The intellectual development of Yuji Ijiri

Abstract

This study investigates the contextual background and development of Yuji Ijiri’s thought. Ijiri was inducted into the Accounting Hall of Fame in 1989 for his work on the dynamic structure of accounting measurements and retired from Carnegie Mellon University in 2011. He passed away on 18 January 2017. His dynamic structure provides both historical cost information and information relevant to managers, based on areas including cost accounting, matrices, and physics. He was influenced by his elders, and his work emphasized the importance of scientific and systematic calculation and represented a big step forward in accounting research on measurements.

Keywords

causal double-entry bookkeeping dynamic structure of accounting measurements historical cost accounting momentum accounting triple-entry bookkeeping Yuji Ijiri

Personal profile

Yuji Ijiri was born on 24 February 1935 in Kobe, Japan (Cooper, 1997, personal communication; The Ohio State University). He learned arithmetic from his father Takejiro, a baker and confectioner (Burns, 1989; Cooper, 1997, personal communication), and this early exposure sparked his interest in mathematics (Ijiri, 1997, personal communication). At the age of six years, Ijiri began formal training in the use of abacus calculations (Burns, 1989). During World War II (WWII), Kobe was a major industrial center and port and came under intensive aerial bombardment. Nine-year-old Ijiri and his classmates were evacuated to a temple in the countryside with a math teacher who taught them algebra until the war ended (Burns, 1989; Cooper, 1997, personal communication). During the war, Ijiri found solace and intellectual stimulation through his exposure to religion and mathematics.

Ijiri began to develop an interest in accounting at the age of 14 years when his father put him in charge of the books at his bakery-confectionery (Burns, 1989; Cooper, 1997, personal communication). Over his father’s opinion that on-the-job training was more than sufficient, Ijiri attended night school at Doshisha Junior College in Kyoto to learn more about accounting and later became the youngest person in Japan on record to receive a Certified Public Accountant (CPA) certificate (Burns, 1989). He later practiced as a CPA for a small firm and then at Price Waterhouse, where he audited several listed companies (Burns, 1989).

Ijiri’s love of mathematics led him to develop interests with a quantitative dimension, including haiku (short poems), computers, and shogi (Japanese chess). To Ijiri (1984), the beauty of haiku lies in its “simplicity in expression without compromising the content.” The dynamic structure of accounting measurements which he developed is a 4×4 matrix that provides aggregated numbers rather than detailed numbers, in which the former are simplified presentations of the latter. Haiku’s directness of expression is similar to the use of aggregated numbers to express a company’s financial performance in dynamic structure of accounting measurements. On the other hand, in shogi, blocks are analogous to sectors in the dynamic structure of accounting measurements. Pieces in shogi are placed in a certain order and can move in certain directions, which is analogous to the cause-and-effect relations in causal double-entry bookkeeping and integral/derivative relations among horizontal and vertical sectors in the dynamic structure of accounting measurements.

In addition, Yuji enjoyed computers and electronic applications. Yuji bought any new electronic gadgets, noted Itami¹ (1997, personal communication). Ijiri’s interest in APL² began in 1978 when Charlie Kelly, then a doctoral student at Carnegie Mellon University (CMU), gave him a copy of APL: An Interactive Approach, by L. Gilman and A.J. Rose, as a Christmas present (Ijiri, 1984).

Yuji also enjoyed games, pointed out Sunder (1997, personal communication), and, as noted, shogi was a particular favorite. He had a special fondness for chess puzzles created by a mathematician and philosopher named Raymond Smullyan (Cooper, 1989). Smullyan (1983) cited the following two philosophers in his work: Willard van Orman Quine promoted linking everything with simplicity, and Oscar Mandel³ encouraged inventing things that did not exist before. Ijiri incorporated his hobbies into his thought on the dynamic structure of accounting measurements, and these formative experiences helped him develop his aptitudes for advanced mathematics.

This article studies the contextual background and development of Yuji Ijiri’s thought. The remainder of this article is organized as follows. The section “The intellectual context as impetus for Ijiri’s thought” provides a review of various people and disciplines that may have influenced Yuji Ijiri’s thought. The section “Academic influences in the United States” presents the influence of Ijiri’s education in the United States on his thought. The section “Ijiri’s main contributions: American Institute of Certified Public Accountants–American Accounting Association notable contributions to the accounting literature” provides descriptions of Ijiri’s main publications and their contributions to the accounting literature. The section “Assessments of Ijiri’s contributions” includes a discussion of his work and its impact on the field of accounting. The final section draws conclusions and implications.

The intellectual context as impetus for Ijiri’s thought

Ijiri studied at Ritsumeikan University, and his accounting teacher Taminosuke Nishimura (Cooper, 1997, personal communication; The Ohio State University, 1997) influenced him in two important ways. The first way was in “the use of analogy as a guide regarding beauty and to unite, with elegance, seemingly separate fields of inquiry in previously unperceived ways” (Cooper, 1997, personal communication). Such a broad intellectual interest was common in Japan at the time (Simon, 1997, personal communication). Nishimura’s second influence on Ijiri (1975) was imparting the idea that accounting is a social convention, and that “it is, therefore, a mistake to think that accounting has given up its dogmas and conventions completely in order to serve the user’s need better” (p. 31). These ideas later became the cornerstone of Ijiri’s research.

Ijiri’s research was also the outcome of general education trends in Japan and in other parts of the world, as well as from the development of various disciplines. In Japan, during the 1940s, the Klein movement⁴ became influential, promoting the application of mathematics and physics to technology and mechanics (Bussi, 2010). Following WWII, Japan’s civil education underwent a process of reform. From 1947 to 1955, social studies and problem-solving methods such as research and discussion were introduced (Ikeno, 2005). From 1955 to 1985, the emphasis turned to intellectualism, founded in disciplines including mathematics, science, and social studies (Ikeno, 2005).

Also after WWII, Edwards Deming, an American mathematician and physicist, taught Japanese executives, engineers, and scholars about statistical process control (SPC) and quality control techniques.⁵ Quantitative methods introduced by Deming and others achieved popularity in Japan and had a huge impact on young Japanese students who were enthusiastic in pursuing new forms of knowledge to restore Japan’s economy. In addition, Japanese engineers studied literature provided by engineers from the Bell Laboratories, for example, Walter Shewhart, who worked on General MacArthur’s staff (Deming, 1986: 2–4). Deming helped Japanese industry to improve product quality, which assisted the country to capture world markets within four years (American Society for Quality, 2017). Ijiri’s mathematical aptitude served him well in Japan, as the education trend and new methods introduced by foreigners were mathematically oriented.

Ijiri’s dynamic structure of accounting measurements is the outcome of applying physics to accounting. Equations of motion were used in mathematical physics to describe the behavior of a physical system through a set of mathematical functions with dynamics variables. Dynamics is a general description of motion that comprises momentum, force, and energy. The term dynamics is sometimes used to describe the differential equations that a system satisfies or is the solution to the equations.

Academic influences in the United States

In 1959, at the age of 24 years, Ijiri emigrated to the United States. The following year, he earned his master’s degree from the University of Minnesota (Cooper, 1997, personal communication). He later pursued his PhD at CMU in Pittsburgh, Pennsylvania – America’s great steel manufacturing center. The Ford and Carnegie Foundations had separately published reports⁶ in 1959 criticizing business and accounting education at the time (Whitley, 1988) and promoting a more scientific approach. Ijiri’s strong aptitude in mathematics gave him an edge in this trend, and he received a Ford Foundation fellowship to pursue quantitative approaches to accounting (Burns, 1989).

Young scholars at the time were attempting to raise the prestige of accounting and business research in the academic community by developing new paradigms and by building intellectual bridges between accounting and other disciplines with mathematical roots. Two professors at CMU had a particular significant impact on Ijiri: William W. Cooper and Herbert Simon. Cooper, the 1995 inductee of The Ohio State University’s Accounting Hall of Fame, specialized in quantitative approaches. Ijiri took Cooper’s seminar called “Quantitative Methods in Business,” and

in the second part of the semester, he worked in a team project with F.K. Levy and R.C. Lyon called “Matrix Formulations of Accounting Ideas and the Use of Dual Relations to Evaluate Cost Plans,” which was later cited in Ijiri’s dissertation (Cooper, 1997, personal communication).

Cooper said “the idea was very new and became immediately very popular.” Under Cooper’s guidance, Ijiri (1963), in his dissertation, Activity Analysis and Activity Accounting, used different linear model forms of breakeven analysis to investigate relations and interactions between overall goals of top management and the sub-goals of the entity (pp. 1–12, 82–131). His thesis was later published as Management Goals and Accounting for Control (Ijiri, 1965).

Ijiri et al.’s (1963) “spreadsheet” idea first appeared in his dissertation and later in his co-authored paper, A Linear Programming Model for Budgeting and Financial Planning. Charnes et al. (1963) related the spreadsheet notion to the matrices theory in linear programming and used linear programming, double-entry bookkeeping, and spreadsheets to forecast various balance sheet and income statement accounts. Cooper (1997, personal communication) recalled, “we … initiated the spreadsheet notion – first time used in operations research. We showed how to do double-entry bookkeeping on computers. One side of the equation (debit) by the column, and the other side (credit) by the row.”

Cooper had worked with the late Eric Louis Kohler, the 1961 Accounting Hall of Fame inductee and a defender of historical cost accounting. Hence, there is a continuity of thought from Kohler to Cooper to Ijiri. Cooper described the impact of the former two on Ijiri as, “Yuji’s thesis showed how to apply historical cost to planning and control simultaneously” (Cooper, 1997, personal communication).

Herbert Simon, a Nobel Prize winner in economics and econometrics, was Ijiri’s professor in a course that was probably called “Mathematical Methods and Social Sciences” (Simon, 1997, personal communication). Through Simon’s courses and book, titled Organizations (March and Simon, 1958), Simon influenced Ijiri’s use of the “satisficing” model. Ijiri’s (1963) dissertation used breakeven analysis to help managers determine whether a breakeven point or a profit goal had been achieved, which is similar to the notion of “satisficing” a certain goal.

Demski et al. (2002) argued that the business innovations that emerged from CMU resulted from researchers with expertise in basic disciplines applying their knowledge to subjects such as accounting. They stated that mathematics was the earliest basic discipline that was connected to accounting. Cooper, Ijiri, Kaplan, and others are widely seen as pioneers in applying mathematics to accounting (Demski et al., 2002).

Ijiri began his teaching career at Stanford University in 1963. When not teaching, Ijiri also audited courses in physics, mathematical logic, and philosophy (Cooper, 1997, personal communication). By this time, Cooper (1997, personal communication) noted, Ijiri was well-equipped for research and began work that would contribute to the body of knowledge in fields including accounting, economics, econometrics, statistics, operations research, organization theory, mathematics, physics, mechanics, and logic. Ijiri, with his strong aptitude in mathematics, sought to exploit accounting’s analytical power by applying insights from statistical, mathematical, and physical models. He was able to do this by following the examples of operations research and management science.

The above backdrop indicates the extent of the various influences on Ijiri. While Ijiri was swayed by the then current trends in scientific research, he was also beginning to establish new trends by promoting new ways to record transactions (Charnes et al., 1963), for example, spreadsheets and matrix-based financial modeling software. Without his distinctive background, Ijiri may not have been able to develop his dynamic structure of accounting measurements.

Ijiri’s main contributions: American Institute of Certified Public Accountants–American Accounting Association notable contributions to the accounting literature

From practice, Ijiri induced that accounting is a social convention and an economic performance measurement, making it counter-productive to abandon historical cost accounting and double-entry bookkeeping. Hence, the goal of accounting should be “accountability” (Ijiri, 1975: 33). He posited that historical cost accounting is low on decision usefulness (relevance) but high on accountability. He extended historical cost accounting to add decision useful information to his dynamic structure, which served as a solution to the deficiencies in historical cost accounting (Ijiri, 1982: 45, 1989: 100).

The following subsections provide descriptions of four publications in which Ijiri made notable contributions to the accounting literature.

Reliability and objectivity of accounting measurements

Ijiri and Jaedicke (1966) discussed the reliability of decision usefulness, and how the former relates to objectivity. They set x as an accounting measure and y as the value that users seek to know or predict, for example, a stock price. The user’s decision function is y = fn(x), where the accounting measure x can be used to predict the future stock price y. They provided a “realistic” definition of objectivity as “the consensus among a given group of observers or measurers” (Ijiri and Jaedicke, 1966). The three factors of measurement are (1) the object to be measured, (2) the measurement system comprising rules and instruments, and (3) the measurer. The more detailed the measurement rules and the better match between the measurement system and the object to be measured, the more objective the output (measure). Measurers with accounting expertise can produce a higher level of consensus. The more objective the measurement, the smaller is the impact of subjective judgment. In addition, objectivity is a relative concept and exists on a continuum. The level of objectivity for a measurement system is often measured as the variability of measures as regards a given object. Furthermore, the objectivity of a measurement can be decided independently of its use.

The degree of reliability depends on the closeness between the actual measurements and the alleged value⁷ and can be measured using Mean-Square-Error. The degree of objectivity depends on the closeness between actual measurements and the mean of measures for the object. The relation between the two concepts can be written as reliability = objectivity + bias, where bias is the difference between the forecast value and the mean value. The equation shows that the degree of reliability is at least as large as the degree of objectivity, and that both are related. However, even if a measure is objective, it is not necessarily reliable. Ijiri and Jaedicke (1966) explained that bias occurs from accountants misunderstanding what the user of the accounting data needs and wants. The usefulness of accounting measure affects bias and hence reliability, but not objectivity.

Theory of accounting measurement

Accounting as an accountability system

Ijiri’s (1975) work is based on the accountability view, yet at the time, the decision usefulness view was dominant. He (Ijiri, 1975: 31–32) argued that this is because fundamental accounting principles are still based on historical cost, despite the interpretation of accounting principles having shifted to a more user-oriented approach in the 1970s. Accountability emphasizes the relationship between the accountor (e.g. a manager) and the accountee (e.g. an investor), where the accountor must account for his or her behavior for the benefit of the accountee. The accountant and the auditor are intermediaries in the accountability relationship (Ijiri, 1975: ix). Ijiri focuses on the role of the accountant as providing the accountee with performance information regarding the accountor. Hence, Ijiri argued that accounting measurement is founded on accountability. However, Ijiri (1975: 33) contended that historical cost accounting can be extended so that the accountor can be accountable to his or her headquarters and its shareholders for past, present, and future activities.

Historical cost accounting

Ijiri (1975) noted that historical cost accounting requires firms to record actual past transactions. This is the foundation of accountability whereby agents report how they utilize resources entrusted to them. He suggested that historical cost accounting is better than other approaches in terms of (1) discharging accountability, (2) performance measurement, and (3) enabling economic decisions (Ijiri, 1975: 86). The accountability advantage arises from historical cost accounting providing information for every transaction in the past (Ijiri, 1975: 32). It also serves as a better performance measurement since it contains all information, while only partial information is required for various decision-making tasks. In terms of economic decisions, historical cost valuation (past data) is crucial when measuring firm past performance and estimating future performance.

Ijiri (1975) disaggregated the measurement structure of historical cost valuation into two parts: axioms and valuation rules (p. 71). According to Ijiri, judgments regarding historical cost valuation include three axioms: control, quantities, and exchanges. The axiom of control refers to the set of all resources under the control of an organization. The axiom of quantities is defined as all resources under the control of an organization that can be categorized into classes such that each class has a nonnegative quantity. The axiom of exchanges is that every change of resources under the control of an organization can be defined as the initiator of a new exchange or the terminator of an old exchange. Ijiri (1975) argues that the mechanical processing of historical cost data is an application of valuation rules (p. 74).

He also provided alternatives for extending historical cost to maintain its advantages while addressing some of its shortcomings. Hence, modifications or supplements may be made to make accounting information more decision-relevant. For example, he states, fair value accounting shares the same judgments as historical cost accounting with regard to the axioms of control and quantities. Different measurements vary only with regards to the axiom of exchanges (Ijiri, 1975: 93), and their values are the products of prices and quantities (Ijiri, 1975: 104–105). Therefore, transactions can be recorded in quantities and then reported based on different prices when compiling specific reports.

Causal double-entry bookkeeping

The accountability view of accounting integrates historical cost accounting and causal double-entry bookkeeping. Ijiri argued that an entity’s behavior (e.g. manager performance) is partly determined by its recognition of the cause-and-effect relationships of changes in resources it controls. In causal double-entry bookkeeping, the value of an increment (debit) is equal to the value of its corresponding decrement (credit). These are the causes and effects of transactions (Ijiri, 1975: 81). He noted that, under the historical cost principle, the value of increments is the same as the value of decrements in an exchange. This is similar to the concept that debit equals credit in a causal double-entry system. Hence, double-entry bookkeeping and historical cost accounting are tightly linked and form the foundation of accountability (Ijiri, 1975: 84).

Triple-entry bookkeeping and income momentum

Ijiri (1982: 4–5) extended double-entry accounting to include future objective information. He developed equation (4), wealth = capital, as the basis of the dichotomy underlying double-entry bookkeeping (Ijiri, 1982: 6–7). In the equation, wealth = assets − liabilities, and wealth accounts are “stock” accounts. That is, they represent a firm’s present financial status. On the other hand, capital accounts are “flow” accounts, that is, changes in a firm’s past wealth (Ijiri, 1975: 19). Hence, stock = flow (Ijiri, 1975: 8). Therefore, the stock of wealth is fully depicted by the flow of capital. If the stock changes continuously, the flow account would be the “derivative” (i.e. the rate of change) of the stock account. In other words, the change in income accounts, that is, the change in revenues or expenses, is the derivative of capital, which is the derivative of wealth. Since a derivative means the rate of change, capital is then the rate of change in wealth multiplied by the length of time during which the change in wealth took place (Ijiri, 1975: 20).

Ijiri (1982: 20) further employed concepts used in physics to describe the motion of an object.⁸ He stated that position x is a frame of reference measured with respect to a coordinate system. Velocity v is the rate of change in the position with respect to time t, that is, dx/dt. Acceleration a is the rate of change in the velocity with respect to time t, that is, dv/dt. Assume that the mass of an object is m. Momentum p is then calculated as p = mv, that is, mass times velocity. Force f is calculated as f = ma, that is, mass times acceleration. Income is the notion of the increase in wealth during a certain period. Income momentum is the ability for an entity to continuously generate income at a certain rate. The concept of income momentum can be applied to momentum p in physics. Hence, p = mv = (f/a)×v, that is, force influences income momentum. The term “earnings power” is equivalent to “income momentum,” and internal and external forces affect the way income changes from this period to the next. Then, Ijiri (1982) extended the dichotomy in double-entry bookkeeping to a trichotomy, where wealth = capital = force. In the equation, force measures the change in income. Wealth is the integration of capital, which is the integration of force. This can be used to create a statement of force (Ijiri, 1982: 22).

Ijiri was concerned that “managers have an incentive to change income numbers up or down for various reasons … human behavior influences accounting” (Sunder, 1997, personal communication). Hence, Ijiri (1982) attempted to create “objective”⁹ and “hard”¹⁰ information (p. 35) by systematically calculating integrals or derivatives of other cells in his dynamic structure of accounting measurements. The predictive information in the structure is based on a systematic calculation of “the change from the present numbers” rather than an actual estimation of future numbers. Ijiri (1982: 160) stated that the information is consistent with investors appreciating firms with smooth earnings growth and is more reliable than current value. Ijiri (1989) showed that the system makes judgments more consistent, systematic, and uniform (Chapter 9) and achieves the goal of objectivity (Ijiri, 1982: 20).

Momentum accounting and triple-entry bookkeeping: exploring the dynamic structure of accounting measurements

Ijiri (1989) expanded upon his previous developments by introducing a dynamic structure of accounting measurement (see Table 1) which includes various bookkeeping systems (pp. 5–6). The structure is a four-by-four arrangement of 16 sectors of measurements where w represents wealth and serves as the base measurement. In the structure, each sector is the cause of the measure directly below it and of the measure to its left.

Table 1.

Dynamic structure of accounting measurements.

A dynamic structure of accounting measurements
	12/31	12/31		12/31	12/31		12/31	12/31		12/31	12/31
	19×0	19×1		19×0	19×1		19×0	19×1		19×0	19×1
[Sector A1] $Δ^{- 3} \overset{\cdot\cdot}{ω}$			[Sector B1] $Δ^{- 2} \overset{\cdot\cdot}{ω}$			[Sector C1] $Δ^{- 1} \overset{\cdot\cdot}{ω}$			[Sector D1] $\overset{\cdot\cdot}{ω}$
Benefit 3rd derivatives			Wealth 2nd derivatives			Momentum derivatives			Forces
	$/ $m o^{2}$	$/ $m o^{2}$		$/ $m o^{2}$	$/ $m o^{2}$		$/ $m o^{2}$	$/ $m o^{2}$		$/ $m o^{2}$	$/ $m o^{2}$
Financial			Cash		−0.5	Revenue			Owners’ contributions
Benefits		−0.5	Equipment			Depreciation			Owners’ contributions
Trading benefits			Loans payable			Operating expense		−0.5	A computers		−0.2
			Capital stock			Interest expense			B computers		−0.3
			Dividends						B computers		−0.3
Benefit 3rd			Wealth 2nd			Momentum
Derivatives	0	–0.5	Derivatives	0	–0.5	Derivatives	0	–0.5	Net forces	0	–0.5
[Sector A2] ∆–2 $\overset{\cdot}{ω}$			[Sector B2] ∆–1 $\overset{\cdot}{ω}$			[Sector C2] $\overset{\cdot}{ω}$			[Sector D2] ∆ $\overset{\cdot}{ω}$
Benefit 2nd derivatives			Wealth derivatives			Momenta			Impulses
	$/mo	$/mo		$/mo	$/mo		$/mo	$/mo		$/mo	$/mo
Financial			Cash	20	35	Revenue	30	52	Owners’ contributions	3	3
Benefits	20	35	Equipment	−10	−20	Depreciation	−10	−20	Owners’ contributions	3	3
Trading benefits	−10	−20	Loans payable			Operating expense	−9	−15	A computers	7	5
			Capital stock			Interest expense	−1	−2	B computers		7
			Dividends
Benefit			Wealth
2nd derivatives	10	15	Derivatives	10	15	Net momenta	10	15	Cumulative impulses	10	15
[Sector A3] $Δ^{- 1} ω$			[Sector B3] ω			[Sector C3] ∆ ω			[Sector D3] ∆2 ω
Benefit derivatives			Wealth			Income			Actions
	$	$		$	$		$	$		$	$
Financial			Cash	244	226	Revenue	360	852	Owners’ contributions	36	72
Benefits	−120	−190	Equipment	240	460	Depreciation	−120	−300	Owners’ contributions	36	72
Trading benefits	240	460	Loans Payable	−100	−200	Operating expense	−108	−252	A computers	84	156
			Capital Stock	−300	−300	Interest expense	−12	−30	B computers		42
			Dividends	36	84
Benefit
Derivatives	120	270	Earned wealth	120	270	Cumulative income	120	270	Cumulative actions	120	270
[Sector A4] $\int ω d t$			[Sector B4] $Δ \int ω d t$			[Sector C4] $Δ^{2} \int ω d t$			[Sector D4] $Δ^{3} \int ω d t$
Benefits			Wealth utilization			Income utilization			Action utilization
	$/mo	$/mo		$/mo	$/mo		$/mo	$/mo		$/mo	$/mo
Financial			Cash	1,602	4,047	Revenue	1,980	8,610	Owners’ contributions	198	828
Benefits	−3,000	−5,295	Equipment	3,660	8,130	Depreciation	−660	−2,910	Owners’ contributions	198	828
Trading benefits	3,660	8,130	Loans payable	−1,200	−3,000	Operating expense	−594	−2,574	A computers	462	1,902
			Capital stock	−3,600	−7,200	Interest expense	−66	−291	B computers		105
			Dividends
Benefits	660	2,835	Wealth utilization	660	2,835	Income utilization	660	2,835	Action utilization	660	2,835

Source: Ijiri, 1989: 82–83, Table 6D.

Horizontally, each Sector is the difference of the one to its left and is the anti-difference of the Sector to its right. In the structure’s embedded double-entry accounting, income (Sector C3, credit) is the cause of changes in wealth (Sector B3, debit) (Ijiri, 1989: 8). That is, earned wealth (stock account) = cumulative income (flow account) (Ijiri, 1989: 31). Hence, stock accounts (∑ stock) = flow accounts (∑ flows) (Ijiri, 1989: 38). In the equation, earned wealth ω = ω₁ + ω₂ + … + ω_n = y₁ + y₂ + …+y_m = y cumulative income, ω₁,ω₂,…ω_n comprises assets (positive), liabilities (negative), contributions by owners (negative), and distributions to owners (positive), while y₁, y₂,…y_m comprises revenues (positive) and expenses (negative) (Ijiri, 1989: 23). The right hand side of the equation represents sources of income, which explain changes in the amount of wealth created by income on the left hand side. The components of wealth and those of cumulative income can be used to form a wealth-income statement (Ijiri, 1989: 24).

Triple-entry bookkeeping is expanded from double-entry by including action accounts (Table 1, Sector D3). Actions (Sector D3, trebit) are the cause of changes in income (Sector C3, credit), which in turn cause changes in wealth (Sector B3, debit) (Ijiri, 1989: 9). The array of Sectors in row three is called wealth accounting. In the row directly above these Sectors (i.e. row two), impulse (Sector D2) explains the reasons for changes in momenta (Sector C2), and a momentum-impulse statement can be made to explain the relation between the two Sectors. The structure that includes all Sectors in row two is called momentum accounting (Ijiri, 1989: 10).

Vertically, each Sector in the dynamic structure of accounting measurements (Table 1) is the time derivative of the one directly below it and the time integral of the Sector directly above it (Ijiri, 1989: 5). The encompassed three-dimensional structure of accounting measurements, a three-by-three arrangement of nine Sectors in rows one to three includes three layers, that is, $, $/mo, and $/mo². In the structure, forces (Sector D1, $/mo²) are the time rate of changes in impulses (Sector D2, $/mo), which in turn are the time rate of changes in actions (Sector D3, $) (Ijiri, 1989: 72).

Sectors in the third row of Table 1 times duration equal Sectors in the fourth row. That is, the sectors in the fourth row of Table 1 are benefit (Sector A4), wealth utilization (Sector B4), income utilization (Sector C4), and action utilization (Sector D4) (Ijiri, 1989: 84). Wealth utilization measures the amount of wealth that managers are able to utilize (enjoy) during the period. Similarly, income utilization and action utilization are the amounts of income and action available for use during the period. The benefit Sector (A4) shows the amount of benefits received from the utilization of wealth. In other words, wealth utilization measures the changes in net benefits. Utilization measurements can be presented in the utilization statement. Hence, four types of management – namely (1) benefit management, (2) wealth management, (3) momentum management, and (4) force management – can be achieved using the corresponding performance measurements in the four-by-four arrangement of 16 sectors, which form the dynamic structure of accounting measurements (Ijiri, 1989: 87). From the dynamic structure, accountants and information users can set up different financial statements based on their particular needs.

In Ijiri’s (1989) view, the true contribution of double-entry bookkeeping is not its recording format, but how the format sensitizes managers and accountants to income (p. 106). Similarly, the true contribution of momentum accounting is in inducing managers and accountants to be sensitive to factors which contribute to improving the firm’s income momenta, that is, its impulse. Hence, dynamic structure of accounting measurements can result in increased sensitivity, thus influencing managerial behavior with regard to various aspects of firm performance.

Other contributions

In his later works, Ijiri provided examples relating to financial accounting. In “A Framework for Triple-entry Bookkeeping,” he (Ijiri, 1986) attempted to demonstrate the practicality of the system through an example of triple-entry bookkeeping which integrates management accounting with financial accounting. The article provides an illustration which depicts the system framework, along with a worksheet, journal entries, and three basic financial statements. The discussions in the article are geared toward enhancing management sensitivity to income.

Assessments of Ijiri’s contributions

Ijiri was classified as an a priori scientist (Gaffikin, 1988) who sought a more scientific way to conduct research.¹¹ Rather than generating work that is purely descriptive, Ijiri developed axioms, which later served as the bases for a system that provides both historical cost and decision useful information. The golden age a priori research has largely been replaced by positive accounting research, partly due to academic politics (Gaffikin, 1988). However, the efforts of a priori researchers, including Ijiri, in making accounting a scientific discipline by integrating physics and mathematics,¹² have had a huge impact on positive accounting (Gaffikin, 1988), which emphasizes objectivity and scientific rigor using statistical tests and large sample sizes in research.¹³ Ijiri’s works have been cited by many scholars, with Google Scholar search showing 5,939 citations for Ijiri’s work, as opposed to 2,468 for Mattessich, and 2,664 for Chambers.

Central to Ijiri’s thinking was his analogous reasoning ability, cultivated by his undergraduate accounting teacher and the work of Willard van Orman Quine. Ijiri might also have been inspired by advances in telecommunications technology.¹⁴ The telephone took advantage of the transferability of wave patterns in audio and electrical environments, thus exploiting an underlying phenomena in two different states of nature. Ijiri may have been trying to accomplish something similar in designing an accounting system based on his comprehension of physical dynamics.

Ijiri’s creation of objective measurements remains important because a crucial problem underlying the choice of accounting measurements is the existence of human bias and dishonesty. For example, the stock market crash of 1929 was partially caused by abuses in financial reporting (Scott, 2012: 3). In addition, since the early 2000s, accounting scandals at firms such as Enron have posed significant threats to accounting credibility.

Ijiri utilized whichever research method best helped him. He was a theorist who conducted empirical testing when he had access to data (Glover, 2016, personal communication). For example, he used the Indiana Telephone Corporation as an example in his argument on price-level information (Ijiri, 1976: 232). In most instances, he provided sample formats for his creations using hypothetical numbers so that they could be applied in practice.

Ijiri (1975) also used both inductive and deductive methods in research (pp. 26–27). He inductively derived the goal of accounting, that is, accountability, based on empirical observations. He then tried to improve upon actual practice using decision usefulness, the objective of financial statements developed by the American Institute of Certified Public Accountants’ Accounting Objectives Study Group in 1973 and the Financial Accounting Standards Board (FASB) in 1978. Ijiri argued that accountability is the basis of accounting, and that firms can account for past, present and future information. He also reasoned that historical cost accounting and future oriented accounting need to be reconciled and integrated (Ijiri, 1975: 160). Later, Ijiri (1989: 100) deductively developed the postulates (i.e. axioms and accounting equations) underlying accounting principles, which in turn can provide guidelines for accounting practice. He claimed that by applying theory from physics, the alternatives for triple-entry accounting are limited to objective measures (Ijiri, 1982: 4–5).

Information regarding every transaction is provided under accountability, while only selected information provided under decision usefulness (Ijiri, 1975: 32). The criterion for information release under accountability is the users’ right to know, while that under decision usefulness is users’ need to know (Ijiri, 1975: 33). Ijiri (1989) claimed that it is crucial to first consider internal users (managers) as main users, and that the needs of external users can be taken into account when the system for momentum accounting becomes mature (pp. 99-100). He also acknowledged that measures may vary depending on the target users (Ijiri, 1989: 1). However, in Ijiri (1986), both managers and investors are users, whereas in Ijiri (1989: 109–113), only investors are information users. It was his intention to use the vast amount of information embedded in the dynamic structure of accounting measurements to satisfy both the goals of accountability and decision usefulness, along with the needs of both managers and investors. While multipurpose accounting may achieve different goals and purposes, it may be difficult for practitioners and standard setters to accept such a comprehensive accounting structure. To date, few empirical studies have sought to determine if all goals and purposes can be simultaneously met.

Over the past decade, researchers have provided evidence that Ijiri’s momentum accounting, which only requires a minimum of three cells, is objective, predictive, and value relevant. Melse (2004) provided an example from the return to equity ratio to promote triple-entry accounting and momentum accounting as an objective and reliable alternative to forward-looking information. Jorgensen and Mikkelsen (2001) provided empirical evidence that abnormal momentum is value relevant. Furthermore, Melse (2004) empirically tested Ijiri’s (1989) theory using a momentum accounting model, finding that momentum accounting (ex post net wealth) can be predicted one to three years beforehand. These results are consistent with Ijiri’s (1982) argument that what is empirical in physics (Newtonian mechanics) is also empirical in accounting.

Other researchers extended Ijiri’s momentum accounting. Jorgensen and Mikkelsen (2001) cited Ijiri (1989) in developing a valuation model where abnormal momentum, that is, changes in residual income, is a determinant of firm value. Melse (2008) extended Ijiri’s momentum accounting and developed a common-size-format model of balance sheet momentum as an approach to analyzing financial statements. He also developed common-size-format momentum ratios to measure changes in business performance. In addition, Govindaraj and Ramakrishnan (2001) developed a continuous time earnings model which uses the earnings rate,¹⁵ rather than an earnings aggregate over a period of time.

The reception of Ijiri’s inventions has possibly been limited by the use of the traditional term “bookkeeping” and the complications and costs of implementing his dynamic structure. In addition, the application of physics equations and the use of multiple measures¹⁶ increases the level of difficulty of accountants’ work and creates significant barriers to use by managers and investors. Also, the narrow range of research methodologies that are accepted by current academics also limited the recognition of Ijiri’s creations (Glover, 2016, personal communication).

Ijiri’s works can be further developed to gain wider acceptance by standard setters and financial accounting practitioners. Researchers can focus on investors’ needs¹⁷ and the level of understanding and cost/benefits for firms and society. Additional empirical testing of the dynamic structure of accounting measurements can be undertaken to help standard setters determine which of the 16 cells are desired, which accounts to utilize, and what statements to generate. This will reduce the extent of subjective judgment needed at the firm level and enhance the objectivity and usefulness of financial statements. Support from analysts will be required to help information users understand the nature of the information provided by Ijiri’s dynamic structure. Of course, future technological advances could make the dynamic structure easier to implement, and further accounting scandals could raise the call for new approaches.

Conclusion

The critical factors for Ijiri’s accomplishments include his mathematic aptitude, the timing of important events in his life, and his competence in analogous reasoning. Ijiri’s contributions are grounded in his aptitude for mathematics, which was developed at an early age. His forced evacuation due to the war was a blessing in disguise in that it exposed him to religious belief and mathematics teachings which not only helped him survive but also became a source of solace and strength for him. Mathematics eventually became the key to his success.

It was also fortunate that relations between the United States and Japan had strengthened by the time Ijiri reached adulthood and that these closer ties coincided with an increased emphasis on applied mathematics among US business researchers. These developments helped him obtain admission to CMU, where his research abilities developed based on his interest in mathematics and accounting.

Ijiri’s mode of reasoning was based on analogy, which was well-established in the physical sciences. Ijiri took a different approach than his contemporaries by applying physical kinetic concepts to financial reporting and budgeting. In his 1982 work, Ijiri linked managerial accounting with financial accounting, which are applications of quantitative theoretical models and are a part of dynamic continuum. As a theorist, Yuji was an unusually broad thinker and pursued a broad range of research topics (Glover, 2016, personal communication). A good theory, such as Ijiri’s, can withstand the passage of time.

Footnotes

Acknowledgements

I very much appreciate the comments from Robert Bricker, Gary Previts, Jonathan Glover, Michael Sperr, Dawn Medlin, Jonathan Brody, and anonymous reviewers on the previous versions of this paper. Furthermore, I extend special thanks to Yuji Ijiri, William Cooper, Richard Cyert, Charles Horngren, Gary Previts, Jonathan Glover, Herbert Simon, Shyam Sunder, and Hiroyuki Itami for their participation in my interviews. I also appreciate research assistance from Hong Lun Lu and Hui Xin Yang. All mistakes in this text are my own.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and /or publication of this article: The author(s) received financial support from National Chung Cheng University for research assistance.

Notes

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