THE RISE AND SIGNIFICANCE OF
MODERN ANALYTICAL METHODS
A Review Essay of the Economics of
Accounting, Vol. I,
of P. O. Christensen and G. A. Feltham
University of British Columbia, B.C. Canada
This is Part II of some review essays dealing with the development of analytical accounting, and partic -ularly, the application of information economics to accounting [for Part I, see Mattessich 2003a]. Thecurrent essay discusses the Economics of Accounting
; Volume I: Information in Markets
by Peter O.
Christensen and Gerald A. Feltham . Although this book deals with the same subject matter as theone discussed in Part I [i.e., Christensen and Demski, 2003], the “new” work is not only more compre-hensive but offers a better overall survey of information economics as applied to accounting. Thus it mayalso serve as an excellent and rigorous reference work, offering a large number of mathematical theo-rems and their proofs. On the other side, it has hardly any intuitive illustrations and is less pedagogical-ly oriented than the book discussed in Mattessich [2003a]. The first volume (here discussed) deals withthe basic decision-facilitating role of information and, above all, with public information and privateinvestor information as well as the disclosure of private information (by owners), all in equity markets(in contrast to the second and forthcoming volume that has a more internal orientation, dealing withPerformance Evaluation and Agency Theory).
accounting, decision theory, information economics, equity markets,
disclosure of information.
In the late 1970s Joel Demski and Jerry (G.A.) Feltham intended to write on invi-tation of the American Accounting Association a monograph on “the state of the artin information economics and its impact on accounting”. But after years of experi-mentation they found the pertinent literature not complete enough. At first, theypostponed the project and ultimately abandoned it. But twenty years later, after
ISSN 1666-5732 v.3 nº 1-2 pp.157-167 2004
much new research by an ever-increasing number of scholars (above all, byFeltham, Demski and Ohlson), the idea of this project found realization in the workby Christensen and Feltham [2003 (and 2005, forthcoming)]. It is based on repeat-ed improvements and expansions of the lecture notes used in two doctoral seminarsoffered by Feltham at the University of British Columbia in Vancouver (PeterChristensen is a former student of Feltham, and now Professor at the SouthernUniversity of Denmark-Odense; he collaborated for years with Feltham on bothvolumes of this book).
2. General remarks
Despite the authors’ assertion that they mainly concentrated on fundamentals, thematerial offers a fairly closed overview of this “new” trend. Only a few areas wereneglected, such as the economics of auditing, tax and bankruptcy issues, as well asaccounting reports for the use of debt holders (so far little explored in the analyti-cal literature). More surprising is that such traditionally important areas as inflationand current value accounting remain virtually unmentioned. The justification forthis may be that in Christensen and Feltham [2003, and 2005] all accounting sys-tems are claimed to be ‘equivalent’; in other words, their theory does not apply tonormative statements about which system is better for a particular situation.
The book title, Economics of Accounting,
may remind the reader of a renownedwork by Canning , The Economics of Accountancy
. Yet this latter book hadthe sub-title “ACritical Analysis of Accounting Theory”—something fully justifiedby a conceptual basis that was more closely tied to traditional accounting. The twovolumes by Christensen and Feltham [2003, 2005], on the other hand, belong to avery different realm, though it must be admitted that there is some endeavour torelate it to traditional accounting (for details, see below)—after all, Feltham wastrained as a Chartered Accountant (in contrast to many other scholars working inthis particular area of specialization). Nevertheless, we are here dealing with a spe-cific perspective of accounting, namely its economic analytical aspect. And thiscross-pollination of ideas may become a trend that may well dominate our field inthe 21st century. Because in addition to the economics of accounting, there is, forexample, emerging a philosophy of accounting
, with its own ontology, epistemolo-gy, methodology and ethics (see Mattessich [1970, 1995, and 2003b], and as a gen-eral philosophic foundation to it Mattessich ). There also exists the behav -ioural science of accounting
, with its own sociology and psychology. To this haveto be added further specializations of more traditional fields such as the history ofaccounting
, or the technique
as well as technology of accounting
, with the adventof computerized spreadsheets and other “innovations”.
If such a general trend should continue, it would enrich the scientific status andsophistication of our discipline, but it also might endanger its unity and the ultimategoal of economic and administrative stewardship. Though the desirability of such atendency may be a matter of debate, the centrifugal forces of specialization seem tobe the inevitable cost of scientific “progress”. Perhaps we can create a counter-forceby avoiding a one-sided training of accounting students and young scholars. Thus,by offering them an education that is broad and well rounded (e.g., impregnatingthem with a philosophic point of view), the dangers of over-specialization may bemitigated. Nevertheless, the most important factor in favour of this new economicsof accounting (as presented in the book under consideration) is the undeniable factthat it constitutes a scientific training more rigorous than any other encountered inour discipline. A very different question is whether the immense effort expendedduring recent decades by economists and accountants in exploring intricate mathe-matical models (accessible only to a small minority of colleagues) is a worthwhileeffort. Boland , in the first issue of Energeia,
seems to question such anundertaking. But should this be a reason for not discussing
a trend that has capturedmany leading scholars of economics, finance and accounting of North America?
Nevertheless, the question arises to what extent such an abstract analytical method-ology (relying on innumerable simplifying assumptions) can be fruitful to anapplied science such as accounting or even to accounting practice. If it were mere-ly a cost/benefit problem of serving present-day accounting practice, there can belittle doubt that improving the ethics of executives in business and public account-ing firms would have been a better educational investment—at least in the shortrun. But this is not the way science works. When we are confronted with a seriousand rigorous scientific approach, we are obliged to respect it and await its long-termresults.
At this juncture one may invoke some words emphasized in the Foreword by thebook’s serial editor: “the challenge Peter and Jerry provide is not simply to masterthis material. It is to digest and act upon it, to offer accounting thought that ismatched, so to speak, to the importance of accounting institutions” [Demski, p. xv,in Christensen and Feltham 2003].
3. Structure of the book
This volume deals with investor preferences relating to the firm’s operations, con-centrating on “decision facilitating information” or simply on information econom-ics as applied to investment activity in equity markets. Vol. II (still to be published)forms the basis for examining the intricacies of Performance Evaluation (and “deci-
sion influencing information” for motivating managers) and tackles, what I wouldcall, the mathematical version and extension of agency theory.
The first volume—consisting (apart from an introductory chapter explaining the
notion of “information in equity markets”) of four Parts (A to D)—deals with the
significance of information in capital markets. Part A (Chapters 2 to 4) explains
basic concepts and relations of information economics and decision theory. Part B
(Chapters 5 to 10) deals with public information available in equity markets (e.g.,
information released by corporations) while Part C (Chapters 11 and 12) explains
the impact of private information held by investors in such markets (e.g., informa-
tion available to managers, majority shareholders) in such markets. Finally, Part D
(Chapters 13 to 15) deals with the disclosure of private owner information in equi-
ty as well as product markets.2 The total of 15 chapters (including the introductory
one) are highly structured (i.e., each with between three to seven sections, and many
subsections) comprising a total of xx + 593 pages (including references sections for
each chapter; and at the end, an Author Index of 3 pages, and a Subject Index of
almost 9 pages). The total number of mathematical “propositions” (i.e., theorems
with rigorous proofs) in the first volume alone is some hundred twenty-four.
4. Essence and content
Chapter 1 (Introduction to Information in Markets [for products and capital]) offersa non-mathematical but fairly rigorous survey of the entire book, explaining keyconcepts and basic ideas. This volume (in contrast to the second one) does notexplicitly regard managers as economic agents with personal preferences and inneed of particular incentives.
Chapter 2 (Single Person Decision Making under Uncertainty) presents conciselyand rigorously the probabilistic tools and concepts for decision making underuncertainty. It begins with single person decision making, discusses the representa-tion of uncertainty, the nature of random variables, different forms of probabilitydistributions, the representation of preferences (e.g., over lotteries) by means ofvarious utility functions, risk aversion, mean variance approximations and prefer-ences, stochastic dominance, etc.
Chapter 3 (Decision-Facilitating Information) offers an intense recapitulation of thebasic notions of information economics. Since the reader of this paper may be unfa-miliar with the idea of information economics (which after all is the basis of thisbook), I shall first try to outline its essence in a much simpler fashion than done inthis book. Information economics grew out of statistical decision theory
best be illustrated by comparing it with the basic decision model,
then pointing outthe differences.3
Statistical decision theory conceives a pay-off matrix that relates to different eventsor “states of nature” (columns) with a variety of human actions or “strategies”(rows). Thus each individual cell in the pay-off matrix reveals either the utility or,more simply, a $-amount to be received for each action, given a certain eventoccurs. It assumes the probability of each event (occasionally called the “prior”probability or belief) is known. With these data it is possible to calculate the“expected value” (i.e., the mean value) of each action by weighting the correspon-ding event probability with each pay-off for a specific action. From the expectedvalues attributed to the various actions one chooses the highest value. This in turnindicates the optimal action to be chosen (though other decision criteria may alsobe chosen, depending on a person’s attitude towards risk and other circumstances).
Information economics extends this decision model by introducing an informationsystem that supplies information for each action, given the occurrence of a certainevent, in form of conditional probabilities (also called “posterior” probabilities orbeliefs). Thus, in the search for the optimal action, it is no longer sufficient tochoose the action with the highest extant expected value maximized among theexpected values for all actions (as in the simple decision model). Now the optimalaction can only be chosen after observing the information “signal”. The value of theinformation is determined by selecting the action that has the highest value for agiven signal; then, these values are weighted by the probability of each signal. Theresult is a kind of “gross-gross” value of a particular information system. However,this value still has still to be compared with the optimal value from the simple deci-sion model (otherwise the advantage of the information system would not be evi-dent). The difference between those two values is the “gross value” of the particu-lar information system. But if this system is not costless, the information costs haveto be deducted from it to yield the net value of this particular information system.
If several information systems are available, the previous procedure has to berepeated for each of those systems. Only then can a choice of the optimal informa-tion system be made, namely by selecting the highest value from all competinginformation systems. As Christensen and Feltham  point out, for such a sys-tem to have economic value to a decision maker, the latter must deem that his out-come beliefs will be changed by some possible signals and, for at least some of thesignals, those belief changes will be sufficient to alter his action preference.
Chapter 4 (Risk Sharing, Congruent Preferences, and Information in Partnerships)deals with multi-personal
decision making as encountered in dual or multiple part-
nerships where partners agree on some sharing rules
despite their personal prefer-ences and their different risk tolerances
. Risk sharing of the outcome is solved bythe well-known notion of Pareto efficiency
Part B (Chapters 5 to 8) deals with public information in equity markets and empha-sizes the clean surplus model
(for details, see [Mattessich 2002], in Energeia
). Herethe emphasis is on the relationship between dividends and stock values in terms offuture expectations. The first three of these chapters deal with pure exchange andthe exogenous
production choice of the manager (in Vol. II these choices becomeendogenous to the model). In such a setting, changes in public information(accounting reports) do not facilitate a Pareto Equilibrium. A major feature of PartB is the addition of further assumptions (e.g. that of ? clean surplus?) to the divi-dend discount model, and the creation of an accounting valuation model. The lattercan be separated into “financial” and “operative” activities. But as Christensen andFeltham [2003, p.11] point out: “The key insight is that we only need forecasts ofthe operating activities”.
Chapters 5 and 6 (Arbitrage and Risk Sharing in Single-period Markets, andArbitrage and Risk Sharing in Multi-period Markets, respectively) stress theassumption of no-arbitrage (stipulating that a portfolio and its prices are such thatis impossible “to get something for nothing”). As the titles of these chapters reveal,the main difference lies in the change from single-period to a multi-period situation,as well as the examination of the relation between equilibrium and efficient risksharing.
Chapter 7 (Public Information in Multi-period Markets) begins by examining theefficiency of an information system and the impact of public information on secu-rities markets. Further topics are the relations between information and prices aswell as trades volumes, etc. When assessing the conditions under which a moreinformative system is Pareto preferred, the authors admit that “to be honest, for anaccountant, the results are disappointing!” [Christensen and Feltham, 2003, p.245].
Chapter 8 (Production Choice in Efficient Markets) switches to production activi-ties and examines the impact of changes in the information system under variousconditions (e.g., under the impact of public information, in two-period economies,etc.). The chapter also raises the question whether general equilibrium analysis canbe usefully employed for accounting (answered in the affirmative by our authors).
Chapter 9 (Relation Between Market Values and Future Accounting Numbers)endeavours to examine the crucial relationship between accounting and equity val-
ues whereby security prices are expressed in relation to current book value (of equi-ty) and future expected (residual) income. Although different accounting policiesmay be differently affect the current book value and expected income, the marketvalue of owner’s equity will be unchanged under certain assumptions. A majorfocus is on the separation between financial and operating activities as well as onanticipated equity transactions (including new stock issues and contingent debtclaims).
Chapter 10 (Relation between Market Values and Contemporary A c c o u n t i n gNumbers) continues to examine how market values (of shares) relate to contemporaryaccounting numbers. But this “analysis merely describes the representational eff e c t sof accounting policies—there are no normative statements with respect to what theaccounting policies should be” [Christensen and Feltham, 2003, p.315]. T h e i rassumptions express the belief that the operating activities (rather than those offinancing) are critical for accounting valuation. An important task of this chapter isto show how to infer “other information” from analyst’ forecasts by discussing theproblems of non-accounting information
and other complicating aspects (includingsuch basic questions as “how to infer private information from equilibrium prices?”
Chapter 11 (Impact of Private Investor Information in Equity Markets) is, to someextent, an extension of Chapter 7. It demonstrates how uninformed investors caninfer from equilibrium prices the private information held by informed investors. Itemploys two major models (GS and HV) dealing with rational investors assumedto be “risk avers price takers”. The GS type model supposes all investors have iden-tical and constant risk aversion and are able to obtain shared private signals. TheHVtype, on the other hand, assumes investors having different degrees of risk aver -sion
and being able to procure different private signals
or infer the competitors? pri-vate information from market prices. Hence risk aversion and the investor’s reac-tion to private information as well as the impact of and the interrelation with pub-lic reports (e.g., from accounting) are major issues. Further concerns (of this and thenext chapter) are variability in equity prices, the impact of trading volumes, and thetiming of the release of public information.
Chapter 12 (Strategic Use of Private Investor Information in Equity Markets)extends this investigation to the equilibrium investments made by insiders
trying tohide (at least to some extent) their private information. It also introduces the notionof the market-maker
and deals with the endogenous and exogenous informativenessof private information as well as public reports.
Chapters 13 to 15 investigate the relationship between current owners
information) and new investors
(lacking such information). To some extent the for-mer group is interested in revealing information (based on auditors verifications,etc.) in order to encourage new investments by outsiders—thereby the well-knownnotion of Nash Equilibrium
and other game-theoretic tools are employed. WhileChapter 13 (Disclosure of Private Information by an Undiversified Owner) assumesa single risk averse owner
, the subsequent two chapters deal with well-diversifiedrisk neutral
Chapter 14 (Disclosure of Private information by Diversified Owners)—assuming(as in Chapter 8) that investors are well-diversified in a setting of perfect and, later,imperfect competition—concentrates on a manager who maximizes the marketvalue of the firm
. Thereby the amount of information released by the manager, andthe possibility of investments open to new owners become important. A series ofpossibilities and variations as to the pertinent information (complete vs. incompletedisclosure, costless vs. costly, exogenously vs. endogenously generated, etc.) areconsidered.
Chapter 15 (Disclosure of Private Information in Product Markets)—assuming sim-ilar conditions as in the previous chapter—now deals with two competing firms
(duopoly) in a setting with products subject to downward sloping demand curvesand either Cournot
or Bertrand competition
. The problem of ex ante
versus ex post
disclosure or even lack of disclosure
(by the manager to the owners) is central tothis discussion.
This book, as a synthesis of the information economics approach to accounting, hasa good chance of becoming a classic.4 Apart from the immense, systematic and con-centrate labour invested in it, it not only is an excellent and integrated survey of theentire field, but also offers a great wealth of details necessary to train doctoral stu-dents for pertinent research. Although it may have been intended as a textbook fordoctoral students, it definitely goes beyond it. In contrast to the book by J. A.
Christensen and Demksi  with which it overlaps in some respects, the workunder review possesses to a much lesser extent features of a textbook. On the oneside, it lacks the many numerical examples and possibly other pedagogic charac-teristics. On the other, this work (particularly if one takes both of its two volumesinto consideration) constitutes, as a synthesis, a comprehensive and rigorous theo-ry with numerous assumptions, definitions and, for both volumes, over 250 propo-sitions, lemmas and corollaries, many of them with mathematical proofs.5 Thiswork may not only serve the future academic accounting community at large, it also
constitutes an economic theory of accounting
unmatched by any other extant theo-ry related to accounting. Some experts might even be tempted to compare the com-piling of this masterwork with the heroic efforts invested in generating thePrincipia Mathematica
by Whitehead and Russell [1910-1913] over ninetyyears ago. Even if this comparison may go too far for many experts, the twovolumes by Christensen and Feltham [2003, 2005] seem to be the mathemati-cally most sophisticated survey of the economics of accounting available at thiss t a g e .
But the mentioning of Whitehead and Russell invokes a saying attributed to the for-mer in a conversation with the latter. Whitehead said to Russell (and I paraphrase):there exist only two kinds of scholars, simple-minded ones, as you Bertie, and mud-dle-headed ones, as myself.6 The wisdom of such a statement might no less be ingood stead for accountants. The more we benefit from the high precision of themathematical approach, the more we suffer from its many simplifying assumptions.
So some of us try to compensate with a more realistic and sweeping view ofaccounting, only to suffer from its vagueness and imprecision. Nevertheless, thebook may well serve accountants and other academics to inform themselves aboutthis kind of research, provided they are willing to absorb the esoteric conceptualapparatus required to master this fairly difficult material. My major criticism is thelack of intuitive illustrations—but this might have required three instead of two vol-umes.
1 Financial support from the Social Sciences and Humanities research Council of Canada for this proj-ect is gratefully acknowledged.
2 Volume II of the same work [Christensen and Feltham, 2005, still forthcoming] deals with perform-ance evaluation that also has four Parts (E to H) and gradually builds up by stepwise relaxing more andmore restrictive assumptions and/or introducing further complications. Thereby Part E deals with theevaluation in a situation of single-period and single-agent; Part F deals with information disclosure ofprivate management information for single periods and a single agent; Part G illuminates contractingactivity in a multi-period situation with a single agent; while Part H deals with such contracting whenseveral agents are involved.
3 For a more detailed overview of the development of statistical decision theory and the emergence ofinformation economics, see Mattessich [1978, pp. 197-233].
4 In this paper, only volume 1 of this work will be discussed. The thrust lies in conveying to the read-er, uninitiated
in analytical accounting, the essence of this work in rough strokes, but without going intotechnical details.
5 In mathematical economics and financial texts it is often customary to deal with the assumptions(axioms) informally in the text, while the definitions, lemmas, propositions and their proofs are being
given much better visible and mathematical exposure. One wonders whether the reason for this practicemay lie in the often embarrassingly unrealistic or oversimplified nature of those assumptions. Anotherpeculiarity is the usage of calling the conclusions “propositions” instead of addressing them as “theo-rems” — particularly when considering that there exist so many propositions in science, philosophy andevery-day life that are not conclusions at all, but assertions or other statements.
6 It is no secrete that the impetus to writing the Pricipia Mathematica
as well as most of the contribu-tions to it came from Russel (although he listed himself as second co-author—probably due to the ref-erence he had for his teacher). Whitehead, as his later publications revealed, leaned less to the precisephilosophical-mathematical thinking of the “simple-minded” Russell, but was more prone to metatha-physical speculations.
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