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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
