An Updated Measurement Theory Perspective on Accounting

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T.J. Mock

UCR and U. of Maastricht

M.A. Vasarhelyi

Rutgers University

Silvia Romero

Montclair State University

September, 2011

Abstract

Over the last five centuries, the evolution of the traditional accounting model has resulted

in an ever-wider set of business practices and measurement conventions. These have

served business well, but are continually losing relevance. The PCAOB’s (2011)

considerationof a more informative audit report and the FASB’s (2011) reconsideration

of the concepts of income illustrate, in a limited sense, discomfort with the restrictions of

the traditional model. This paper considers a wider frame of business representations,

discussing business measurement under the frame of measurement theory.

In this paper, we discuss a business measurement model which includes three layers: the

disclosure value chain, the point measurement of each datum, and the level of desired

contingency measurement. The disclosure value chain includes: 1) environmental

conditions, 2) business plans, 3) lead actions that are added to the current 4) business

activities measurement, and 5) subsequent events. In examining the point measurement of

each datum, we argue that measures are not deterministic, but rather contingent on time,

the nature of the decision being supported, the level of precision, related future events,

and inherent uncertainty. Finally, the level of desired contingency measurement

determines the information structure around the business processes and its measurement

that is needed in each specific decision context.

The business measurement model has been stagnant for a long period, and we suggest

major changes in the model through measurement theory, incorporating stochastic

thinking and considering the capabilities of modern data processing. Many of these

proposed changes could be implemented through a modified XBRL tagging.

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The authors are appreciative of the comments in multiple seminars this paper was presented and the

subtantive contributions of Mr. J.P.Krahel.

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Introduction

This paper applies concepts from measurement theory and information economics to

revisit critical issues in business measurement as provided by accounting information

systems. The essential features of the current accounting model have remained

unchanged since Luca Pacioli’s introduction of the double-entry system

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over five

centuries ago.

Business measurement initially evolved from basic business needs and was geared to the

internal management of manufacturing entities. While it supported basic processes such

as inventory management and sales recording, it also supported summary financial

reporting which facilitated performance measurement and accountability reporting to

many stakeholders.

Two basic phenomena have molded the evolution of the reporting model: the ever–

increasing complexity of business processes, and recent dramatic changes in information

technology. At the same time, the development of modern society has increased the

resources necessary for roads, police and defense; more relevant, valid, reliable and

verifiable measurement of wealth, income and other attributes of enterprises, are

necessary to maintain an equitable taxation system.

The effects of increased business process complexity and information technology

development have permeated the business environment, forcing rapid change and the

abandonment of obsolete business methods and regulations. This change is reflected in

current discomfort with reporting and assurance and efforts toward redevelopment. The

PCAOB’s (2011) advocation of a more informative audit report, and the FASB’s (2011)

reconsideration of income concepts illustrate, in a limited sense, this discomfort with the

restrictions of the traditional model.

The changing needs of three basic stakeholder types- internal management, equity

owners, and taxing authorities- have stimulated the evolution of entity reporting and

business measurement. While necessary and beneficial, this evolution has nevertheless

been haphazard and impounded serious weaknesses that derived in cases like Enron in

the 2000’s and the Ponzi scheme these days, that have generated significant costs to

society.

Several weaknesses of the current model can be considered from a social welfare

perspective:

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“Summa de arithmetica geometria proportioni and proportionalita”, Luca Pacioli (1494).

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• A dual reporting system with tax reporting structures very different from

traditional financial reporting structures, which sometimes requires duplication of

efforts.

• Private entities use roads, hire people, and benefit from police and national

defense, but are largely exempted from social accountability and public

reporting. This exemption creates incentives for organizations to stay out of the

public reporting arena, resulting in misallocation of national resources, because

these entities are- by choice- neither publicly measured nor public targets for

investment

• Internal management reporting structures have shifted from traditional costing to

complex, multi-element, predominantly non-financial reports while external

reporting structures have remained essentially stagnant.

Alles and Vasarhelyi (2006) have discussed some difficult, perhaps intractable, problems

of the current accounting and reporting system. All of the following problems have been

extensively “addressed,” but not resolved, by standard setters:

1. Aggregation issues:–the boundaries of the business organization are

fuzzy, financial statements differ across industries, and the resulting

measures from aggregation and consolidation often are not homogeneous

to be added (additive).

2. Reliability issues:– current methods produce numerical assignments that

are unreliable, time dependent, and also not additive as they aggregate

measurements with different scales. Furthermore, measurements provided

lack transparent reliability. While some measures are accurate (e.g. cash)

others are of questionable reliability, to the point of irrelevance (e.g.

goodwill).

3. Completeness issues: There is lack of disclosure of relevant business

features such as contractual obligations.

4. Valuation issues: Elements are valued based on obsolete economic

situations and there is little disclosure of contingencies in these

valuations.

5. Scale issues: Verbal descriptions of accounting phenomena are used even

in cases where quantitative scales are feasible. For example contingencies

are often neglected or qualitatively described when they could be

statistically described.

Some basics of measurement theory

Mock and Grove (1979) define a measurement system as “a specified set of procedures

that assigns numbers to objects and events with the objective of providing valid, reliable,

relevant, and economical information for decision makers” (page 3). Formal

measurement theory is based on mathematics, particularly set theory, wherein a set of

numbers is assigned to different attributes of phenomena of interest via a mapping

process. For example, in a dividend payment decision, a dollar value is assigned to an

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attribute (Cash on hand at the time of the decision) to determine how much can be

distributed.

In this paper, we argue for a substantial extension of traditional external reporting by not

only modifying the procedures of assigning values to objects, but also enhancing the

declarations that describe the underlying events. This change is enabled by the presence

of relevant data (e.g. purchase orders and information about existing contracts) within

currently existing Enterprise Resource Planning systems (ERPs,), such as SAP and

Oracle. These arguments are based partly on the following observations:

• ERPs extend numeric assignments to both financial and non-financial attributes

(quantitative and qualitative), demonstrating management’s need for a much more

extensive set of non-financial measures. While these information structures exist

in a majority of large companies, they have not been utilized to tell a more

complete story of the measurement of business and income. Sample reports and

updated standards are needed.

• Methods of measurement implemented in ERPs are typically designed to support

particular business requirements and decisions (e.g. OSHA reporting, retirement

planning for employees, optimal inventory reordering), not to meet the decision

needs of investors, analysts, suppliers, clients, localities or other business

stakeholders. Expanding the scope of ERPs could result in a more valuable

business reporting system.

The ERS vs the NRS

To understand the potential benefits of applying basic measurement concepts within

current business information systems, it is necessary to summarize some of the basics of

measurement theory. Mock (1976) discussed these ideas in an accounting context

beginning with the relationship between the Empirical Relational System (ERS) and the

Numerical Relational System (NRS). The relationship’s basic measurement constructs

are represented in Figure 1.

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ERS

(Empirical Relational

System)

NRS

(Numerical Relational

System)

Mapping

Represents the “real”set

of events and relationships in

the economic system

Represents the set

of relationships that exist

In the measurement system:

numerical, semantic,

representational and relational

•Business Sales Events

•Right to Collect from Customers

•Obligations to pay

•Obligation to perform services

•Business Relationships

•Sales ledgers

•Accounts receivable

•Accounts payable

•Accruals (# of pending orders)

•Order, production and shipping

details

]’

Figure 1: A Basic Measurement System

The ERS represents the objects (e.g. resources) and events (e.g. economic transactions) to

be measured, as well as the relationships between these objects and events as defined by

McCarthy (1982). The same object might have different attributes of interest in different

decision situations. For example, the same product might be measured in terms of

variable cost for production decisions, total cost for profitability analysis, or level of

obsolescence for capital budgeting decisions. Recent fair value discussions (Laux and

Leuz, 2009, Plantin et al., 2008, Wallison, 2008) and standards (e.g. Fasb 159) show a

plethora of potential fair values for a particular measurement

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. Where feasible and

economical, such attributes need to be measured, stored, and communicated to various

stakeholders.

The NRS includes a set of numbers and a set of fundamental numerical relations, for

example the ‘less than’ ( < ), that are defined for the particular scale being used. The

particularities of the ERS determine which scales are valid.

The measurement system assigns numbers in the NRS to represent attributes of interest

from the ERS in a process referred to as numerical mapping. In formal measurement, this

mapping requires the assignment of a unique number to each object or event which

represents an attribute of interest (e.g. ‘incremental cost’), and requires that the

assignments be homomorphic. To be homomorphic, the mapping must preserve the

actual relationships in the ERS. For example, ‘variable cost’ is mapped with a unique

number representing the variable cost, while ‘total cost’ is mapped with a unique number

representing the total cost, and the relationship between the actual attributes is the same

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Fair values have been blamed for market collapses. Both the FASB and the IASB have undertaken a

review of fair value. Decision-based valuations, as proposed later in this paper, might resolve this issue.

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as the relationship between the mapped numbers. If the mappings are valid, then the

variable cost measure will be “less than” the total cost measure.

Cost Attributes versus Value Attributes

Cost attributes form the base of the traditional external reporting structure. Mattessich

(1964) states that the cost basis is the most reliable method if the purpose of accounting is

the presentation of data which can be verified at a comparatively “high degree of

objectivity” (Page 162). He also explains different treatments to which the measurement

of marginal utility (value) has been associated in economic theory, and how the

difficulties found in quantifying them led to an indirect measurement of value through the

price paid for the commodity.

While cost attributes are fixed in traditional reporting, current values are dependent on

factors like time and are contingent on changes in the measuring scales, as well as on

circumstances (Mattessich 1964, P. 163).

Values are time-dependent

Many business measurements are time-dependent, and this dependence is only

considered on an ad hoc basis. Some assets (e.g. cash) are expressed in current-day

dollars, others have values that are affected by price changes, for example:

• A/R and A/P includes 30, 60 and more days collectibles and discounts which are

not expressed at their present value.

• Inventory includes purchases over time, leading to LIFO, FIFO and standard cost

valuations

• All financial paper is affected by existing and changing interest rates. The longer

the maturity period, the potentially stronger this effect.

• Advanced financial derivatives present an even more complex effect.

• Retained earnings measures combine accumulated dollars of very different values.

The new business measurement model has to be formulated with these issues in mind.

Even simple spreadsheet representations of company wealth and income flow can be

made time dependent, providing interest rate sensitivity information.

Values are contingent on information usage

The literature has been prolific in establishing valuation bases for business, for example:

• Exit value for liquidation situations ((Parker, 1975); (Chambers, 1979); (Mock &

Collins, 1979))

• Present value of future cash flows for investors that hold titles ((Staubus, 1971);

(Ijiri, 1979); (Sloan, 1996))

• Market value for trading situations, for natural resources ((Harris & Ohlson,

1987); (Barth, 1991); (Barth, 1994))

These alternate valuation bases are contingent on a particular view of business that in

economic terms could be maintenance of capital, maintenance of purchasing power,

maintenance of purchasing capacity, or value for liquidation.

Values are contingent on level of precision

Measures are of limited relevance if their measurement precision is not understood. In the

physical sciences, the degree of precision of the measurement is often explicit. A weather

forecast may include its level of precision, while a measure of pressure will include the

measuring tool used (e.g. barometer) or the measuring units (Pascals) that indicate the

precision of the measure.

When measures with different degrees of precision are combined, the resulting measure

exhibits precision equal to that of the least precise component measure. However,

traditional financial statements mix different precision schema, hindering assessments of

precision. Figure 2 displays different assets disclosed in the balance sheet with an

example of the level of precision of their measures (the levels of precision have to be