J. Account. Public Policy 31 (2012) 341–355

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J. Account. Public Policy

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Hail, Procrustes! Harmonized accounting standards as aProcrustean bed q

Jack Stecher a, Jeroen Suijs b,⇑a Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA 15213, USAb Tilburg School of Economics and Management, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, Netherlands

a b s t r a c t

0278-4254/$ - see front matter � 2012 Elsevier Inhttp://dx.doi.org/10.1016/j.jaccpubpol.2012.05.003

q This paper benefited from participants’ commein Fribourg, the American Accounting Association acongress in Rotterdam.⇑ Corresponding author. Tel.: +31 13 4663339; f

E-mail addresses: jstecher@cmu.edu (J. Stecher)1 Or does it? Could harmonization simply mean re

3 that it cannot.

This article finds that the use of a harmonized accounting standard,such as the International Financial Reporting Standards, increasesthe information available to markets only if institutional differ-ences across countries using the harmonized standard are insignif-icant. In all other cases, harmonization of reporting standardsdestroys information rather than increasing it. This article also con-tributes to methodology, introducing techniques for studying non-partitional information structures.

� 2012 Elsevier Inc. All rights reserved.

1. Introduction

Conventional wisdom is that the economy would benefit from using a single, global set of account-ing standards. This article shows that the main benefit of a harmonized accounting standard, compa-rability, comes at the cost of lower reporting quality when the countries using the harmonizedaccounting standard have significant institutional differences. Comparability requires that the inter-pretations of a firm’s financial report be the same, irrespective of the home country of the firm orthe user of the financial report.1 It thus confines a harmonized standard to being mutually compatiblewith the countries’ local institutions. Consequently, high-quality harmonized accounting standards seeman impossible mission in a setting with institutional differences. Higher financial reporting quality is

c. All rights reserved.

nts at the University of Stavanger, the Fifth Accounting Research Workshopnnual meetings in Chicago, and the European Accounting Association annual

ax: +31 13 4668001., jeroen.suijs@uvt.nl (J. Suijs).porting in the same way, regardless of the interpretation? We argue in Section

342 J. Stecher, J. Suijs / J. Account. Public Policy 31 (2012) 341–355

achieved through mutual reconciliation of different practices rather than through the use of a uniformstandard.

Our finding that harmonization may not be desirable is similar to the position taken by Walker(2010). Walker’s argument focuses on varieties of capitalism (i.e., institutional differences), with eachvariety having its own set of optimal accounting standards. Accounting standards that suit liberal mar-ket economies like those of the United States and United Kingdom may be inappropriate for coordi-nated market economies like that of Germany or for state-led capitalism such as found in France.We take Walker’s argument one step further and show that imposing a harmonized accounting stan-dard on different forms of capitalism will lead to lower-quality financial reporting.

We stress that our result is not an artifact of choosing a particular equilibrium or even a conse-quence of strategic interaction; instead, we address the amount of information one could possiblycommunicate when using a harmonized accounting standard. This puts our work in the tradition ofIjiri (1975) and Jordan and Xu (1999). We view this question of the bandwidth of a noisy channelas more fundamental than the question of what messages agents choose to send given the bandwidththey face.2

Empirical evidence with respect to the introduction of IFRS seems consistent with our findings.Atwood et al. (2011) show that earnings reports under IFRS are less informative about future cashflows than those under US GAAP. Carmona and Trombetta (2008) argue that the flexibility ofaccounting standards enables the application of such accounting standards by countries with diverseaccounting traditions and institutional environments. Daske et al. (2011) find that some firms use theflexibility offered by IFRS and continue using their usual financial reporting policies. Chua and Taylor(2008) find that there is little to no evidence that the adoption of IFRS has resulted in economicbenefits attributable to improved comparability; instead, improvements in financial reporting qualityseem to be the source of any economic benefits of IFRS adoption. Similarly, Daske et al. (2008) find thateconomic benefits of IFRS adoption are lower for countries whose local Generally Accepted AccountingPrinciples (GAAP) are closer to IFRS, while Shima and Gordon (2011) find that IFRS adopters attractforeign investment only if other strong institutions are in place to protect investors.

The structure of the rest of the article is as follows. Section 2 provides our model of financial report-ing. In particular, it focuses on modeling differences in institutional environments. Section 3 intro-duces the concept of a harmonized accounting system and presents our main result. Section 4discusses mutual reconciliation as an alternative to harmonization. A final section concludes and re-lates our findings to the increasing adoption of IFRS and the convergence project of the InternationalAccounting Standards Board (IASB) and the Financial Accounting Standards Board (FASB).

2. A model of jurisdictional reporting

The question of harmonized accounting standards arises only when local accounting standards dif-fer from each other. We assume throughout that such local differences originate from cultural, insti-tutional, or legislative differences across countries. More abstractly, we envision local differences inaccounting standards arising when people in different jurisdictions have different perceptions ofthe world or of the meaning of various events.

Jurisdictional differences may have far-reaching consequences for the financial reporting process.To illustrate, consider restatements of financial statements. In the United States, a restatement is con-sidered a disclosure with no legal consequences. In the Netherlands, however, a restatement nullifiesthe original financial statements, implying that shareholders need to give again their approval of therestated financial statements and that any declared and paid dividends based on the original financialstatements have become illegal. This jurisdictional difference may, to a large extent, explain the higherfrequency of restatements in the United States relative to the Netherlands.

As another example, consider a recent clash between the German Commercial Code and interna-tional accounting standard (IAS) 32, which concerns presentation of financial instruments as equityor liability. German law mandates that private partnerships allow owners to withdraw their

2 For an example of the latter approach, see Barth et al. (1999). For discussion on the choice reporting entities might make whenoffered alternative standards, see Dye and Sunder (2001) and Sunder (2002).

J. Stecher, J. Suijs / J. Account. Public Policy 31 (2012) 341–355 343

contributed capital. Prior to 2008, however, this legal requirement meant that under IAS 32.18(b), allowners’ contributions to a private partnership were classified as liabilities, as they are puttableinstruments, whereas German law views owners’ contributions as equity. The international standardthus restricted recognizing paid-in capital to a setting that the German law forbids. In February 2008,the IASB amended the standard to allow classification of puttable instruments as equity, provided thatthe obligations could only arise on liquidation. So to make the standard compatible with German law,the IASB needed to broaden the meaning of equity.

The German example is a stark illustration, but there is a large body of literature suggesting that usersof harmonized standards restate or adapt them to local conditions, essentially replacing them with juris-dictional GAAPs. Delvaille et al. (2005) provide additional examples from Europe. Chamisa (2000) andTyrrall et al. (2007) show results from developing and transitional economies. Chamisa (2000) docu-ments Zimbabwe’s rejection of IAS 29, which covers hyperinflationary economies, as inappropriatefor Zimbabwe. Tyrrall et al. (2007) present similar evidence for Kazakhstan and cite similar findingsin other studies of transitional economies. In each case, the pressure seems to be away from using a har-monized standard and toward a local GAAP, often presented as more informative for local conditions.

Why would the IASB not simply add new terminology to accommodate cases such as the Germanexample? A natural explanation is that while the IASB could create a new category, such as puttableowners’ equity, that might only apply in Germany, an audience outside Germany would not knowhow to interpret such a report, as puttable owners’ equity is an unknown concept to them. This ideahas appeared many times informally in the accounting literature (e.g., Avery, 1953; Wilkinson,1964; Ball, 1995) and is recognized explicitly by the FASB (1978) in its first Statement of FinancialAccounting Concepts, which states that financial reporting information ‘‘should be comprehensibleto those who have a reasonable understanding of business and economic activities and are willingto study the information with reasonable diligence.’’ (Section 34, p. 11).

In what follows, we present a model of jurisdictional reporting that captures the idea of reportsbeing meaningful in one jurisdiction yet unclear in another. Our model has two building blocks.The first, which we refer to as an agent’s perception of the world, models institutional, legal, or culturaldifferences across jurisdictions. The second is the financial reporting environment. A perception of theworld describes the observable characteristics of each transaction recognized within a jurisdiction.Perceptions of the world determine what a company in a given jurisdiction can meaningfully report.Different perceptions across jurisdictions may result in different reporting languages, that is, differentGAAPs. We describe both building blocks next.

2.1. Perceptions of the world

We define a world as a pair hX ;Ai, where X denotes the set of real-world objects or events and Adenotes the set of possible observable characteristics of objects or events. In accounting terms, onecan think of A as the set of characteristics used to describe the transactions in which a firm can engagesuch as a sales agreement or debt contract. We assume that objects or events x 2 X are not directly ob-servable but that only the characteristics that x is perceived to have are observable. Then a perception pof a world hX ;Ai is a correspondence, assigning to each event x 2 X the characteristics pðxÞ � A thatevent x is seen to possess. We assume that for every x 2 X ; pðxÞ– £; this just rules out events thathave no observable characteristics.

One can interpret perceptions as describing the institutional, cultural, and legislative setting ofjurisdictions. For example, the additional feature of private partnerships that allows owners to with-draw their contributed capital would be an observable characteristic in Germany but not in otherjurisdictions, where German law may be unfamiliar. Similarly, restatements of financial statementswould come with different observable characteristics in the Netherlands than they would in the Uni-ted States. For expository purposes, we use a stylized example related to financial obligations.

Example 2.1. Let X be the set of financial obligations a firm can face. Possible characteristics of suchobligations are the likelihood of a future cash outflow, the amount and timing of the cash outflow, or theidentity of the counterparty. For simplicity, we confine attention to the first characteristic and writeX ¼ ½0;1�, with x 2 X denoting the likelihood of an obligation resulting in a future cash outflow. In a

344 J. Stecher, J. Suijs / J. Account. Public Policy 31 (2012) 341–355

world of known risks, one could perfectly assess the likelihood of a cash outflow so that A ¼ ½0;1� andp(x) = x. But if there is no basis for assessing risks, one might only be willing to commit to an impreciseestimate of the likelihood of a cash outflow. A perception that allows for a 20% error would bep(x) = [max{x � 0.1,0}, min{x + 0.1,1}]. Alternatively, one could classify obligations qualitatively usingA ¼ fhighly likely; likely; unlikelyg and perception p with p(x) = {highly likely} for x 2 [0.8,1], p(x) = {li-kely} for x 2 [0.3,0.9] and p(x) = {unlikely} for x = [0,0.3). In that case, obligations in [0.8,0.9] can beperceived as either highly likely or likely. This reflects the inherent ambiguity in the classification.3

As agents do not observe events x 2 X , they use observable characteristics to make distinctions be-tween events. We say that perception pdistinguishes events x1 and x2 if there exist characteristicsa1; a2 2 A such that

3 Witprobabiterms, a

4 Disthe predistingureader t

5 Thenoted, i

ðiÞ a1 2 pðx1Þ and a1 R pðx2ÞðiiÞ a2 R pðx1Þ and a2 2 pðx2Þ

:

These conditions state that x1 and x2 have distinct observable characteristics. Perception p weaklydistinguishes x1 and x2 if either (i) or (ii) holds.

Example 2.2. Let X ¼ ½0;1� denote the likelihood of an obligation resulting in a future cash outflow,and let A ¼ fhighly likely; likely; unlikelyg. Suppose perception p is given by p(x) = {highly likely} forx 2 [0.8,1], p(x) = {likely} for x 2 [0.3,0.9], and p(x) = {unlikely} for x = [0,0.3). The obligations in theinterval (0.9,1] are distinguishable from the obligations in [0,0.8) and are weakly distinguishable from[0.8,0.9]. Obligations in [0.8,1] are indistinguishable from each other (even though some are weaklydistinguishable from others).4

To describe when jurisdictions coincide in their interpretation of events, we introduce a notion ofconsensual validation. For this purpose, let the inverse image p�1ðAÞ ¼ fx 2 XjA � pðxÞg describe allevents x 2 X that possess all of the characteristics in A � A.5 Let hX;pi;Aiii2I be a family of worldsand perceptions for some set I of jurisdictions. Suppose that for each i 2 I , there is an Ai � Ai such thatfor all i; j 2 I , the respective inverse images agree: p�1

i ðAiÞ ¼ p�1j ðAjÞ. Then there is consensual validation

among the jurisdictions in I of the characteristics in fAigi2I . Consensual validation implies that the juris-dictional perceptions agree on the events with characteristics in fAigi2I .

Example 2.3. Consider the situation in Example 2.2. Let p1 and p2 be such that p1(x) = p2(x) = {highlylikely} for x 2 (0.95,1], p1(x) = {likely} for x 2 [0.3,0.95], p2(x) = {likely} for x 2 [0.4,0.95], p1(x) = {unli-kely} for x 2 [0,0.4), and p2(x) = {unlikely} for x 2 [0,0.5). Then there is consensual validation on highlylikely but not on likely or unlikely. In both perceptions, an obligation that is highly likely yields a cashoutflow with a probability of at least 95%.

Example 2.4. Consider the situation in Example 2.2. Let perception p1 be such that p1(x) = {highlylikely} for x 2 (0.95,1], p1(x) = {likely} for x 2 [0.3,0.95], and p1(x) = {unlikely} for x 2 [0,0.4). Next, letp2 be such that p2(x) = {highly likely} for x 2 (0.9,1], p2(x) = {likely} for x 2 [0.3,0.9], and p2(x) = {unli-kely} for x 2 [0,0.5). There is no consensual validation on highly likely, likely, or unlikely, but there isconsensual validation on {highly likely, likely}. In both perceptions, an obligation that is likely or high-ly likely results in a payment with at least 30% likelihood.

Unlike in the preceding stylized examples, events x 2 X are typically not (fully) characterized by asingle characteristic a 2 A. Besides the likelihood that a future cash flow occurs, an obligation is alsocharacterized by the amount due and the settlement date. As another example, a sales transaction has

hout ambiguity in perceptions, an obvious solution would be simply to require a given accounting treatment if thelity of cash outflows lies in some given range. With ambiguity, establishing a fixed cutoff is infeasible. In mathematicalmbiguous information is a notion of being within a tolerance and hence does not induce a partition.

tinguishability is an incomplete partial ordering, but it is the standard one to use with nonpartitional information, if (as insent case) the information structure is of a topological nature. What we call distinguishability (respectively weakishability) is called Hausdorff (respectively Kolmogorov) separability in the topology literature. We refer the interestedo a standard text on topology, such as Kelley (1975).re are four possible ways to define the inverse image of the correspondence p. The definition we use, unless otherwises known as the strong dual image. For other possible definitions and their properties, see Sambin (2012).

J. Stecher, J. Suijs / J. Account. Public Policy 31 (2012) 341–355 345

many attributes: what stock-keeping unit is sold, whether the sale is cash or credit, when the productships, whether it is sold with a warranty, and so on. It would thus be more realistic to describe a trans-action by a subset of characteristics A � A. Consensual validation of A then means that two jurisdic-tions agree on this particular type of transaction.

Just like in Example 2.4, where two jurisdictions have consensual validation on the collection ofcharacteristics {highly likely, likely} but not on the characteristics highly likely or likely individually,it may happen that two jurisdictions have consensual validation on a collection of transactions butnot on each transaction individually. To accommodate such cases, we extend the definition of consen-sual validation to a collection of subsets of A.

Let PðAÞ denote the collection of all subsets of A. For two perceptions p1 and p2 on hX ;Ai and forsome index sets I1, I2, we say that there is consensual validation of fAi1gi12I1

� PðAÞ withfAi2gi22I2

� PðAÞ if fx 2 Xj9i1 : Ai1 � p1ðxÞg ¼ fx 2 Xj9i2 : Ai2 � p2ðxÞg.

2.2. Financial reporting environment

The accounting standards of a jurisdiction prescribe how events will be recorded in the financialstatements. As events are not directly observable, accounting standards have to be based on the ob-servable characteristics A. We define an accounting standard in world hX ;Ai as a pair S ¼ hR; T i, whereT denotes a set of terms or reports and R � PðAÞ � T denotes a binary relation between the power setPðAÞ of A and T . One can think of t 2 T as a separate line item in the balance sheet or income state-ment, a footnote disclosure, or a part of management discussion. For A � A and t 2 T (A, t) 2 R meansthat an agent can report any event possessing all characteristics a 2 A as t; that is, an auditor familiarwith the standard S would approve the report t.

To analyze the information that an accounting standard communicates, some additional terminology isneeded. We denote by R�1ðtÞ ¼ fA � AjðA; tÞ 2 Rg the information communicated by report t. In other words,when observing the report t 2 T , one knows an event x 2 X has occurred with characteristics A 2 R�1(t). Soeach A 2 R�1(t) represents a collection of characteristics that suffices for an event x 2 X to be reported as t.The collection of characteristics

T{AjA 2 R�1(t)} is necessary for an event x 2 X to be reported as t.

Example 2.5. Consider the situation in Example 2.3. An accounting standard for the recognition ofliabilities can be described by S1 ¼ hR1; T 1i, with T 1 ¼ fliability; other commitmentg, and R1 such that

6 Recwith thmathem

R1 ¼ fðfhighly likelyg; liabilityÞ; ðflikelyg; liabilityÞ; ðfunlikelyg; other commitmentÞg:

Hence, when a liability is recognized, one knows that a future cash outflow is (highly) likely to hap-pen, that is, R�1

1 ðliabilityÞ ¼ ffhighly likelyg; flikelygg. However, one does not know which of these actu-ally applies (i.e., whether a future cash outflow is highly likely or likely). When a liability is notrecognized, one knows for certain that a future cash outflow is unlikely to happen, asR�1

1 ðother commitmentÞ ¼ funlikelyg.Given a perception p, the reportable image s(x) of an event x 2 X in accounting standard S is the set

of all feasible reports of x; that is,

sðxÞ ¼ ft 2 T j9A 2 R�1ðtÞ : A � pðxÞg:

Observe that event x can be reported as t only if event x possesses the sufficient characteristicsA(i.e., A � p(x)) required by the accounting standard S (i.e., A 2 R�1(t)). Conversely, s�1(t) denotesall events x 2 X for which t is a feasible report in accounting standard S; that is,6

s�1ðtÞ ¼ fx 2 Xj9A 2 R�1ðtÞ : A � pðxÞg:

An accounting standard S ¼ hR; T i distinguishes between events x1; x2 2 X under perception p ifthere exist reports t1; t2 2 T such that t1 is a feasible report for x1 but not for x2 and such that t2 isa feasible report for x2 but not for x1:

all that p�1(A) is defined as the set of events that have characteristics in A. To capture the definition of s�1, we need to worke weak inverse image, at least if we want to think of s�1 as equivalent to p�1�R�1. See Sambin (2012) for a discussion of the

atical properties of the weak inverse image.

7 Hen8 The

necessawhich ofinenes

346 J. Stecher, J. Suijs / J. Account. Public Policy 31 (2012) 341–355

ðiÞ t1 2 sðx1Þ and t2 R sðx1ÞðiiÞ t1 R sðx2Þ and t2 2 sðx2Þ

:

We say that S weakly distinguishes x1 and x2 if either (i) or (ii) holds.

Example 2.6. Consider the accounting standard S ¼ hR; T i of Example 2.5 and perception p1 ofExample 2.3, that is, p1(x) = {highly likely} for x 2 (0.95,1], p1(x) = {likely} for x 2 [0.3,0.95], andp1(x) = {unlikely} for x 2 [0,0.4). The reportable image satisfies s(x) = {liability} for x 2 [0.4,1], s(x) ={liability, other commitment} for x 2 [0.3,0.4), and s(x) = {other commitment} for x 2 [0,0.3). Hences�1(liability) = [0.3,1] and s�1(other commitment) = [0,0.4). The obligations in [0.4,1] are indistin-guishable from each other; however, they are distinguishable from the obligations in [0,0.3), and theyare weakly distinguishable from obligations in [0.3,0.4). The obligations in [0.3,0.4) are only weaklydistinguishable from the obligations in [0.4,1] and [0,0.3).

Accounting systems like US GAAP, IFRS, and other local GAAPs are collections of accounting stan-dards. We thus define an accounting system S as a collection of accounting standards S ¼ fS1;S2; . . . ;

Sng. By straightforward aggregation of the individual accounting standards Si ¼ hRi; T ii, one canrepresent an accounting system by S ¼ hR; T i, where T ¼ [n

i¼1T i and (A, t) 2 R if (A, t) 2 Ri for somei = 1, 2, . . .,n. Hence all previously defined concepts for accounting standards also apply to accountingsystems.

With respect to perception p, we say that accounting system S is at least as informative asaccounting system S0 if every pair of events x1; x2 2 X that is (weakly) distinguishable in S0 is also(weakly) distinguishable in S. Accounting system S is more informative than accounting system S0if S is at least as informative as S0 and there exists a pair of events x1; x2 2 X that is distinguishablein S but not in S0. Accounting systems S and S0 are equally informative if S is at least as informativeas S0 and S0 is at least as informative as S. Finally, an accounting system S� is maximally informativeif there exists no accounting system that is more informative than S�.7 Accounting systems are thuspartially ordered by their informativeness. Two accounting systems S; bS need not be comparable inthat neither might satisfy the definition of being at least as informative as the other. We cannot con-sider two such systems as equally informative as this would make the notion of being equally infor-mative intransitive.

Example 2.7. Consider the accounting standard S ¼ hR; T i and perception p1 of Example 2.3. Noticethat S is not maximally informative. A maximally informative accounting system is S� ¼ hR�; T �i withT � ¼ fliability; provision; other commitmentg and

R� ¼ fðfhighly likelyg; liabilityÞ; ðflikelyg; prov isionÞ; ðfunlikelyg; other commitmentÞg:

This accounting system distinguishes the same events as the perception p1 does. In other words,the maximally informative accounting system just reports the perceived characteristics of each event.In practice, however, one may not observe maximally informative accounting systems as one purposeof accounting is to aggregate information; that is, events with sufficiently similar characteristics arecombined and reported as the same event. The literature discusses why aggregation arises (e.g.,Dye and Sridhar, 2004; Arya et al., 2006), and we do not revisit this issue here.

As noted in Section 1, our interest is in the amount of information that one can communicate withharmonized accounting standards. We focus on the partial ordering of accounting systems that differ-ences in perceptions induce (see Footnote 4 for our reason for choosing this ordering). We view this asa prior question to that of considering a particular decision problem in which we can rely on the deci-sion makers’ preferences.8

ceforth we denote maximally informative accounting systems by a superscript asterisk.results of Demski (1973) might seem to imply that in a setting as general as ours, any ordering of accounting systems

rily satisfies our ordering criteria. However, we urge caution in making this inference. Demski (1973) discusses settings inne cannot rank information systems by their fineness, in the Blackwell (1951) sense. This differs from our notion of

s, and we claim only that the results of Demski (1973) are suggestive.

J. Stecher, J. Suijs / J. Account. Public Policy 31 (2012) 341–355 347

2.3. A note on partitional information structures

The purpose of this subsection is to show that nonpartitional information structures better suit thecontext of accounting information than partitional information structures. Partitional informationstructures arise when the perception p is constrained to be a function instead of a correspondence.Then the inverse image p�1(�) induces a partition of X . The axioms of Savage (1972) and the resultsof Blackwell (1951) require partitional information structures.

Example 2.8 illustrates how the information structures we consider relate to information parti-tions. While {[0,0.3), [0.3,1]} is the finest information partition in the example, there is more structurewithin the partition set [0.3,1]. A Savage-rational agent ignores this additional structure, whereas theagents in our model pay attention to it. Put differently, agents in our model would be considered neo-classically irrational because they do not throw information away. To us, this seems a strange propertyof the standard notion of rationality. Furthermore, the interpretation of partitional information struc-tures may be inconsistent, as the following example shows.

Example 2.8. Let X ¼ ð0;1Þ denote the likelihood of an obligation resulting in a future cash outflow.Let the perception p1 be such that p1(x) = k when x 2 (k � 0.1,k + 0.1] for some k 2 {0.1,0.3, . . . ,0.9}.Furthermore, let perception p2 be such that p(x) = (max{x � 0.1,0},min{x + 0.1,1}]. Both perceptionscan be interpreted as allowing for 20% error in assessing the likelihood of a future cash outflow. Theperception p1 yields the information partition {(0,0.2], (0.2,0.4], . . . , (0.8,1)}, implying that one is notable to distinguish any two different likelihoods in the interval (0,0.2]. For example, one would not beable to distinguish between x1 = 0.01 and x2 = 0.2. Strangely, however, the perception p1 would be ableto distinguish between 0.2 and 0.2 + e for arbitrarily small positive values of e. Nonpartitionalinformation structures like p2 resolve this inconsistency as one cannot distinguish between any twolikelihoods for which the difference is less than 20%.

Nonpartitional information structures allow for ambiguity in perception and vagueness in termi-nology, and these are desirable properties when studying accounting systems. For example, an auditormust decide whether differences in the client’s financial statements and the auditor’s calculations arematerial. It is easy to see that the notion of being immaterial is intransitive: an accurate report candiffer immaterially from a report with a small error, which can differ immaterially from a report withtwo small errors, and so forth.

There are many other instances in which accounting would naturally fit with a nonpartitionalinformation structure. Issues involving judgments seem like a natural setting. Revenue recognitiondepends on judgments about whether benefits are likely to be received (whether they are realizable).Fair value accounting for assets that are not actively traded depends on judgments about which assetshave similar cash flow profiles. This is easily seen to be a nonpartitional structure: one asset can have asimilar cash flow profile to two other assets, neither of which would be considered similar to the other.As a final example, accounting for acquisitions prescribes that the acquirer determines the fair value ofthe acquired firm’s assets. This presumes that the acquirer is able to distinguish the impact of the var-ious assets on the total market value of the firm. If the acquirer cannot unambiguously attribute everydollar of market value to a specific asset, vague accounting terminology is necessary to properlydescribe the valuation problem.

3. Harmonized accounting standards

When different jurisdictions use different reporting systems, communication across jurisdictions isnot straightforward as reports may not be comparable across jurisdictions. Reports in one jurisdictionmay have no or different meaning in other jurisdictions. Recall our example of equity in German pri-vate partnerships, which has the character of puttable owners’ equity and may not be perceived asequity in other countries. One way of establishing communication across jurisdictions is by meansof a harmonized accounting system. A possible interpretation of a harmonized accounting system isone set of rules that all jurisdictions apply. The major drawback of this approach is that reports stillneed not be comparable across jurisdictions.

348 J. Stecher, J. Suijs / J. Account. Public Policy 31 (2012) 341–355

Example 3.1. Consider the situation in Example 2.2 with

A ¼ fhighly likely; likely; unlikelyg:

Suppose p1(x) = {highly likely} for x 2 (0.8,1], p1(x) = {likely} for x 2 (0.4,0.8], and p1(x) = {unlikely}for x 2 [0,0.4]. For perception p2, suppose p2(x) = {highly likely} for x 2 (0.9,1], p2(x) = {likely} forx 2 (0.4,0.9], and p2(x) = {unlikely} for x 2 [0,0.4].

Suppose that S ¼ hR; T i with

T ¼ fliability; provision; other commitmentg

and that

R ¼ fðfhighly likelyg; liabilityÞ; ðflikelyg; provisionÞ; ðfunlikelyg; other commitmentÞg

is the accounting system that both jurisdictions use. For this accounting system, the report other com-mitment is comparable across both jurisdictions as both interpret other commitment as an unlikelycash outflow; that is, a cash outflow arises with 40% probability or less. The reports liability and pro-vision are not comparable. When a firm incorporated in jurisdiction 2 reports a liability, investors injurisdiction 2 will interpret this report as the likelihood of a cash outflow being at least 90%. However,investors in jurisdiction 1 will interpret this report as the likelihood of a cash outflow being at least80%. They would thus underestimate the likelihood of a cash outflow. Conversely, when a firm incor-porated in jurisdiction 1 reports a provision, investors in jurisdiction 2 would overestimate the likeli-hood of a cash outflow. Thus a common accounting system need not provide each jurisdiction with thesame information.

Comparability is commonly seen as the major benefit of a harmonized accounting system. For thisreason, we define a harmonized accounting system as a common language that enables undirectedcommunication across jurisdictions. To be precise, let pi be the perception of jurisdiction i 2 I . Wesay that an accounting system S is harmonized for ðpiÞi2I if, for all i; j 2 I and all reports t 2 T ,

s�1i ðtÞ ¼ s�1

j ðtÞ:

Condition (1) says that users of S interpret all reports in the same way; that is, reports are compa-rable across jurisdictions.

Example 3.2. Consider the situation in Example 2.2 with

A ¼ fhighly likely; likely; unlikelyg:

Suppose p1(x) = {highly likely} for x 2 (0.8,1], p1(x) = {likely} for x 2 (0.4,0.8], and p1(x) = {unlikely}for x 2 [0,0.4]. For perception p2, suppose p2(x) = {highly likely} for x 2 (0.9,1], p2(x) = {likely} forx 2 (0.4,0.9], and p2(x) = {unlikely} for x 2 [0,0.4]. Let accounting systems S1 and S2 be such thatT 1 ¼ fliability; other commitmentg; T 2 ¼ fliability; provision; other commitmentg, and

R1 ¼ fðfhighly likelyg; liabilityÞ; ðflikelyg; liabilityÞ; ðfunlikelyg; other commitmentÞg;R2 ¼ fðfhighly likelyg; liabilityÞ; ðflikelyg; provisionÞ; ðfunlikelyg; other commitmentÞg:

A harmonized accounting system for perceptions p1 and p2 is S ¼ hR; T i withT ¼ fliability; other commitmentg and

R ¼ fðfhighly likelyg; liabilityÞ; ðflikelyg; liabilityÞ; ðfunlikelyg; other commitmentÞg:

It holds that

s�11 ðliabilityÞ ¼ s�1

2 ðliabilityÞ ¼ ð0:4;1�;s�1

1 ðother commitmentÞ ¼ s�12 ðother commitmentÞ ¼ ½0;0:4�:

Our first result shows what a harmonized accounting system can convey.

J. Stecher, J. Suijs / J. Account. Public Policy 31 (2012) 341–355 349

Proposition 3.1. If S is a harmonized accounting system for perceptions p1 and p2, then there is consensualvalidation on the characteristics underlying each report in S; that is, for all t 2 T , there is consensualvalidation on R�1(t).

All proofs are in Appendix A.There may be many harmonized accounting systems for given perceptions. Restricting the notion

of informativeness from Section 2 to harmonized systems, we call harmonized accounting system Smaximally informative if no harmonized accounting system S0 is more informative than S. Observe thatthe harmonized accounting system in Example 3.2 is maximally informative.

Proposition 3.2. A harmonized accounting system S� is maximally informative with respect to perceptionsp1 and p2 if and only if S� distinguishes all events that both perceptions can distinguish, that is, if and only if,whenever x1 2 X and x2 2 X are distinguishable in p1 and p2, it is also the case that x1 and x2 aredistinguishable in S�.

The intuition for this result is straightforward. When agents in a jurisdiction do not see the differ-ence between events x1 and x2, the harmonized accounting system cannot distinguish these events.Even when the harmonized accounting system would report x1 and x2 differently, agents would justinterpret these reports as one and the same message, that is, as synonyms.

Next, we turn to the main issue of this article: do agents benefit from using a harmonized account-ing system?

Theorem 3.1. Let ðpiÞi2I be the perceptions of jurisdictions in I .

3.1a When perceptions are homogeneous (i.e., for all i; j 2 I ; pi ¼ pj), then for each i 2 I , it holds that themaximally informative harmonized accounting system S� is at least as informative as any localaccounting system Si. S� is strictly more informative than Si when, for some j 2 I , there exist eventsx1; x2 2 X that are distinguishable in Sj but not in Si.

3.1b When perceptions are heterogeneous (i.e., there exist i; j 2 I such that pi – pj), for each i 2 I , it holdsthat the maximally informative local accounting system S�i is at least as informative as any harmo-nized accounting system S. S�i is strictly more informative than Si when, for some j 2 I , there existx1; x2 2 X that are distinguishable in pi but not in pj.

Theorem 3.1a applies to a setting that is consistent with a neoclassical world, in which all agentsperceive X in the same way (even if they may be restricted on what they can observe). Because per-ceptions are homogeneous, there is consensual validation on the characteristics a 2 A. Hence allagents agree on what characteristics describe each event. In such a setting, all agents prefer the useof a maximally informative harmonized accounting system, in the absence of other strategic consid-erations. The intuition is straightforward: because agent i can understand the reports of accountingsystem Sj, one can construct a harmonized accounting system as the join of the local accounting sys-tems: S� ¼ [i2ISi.

Theorem 3.1b shows that the result reverses when perceptions are heterogeneous because themaximally informative harmonized accounting system is now the common denominator of the per-ceptions: S� can only distinguish those events that all perceptions distinguish. Consequently, any dis-tinction that at least one agent cannot perceive is lost in S�. For this reason, maximally informativelocal accounting systems are at least as informative as any harmonized accounting system.

Notice that Theorem 3.1b holds for only the maximally informative local accounting system andnot for any local accounting system. This implies that a harmonized accounting system may improvecommunication when the local accounting standards are of sufficiently low quality.

4. Reconciling accounting systems

Theorem 3.1b shows that harmonization coarsens the amount of information an accounting systemcan convey. An alternative to harmonization is mutual reconciliation of accounting systems. Let p1 and

350 J. Stecher, J. Suijs / J. Account. Public Policy 31 (2012) 341–355

p2 denote the perceptions of jurisdiction 1 and 2, respectively. Let S1 and S2 denote the respectiveaccounting systems. Then we say that accounting system S1 is fully reconcilable with accounting sys-tem S2 if there exists a correspondence T f

1T 2 such that for each t1 2 T 1,

9 Oneaccountis reconall t1 2

s�12 ðf ðt1ÞÞ ¼ s�1

1 ðt1Þ: ð1Þ

To explain expression (1), observe that s�11 ðt1Þ represents how the users in jurisdiction 1 interpret

the report t1, while s�12 ðf ðt1ÞÞ represents how the users in jurisdiction 2 interpret the collection of re-

ports f(t1). One can thus view f(t1) as the translation of report t1 in the reporting language of jurisdic-tion 2. Notice that the translation f need not be a word-for-word agreement as f is not required to beinjective; that is, two different reports in accounting system S1 may correspond to the same report inaccounting system S2. Conversely, f also need not be surjective; that is, a report in accounting systemS2 may be meaningless to the users in jurisdiction 1.

Example 4.1. Consider the situation in Example 3.2. Accounting system S1 is fully reconcilable withaccounting system S2. The translation that establishes reconciliation is

f ðliabilityÞ ¼ fliability; prov isiong;

f ðother commitmentÞ ¼ fother commitmentg:

Users in jurisdiction 2 interpret a liability in accounting system S1 as either a liability or provision inaccounting system S2. Our notion of reconciliation is thus one of embedding: a company in jurisdic-tion 1 complies with S2 by adding to its footnotes, ‘‘Both provisions and liabilities are considered lia-bilities in these statements, in accordance with accounting system S1.’’ Everything expressible in S1

can be conveyed if the reporting entity uses S2.

Proposition 4.1. Let p1 and p2 be two perceptions with accounting systems S1 and S2, respectively. Ifaccounting system S1 is fully reconcilable with accounting system S2, then accounting system S2 is at leastas informative as accounting system S1.

Proposition 4.1 implies that reconciliation is not symmetric. When accounting system S1 is recon-cilable with accounting system S2; S2 may be irreconcilable with S1 (cf. Example 4.1).

Proposition 4.1 imposes a strong necessary condition for reconciliation of accounting systems to befeasible. Any two accounting systems that provide more detailed information on different topics areirreconcilable. For example, if S1 provides more detailed information on business segments than S2,while S2 provides more detailed information on executive compensation than S1, then there can beno full reconciliation between S1 and S2.9

Theorem 4.1. For any maximally informative harmonized accounting system, there exist local accountingsystems and (partial) reconciliations that enable at least as much communication across and withinjurisdictions as under a maximally informative harmonized accounting system.

The following examples illustrate the ideas behind Theorem 4.1.

Example 4.2. Let p1 = p2 be the identity function on X , and let A ¼ X . Suppose that for allx 2 X ; p3ðxÞ ¼ A. Then the maximally informative harmonized standard among all three jurisdictionsis completely uninformative: T must be a singleton. Conversely, under reconciliation, communicationbetween jurisdictions 1 and 2 is perfect.

Example 4.3. Consider the perceptions of Example 3.2. A maximally informative harmonizedaccounting system is S ¼ hR; T i, with

can relax the results for reconcilability in the natural way to results for partial reconcilability. To be precise, we say thating system S1 is partially reconcilable with accounting system S2 if only some subset of reports T1 of accounting system S1

cilable with accounting system S2, that is, there exists a correspondence Tf1T2 with Ti � T i such that s�1

2 ðf ðt1ÞÞ ¼ s�11 ðt1Þ for

T1.

J. Stecher, J. Suijs / J. Account. Public Policy 31 (2012) 341–355 351

T ¼ fgeneral liability; other commitmentg;

R ¼ fðfhighly likelyg; general liabilityÞ; ðflikelyg; general liabilityÞ; ðfunlikelyg; other commitmentÞg:

The maximally informative harmonized accounting standard S ignores the local distinctionbetween obligations (0.8,1] and (0.4,0.8] in jurisdiction 1 and the local distinction between obligations(0.9,1] and (0.4,0.9] in jurisdiction 2. More communication within each jurisdiction is established bythe local accounting system Si ¼ hRi; T ii, with

T i ¼ fgeneral liability; liability; prov ision; othercommitmentg;

R ¼ fðfhighly likelyg; general liabilityÞ; ðflikelyg; general liabilityÞ ðfhighly likelyg; liabilityÞ;ðflikelyg; prov isionÞ ðfunlikelyg; other commitmentÞg:

Both local accounting systems now include a more detailed specification of the report generalliability. A general liability can either be a liability or a provision. Communication between the two juris-dictions is established by the partial reconciliation T fij

i T j, with

T i ¼ fgeneral liability; liability; provision; other commitmentg;T j ¼ fgeneral liability; other commitmentg;

fijðtÞ ¼other commitment; if t ¼ other commitment;

general liability; if t – other commitment:

�

Jurisdiction i interprets a general liability reported by the accounting system of jurisdiction j aseither a general liability, liability, or provision in terms of its own accounting system. The specificationof a general liability in a liability or provision that jurisdiction j makes is meaningless in jurisdiction i.Consequently, only the report general liability is meaningful to both jurisdictions. The reports liabilityand provision have jurisdiction-specific meanings. Observe that across jurisdictions, the same informa-tion is communicated as in the harmonized accounting system S, but that within each jurisdiction,more information is communicated than in S.

5. Discussion and concluding remarks

So where does this leave us? Would a unique global financial reporting system improve the abilityof firms to provide information to markets, or must IFRS and all similar projects turn out to be a Pro-crustean bed? The answer depends on a deeper question of how well the axioms of Savage and Black-well describe the information that market participants are likely to face.

In a neoclassical world, all agents have homogeneous perceptions and understand the nature of anyuncertainty with infinite precision. Agents may differ in the signals they can observe, but neoclassical-ly, everyone has the same underlying state space. Theorem 3.1a shows that the neoclassical frame-work predicts that a shared accounting standard can improve the amount of information availableto markets, at least in the absence of other strategic considerations. An ideal global accounting systemwould make any distinctions that any agent could observe (i.e., one in which there is consensual val-idation on each characteristic a 2 A).

Yet this prediction is not robust even to a small departure from the Savage axioms. Specifically, wehave shown that if agents have any heterogeneity in what they perceive, then a global accounting sys-tem becomes at best a lowest common denominator, capturing only distinctions that everyone inevery jurisdiction can make.

There are two forces that drive this result. First, there is the interference caused by outside parties.Imagine, for example, that a French company lists on a Spanish exchange. Both jurisdictions are capa-ble of perceiving the difference between puttable instruments and contributed capital, but because ofa limitation in the perceptions of Germany—an unrelated party—the French company is preventedfrom reporting this distinction, even though the Spanish audience would have no trouble interpreting

352 J. Stecher, J. Suijs / J. Account. Public Policy 31 (2012) 341–355

it. In this sense, the use of a harmonized accounting system is a Procrustean bed. Rather than beingone size fits all, the global standard forces all to fit one size.

A second, related force is that the informativeness of an accounting system is meaningful onlyagainst the backdrop of what its users can perceive or, alternatively, relative to what is meaningfulwithin an institutional environment. The level of detail that can be meaningful in different jurisdic-tions is a partial ordering, roughly because different aspects of information will be more crucial in dif-ferent environments. This means that the greatest lower bound on the information two jurisdictionscan consensually validate will, in general, be a strict coarsening of what either jurisdiction can indi-vidually discern. Thus, even without the interference of external parties, the introduction of asymmet-ric institutions or asymmetric perceptions implies that standards can only converge by discardinginformation.

Agents who differ in their perceptions can do better under reconciliation with local, country-specific accounting standards than with a single harmonized system. There are two main reasons.First, reconciliation enables the choice of reported information to be adapted to the intendedaudience: outside parties do not affect communication. Second, reconciliation is by natureasymmetric. This enables a cross-listing firm to convey information in the home jurisdiction thatwould be meaningless in the foreign GAAP and thereby to improve on the greatest lower boundon shared information.

As our modeling approach leads to drastically different predictions from the standard neoclassicalmodel, it seems worthwhile to consider some results from the empirical literature. One commonfinding is that IFRS and its predecessors are applied differently across jurisdictions (see, e.g., Joosand Lang, 1994; Chen et al., 2002; von Keitz, 2006). This is consistent with the prediction ofharmonized systems evolving toward systems that allow for local interpretations of the accountingstandards. This enhances financial reporting quality at the country level, but at the expense ofcomparability.

Indirect evidence might also be assessed by looking at how IFRS adoption changes a firm’s cost ofcapital to the extent that more informative reports lead to reductions in the cost of capital.Jermakowicz and Gornik-Tomaszewski (2006) report the results of a survey of firms that facedmandatory adoption of IFRS. They report that firms adopting IFRS did not expect reductions in theircosts of capital and that 70% of first-time adopters stated that they would not use IFRS if they had achoice. Cuijpers and Buijink (2005) find higher costs of capital for firms that adopted IFRS, at a timewhen adoption of IFRS was still voluntary.

Market returns for IFRS adopters may also provide suggestive evidence on the predictions of thecompeting models discussed here. Although the results are mixed, the following findings arenoteworthy. First, Armstrong et al. (2010) find a generally positive market response to IFRSadoption; however, for firms located in jurisdictions with high-quality local GAAPs, they find noimprovement. Barth et al. (2008) likewise find that gains from IFRS adoption come chiefly fromfirms in countries with poor-quality local GAAPs. To the extent that local GAAPs are not maximallyinformative for their jurisdiction, a move to a harmonized system could be an improvement, evenin the non-Savage setting on which we concentrate. Such improvement, however, stems from theharmonized accounting system being just a more informative system than the local one, notbecause it is a harmonized system. Second, the market’s positive reaction to IFRS adoption seemsshort-lived. Karamanou and Nishiotis (2009) find that firms voluntarily adopting IFRS showshort-run improvements in their returns but that long-run returns are significantly lower. Althoughthis could be attributed to improved costs of capital, the evidence cited earlier would suggestotherwise.

In sum, the empirical evidence is at least suggestive that reporting entities do not see harmonizedreporting standards as improving the quality of information, that the market’s skepticism increasesover time, and that reports under harmonized standards become increasingly vague in their meaning,allowing for a wide range of local interpretations—exactly what our results predict. We end by notingthat these results are not a complete surprise: decades ago, Haried (1972) raised the question ofdifferent semantic interpretations of a common reporting system, and Dickhaut and Eggleton(1975) provided laboratory evidence of subjects having different perceptions of numerical stimuliin different accounting contexts.

J. Stecher, J. Suijs / J. Account. Public Policy 31 (2012) 341–355 353

Acknowledgements

Thanks especially to Eva Labro, Martin Loeb, Garen Markarian, Holly Monteith, Lin Nan, MarcoTrombetta, Stefan, Wielenberg, and two anonymous referees for their detailed comments andsuggestions.

Appendix A. Proofs

Proof of Proposition 3.1. This follows from the definition of s�1 and the definition of consensualvalidation of a collection of subsets fAigi2I1

� PðAÞ. h

Proof of Proposition 3.2. First, we show that if x1 and x2 are distinguishable in a harmonized account-ing system S, then x1 and x2 are distinguishable in p1 and p2. The condition in the proposition thenimplies that x1 and x2 are also distinguishable in S� so that S� is maximally informative. Denote bysi the reportable image of perception i. Let reports t1 and t2 be such that t1 2 si(x1), t2 2 si(x2), t1 R si(x2),and t2 R si(x1). Because t1 2 si(x1), there exist A1 2 R�1(t1) such that A1 � pi(x1). Furthermore, becauset1 R si(x2), it follows that A1 å pi(x2). Hence there exists a1 2 A1 � pi(x1) such that a1 R pi(x2). Similarly,t2 2 si(x2) and t2 R si(x1) imply that there exists A2 2 R�1(t) such that A2 � pi(x2) and A2 å pi(x1). Takinga2 2 A2 such that a2 R pi(x1) then proves that x1 and x2 are distinguishable in pi.

Conversely, let x1 and x2 be distinguishable in p1 and p2. There exists ai1; ai2 2 Ai such thatai1 2 pi(x1), ai2 2 pi(x2), ai1 R pi(x2), and ai2 R pi(x1). Define the accounting standard S ¼ hR; T i byT ¼ ft1; t2g and R = {(a11, t1), (a21, t1), (a12, t2), (a22, t2)}. Because t1 2 si(x1), t2 2 si(x2), t1 R si(x2), andt2 R si(x1), x1 and x2 are distinguishable in S. Every pair of events that is distinguishable in p1 and p2

gives rise to an accounting standard that can distinguish between these two events. Let the accountingsystem S0 consist of all these accounting standards. Then either S0 is maximally informative or, bydefinition of maximal informativeness, the maximally informative accounting system S� distinguishesall events that S0 distinguishes; that is, if x1; x2 2 X are distinguishable in p1 and p2, then x1 and x2 aredistinguishable in S�. h

Proof of Theorem 3.1. We start with proving 3.1a. Define the harmonized accounting system S as thejoin of all local accounting systems ðSiÞi2I ; that is, S ¼ hR; T i with T ¼ [i2IT i and (A, t) 2 R if and onlyif (A, t) 2 Ri for some i 2 I . Observe that S is a harmonized standard because pi = pj implies that

s�1i ðtÞ ¼ fx 2 Xj9A 2 R�1ðtÞ : A � piðxÞg ¼ fx 2 Xj9A 2 R�1ðtÞ : A � pjðxÞg ¼ s�1

j ðtÞ

for any t 2 T .It holds that S is at least as informative as Si. Let x1; x2 2 X be distinguishable in Si. Then there exist

reports t1; t2 2 T i such that t1 2 s0iðx1Þ; t2 2 s0iðx2Þ and t1 R s0iðx2Þ; t2 R s0iðx1Þ, where s0i denotes thereportable image of events in accounting system Si. Because t1 2 s0iðx1Þ implies that there existsA 2 R�1

i ðtÞ such that A � pi(x1), it follows from the definition of S that t1 2 si(x1); that is, x1 can bereported as t in the harmonized accounting system. Hence, by repeating this argument, it follows thatx1, x2 are distinguishable in S.

Assume that there exist events x1; x2 2 X that are distinguishable in Sj but not in Si for some j 2 I .As shown earlier, x1 and x2 are distinguishable in the harmonized accounting system S. Hence S ismore informative than Si.

To prove part Theorem 3.1b, observe that when S�i is maximally informative, then any x1; x2 2 Xthat are distinguishable in pi are also distinguishable in S�i . By definition of a harmonized accountingstandard S it holds that if two events x1; x2 2 X are distinguishable in S then x1, x2 are distinguishablein perception pi. Hence, x1, x2 are also distinguishable in S�i .

Let x1; x2 2 X be such that they are distinguishable in pi but not in pj. The latter implies that x1, x2

are not distinguishable in the harmonized accounting standard S. Since events x1, x2 are distinguish-able in S�i ; S�i is strictly more informative then S. h

354 J. Stecher, J. Suijs / J. Account. Public Policy 31 (2012) 341–355

Proof of Proposition 4.1. Without loss of generality, suppose that there exists x; y 2 X and t 2 T 1

with t 2 s1(x) and t R s1(y). By hypothesis, S1 is fully reconcilable with S2, so let f be the translationcorrespondence T 1!

f PðT 2Þ. Because s�12 � f

� �ðtÞ ¼ s�1

1 ðtÞ, we must have x 2 s�12 ðf ðtÞÞ and

y R s�12 ðf ðtÞÞ. This implies that there is some t̂ 2 f ðtÞ � T 2 with x 2 s�1

2 ð̂tÞ, while for every t̂ 2 f ðtÞ,we must have y R s�1

2 ð̂tÞ. This means that if x is weakly distinguishable from y in S1, it must be weaklydistinguishable from y in S2. An analogous argument applies when there is also some way of reportingy in T 1 that is not a valid report of x under S1; this shows that if x and y are distinguishable under S1,they must be distinguishable under S2. h

Proof of Theorem 4.1. Let S� ¼ hR�; T �i be the maximally informative harmonized accounting systemfor perceptions {p1,p2, . . . ,pn}. Next, define for each perception pi the local accounting systemS�i ¼ hR

�i ; T

�i i as follows. If, for a perception pi, all events x1; x2 2 X that are distinguishable in pi are also

distinguishable in S�, let the local accounting system S�i be equal to S�. Otherwise, if, for a perceptionpi, there are events x1; x2 2 X that are distinguishable in pi but not in S�, extend the reporting space T �iwith two new reports t1 and t2, that is, T �i ¼ T

� [ ft1; t2g with t1; t2 R T �. Define R�i ¼ R� [ fðpiðx1Þ;t1Þ; ðpiðx2Þ; t2Þg.

Observe that for each jurisdiction i, the accounting system S�i is at least as informative as theharmonized system S�. Furthermore, any two accounting systems S�i and S�j are partially reconcilablewith respect to T � by using the translation fij(t) = t for all t 2 T �. Hence any information that can becommunicated using the harmonized accounting system S� can also be communicated using the localaccounting systems S�1;S�2; . . .S�n and the appropriate partial reconciliations. h

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