A Two-step Representation of Accounting Measurement 1 An incorrect belief Pingyang Gao The University of Chicago Booth School of Business November 27, 2012 How does accounting provide information? Empirically, to provide information, accounting relies on an elaborate, distinct measurement system. Examples of the system s institutional features include: exclusive reliance on rules (created by fiat or by social norms) while simultaneously being plagued by rule manipulation, various patterns of conservatism in accounting rules, pervasive use of binary classifications and thresholds, and emphasis on the difference between recognition (financial statements) and disclosure (footnotes). Conceptually, an accounting system uses rules to convert a firm s transactions into an accounting report, aiming to capture the transactions economic substance as accurately as possible. But what is an accounting rule? How does a rule relate a transaction s economic substance to an accounting report? What are the major frictions in the process? What instruments does a rule designer (or standard setter) control to influence properties of the report? These definitional questions arise naturally when we seek to understand an accounting system s institutional features. In my opinion, we still do not have good answers to the question of how information is generated through a measurement system. Consider two common approaches to this question in accounting theories. The first approach formulates the problem as a general reporting game in which we design a manager s incentive contract to solicit her private information optimally. For example, the optimal bonus coeffi cient is reduced if the manager s cost of misreporting becomes lower. The other approach treats accounting measurement as a black box that emanates a signal with certain statistical properties. The question of accounting measurement is dealt with indirectly by linking these properties to accounting s institutional features. For example, we define conservatism as trading a higher false negative error for an equal amount of reduction in the false positive error. As such, we conveniently transform the evaluation of accounting s institutional features to an evaluation of a signal s economic consequences. While both approaches have greatly advanced our understanding of the economic consequences of information production, neither tackles directly the question of the supply of information through the accounting measurement system. 1 Even after an accounting signal with certain statistical properties has been identified as desirable (by answering the economic 1 The lack of accounting content in analytical models has also been pointed out by Dye (2001). 1
consequences question), we are still left with the task of generating such a signal through the design of the accounting measurement system. After all, it is the measurement system that determines the signal s actual properties (and is presumably the core of accounting as an independent academic discipline). 2 One remedy: a two-step representation of accounting measurement One way to open the black box of accounting measurement is to formalize a two-step representation of accounting measurement. 2 First, the state of nature, interpreted as a transaction s or event s economic substance or economic earnings, manifests itself in various transaction characteristics. Second, a measurement rule prescribes a mapping from transaction characteristics to an accounting report. While the rule aims to measure the state as accurately as possible, it is restricted to be written on transaction characteristics. This restriction introduces a natural representation of two major frictions in accounting measurement. First, the correlation between a transaction s economic substance and its characteristics is likely to be imperfect, even in the absence of managers influence. This correlation might be interpreted as a transaction characteristic s relevance. Second, managers can influence a transaction s characteristics without improving its economic substance. These influence activities might be interpreted as earnings management, which ranges from outright fabrication of evidence to the sophisticated accounting-motivated transactions such as offbalance-sheet financing activities. A transaction characteristic s vulnerability to earnings management is one measure of its reliability. Earnings management is often ex post rational for managers but ex ante ineffi cient. Facing these two frictions, the rule designer controls at least three instruments to influence the report s informational properties. First, what transaction characteristics are admitted to a rule? Second, how much verification is required before a transaction characteristic is accepted? Finally, what is the evidence threshold above which an accounting treatment is accorded, despite residual uncertainty about the economic substance? state (substance) of a transaction } {{ } firm influence (earnings management) characteristics of a transaction } {{ } rule design (three instruments) accounting report To make the two-step representation more concrete, consider as an example a typical revenue recognition rule. The economic substance the rule aims to capture is the revenue earning process in a transaction. Transaction characteristics include terms like cash receipt, product delivery, and warranty. These characteristics are imperfectly correlated with the revenue earning process and are vulnerable to managers influence. For example, even if a firm has not earned revenue from a transaction, the manager may simply lie about product delivery or accelerate product delivery through channel stuffi ng. A revenue recognition rule 2 This two-step representation and its importance for understanding the design of accounting rules have long been noted in the classical accounting literatures, e.g., Ijiri (1975), Ball (1989), Leuz (1998b) and Leuz (1998a). 2
has at least three components. It identifies the subset of transaction characteristics to be used, imposes a verification requirement for each transaction characteristic, and prescribes a threshold of evidence above which revenue is recognized. 3 What can we do with this two-step representation? Not only is this two-step representation somewhat empirically descriptive, but also it provides a tractable framework to study the design of the accounting measurement system. Here, I describe a few examples. 3.1 Relevance and Reliability Leuz (1998b) and Dye and Sridhar (2004) study the design of the first instrument, the subset of transaction characteristics to be admitted in a rule. In the context of designing a measurement rule based on which dividend covenants are implemented, Leuz (1998b) considers what transactions and events to be included (or excluded) in an accrual rule. Relative to a cash-based rule, the accrual rule could be superior because of its ability to actively choose non-cash contingencies that are relevant for the agency problems at hand. However, the inclusion of non-cash contingencies also makes the accrual rule more vulnerable to managers manipulation. This trade-off of relevance and reliability constrains the design of the accrual rule. Dye and Sridhar (2004) considers a model with two transaction characteristics, one more relevant and one more reliable. They study the trade-off in the context of designing the optimal aggregation rule that combines the two transaction characteristics in generating an accounting report issued to a competitive capital market. They also prove that aggregation is endogenously optimal (relative to disclosure of two separate transaction characteristics). 3.2 Conservatism The general value of conservatism as a measurement principle has been controversial. In this two-step representation of accounting measurement, conservatism can be defined directly as a differential verification requirement, a property of the second instrument. With this definition, Gao (2012b) shows that conservatism is optimal as long as the manager has the ability and incentive to inflate transaction characteristics, consistent with the long-lasting intuition in the empirical and classic literatures. The previous analytical literature often treats accounting measurement as a black box and models it as a one-step process from economic earnings (the state) to an accounting signal (the report). Accordingly, conservatism is defined indirectly as an informational property of the accounting signal. The evaluation of conservatism is then conveniently transformed to an evaluation of the signal s economic consequences. As a result, the previous literature concluded that conservatism is effi cient if and only if the false negative error is less costly than the false positive error, a condition whose generality is apparently questionable. 3.3 Binary Classifications and Thresholds A binary classification uses a threshold to partition raw evidence. Compared with disclosing the raw evidence, a binary classification suppresses information. Yet, such classifications are pervasive in accounting rules. Using the two-step representation of accounting measurement 3
and focusing on the third instrument (evidence threshold), Dye (2002) takes the binary classification as given and studies the interaction between the design of the threshold and the capital market pricing. Gao (2012a) goes further to explain one benefit of a binary classification as the optimal response to managers opportunistic influence on raw evidence. A threshold affects not only the ex post use of information by stakeholders but also the ex ante earnings management by managers. These dual functions differ qualitatively. As a result, the ex ante optimal threshold is not ex post effi cient, creating a time inconsistency problem. By suppressing ex post information, a binary classification serves as a commitment device to implement the ex ante optimal threshold and makes the accounting report more informative overall in equilibrium than the disclosure of raw evidence. 3.4 Rule-based versus principle-based standards So far, we have focused exclusively on the design of accounting rules. We could introduce auditors professional judgment to the framework and use it to study the trade-off of rule-based versus principle-based standards. A rule-based standard prescribes a definitive mapping from transaction characteristics to an accounting report; a principle-based standard leaves the determination of the mapping to auditors professional judgment. A rule-based standard is vulnerable to non-contractible earnings management even if it is ex post observable. In contrast, the principle-based standard allows auditors to utilize soft information ex post and thus overcomes transparent earnings management. Its disadvantage, however, is that it relies more heavily on the auditors knowledge and incentives. Thus, this two-step representation of accounting measurement can help identify the determinants of the relative effi ciency of a rule-based versus a principle-based standard. 3.5 Two types of agency problems This representation also clarifies two types of agency problems, one with primary activities in a model and the other with the measurement process. They serve different purposes. Agency problems in the primary activities generate a demand for accounting information. For example, the primary activity could be effort provision in a moral hazard problem. The problem s solution demands the measurement of the output of the effort. For another example, the primary activity could be asset substitution in project financing. Its solution demands a measurement-contingent covenant. In contrast, agency problems with the measurement process, or earnings management, constrain the supply of accounting information through the design of measurement rules. 4 The implications Treating accounting measurement as a black box has various consequences. I illustrate them with two examples. First, the "impossibility theorem" of Demski (1973) has foreshadowed a formidable gap between accounting standard setting and academic research that treats accounting measurement as a black box emanating a signal. Conceptualizing accounting standard setting as a choice of the statistical properties of signals generated by the standards, Demski (1973) points out that the value of a signal depends on the specifics of the problems whose solutions 4
rely on the signal. Because two signals that are not Blackwell comparable cannot be universally ranked, it is impossible to establish the general value of any accounting standard even in a single person decision-making setting. While this fundamental insight has accentuated the issue of the proper mandates for standard setters, it has also, inadvertently, distracted attention away from the issue of designing accounting standards for a given mandate. As important as the debate on the proper mandates for standard setting is, standard setters in practice have to deal with the design of accounting standards to fulfill a given mandate, about which academic research following the impossibility theorem does not have much to say. To do so, we need to open the black box of accounting measurement. Second, treating accounting measurement as a black box may have also mixed the two types of agency problems discussed in Section 3.5. As a result, the second type of agency problems, i.e., managers opportunistic influence on transaction characteristics, is often downplayed, if not ignored, in accounting standard setting. The underlying premise is that the production and use of accounting information could be separated and that managers incentives should be dealt with by users of the information. FASB s new conceptual framework (FASB (2010)) is a case in point. For example, it eliminates conservatism as a measurement principle, partly based on the doubt about its general value. Such doubt, as I have discussed in Section 3.2, is predicated on the reduced-form representation of accounting standards as a black box but not founded in the two-step representation that features managers opportunistic influence on accounting measurement. In sum, as accounting scholars, we all strive to understand accounting s institutional features that generate accounting information. We could advance our knowledge along this line by treating the structure of the measurement system more concretely. The two-step representation of accounting measurement serves as a starting point. References Ball, R., 1989, The firm as a specialist contracting intermediary: Application to accounting and auditing, unpublished manuscript. Demski, J.S., 1973, The general impossibility of normative accounting standards, The Accounting Review 48, 718 723. Dye, R.A., 2001, An evaluation of "Essays on Disclosure" and the disclosure literature in accounting, Journal of Accounting and Economics 32, 181 235., 2002, Classifications manipulation and Nash accounting standards, Journal of Accounting Research 40, 1125 1162., and S. Sridhar, 2004, Reliability-relevance trade-offs and the effi ciency of aggregation, Journal of Accounting Research 42, 51 88. FASB, 2010, Statement of financial accounting concepts no. 8, Financial Accounting Standards Board of the Financial Accounting Foundation. Gao, P., 2012a, A measurement approach to binary classifications and thresholds, working paper, University of Chicago., 2012b, A measurement approach to conservatism and earnings management, Journal of Accounting and Economics Forthcoming. Ijiri, Y., 1975, Theory of Accounting Measurement (American Accounting Association Studies in Accounting Research, No. 10. Sarasota, FL). 5
Leuz, C., 1998a, Embedded contingencies in earnings-based contracts, unpublished manuscript., 1998b, The role of accrual accounting in restricting dividends to shareholders, European Accounting Review 7, 579 604. 6