leave it alone (i.e., truthtelling) or add that amount to the first period output (i.e., borrow). For example, some revenue can be recognized earlier. When z= d, the agent knows there will be a decrease. Again, he can leave it alone (i.e., truthtelling) or take the hit in the first period (essentially lending some output to the next period). For example, some expense recognition can be made earlier. The only recognition decision made by the agent is regarding the shock term z. The accounting recognition of any other portion, such as the labor driven portions (i.e., a1, k, a,+k2 a) and the random portions (i.e., E1, e2), is not controlled by the agent. We assume no other (self)reporting mechanism exists.54 The linear contract takes the form: 6' = [61, 6] and r' = [y,, yj. To induce a particular reporting option, denoted ( e 'F, and desired labor input pair, the principal's problem can be written as the following optimization programs5 C'(i,) minimum E[I(y,, y2) H, a", q]J (13) 60 6, 62 54 To reduce the complexity, we rule out mixed reporting strategies. 55 The agent's induced decision tree under the accounting report regime is: [A 4 %a a a X l(y,, y,) alE{H,L) xE R z,e{d,d} y, e a2E{H,L} x, e R x = xj+x2 {x,,x,+z} y, =xy, 56 Subject to E[U(I(.); ")H, a", ] U (14) E[U(I(.); )IH, a", 4r] 2 E[U(I(.); *)a, a, irj'] V a, a, iji' (15) Proposition 4.1: In the accounting regime, the Truthtelling option is weakly dominated by the other two options. Furthermore, if a is "sufficiently large" and d is "sufficiently small, then (1) when k2 > k, +1, the Borrowing option (f1) is preferred to the Truthtelling option (r'); and (2) when k. < ki +1, the Lending option (0b) is preferred to the Truthtelling option (01). If the principal decides to induce the Truthtelling reporting option, he must deter both Borrowing and Lending incentives, and the only way to do that is to equate 6, to 62, which essentially leads to the optimal contract under aggregate output observation. Inducing other reporting options makes it possible to utilize the natural incentive to the principal's advantage. Specifically, when k2 > k, + 1, the natural incentive for the agent is to borrow output from the second period, and the principal may be better off encouraging the agent to use the Borrowing option as opposed to the Truthtelling option. On the other hand, when k2 < k, + 1, the natural incentive for the agent is to lend output to the second period, and the principal may be better off encouraging the Lending option. By encouraging a reporting scheme other than truthtelling, the principal can reduce the total variance of the compensation package and therefore reduce the risk premium that must be paid to the agent. However, inducing the Borrowing (respectively, Lending) option also causes the principal to "overpay the bonus" when the agent does borrow (respectively, lend). When the risk premium effect overcomes the additional bonus effect,"5 it is worthwhile for the principal to invite the agent to manage his reported performance. 56 This gives rise to the condition that a is "sufficiently large" and d is "sufficiently small" in Proposition 4.1. In the numerical example with k2 = 1, inducing the *L option is more attractive than any other option. It involves setting I'(y,, y2)= 15,730 + 10 y, + 20 Y2, and the expected compensation is E[I*(y,, y2)] = 21,230. Inducing any other option requires writing a contract that is identical to the aggregate output observation case, which is I'(y1, y2)= 17,701 + 20 (y, + Y2), yielding an expected compensation of 22,701. On the other hand, when k2 = 2, inducing "' is better than any other option. The optimal contract is I'(y1, y2)= 15,750 + 15 y, + 10 Y2, and the expected compensation is E[I*(y,, y2)] = 20,500, while to induce Truth telling (or Lending) the optimal contract is Il(y1, y2)= 16,002 + 13.33 (y, + y2), with an expected compensation of E[I'(y,, y2)] = 20,668. Discussion Blocked communication and linear contracts are the keys to the results. Under these two conditions, one cannot appeal to the Revelation Principle, where equilibrium truthful reporting prevails. In this model, communication is blocked because the only communication channel (i.e., an accounting report) is restricted by accounting articulation requirements as well as by the number of options allowed by the auditor. In addition to communication limitations, contracts are required to be linear, which reduces the flexibility of the incentive design. These are the keys for performance management to be equilibrium behavior in our setting. Similar restrictions are present in related studies. In Demski [1998], communication is blocked between the agent and the principal but there is no restriction on contractual form. When the agent's ability to manage performance measures is linked to his other productive activities, smoothing appears as equilibrium behavior. In Arya, et al [1998], the lack of commitment (e.g., atwill contracts) implies that the Revelation Principle does not apply. Tolerating smoothing serves as a "device that effectively commits her to making firing decisions that are better from an ex ante perspective." (p.4) In all such studies, "truthful" reporting may not be desired and contracts are designed to cope with the limitations, which may involve letting the agent manipulate performance measures in equilibrium. The manipulation is by design and, in fact, encouraged to combat contracting frictions. Empirical Considerations Now take a giant step and suppose we have a sample of data from firms well described by the modeling assumptions here. Suppose (1) k2 > k, + 1 and (2) o and d satisfy the conditions in Proposition 4.1, the optimal linear contract will induce the agent to adopt the Borrowing option and the equilibrium accounting reports (y,) are given by the following: i(H)+ z + E, z>0 y= p(H)+t z<0 (T1) (k+ k2)p(H)+E2 z>0 Y2 (k,+k2)p(H)+z+E2 z<0 (T2) Based on TI and T2, we specify the following empirical truncation models regarding the equilibrium reporting behavior for the above models. Let index i (i=l,2,...N) denote the individual firms in the sample of interest. We obtain the following empirical models: = X,, + z, + & z'< z, <" Yil= iX,,+I ,, z ,< z (El) P, Xi2 + Ei Z < Z The dependent variable, y,, is the reported performance measure. The vector X,, represents control variables for firm i in year t. There are two random shocks in the system, z, and e,,. Based on the theoretical model, the e.'s are independently identically distributed random variables that follow the classical Gaussian assumptions. However, the other unobservable random shock (z,) is truncated to zero when z, is below (resp. above) some threshold z* in El (resp. E2). These empirical models help us identify the following important econometric issues. We shall use El and E2 as examples for illustration. CrossSectional Estimation Issue Most empirical studies on performance management involve estimating the discretionary component of the total accruals. The most common model is the Jones' [1991] model. It looks somewhat like El, where the dependent variable is total accruals and the control variables include current year revenues (or their first difference) and gross property plant and equipment (GPPE). All variables are scaled by last year's total assets. One major difference is that, unlike this model, existing models assume that researchers can observe a so called partitioning binary (or dummy) variable (the PART variable in Dechow et al. [1995] and Kang and Sivaramakrishnan [1995]) for all observations, indicating whether the manager has the incentive to manage earnings. Regression analysis is typically carried out with this partitioning variable in the regression. Statistical inference is drawn using a test of whether the coefficient on the partitioning variable is different from zero. Our model, however, suggests an unobservability issue. That is, in our model, the partitioning variable z is unobservable to outside researchers. As a result, models El and E2 involve truncation. An Ordinary Least Square (OLS) estimator of the unknown coefficient P is biased because the model is misspecified. An unbiased and asymptotically efficient estimator can be generated using the Maximum Likelihood Estimator (MLE), which is based on some assumed moment conditions among the random terms (e.g., all three error terms are independent and the e1i's are normal). For model El, the MLE of 3, is defined by: 60 MLE E argmax In f(y, PIX,,o2)p(z,)dz, + Jf(y, pIXi + zi,2 )P(z)dz where f(t, ao) is the normal density function with mean y and variance o2, and 9p(z) denotes the generic density functions of z, which may be characterized by some parameters (e.g., if z is assumed to be normal, yp(z,) can be characterized by two parameters: mean and variance). The threshold z* may be theoretically calculated, but its value may be an empirical question. These and other parameters (e.g., oa, and z') may all need to be estimated along with P, simultaneously. In fact, there may be reasons to believe the magnitude of performance management differs from firm to firm depending on some other observables, say some vector W. If we further assume the discretionary accrual for firm i depends on W linearly, i.e., d, = y,'Wi,, we can estimate vector y, together with all other parameters using a similar MLE. Given large enough N, we can estimate the parameter vector Pi (pIP, o2, z*, Yi) using: pILE e arg max In Jf(y, P1X,,oa2)(z)dz, + Jf(y1, 13X,1 + y ,W,,a')2)(z,)dzj The key differences between the proposed estimator and the conventional (OLS) estimator is that the MLE handles the unobservability of z correctly by taking expectation over z in calculating the loglikelihoods (i.e., integrating z out). Therefore, the estimator considers the potential (accounting) truncation problem generated by the strategic behavior (i.e., the presence of performance management depends upon z).57 If researchers ignore these important 57 The truncation problem has been encountered in some empirical finance studies, especially survivorship studies (e.g., Brown et al. [1995]). There, bad performing portfolios are dropped by some survivorship rule and therefore no longer appear in the observed sample. As a result, the samples may violate classical assumptions and the conventional econometric analysis is not adequate. In our setting, observation stays in the sample but the dependent variables are altered as a result of the performance management, which, similar to survivorship studies, causes the model to violate classical assumptions. implications of the performance management issue, inferences made by treating the residuals from an OLS estimator as the suspected "managed accrual" can be erroneous." Inference Making Issues Moving on to inferencemaking, the common practice in this research has been to use the residual terms from an OLS estimator as estimates of discretionary accruals. In light of the above consideration, the residual term from the MLE estimator, y. 1,"" X,,, belongs to either of the two normal distributions (one with z, as its mean and the other with mean 0). Given the distributional assumptions on the error terms and the stochastic properties of the MLE estimator, the natural inference one can make for each observation is to test the hypothesis that the particular observation is drawn from the performance management population (i.e., mean= z,) against the alternative hypothesis that it is drawn from the no performance management population (i.e., mean=0). As a result, a classification rule can be devised to classify each observation into one of two groups. We propose using such a classification rule, as opposed to taking the residual as the estimate of the discretionary accrual literally, to investigate the motivation for accrual management (e.g., bonus hypothesis, etc.). Next, we provide results of empirical simulations of the MLE estimator and the classification rule. 5' A more serious issue comes from the fact that, as researchers, we do not know whether an individual observation (i.e., a firmyear) is generated by El or E2, or some other model altogether. This unobservability causes severe model switching problems. Some modeling selection criteria may be established. For example, one can apply El and E2 to the same data set to see which model fits the data better. A more sophisticated way is to use an additional parameter, say S, to represent the probability that El is the true model and estimate E along with the other parameters. Alternatively, researchers can search for additional variables to screen and separate the sample into subsamples such that a particular model may be estimated using a particular sample. If one does not consider this issue and fits the data to one model, say El, the consequences of fitting the data set with any empirical model (truncated or not) will include biased estimators to incorrect inferences because the empirical model is misspecified. Empirical Simulations In this section, we provide the results of empirical simulations based on the statistical procedures suggested above. In this simulation, we use "perturbed real data" to study the effectiveness of the estimator. We find the MLE estimator performs fairly well and the classification rule does a good job in separating subjects into suspect groups. We also report simulation results comparing the suggested method to the commonly used methods. To test the effectiveness of the MLE estimation and subsequent inferencemaking, the simulation is carried out using a Bootstrap technique as follows: (1) collect the relevant financial data from COMPUSTAT tapes; (2) randomly select 100 firms; (3) artificially increase the amount of total accruals for 50 of the 100 firms; (4) estimate relevant parameters using the MLE estimator (without using the knowledge of which firm's accruals have been manipulated); (5) calculate the residuals for each observation; (6) use the residuals to classify each observation into either the "managed" or the "unmanaged" group based on a classification procedure; (7) compare the classification with the real classification using a Chisquare test of independence; and finally (8) repeat steps 27 100 times. The sample data collected are 1724 firms from the 1996 PrimarySupplementary Tertiary (PST) file after two screens: (1) the firm must not yield SIC codes 6021 to 6799 (to exclude firms from the financial sector); and (2) the firm must have eight or more timeseries observations (19891996). Both of these two screens are common in the literature. Only 1996 data are used in the simulation to avoid potential specification problems associated with panel data. The model specification is the commonlyused Jones [1991] empirical model of total accruals: A,, 1 AREV,, GPPE,, DA,, NTAi,, NTA,, + NTA,, NTA,,, NTA,,  where (ignoring the firmyear subscripts and A refers to the timeseries first difference): A = accruals = AAR + AINV + AOCA ACL DEP AR = Account Receivable excluding tax refunds (2161)"9 INV = Inventory (3) OCA = other current assets (4123) CL = Current Liabilities excluding taxes and current maturities of longterm debt (5 7144) DEP = Depreciation (14) REV = net sales revenues (12) GPPE = Gross Property, Plant and Equipment (7) DA = Discretionary Accruals NTA = Net Total Assets (6) From each random sample of 100 firms, 50 firms were selected at random to receive the perturbation treatment (i.e., we add 2% to 10% of current year NTA to the total accruals). So the new dependent variable is defined as yi. For the 50 "unperturbed firms", y, is equal to the total accruals. For the other 50 firms, y, is total accruals plus the added accrual. The MLE estimates are derived in the usual fashion, but with all variables scaled by the firm's last year net total assets. The classification rule is as follows. We first calculate the residual y, X, p"LE'. This variable will either have a mean of 0 or added accruals, with identical variance. So the model classifies observation i into the "managed group" (resp. "unmanaged") if y, x, p`"L > (resp. 5 Numbers in parentheses refer to the COMPUSTAT file data item numbers. 64 <) .5 added accruals.' The entire sampleestimationclassification procedure is repeated 100 times and the average classification accuracy is calculated. The repetitions are designed to filter away ongoing performance management in the data and idiosyncratic irregularities such as skewness, and extreme observations. Table 41 presents the results of the simulation. Naturally when we increase the amount of added accruals into the dependent variable the model performs better at classification. For example, if we add 2 % of net total assets, the average classification error is 45.78 (23.98 +21.80) firms out of 100 firms. If we add 10% of net total assets, the average classification error is 28.59 (14.64+13.95) firms. The model does a fairly good job of predicting the total number of firms in the "managed" group, ranging from 50.69 to 52.18 firms compared with the actual number of 50 (i.e., the number of those firms whose accruals were actually perturbed). The Chisquare tests of independence are significant for the 5% and 10% cases at the conventional level (i.e., 5% type I error tolerance). Now we compare the suggested method and the commonly used models. In existing studies, researchers believe the motivation (or decision rule) is observable. Such models usually involve a partitioning variable (the PART variable in Dechow et al. [1995] and Kang and Sivaramakrishnan [1995]). In our model, however, the variable z is the agent's private information and is reported in an aggregated and truncated manner (i.e., z is part of y, the total performance measure, only some of the time). One potential way to unify the two models is to 6 Technically, the two distances should be scaled by the standard deviations of the residual and the reference point should be picked based upon the variances of the two populations ("managed" and "unmanaged"). However, since we assume that the error term e is independent of z, the variance of the two residual populations is identical, and the reference point is the midpoint between the two means of the population (i.e., added accruals for "managed" and 0 for "unmanaged" population). We repeat the MLE procedure without the knowledge of amount of added accruals (i.e., 2%, 5%, and 10% of NTA) and the prior probability of performance management occurrence (i.e., 50%). These two parameters are instead estimated by the MLE model. The results stay the same with some loss of power. treat the PART variable as a noisy indicator (or signal) of the unobservable z and assume that PART is not available for contracting purposes. We conduct additional empirical simulations to evaluate the relative effectiveness of the two methods. The simulation procedure is the same as before except we introduce a binary variable PART (zero or one) as a noisy indicator of whether z is positive. We seed errors in PART to reflect its measurement error. For example, a 20% error rate means that when z is positive (therefore the manager will borrow), PART is equal to one only 80% of the time. We estimate the coefficient on the PART variable using the conventional OLS model and the MLE model and test the null hypothesis that the coefficient is zero (i.e., no performance management). Table 42 reports the rejection frequencies for different simulation parameters. Since we have seeded the added accruals, these rejection frequencies measure the type II errors of the two models. Notice when the added accruals are 2% of the net total assets, the OLS model rejects the null hypothesis 29% (respectively 28%) of the time with a 40% (respectively 20%) measurement error." The MLE model rejects the null hypothesis more frequently for every added accruals level (i.e., 2%, 5%, and 10% of net total assets) and every measurement error rate (i.e., 20% and 40%). Also, when there is less error in PART, the MLE model is able to use the information in PART better and therefore exhibits more power. For example, when the error rate drops from 40% to 20%, the MLE model's rejection frequency increases from 49% to 89% for the case of 10% added accruals. The problem of measurement errors (in PART) is further confounded if the amount of added accrual is random as opposed to fixed at a certain percentage (e.g., 5%) of net total assets. To explore this interaction between measurement error in PART and random effects, 61 These two power measures are similar to those reported by Kang and Sivaramakrishnan [1995]. 66 we modify the simulation such that the amount of added accruals is independently drawn from a normal distribution with mean of 5 % and a standard deviation of 1%. The result shows that the coefficient estimates on PART by the OLS model is biased downward when there are measurement errors in PART. For example when the measurement error rate is 40% (respectively 20%), the average estimated coefficient on PART is .24% (respectively 1.29%). When the measurement error is zero, the average coefficient estimate is 5.06%, statistically the same as the population mean of 5 %. An open question is performance of the maximum likelihood estimator in this setting. Conclusions In this chapter, we introduce performance management issues. Recognition rules are used to shift a portion of "reported" performance measures across periods. We modify the agency model constructed in Chapter 3 such that (marginal) performance management may occur. We first showed that limited communication and contract restriction can lead to the conclusion performance management is equilibrium behavior that is induced by the principal. Then we derived the empirical implications of this concept. Econometric issues regarding the crosssectional estimation of discretionary accruals are raised, which have direct relevance for attempts to identify the discretionary component of the total accruals. We perform an empirical simulation based on "perturbed real data" to evaluate the performance of the statistical procedures we have suggested. The results of the simulation indicate that the statistical procedures hold fairly well. Understandably, the higher the suspected manipulation amount, the better the model is able to predict suspect firms. We also compare the type II 67 errors of the MLE model to the commonly used OSL model. The MLE model outperforms that of the OLS model for all specifications. Figure 41: Event Sequence of Models in Chapter 4 t= t=2 agent's inputs a, e {H, L} agent's private information output accounting report options: Truthtelling (p') Borrowing (t111) Lending (*11L) agent's net compensation principal's net cash flow a2 c {H, L} z e {d, d} Yi = x y, = x, + d, ifz=d y, = x, if z=d y, = x,, ifz=d yj = x, d, if z=d I,c(a,) y, = x2 y, = x2d, ifz=d Y2 = x2, ifz=d Y2 = x2, if z=d y, = x, + d, if z=d I,c(a2) X = X, + X2 qx 13 Table 41 Simulation Results From the MLE model Amount added True classification 2% of NTA Managed Unmanaged Total Chisquare statistic (d.f. = 5% of NTA Managed Unmanaged Total Chisquare statistic (d.f. = 10% of NTA Managed Unmanaged Total Chisquare statistic (d.f. = MLE model classification Managed Unmanaged Total 28.20 21.80 50 23.98 26.02 50 52.18 47.82 100 1): 0.90 (pvalue < 0.30) Managed Unmanaged Total 31.55 18.45 50 20.12 29.88 50 51.62 48.38 100 1): 5.38 (pvalue < 0.025) Managed Unmanaged Total 36.05 13.95 50 14.64 35.36 50 50.69 49.31 100 1): 18.35 (pvalue <0.005) Notes: The simulation is based on 100 repetitions of the sampleestimationclassification procedure. Each sample of 100 firms is randomly selected from the pool of 1724 firms contained in COMPUSTAT PST file. Random numbers are generated by the FishmanMoore procedure with replacement. 50 firms were selected at random to receive the perturbation treatment (i.e., we add 2% to 10% of current year NTA to the total accruals). Table 42 Comparisons of the MLE model and the OLS model Measurement error rate in PART 20% 40% 20% 40% 20% 40% 5 % Reiection Region OLS rejection MLE rejection frequency frequency Notes: The simulation is based on 100 repetitions of the sampleestimationclassification procedure. Each sample of 200 firms is randomly selected from the pool of 1724 firms contained in COMPUSTAT PST file. Random numbers are generated by the FishmanMoore procedure with replacement. 100 firms were selected at random to receive the perturbation treatment (i.e., we add 2% to 10% of current year NTA to the total accruals). Measurement errors in PART are seeded such that PART correctly identifies the firms received additional accruals with 20% or 40% error. Rejection frequency is the frequency the model rejects the null hypothesis of no performance management. Amount added 2% of NTA 5% of NTA 10% of NTA CHAPTER 5 CONCLUSIONS This dissertation revisits the ageold issue of recognition. An extensive review of the (historical and contemporary) literature leads to the conclusion accounting recognition issues are of fundamental importance to accounting theory. Most controversial debates in accounting, such as historical cost or revenue recognition, hinge on recognition criteria. Today, recognition debates continue to take place as researchers, practitioners, and standardsetters struggle to cope with the accounting challenges (e.g., accounting for financial derivatives) presented by the everchanging landscape of modern economic environments. Chapter 2 explained that the literature on recognition has undergone a considerable transformation during this century. The elegance of the measurement perspective certainly has its theoretical appeal. However, incomplete and imperfect market conditions make it difficult to use the measurement perspective to provide insights into the role of accounting in economic settings. Therefore, the information content perspective is widely adopted as the research paradigm in contemporary accounting literature, including this dissertation. Within the information content perspective, we focus on an incentive setting where information is extracted to the fullest extent to combat moral hazard and to alleviate information differences among the players. Such a decisionmaking setting has an analytic advantage in that we can explicitly attach economic values to alternative accounting reporting 72 regimes. Furthermore, the interactions between accounting and other information sources may be studied. Building on earlier work on accounting structure, we consider suggestive versions of accounting structures that include two important issues regarding recognition. First, we examine the economic tradeoff between early and late recognition. Second, we consider managers' discretion over recognition rules and their incentive to "manage" accounting reports to their advantage. These two structures provide the accounting context in which information content analysis is carried out. By bringing the information content and accounting structures together, this dissertation expands the discussion of this traditional accounting issue and exposes it to considerations that were not available without the union of the two literatures. This union enables us to explicitly and carefully consider the comparative advantage of accounting, which, we have argued, lies in its credibility as a source of information. This allows us to think of the role of accounting more broadly in that accounting is most important in serving its disciplining and confirmatory roles through its interactions with other information sources. There are limitations to our analysis. Only an incentive decision context is considered. Other contexts (production and consumption concerns) are intentionally neutralized. It helps us to pinpoint the incentive use of information, but we pay the price of not being able to explore the interactions among different demands for accounting information. Similarly, by assuming full commitment power, we forgo the opportunity to study the effect of limited commitment on the recognition issue (e.g., hiring and firing decisions and renegotiations). In addition, we leave most of the empirical work outside of the dissertation (except the simulation work to explore certain properties of the statistical procedures suggested). We suggest that future researchers study a particular setting (e.g., an industry or certain transactions) carefully and model the underlying performance management incentives. Testable hypotheses can be developed and the suggested estimators and inferencemaking methods can be utilized. These types of empirical work certainly will complement work done in this dissertation. To conclude the dissertation, we put our journey into better understanding accounting recognition in a philosophical perspective of social science theories. Under this perspective, articulated by Professor Christopher Sims [1996], the purpose of theory is to discover ways to reduce data with little loss of information, as opposed to the view that the purpose of theory is to be confronted by data and is claimed false if the data do not agree with the theory. Further, with regards to methodology in social sciences, Professor Sims sees rhetorical arguments as secondary to scientific inquiries and warned of the danger of relying too much on rhetoric. We have, through the review of the history of accounting thought, encountered a number of approaches to the subject of accounting. Various approaches view accounting differently (e.g., carrying information content or measuring economic stocks and flows) and employ different methods (e.g., empirical investigations, economic modeling of information, or rhetorical claims from standardsetting bodies like the FASB). The discussion of topics as important as recognition should not be left solely to the policy and practical arenas. Scholarly inquires into recognition as well as other fundamental accounting concepts are seriously needed; they become the building blocks of a contemporary accounting theory based on (social) science rather than rhetoric. Clearly, in this dissertation, arguments are made from an information content view of accounting. We draw conclusions based in analytic results from studying suggestive economic settings in which accounting is treated as a source of information. The methods used in this dissertation are economic and econometric modeling. 74 Consistent with Sims [1996], we view our endeavor as an attempt to reduce the complex phenomena of accounting recognition to a few important and insightful economic attributes (e.g., incentive use, other competing sources of information, and contractual frictions). We acknowledge the limitations of such an approach and do not wish to claim this is the only "right" way to study the subject matter. However, we reject the notion that this type of analytic modeling of accounting is useless because it does not easily lead to empirically testable hypotheses. Sims [1996] used the example of Kepler's theory of planetary motions to convey an important idea. That is, good theories help us understand the world better, they do not necessarily predict the world very precisely. The limitations of our analysis do not deny the usefulness of carrying out our inquiries. APPENDIX I PROOFS FOR CHAPTER 3 Proof of Proposition 3.1: We begin with the basic model: C' minimum E[I(x) I H, a"] = Ex P(x I HH)I(x) (1) I(x) Subject to E[U(I(x);) I H, a"] 2 M (2) E[U(I(x); *)H, a"] 2 E[U(I(x); *)a, a] V a,, a (3) with a, E {H, L} and a: {G, B} {H, L}, the agent has eight possible strategies: Strategy at a a(G) a(B) (i) H H H (ii) H L H (iii) H H L (iv) H L L (v) L H H (vi) L L H (vii) L H L (viii) L L L In general, there are seven IC constraints in the basic model (e.g., strategy (i) is preferred to (ii), (iii)). We label the seven IC constraints by their offequilibrium strategy numbers, (ii) through (viii). Given [Al] and [A2], we can collapse the seven IC constraints into two IC constraints. To proceed, constraint (ii) requires: P(GIH) E[UIG, HH] + P(BIH) E[UIB, HH] P(GIH) E[UIG, HL] + P(BIH) E[UIB, HH] Canceling common terms, the constraint simplifies to: E[U I G, HH] 2 E[U  G, HL] (Al1) [Al] implies P(x, z2,zZ, ai, a2)=P(xlai, a2)P(z21a) for all z,, z2, and (a,, a2). Therefore, constraint (ii) reduces to: E[UI HH] E[U I HL] (AI2) where E[U a, az] Ex P(x I a,, a2) U(I(x); a,, a2) (AI3) Similarly, by [Al], constraints (iii) and (iv) are identical to (Al1). Thus, constraints (ii), (iii), and (iv) can be replaced by (Al1), which we rename the secondperiod IC constraint. Similarly, [Al] simplifies constraints (v) through (viii) to these four inequalities: constraint (v): E[U I HH] E[U I LH] constraint (vi): E[UIHH] t P(G L) E[U LL] + P(BL) E[UIL LHI constraint (vii): E[U  HH] 2 P(G  L) E[U I LH] + P(B  L) E[U LL] constraint (viii): E[U HH] E[U I LL] Clearly constraints (v) and (viii) imply constraints (vi) and (vii). Given [A2], the CDFC assumption, it is easy to verify constraint (viii) does not bind. We rename constraint (v) the firstperiod IC constraint. Thus far, all but the following three constraints in the basic model have been eliminated: (1) the IR constraint, (2) the first period IC constraint (constraint (v)), and (3) the secondperiod IC constraint (inequality (Al 1)). Let 1, A., and A2 be the nonnegative Lagrange multipliers associated with these three constraints respectively. We set up the following Lagrangian: af = E[I(x)IH, a"] + A (E[UIHH] M) + ., (E[UIHH] E[UILH]) + A2 (E[UIHH)] E[UIHL]) (AI4) From the firstorder conditions, it is easy to verify that: (i) A > 0 (Holmstr6m and Milgrom [1987]), (ii) if P(x= 11 LH) > P(x= 1 HL), then 1. > 0 and 12 = 0 (because (L, H) dominates (H, L) in the sense of first order stochastic dominance and I(x= 1) > I(x=0) in equilibrium), and (iii) ifP(x=l LH) < P(x=l HL), then z2 > 0and A1 = 0. Now we analyze the usefulness of R,. Under R2, Y2 is just an ex post monitor. From Holmstr6m [1979] and Grossman and Hart [1983] where there is only one binding IC constraint, we know a monitor, say Y2, is useful if the likelihood ratio associated with the constraint is a function of y2 because when P(x= I LH) > P(x= 1 IHL), z, is incentive informative about a, and y2 is a garbling, but not independent, of z,. A parallel argument applies to the case where P(x= 11 LH) < P(x= 11 HL). Now consider R,. First, suppose P(x= 11 LH) < P(x= 11 HL), we claim R, is useless. Under R,, the agent's secondperiod policy is a mapping a: Z Y A. There are now 16 possible a mappings. Mixed with a1, there are 32 possible strategies. To avoid repetition, we replace the 15 IC constraints involving (H, a) (a*a") with the following four constraints: E[UIz,, y, HH] t E[UzI, y,, HL] V z,, y, (AI5) These four constraints imply that the agent, having chosen a,=H, will choose a2=H for all possible realizations of z, and y,. If (AI5) is satisfied, the 15 IC constraints that involve (H, a) (aea") are also satisfied.62 [Al] and the fact y, is a garbling of z, imply P(x z, y1, at, a2) = P(x  a, a2), so (AI5) reduces to the following two constraints: E[Uly,, HH] 2 E[Uly,, HL)] V y, (AM6) 62 To see this, write the 15 constraints as: E[U()IH, a"] E[U() H, a] V a a". But E[U()JH, a"] = Ez, E(UIz, y,, HH) and E[U()IH, a] = E2 y E[UIz, y1, H, a(z,)]. Given (Al 5), each of the four terms in E[U()IH, a"] is greater than or equal to its counterpart in E[U()IH,a]. where E[UIy, a1, a = Ex P(xIa, a2 )U(I(x, y,); ") We solve the optimization problem with only the two constraints in (AI6) and the IR constraint, (ignoring the other 16 IC constraints involving (L, a) for the moment). We obtain the following first order conditions: 1 1 P(xHL)t rV(I(xq.y))k' =P + XM kP(x HH) From here it is clearly that R, is useless if P(x= 11 LH) < P(x= 11 HL), as strict use would needlessly impose risk on the agent. If the principal does not use y,, the omitted IC constraints are clearly satisfied, R, is indeed useless. Now, suppose P(x= 1 LH) > P(x= 1 HL), but let I'(x, y,) = I'(x), where I'(x) is the optimal contract from the basic model. We show this solution violates the optimality conditions in the expanded program. With this supposed solution, the IR constraint binds, only one IC constraint is binding by complementary slackness. The binding IC constraint must involve (L, a"). All other 30 offequilibrium strategies result in input sequence (H, L) or (L, L) with nonzero probability and are, therefore, dominated by (L, a") under incentive scheme I'(x). (CDFC is used here.) The firstorder conditions evaluated using the supposed solution is: ( P(x rH) P(y, z,)P(zf, =L) rV(I,(x,y,))k2= + (Ln y kP(x HH)Z P(yV,)P( =H) (A ) z The righthandside of (AI8) is a nontrivial function of y, because (i) z, is incentive informative about a, and (ii) y, is a garbling but not independent of z,. However, the left handside of (AI8) is not, under the supposed solution. Proof of Proposition 3.2: When only x is contractible, the design program with communication is as follows: C(m) minimum E[I(x, m(z,)) H, mT, a"] 1(*) Subject to E[U(I(); *) H, m', a"] 2 M E[U(I(); )H, mT, a"] E[U(I(); ) ja, m, a] V a, m, a The agent's strategy for the entire game is represented by (a,, m, a). There are four possible selfreporting policies, denoted mT, moo, mBa, and mB, where m' is the truthtelling policy, mrl (resp. ml) is the policy that always reports good news (resp. bad news), and ml is the policy under which the agent always lies. Recall there are four secondperiod input policies (a). Therefore, for the entire game, the agent has 32 possible strategies. The preferred strategy is (H, mT, a"). The design program has 31 IC constraints and one IR constraint. We use a variation argument to prove communication is strictly useful. Let (v,', vo') be the optimal payment scheme, in utility terms, for the mechanism design program without communication. We construct a trial solution vm, x, in utility terms, to the program with communication: vm.,, = v,x V x, m() e Z. Clearly, the solution is feasible. Since P(x=l LH) > P(x=l HL), only 7 of 31 IC constraints are satisfied with equality, which correspond to the following offequilibrium strategies: a, m a H mm aa H mn" aH H mB a" L mT aH L mGG aH L mBB a"t L mB aH Each of the seven strategies has a=a". All other 24 offequilibrium strategies (i.e., (a,, m, a), asa") result in input sequence (H, L) or (L, L) with nonzero probability and are, therefore, dominated by (L, m, a") or (H, m, a") under the trial solution v,,,. Along with the IR constraints, we have the following eight constraints satisfied with equality: E[U] = (vCGI + 9(1CG)VGO + (l) CV5 + (1)(1CB)VBo M > 0 (IR) E[U] [ Cv, + (1Ovoo] > 0 (TTGG) E[U] [CvB + (I )v] 0 (TT0a) E[U] [I oVB1 + (lCG)VBO + (1)CBVGI + (1)(lCsB)v c] > 0 (TTBG) E[U] [ 'kvo + 4(lC')kvco + (1D)C'kvy, + (1 )(1C')kvBo] > 0 (ICT) E[U] [ C'kv, + ( l')klvo] 2 0 (ICGG) E[U] [ C'kv, + (lC')kvl] 2 0 (ICB) E[U] [ C'kv., + (lC')kvBo + (l)C'kv1G + (1 )(1C')kvGo] > 0 (IC ) where: =P(z,=G); C=P(x=lzi=G, HH); C(P(x=l zi=B, HH), C'=P(x=1 LH), C P(x=I HH) = c + (IG)CB and C(G > C > CB > C'. Rewriting the principal's objective function, in utility terms, we have: E[I(x, m())IH, m', a"] = (GV'(V) + G(lCo)V '(VGo) + (IW)BV' ,) + (lD)(ICB)V (VBo) Totally differentiating (IR), (TTGG), (ICBB), and the principal's objective function at the trial solution, we have: AIR = c(dvG1 + W(1C,)dvo + (1 )ddva, + (1 0(1C)dVao ATTGG = AIR Cdvo, (lC)dvGo AICaB = AIR C'kdv,, (lC')kdvo, AE[I()] = aV '/av(v,*)[ CGdvGI + (l Bdvi,] + V '/lv(vo')[ E(l(G)dVcG + (1()(lCB)dve,] For a fixed dvG, > 0, choose dvGo, dvB,, and dveo so that AIR = 0, AICB, = 0, and ATTGG = 0. Therefore we have system of three linear equations with three unknowns. Solving the system", we have: sign[AE[I()]] = sign((a) = sign [((1(')(1) C'CG(O(CB)] Therefore, the expected payment is reduced, i.e., AE[I()] < 0, if (l ') With dvGI, dvGO, dvaB, and dvoo chosen in such a way, we can readily verify that constraints (TTB,), (TTBG), (ICT), (ICcGG) and (ICBG) are satisfied. Proof of Proposition 3.3: The design program with recognition and communication is as follows: C(R, m) = minimum E[I(x, y,, m(zi))  H, mT, a"] (7) I(.) Subject to E[U(I(); )I H, mT, alH] 2 M (8) E[U(I(); ) IH, mn, aH] E[U(I(); *) I a, m, a] V a,, m, a (9) Under R2, the agent has 32 strategies. Let X(a,, m, a) denote the nonnegative Lagrange multipliers and let p denote the multiplier associated with the IR constraint. The first order condition can be written as: 1 rV(l(x,y2,m(.))k2 + (a.).,m(,a)AH(a.,m,) where A(a,, m, a) will be specified in the following. Specifically, the first order condition with respect to I(x, y2, G) can be expanded to: 63 One can readily verify the determinant of the coefficient matrix is not zero, so the solution to the system of three linear equations exists. rV(I(x, y ,G)k 2= + (a,,mT,a)( (aa(G)) P(xz=G,)) + X(am"'a) + ..(a,m ,a)I(a,a(G))P(xlz = Ga,a(G)) (a,..a(B))(1y)P(x:z,=Ba<,(B)) P(xlz, = G,. HH) a( P(xaz, = GHH) + k.(a, m ,a ) I4, ( a,) B)(1 y )P (xlz = B a a (B )) y P(xlz = G,HH) I (AII9) where mGG, mBB, and ms" are defined as in the proof of proposition 2, 4)2 = P(y2lz,=B)/P(y2z,=G), and K(a,,a2)=exp(r(c(a,)+c(a2)2c(H)). Similarly, the first order condition with respect to l(x, Y2, B) can be expanded to: rV(l(x,y,,B)k2= p+.))azm',) a (B zBHK)+ ..(a,. ,) D.a m",as .( .. .... ) P(xlz, = B,a ,a(B)) # _a a 7P(xlz, = G,a,,a(G))) + (a,,m ',a) l (a,,a(G)) yP(x Gaa(G)) (All10) We know 4)2 is a nontrivial function of y2 because Y2 is not independent of z,. If the principal strictly prefers communication with no recognition, then at least one truthtelling constraint is binding, i.e., at least one of the multipliers X.(al, m, a), ;l(a,, m", a), or ;.(al, m", a) is positive. Thus, we have the righthandside of (AII9) as a nontrivial function of y2 (if some ;,(a, m"', a), or X(al, mB, a) is nonzero), or we have the righthandside of (AII10) as a nontrivial function of y2 (if some .(a1, ms", a), or the X(a, m"', a) is nonzero), or both". Therefore, y, is useful for contracting. Now consider R,. First consider the program with no recognition. Let 0 denote the set of offequilibrium strategies in this program, strategies denoted (as, m, a). In the program 64 Note that in the righthandsides of both (All9) and (All10), the coefficients on (02' are either negative or zero. with R1, the agent chooses among strategies (a&, m, a). (We use an underline "_" to denote the elements of strategies in the program with R, to avoid confusion.) Here, a: Z x Y A. There are sixteen possible a mappings. Mixed with a, e {H, L} and m E {mT, mGG, m", m';), the agent has one hundred twentyeight strategies. In this expanded program, we construct an offequilibrium strategies set, denoted C, in the following way. For each strategy (a1, m, a) e 0, find the strategy in the program with R, such that a, = a,, m = m, and a(zj, y,) = a(z,) for all y,. By construction, the agent's secondperiod input is not a function of y1 for strategies in Q. We write a(z,,*) to reflect this fact. Further, we partition Q into four subsets: those that use mT, QT; those that use mm, Q.., etc. Now we take the optimal solution in the program with no recognition to construct a trial solution to the program with R, by setting I(x, Y2, m()) = I'(x, m()). If all constraints involving strategies not in 0 are redundant, (which will be proved to be true later,) we can evaluate the first order conditions in the program with R, at the trial solution as follows: I In 1,( P(x z, = ,a;,o(G,*))) rV(I(x .yG)k + P(x z, = ,G, HH) , + P(Ytz,=G(qcj ,P(xz) ,G'a,(G')) (I )P(xjz,=B'aj(B'*)) + tio....., Is,,"(G,.)) P(z, = G, HH) ,ita,,a(B,.)) yP(x1z, = G,HH) ) + X(A.M. ( . (I y)P(xlz, :Ba,,_(B,)) (All11) and I ,,m (a (G,))yP(xz, = G B B(G,,*)) S, (1( ')P(z B, HH)(l)P(xz,=BHH) Se(, )y P(xy) P(x z, = B,HH)) (AI12) 84 where 4, = P(y, z, =B)/P(y, I z, =G). We know <, is a nontrivial function of y, because y, is not independent of z,. If the principal strictly prefers communication with no recognition, then at least one truthtelling constraint is binding, i.e., at least one of the multipliers 1(a,, mi, a), .(a,, m", a), or A(g, m"e, a) is positive. So we have the righthandside of (All11) as a nontrivial function of y, or we have the righthandside of (AII12) as a nontrivial function of y,, or both. Therefore, y, is useful. Now we prove that under the trial payment scheme, the constraints involving strategies not in Q are, in fact, redundant. Let 0 denote the set of all such strategies. Partition 0 into two subsets denoted Q' and 02. 01 is the set of strategies in which the agent's secondperiod input is a function of y, only when his firstperiod private signal (z,) is z,' and it is not a function of y, when z, = z," z,'. On the other hand, Q2 is the set of strategies in which the agent's secondperiod input is a function of y, when z, = z,' as well as when z, = z," # zi'. We first prove if E[U() IH, mT, aH] 2 E [ Lli i, m, a for (a, m, a) e Q, then E[U() H, mi, a] E[U() a, m__, a] for (a%, m, a) e 0 at the trial solution, i.e., constraints involving strategies in U' are redundant. Second, we prove if constraints involving strategies in 0' are redundant, then constraints involving strategies in 02 are also redundant. First, suppose, without loss of generality, a representative strategy (a4, m, a) E 0 is such that g(z,', y,') g(z,', y,") for z,' equal to, say, good news (i.e., z,' = G), and aJB, y,') = q(B, y,") = g(B,.). Evaluating the agent's expected utility of adopting this strategy, we have: E[U()a, tma = z P(z,, y,'ja,) E[UIz,, y,', a,, m, a] + Sz P(z,, y," a,) E[UIz,, y,", a4, m, g] = P(G, y,'a,) E[UjG, y,', ai, m., (G, y,')] + P(B, yt'lja) E[U B, y,', a,, m, aB. *)] + P(G, y,"Ia,) E[UIG, y,", a, m, a(G, y,")] 85 + P(B, y," a,) E[UIB, y", a, Wm, JB, *)] (All13) Now select a strategy, denoted (ag, m', n') from Q such that: ," = Q, i' = m. a'(G, *) = a(G, y,'), and a"(B, *) = (B, .). The constraint associated with this strategy requires: E[U()IH, mT, a] E[U()a,', m, g'] = P(G, y,'a4) E[UG, y,', a,, m, a'(G, *)] + P(B, y,' a,) E[UIB, y,', a1 m, a'(B, *)] + P(G, y,"a,) E[UG, y,", a, m g(G, *)] + P(B, y,"a,) E[U B, y,", a,, m_, a*(B, .)] Since a'(G, .) = a(G, y,'), and a'(B, .) = aB, *) by construction, the constraint can be written as: E[U() I H, m, a"] E[U()Ia,', m', g~] = P(G, y,'a,) E[UIG, y,', a,, m ajG, y,')] + P(B, y,' a,) E[UIB, y,', a, m, m B, *)] + P(G, y,"Ia,) E[UIG, y,", a,, m, gG, yl')] + P(B, y,"ja,) E[UIB, y,", a, m, a(B, *)] (All14) Combining (Al13) and (All14) yields: E[U()Ia', m', a'] E[U()I, m, a] = P(G, y," a) (E[UIG, y,", a, m, fG, y,')] E[UIG, y,", a,, an., G, y,")]) (AII15) Select another strategy, denoted (ap", m", a*") from a such that: a*' = a, m" = ma, "(G, *) = S(G, y,"), and g"(B, *) = (B, ). In similar fashion, the constraint associated with that strategy can be written as: E[U()IH, m'. a"] E[U()ja,", m", g7] = P(G, y,'ja,) E[UIG, y,', a,, m, aJG, y,")] + P(B, yi'a,) E[UB, y,', a, am, (B, *)] + P(G, y,"jI ) E[UIG, ye", aU, m G, y,")] + P(B, y," ai) E[UIB, y,", a, afB, *)] (AII16) Combining (AII13) and (AII16) yields: E[U()[1a, e%, g] E[U()Ia,, m, a] = P(G, yi'ja) (E[UIG, y,', a,, m,, aG, y,")] E[UIG, y,', a,, m, 4G, y,')]) (All17) Suppose E[U()jai, m, g] s E[U()Ia", m, m", ], constraint (All13) is implied by constraint (All16) and is, therefore, redundant. If E[U()Ia,, m j, > E[U()a_', m", a"]. (AII17) implies: E[UIG, y,', a,, m, a(G, y,')] > E[UiG, y,', a_, m, eG, y,")] But under the trial solution, E[U G, y,', a, m, g(G, y,')] = E[UIG, yi", a, m, q(G, y"')] and E[UIG, y,', Ma, i, (G, y,")] = E[UIG, y,", a, mn, a(G, y1")], so we have: E[UIG, y,", a, m, g (G, y,')] > E[UIG, y,", aj, m_, qG, y,")] By (AII15), this implies E[U()Ia', n.', a'] > E[U()a4, m, aj. So constraint (All13) is implied by constraint (AII14) and is, again, redundant. Therefore, constraint (AII13) is implied by either (All14) or (All16) and can be eliminated under the trial solution. This is true for each strategy in the set 0'. A parallel argument applies to the strategies in O2 so that strategies in the set Q2 can be ignored when the constraints are evaluated at the trial solution. APPENDIX II PROOFS FOR CHAPTER 4 Proof of Lemma 4.1: Under full output observation, the principal's problem is the following mechanism design program: C" s minimum E[I(xl, x2 ) H, a"] (10) 6 6,6,2 Subject to E[U(I(.); *) H, a"] ; U (11) E[U(I(.); *)IH, a"] > E[U(I(.); )a,, a] V a,, a (12) Consider the following restricted version of the above program: minimum E[I(x,, x2 ) H, a"] (AII1) 60 6, 62 Subject to E[U(I(.); *) H, a"] 2 U (AII2) E[U(I(.); I)jH, aH] 2 E[U(I(.); I)jH, aL] (AII3) E[U(I(.); I) H, a"] E[U(I(.); *)1L, a"] (AII4) given assumption [A5] and [A6], we can simplify the program using a riskpremium formulation": minimize RP = 2 c(H) + .5 (612+622) 02 + (1/r) log g(02, 62) 6, 62 Subject to 82 6/k2 (AII5) 6, + k,62 6 (All6) 6 Notice that normal density, negative exponential utility function, and linear compensation contract make expected utility calculation simpler, see e.g., Holmstr6m and Milgrom [1987]. Let A1, 4 be the Lagrange multipliers and we obtain the following first order conditions: 6, o2 12 = 0 or 12 = 61 02 (FOC1) 62 o2 + (1/r) a(log(g(62, 82)))/0 AL k, A2 = 0 (FOC2) To proceed, if 12 = 0, 6, = 0, so (AII6) reduces to 62 6_/kI. But 12 = 0 also means 1, > 0, then (AII6) must bind, or 62 = 6/k2, violating 62 2 6/k, because k2 > ki. Therefore 12 > 0. Given 12 > 0, we have 6, =6 k,62. Substituting 6, and A2 into (FOC2), we have: 1 = (62k,(6 k,62)) o2 + (l/r) 3(log(g(82, 52))/a62 > 0. Both IC constraints are binding, or 62" = 6/k2 and 6,' = (1k,/k2) 6. Notice at the solution to the restricted version of the program, the expected utility of continuation given any (a,, x,, z) history is such that the agent will prefer to provide high effort. So all other input combinations (e.g., a(.) = H some of the time and a(.) = L otherwise) are inferior to (H, a") at the solution. There is no loss of generality to consider the restricted version of the program. Proof of Lemma 4.2: Under aggregate output observation, the principal's problem is equivalent to the full observation case except there is an additional constraint of 6, =62=6. The mechanism design program becomes: minimum RP = 2 c(H) + 62 o2 + (1/r) log (g(6, 6)) 6 Subject to 6 2 6/k2 (AII7) (l +k1) 86 2 (AII8) and since one IC constraint must bind here, we have 6* = max {6/(1 +k,), 6/k2}. Proof of Proposition 4.1: Let E[U(I(y,, y2); ") a, a, ir] denote the agent's expected utility if he provides labor input (a,, a) and adopts reporting option *'. Using CE expressions again, we have: E[U(I(); a*)a, a", *T] = exp(r CE'" (a1, H)) g(62, 82) E[U(I(); *)Ias, a", 40,] = exp(r CE'" (a1, H)) g(6,, 62) E[U(I(); .)a,, a", itL] = exp(r CE~" (a,, H)) g(682, 6) where g(61, 62) = .5 [exp(r 6, d) + exp(r 62 d)] > 0 CE"1 (a,, a) 60 +6,a, +682(ka, +ka2) c(as) c(a2) .5 (8,2 + 822) o2 and similarly for strategies with a'. Now consider the truthinducing program. Two particular IC constraints are of interest here: E[U(I(.); ) IH, a", iT] E[U(I(.); *)IH, a", lp,] and E[U(I(.); ")IH, a", ,1] E[U(I(.); )IH, aH, 1,L]. They readily collapse to 862 6, and 62 6,, or 62 = 16, we are thus back to the aggregate output setting. (The remaining IC constraints are readily verified). Now consider inducing the borrowing policy (H, a", 4,). Notice the optimal T contract is feasible here, as the agent is indifferent among the reporting options. We look for parameter regions where inducing ir' is strictly preferred to inducing 4r. The program to induce (H, a", i"B), is the following: C'(jr=) = minimum E[I(y,, y2) H, a", ,ri] 60 6,8, Subject to E[U(I(.); ) I H, a", ,"2] U E[U(I(.); )IH, a", I"11] z E[U(I(.); .)a, a, r'] Va,, a, ,'e ' For the moment, we solve the related problem based on IC constraints that reflect reporting via 4l,9: E[U(I(.); )IH, a", 1,5] 2 E[U(I(.); *) IH, a1, 4,B] and E[U(I(.); ) IH, a", *,B] i E[U(I(.);)IL, a", *,"]. Once again, they reduce to 6, + k162 >6 _and 82 2a /k,. The riskpremium under the Borrowing option is: RP = E[I(x,, x2 )IH, a", *B] U(E[U(I(x, x2);)H, a", 1 B]) = 2 c(H) + .5 (812+6,2) (2 + (1/r) log (g(6i, 62) + .5 d (61 62) Now we can reformulate the restricted program into: minimize RP = 2 c(H) + .5 (681+682) 02 + (1/r) log (g(82, 62))+ .5 d (6,1 62) 6, 6, Subject to 862 6/k, (AII9) 6, + k6, > 6 (AII10) It is routine to verify that both IC constraints bind, so 6,' = _/k2 and 6,' = (1k,/k2) 6. From here, k2 > 1 + k, implies 62' < 6,*. Finally, it is easy to see this implies all the omitted IC constraints are satisfied. Now compare the riskpremiums under the Borrowing and Truthtelling options: RP(*T) RP(4B) = .5 62 (2 02) .5 (6,2 + 622) o2 (I/r) log [.5 exp(r 6 d) + .5 exp(r 6 (d))] + (1/r) log [.5 exp(r 6, d) + .5 exp(r 62 (d))] .5 d [61 62] Express this as RP(qT) RP(tIB) = DVAR + DBONUS1 + DBONUS2, where DVAR .5 62 02 .5 (62 + 622) o2 DBONUSI a (l/r) log [.5 exp(r 6 d) + .5 exp(r 6 (d))] + (1/r) log [.5 exp(r 6, d) + .5 exp(r 62 (d))] DBONUS2 = .5 d [6, 62. So DVAR is the difference due to the variances of the two schemes and DBONUS1 and DBONUS2 are the differences due to the reporting schemes. Notice the rT contract calls for 6" = max {6/(1 +kj), 6/k2}, in the region k, + I1 < k2 < ki + 1/k1, we have 6 = 8/(l+k1). The IjB contract calls for 6,' = (1 k,/k2) 6.and 62* = _/k2. Substituting the bonus coefficients into DVAR, we have: DVAR = .5 6202 (2/(1+k)2 (1kj/k2)2 1/k22) Observe that: 1 AR 2 (k, k2+ 1) ' DVARIk,=+, = 28 V 2 k k 2 0 and k2< k, + 1/k, insures that: DVAR= 0 2(1 I)(1) (2) k2 k ,k2 I a kI+kk+ > So DVAR > 0. Moving on to DBONUSI, we observe that 6,1 > 6' > 82*, so it must be the case that: [.5 exp(r 6 d) + .5 exp(r 6 (d))] + [.5 exp(r 6, d) + .5 exp(r 62 (d))] < 0 therefore DBONUSI < 0. And it is elementary that: DBOUNS2 < 0. Notice that neither DBONUS1 nor DBONUS2 is a function of o; similarly DVAR is not a function of d. So if o is "sufficiently large" and d is "sufficiently small," the total difference is positive. If that is the case, the expected compensation to the agent is higher in the rT case than in the PB' case. A parallel argument applies for the case of *irL when k, + I > k2. REFERENCES Alexander, S. S., "Income Measurement in a Dynamic Economy," 1948. Revised by David Solomons and reprinted in Studies in Accounting Theory ed. by W. T. Baxter and Sidney Davidson. Homewood, IL: Richard D. Irwin Inc., 1962, p. 126200. American Accounting Association Concepts and Standards Research Committee, "The Realization Concept," Accounting Review (1965): p. 312322. American Accounting Association, Accounting and Reporting Standards Underlying Corporate Financial Statements and Preceding Statements and Supplements. Madison, Wisc: American Accounting Association, 1957. American Accounting Association, "A Tentative Statement of Accounting Principles Affecting Corporate Reports," Accounting Review (June 1936): 187191. American Accounting Association, A Statement of Basic Accounting Theory (ASOBAT), 1966. Antle, R., and J. S. Demski, "Revenue Recognition," Contemporary Accounting Research (Spring 1989): p. 423451. Antle, R., J. S. Demski, and S. G. Ryan, "Multiple Sources of Information, Valuation, and Accounting Earnings," Journal of Accounting, Auditing & Finance (1994): p. 675696. Antle, R., and A. Smith, "Measuring Executive Compensations: Methods and an Application," Journal of Accounting Research (Spring 1985): p. 139. Arya, A., J. Glover, and S. Sunders, "Earnings Management and the Revelation Principle," Working paper, Carnegie Mellon University, January 1998. Baiman, S., R. Verrecchia, "Earnings and pricebased compensation contracts in the presence of discretionary trading and incomplete contracting," Journal of Accounting and Economics (20, 1995): p. 93121. Ball, R., and P. Brown, "An Empirical Evaluation of Accounting Income Numbers," Journal of Accounting Research (Autumn 1968): p. 159178. Bartov, E., "The Timing of Asset Sales and Earning Manipulation," Accounting Review (October, 1993): p. 840855. 
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