Evaluating Heuristics Used When Designing Product Costing Systems

Ramji Balakrishnan Tippie School of Business

University of Iowa Ramji-Balakrishnan@uiowa.edu

Stephen Hansen The George Washington University

shansen@gwu.edu

Eva Labro University of North Carolina, Chapel Hill

Version: July 2009

Please do not cite without permission

We appreciate the many helpful comments from Anil Arya, Romana Autrey, John Christensen, J. Harry Evans, Thomas Hemmer, Susan Kulp, Karen Sedatole, Naomi Soderstrom, K. Sivarama-krishnan, Jeroen Suijs and Directors of the FAR at the Institute of Management Accountants. We also thank workshop participants at the following universities and conferences: Accounting Re-search Workshop Bern, Carnegie Mellon University, Florida International University, George Washington University, GMARS conference Copenhagen, MAS mid-year meetings, Tilburg University, University of Houston, University of North Carolina at Chapel Hill, and University of Southern Denmark. Fang Yang, Saurav Pandit, and Vasu Balakrishnan provided programming assistance. We gratefully acknowledge funding from the IMA Foundation for Applied Research. An earlier version of this paper was titled “Heuristics for Evaluating and Refining Product Cost-ing Systems.”

 

Evaluating Heuristics Used When Designing Product Costing Systems Design choices regarding the features of a product costing system significantly influence the ac-curacy of reported costs used in product- and capacity planning decisions. Using simulations, we examine how an amalgam of system design choices influences the error in reported costs. We focus on popular heuristics / rules for grouping resources into cost pools and on methods for de-termining the driver for cost pools that contain many resources. We also model alternate ways to translate the vague guidance in the literature to implementable rules. We find that correlation-based methods (that follow the prescription to combine “like” resources) are superior to size-based methods (such as the Willie Sutton rule) when selecting the resources combined to form an activity cost pool. Taking information requirements into account, we provide guidance on how such correlation-based rules might be implemented. In addition, we find that combining informa-tion from several resources in an index to use as the cost driver achieves economically signifi-cant gains in accuracy relative to using a driver based on the largest resource and might beat a driver that considers all resources in an activity pool. By varying properties of the underlying production environment, we also speak to the generalizability of our findings. I. INTRODUCTION

Practitioners and academics are well aware that reported product costs contain error

(Cooper and Kaplan 1998a; Noreen 1991). Yet, there is compelling evidence that managers base

long-term product- and capacity-planning decisions on reported product costs (Govindrajan and

Anthony 1983, Shim and Sudit 1995). One explanation of this discordance is that product costs

are the best estimates that a firm can generate regarding the long-run opportunity costs of its re-

sources (Balakrishnan and Sivaramakrishnan 2002). That is, product costing systems are practic-

al models of the underlying economic relation. However, as Cooper and Kaplan (1998a) emphas-

ize, any cost model contains numerous design judgments made on a cost and benefit basis. It is

therefore important to understand the sources of error in a cost system as well as how these fac-

tors interact. With this knowledge, a system designer can make choices that decrease the gap be-

tween reported product cost and the “true” opportunity cost of making a marginal unit of a prod-

uct, thereby increasing the benefit from the cost system.1

In general, product costing systems comprise two stages (see textbooks such as Horngren

et al. 2003). In the first stage, we group resources into cost pools, and in the second stage, we

allocate costs from the cost pools to individual products. However, as system designers, we con-

front myriad design choices when executing these steps. How many cost pools should we form?

                                                            1 Firms also employ cost data to value inventory, modify behavior, evaluate performance, and so on. We focus solely on the use of cost data for making decisions, even though it is known that the data contain error.

2  

How do we decide which resources belong in the same pool? Given that a cost pool may contain

many resources with differing consumption patterns, how should we select the driver for the

pool? Answers to these questions may be complex because environmental features likely influ-

ence the benefits from candidate solutions. For example, job shops and process shops face differ-

ent production environments and thus may need different system configurations.

Unfortunately, textbooks and practitioner publications (see, for example, Cooper 1988,

Turney 1991) offer limited help. With regard to how to pool resources, some authors (e.g., Co-

kins 2001, Hilton, Maher, Selto 2006, Turney 1991) claim that systems that combine unit and

batch costs into the same pool, or systems that combine all costs into few over-sized pools con-

tain significant error. To overcome these problems, many authors (e.g., Cooper and Kaplan 1988,

98) suggest focusing on the most expensive resources, the “Willie Sutton” rule, but do not detail

how exactly to implement this prescription.2 Other authors (e.g., Garrison, Noreen and Brewer

2008, 317; Horngren et al. 2003) recommend grouping “like” resources together. Indeed, one

could view the Activity Based Costing hierarchy as a recommendation to group resources as per

their consumption patterns. In terms of choosing drivers, most authors advocate that managers

consider a cause-effect relation (Garrison et al, 2008, 99; Horngren et al. 2003, 484) but provide

minimal guidance on how to select such a driver. Practitioners suggest the heuristics of using the

driver for the largest resource in the pool, a product-level complexity index, or a weighted-

transaction metric (Cooper and Kaplan, 1998b, 98).3 While all of these heuristics appeal to

common sense, there is limited research that examines their efficacy. Furthermore, the rules are

vaguely defined and this ambiguity limits the practical guidance they provide. We also do not

know how features of production environments influence the performance of particular rules. In

this paper we address the benefits of heuristics for the grouping of resources into cost pools, the

selection of the cost driver for the cost pool, and the impact of environmental variables on the

outcome.

                                                            2 The various interpretations of the Willie Sutton rule we found in the literature all suggest using the larg-est costs as the nuclei of individual cost pools but are silent on concrete implementation guidance. For example, should each large resource form its own pool? What should be done with the smaller, leftover costs? How many large costs (or what percent of total resource cost) should be separated into individual pools? 3 Data availability often hinders the use of statistical methods such as regression analysis to choose among candidate drivers.

3  

Simulations are well suited for exploring our research questions because the method per-

mits the luxury of observing a benchmark system. Further, the method allows for complex inte-

ractions among multiple factors, a feature that is analytically intractable. In particular, we simu-

late a wide variety of benchmark systems by varying fundamental attributes of the production

environment (see figure 1 for an overview of our experiment). In particular, we vary the disper-

sion in resource costs, extent of resource sharing by products, and the correlation in resource

consumption patterns. Thus, we can model a setting (e.g., a job shop) in which overhead com-

prises a few expensive resources and in which products differ greatly in the resources they con-

sume and in the pattern of consumption. We also can also include other settings (e.g., a process

shop) in which resources might trigger similar costs, and in which products consume the same

set of resources in approximately similar proportions. Within each environment, we simulate

numerous detailed benchmark systems that provide us with “true” costs. For each benchmark

system, we simulate various noisy approximations by systematically varying system design fea-

tures such as the number of activity cost pools, how we assign resources to pools, and how we

calculate drivers for the individual pools. We then analyze the relation between the heuristics, the

system error relative to benchmark costs, and the features of the production environment.

Our first set of results pertains to the heuristics employed to group resources into cost

pools. We examine two types of heuristics: those that follow the Willie Sutton rule and create

cost pools based on resource size, and those that create cost pools using resource correlations.

We find that correlation-based assignment rules lead to significantly lower error than size-based

assignment rules do. Indeed, size-based assignments do no better than the random baseline as-

signment. Thus, we find little support for the intuitive and popular “Willie Sutton” rule that asks

system designers to focus on segregating, and allocating well, the largest resources. The domin-

ance of correlation-based heuristics is robust across production environments. In particular, we

find that, over the range of resource dispersion that we consider, the relative gains from using

correlation-based methods do not decrease as resource dispersion increases. Such robustness is

particularly surprising for production environments with high resource dispersion, as typified by

the existence of a few very large cost pools and many small ones, because we expect the Willie

Sutton rule to perform well in such environments.

While correlation-based methods are effective, they are information intensive. A typical

firm is likely to have (accounting) data on resource costs that enable size-based rules, but it

4  

might not have detailed data on how products consume individual resources. As an alternative to

a full-information correlation approach, we examine a hybrid where we use a gross estimate of

inter-resource correlation to initially group resources into tiers and employ a size-based rule to

assign individual resources within a tier to activity cost pools. We find that our hybrid or blended

approach yields results comparable to the full information correlation-based method. This find-

ing supports the ABC prescription to group resources per the cost hierarchy and then forming

separate pools for each tier in the hierarchy.

Our second set of results further develops correlation-based heuristics for assigning re-

sources to cost pools. We explore how the cut-off correlation used to pool resources and the per-

cent of total cost of resources to pool into a miscellaneous cost pool affect system accuracy. In

this variation of our base experiment, we let the number of activity pools be endogenously de-

termined rather than fix it as an experimental parameter. We obtain relatively small errors even

when we use a low correlation cutoff of 0.4 to determine which resources to group together into

the same activity pool. Further, we find that we could group as much as 25% of costs into a mis-

cellaneous cost pool without significantly degrading system accuracy. Thus, we find broad sup-

port for the idea that a relatively small number of cost pools might be enough (in terms of the

cost–benefit tradeoff to adding more pools versus system accuracy) even for firms with large

numbers of resources. These findings support prescriptions by Turney (1991, 51) that “10-20

cost pools might be enough” as well as by Cooper and Kaplan (1998b, 98) that “ABC systems

settle down to between 35-50 activity cost drivers.”

Our final set of results pertains to the guidance offered for selecting the cost driver, the al-

location base, for a cost pool. We find that the common practice of using the driver for the larg-

est resource (e.g., labor hours for the pool of all labor related resources) is inefficient. We obtain

economically significant gains from considering an indexed driver. Such a composite driver,

which combines the largest few (2-5) resources in a given pool into an index, is less information

intensive than a system that considers the drivers for all resources in a pool but delivers a sub-

stantial portion of the potential gains. Indeed, with a medium number of cost pools, we find that

an index method can perform even better than the method that uses information from all re-

sources in the cost pool.

The value of using a composite driver (rather than the driver for the largest resource only)

increases in the sparsity of the consumption matrix (i.e., the extent of traceability of resources to

5  

products). The intuition is that when any particular resource only relates to a small subset of

products, resource consumption patterns within an activity pool exhibit considerable diversity.

Consequently, the system records significant gains by combining the mappings from several re-

sources to generate a cost driver. The gain from using an index also increases with the number of

cost pools. As the number of cost pools increases, the number of resources per pool falls, and an

index with a fixed number of resources in each pool rapidly converges toward the full informa-

tion approach. These findings underscore that driver selection might be particularly important in

job shop type environments in which products exhibit diversity in both the sets of resources they

consume and in the proportion of consumption.

Our analysis is of significant interest to academic and practicing management accoun-

tants because we know that managers use reported product costs to make decisions and that deli-

berate design choices influence the error in reported costs. However, because of the complexity

involved, firms have no choice but to employ rules and heuristics when developing a cost system

that models the economics of the underlying production process. Moreover, existing guidance

such as the prescription to combine “like” resources tends to be vague. In addition, lack of in-

formation about the efficacy of alternate methods in specific settings hampers the choice among

rules. Our paper contributes in this context by taking a holistic view of costing system design

choices to rank rules / heuristics for grouping resources into pools and for deriving driver rates

for activity pools. We also provide guidance on practical methods that a firm might employ to

implement a correlation-based assignment, and generalize our findings to a broad range of pro-

duction settings.

We organize the remainder of this paper as follows. In Section two, we place our research

into the literature. In the third section, we describe our simulation technique. Section four con-

tains our discussion of the properties of the generated systems and provides descriptive data on

the production settings. We consider the performance of the candidate heuristics in section five

and conclude in section six.

II. RELATED LITERATURE

Accountants broadly group a firm’s resources into two categories: direct and indirect. Costs of

direct resources such as raw materials and components are traceable to a product and thus require

no allocation. Indirect resources such as machinery and supervisory personnel, however, benefit

6  

many products. Cost accounting systems divide indirect costs into portions attributable to indi-

vidual products. The literature on product costing focuses on the usefulness of such systems, in

an attempt to reconcile their widespread use with classical economic theory that admits limited

benefits from allocating historical costs.

The literature on product costing comprises two broad strands. The first (e.g., Banker and

Hughes 1994; Balakrishnan and Sivaramakrishnan 2002) considers the economic sufficiency of

allocated costs for decision-making. In particular, the overall research question is whether firms

can use product costs to decompose the complex, multi-period stochastic product and capacity-

planning problem into simpler problems. This literature shows that while economic sufficiency

holds under restrictive conditions, product costs are a reasonable heuristic that help managers

address an otherwise intractable problem. The second strand (e.g., Cooper and Kaplan 1988; Da-

tar and Gupta 1994) focuses on the measurement of product costs. Assuming that the information

is useful for making decisions, this literature considers the ability of observed cost accounting

systems to reflect accurately the costs of shared resources consumed by products. Our paper is

part of this second strand, which we now describe in more detail.

While the many papers on activity-based costing focus on differences among cost sys-

tems, Datar and Gupta (1994), Gupta (1993) and Hwang, Evans and Hegde (1993) are among the

first to study the nature of errors in the reported costs, and their influence on decisions. These

papers classify errors as relating to aggregation (pooling disparate resources together into one

activity pool), specification (using a driver that does not accurately reflect consumption patterns)

and measurement (measuring driver quantities and costs with error). They show that sequential

refinement of systems by focusing on one type of error at a time could increase total error. That

is, breaking a larger cost pool into smaller pools and using better drivers for the two pools could

increase error by removing the offsetting effects of specification and aggregation errors. They

also show an endogenous tradeoff between the magnitude of aggregation and measurement er-

rors. Christensen and Demski (1997) focus on how a linear costing system introduces costing

errors when the underlying cost function is non-linear. They use analytical derivation and simu-

lation with three non-linear overhead costs to show that different costing systems produce dis-

tinct error patterns and to demonstrate that there is no simple method to select the approach that

7  

results in the lowest error. Every linear accounting system produces errors and, when choosing

among cost systems, a firm implicitly chooses among portfolios of errors.4

While analytic works provide precise insights, models often become intractable when we

seek to generalize their findings. Because of this reason, recent research employs simulation me-

thods to study errors in the design of costing systems even though simulations involve some loss

in precision. Balachandran et al. (1997) identify conditions under which using full costs leads to

reasonable solutions to the capacity-planning problem. Labro and Vanhoucke (2007) study the

interaction among the kinds of errors in a costing system, whether these errors offset, and which

types of errors have most impact on overall accuracy. They show that the impact of stage II cost-

ing errors (cost pools to products) on accuracy is more important than stage I costing errors (re-

sources to cost pools). They also demonstrate that partial improvement of the costing system

usually increases the overall accuracy of reported costs, other than in a few exceptional cases.

Labro and Vanhoucke (2008) examine the assertion that settings in which there is high resource

consumption diversity are more sensitive to the introduction of costing errors. Exploring alter-

nate definitions of diversity, they find that this assertion is correct when diversity is defined as

variance in the dollar value of resource cost pools, but incorrect when we define diversity as the

extent of sharing of resources across the cost system.

One feature of the accounting literature to date is that it studies the effects of individual

sources of errors (e.g., aggregation), select economic characteristics (e.g., consumption diversi-

ty), or interactions between two kinds of errors (e.g., aggregation and specification) on cost sys-

tem error. We also note that simulation studies that do consider many dimensions usually look at

two- or (at most) three-way interactions rather than consider all dimensions simultaneously.

However, the error in reported costs is an amalgam of all kinds of errors and economic features.

Thus, analysis of individual aspects of systems is handicapped in yielding an assessment of the

efficacy of alternate heuristics. The handicap arises because interactions among sources of errors,

the used heuristic and economic features of the production environment can be subtle and coun-

ter-intuitive. Our paper therefore models a system that considers all of these aspects jointly.

                                                            4 With suitable relabeling, we interpret the literature on linear valuation rules (see Sunder 2008 for a summary) as examining a dual of our problem. This literature considers assets that are bundles of re-sources. The question is how to group resources into baskets (aggregation), when each resource’s value is subject to errors from price movements (specification) and measurement errors affect the error in valua-tion. Again, this literature emphasizes the complex nature of the tradeoffs among the errors.

8  

III. EXPERIMENTAL DESIGN

To be both tractable and generalizable, our simulation experiment (see figure 1 for an overview)

must capture the essential and salient features of production environments as well as of the re-

searched costing system design heuristics, succinctly. Begin by considering a production envi-

ronment. Conceptually, a production function maps input resources to outputs. A firm with a

given scale and sets of products and resources is a point on a multi-dimensional production func-

tion. We model this simpler vision of a production environment as a set of products and re-

sources with a consumption matrix that links the two sets.

We consider a linear production function with non-substitutable inputs (e.g., Leontief

functions). This specification is the basis for much of the analytic work that has examined prod-

uct costing systems (Banker and Hughes 1994; Balakrishnan and Sivaramakrishnan 2001, 2002)

as well as studies of errors in cost systems (Hwang et al. 1993; Labro and Vanhoucke 2007,

2008). Researchers make this choice because the function is tractable and represents a wide

range of production settings. Further, the Leontief function is the implicit basis for most ob-

served cost systems and we view this assumption as providing a baseline against which we can

test how features such as scale and scope economies (Christensen and Demski 1997) affect the

performance of heuristics.

Even within the class of Leontief functions, production environments exhibit enormous

variation in both the mix of resources employed and in the consumption pattern that maps re-

sources to products. First, some settings might have a few expensive resources supported by

many lower-cost items (high resource dispersion). For example, a firm might have a central ma-

chine that supports its operations, or labor-related costs (e.g., supervision) might be the single

largest component of overhead costs. In this case, we might obtain good approximations of true

product costs even if we only track a few large resources and group all other resources into a

miscellaneous cost pool. Other settings might exhibit considerably lower variation in resource

costs. Size based algorithms for grouping resources might not work well in these settings. Thus,

our design explicitly varies the dispersion of resource costs.

Next, consider consumption patterns. At one end, we might have a process shop that pro-

duces few products that utilize the same set of resources in similar proportions. At the other end,

a job shop might exhibit much variation in the set of resources consumed by a product and in

consumption patterns. It is important to model such variation because high diversity in resource

9  

use is often advanced as a red flag for when we might need a refined cost system (e.g., Cooper

and Kaplan 1998a; Cokins 2001, Labro and Vanhoucke 2008). Conceptually, we use two para-

meters to model this dimension of a production environment. First, we use the density (or sparsi-

ty) of a matrix with cell entries that map the consumption of resources by products to model the

extent of resource sharing by products or how traceable the use of a resource is to a (subset of)

product(s). Further, because two products might consume the same set of resources but in differ-

ent proportions, we use the correlation matrix of consumption patterns to parameterize this as-

pect of diversity in resource use. In sum, a reasonable simulation of production environments

must allow for variation in dispersion of resource costs, in the density of the consumption matrix

and in the correlation among resource consumption patterns.

A cost system is a parsimonious model of the linkages in the production environment.

Firms employ such cost models because individually tracking the costs of a large number of re-

sources is not practical. Following standard practice, we categorize most observed “noisy” sys-

tems as two-stage systems. In the first stage, firms group resources / costs into activity pools.

The source cost data for this exercise come from accounting records. System designers pool re-

source costs in some “reasonable” way to generate a manageable number of activity pools. There

are diverse views on the number of cost pools to form and how best to group resources into

pools.5 In all cases, the existing guidance is vague resulting in system designers confronting

practical questions about implementation. In the second stage, firms allocate costs from activity

cost pools to products. The challenge here is to compute the consumption driver percentages

used to determine the cost allocated to each product. Again, there is limited guidance other than

an exhortation to use a driver that has a “cause-effect” relation with the costs in the activity pool.

How to compute this driver when the pool has many resources (with different consumption pat-

terns) is unclear. Our goal is to make progress on answering these questions and assess the guid-

ance available on how best to group resources into activity pools, how many pools to form, and

how to choose consumption drivers when a pool has many resources.

Our overall design for generating the data comprises three steps.

• First, we generate a set of production environments. These environments vary along the di-

mensions of resource dispersion, density of the consumption matrix and the correlation

                                                            5We abstract away from two additional features of observed systems: systems can have more than two stages, and there can be interactions across cost pools (e.g. service department allocations).

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among consumption patterns. For each combination of these parameters (i.e., for each envi-

ronment), we simulate many benchmark systems. Each of these draws of a benchmark sys-

tem represents a “firm” with 50 resources whose costs are shared by 50 products. For each

draw, we use the associated vector of resource costs and a consumption matrix that maps re-

sources to products to calculate the benchmark vector of product costs. This calculation is of

course an allocation that precisely models the production process for that firm and thus yields

the benchmark or “true” cost of the resources consumed by the products.6

• Next, for each benchmark system, we construct several associated “noisy” systems. These

systems vary along dimensions as proposed by the heuristics for costing system design. For

example, we vary the rules for grouping resources into activity pools and for calculating the

consumption rates used to allocate costs from an activity pool to products. For each noisy

system, we compute the associated vectors of reported product costs.

• Finally, for each combination of a benchmark system and an associated noisy system, we

compute an error metric by comparing the vector of benchmark and reported product costs.

We then analyze how variations in the construction of noisy systems (e.g., use of different

rules for grouping resources) affect the error in reported costs.

Each of the steps described above require detailed choices to implement the simulation model, as

explained below.

Step 1: Creating Benchmark Costs

To calculate a benchmark cost, we model the vector of resource costs and the matrix of the pat-

terns in which products consume resources. We begin by defining a production environment

along three dimensions: variation in the costs of individual resources, extent of resource sharing

by products and the correlation in consumption patterns of resources. (See Appendix A for nota-

tion and Appendix B for a detailed description of the steps.)

We induce dispersion in resource costs by changing the parameter RC_DISP (resource

cost dispersion). Low values of RC_DISP correspond to environments where all resources are of

roughly equal monetary importance. In contrast, high values of RC_DISP indicate an environ-

ment with many small resource cost pools and a few very large cost pools. Our measure is highly

                                                            6 Accounting records provide data on resource costs, albeit with aggregation error. However, much of the data in the consumption matrix would not be observable or easily measured in many settings. Thus, we cannot calculate benchmark costs and this lack of data precludes the use of archival and/or field data to validate/refine heuristics.

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correlated with other measures of dispersion such as the standard deviation in resource costs and

the Herfindhal index.

We use the parameter DENS (density of consumption matrix) to model differences in the

patterns in which products consume resources. This parameter determines the number of positive

entries in the resource consumption matrix. When DENS is low, the resource consumption ma-

trix is sparse meaning that only a few products consume any given resource (that is, we have

many zeros in the consumption matrix.) As might occur in a job shop, there is little resource

sharing by products and high traceability of costs to products. On the other hand, a dense matrix

implies a setting with many common costs, many cost objects sharing any given resource, and

low traceability. A process shop is a good example.

The final environmental parameter (COR) captures the correlation between resources

whose consumption varies with production volume (volume-based resources) and with the num-

ber of batches (batch-level resources). A large positive value induces similarity between the con-

sumption patterns of batch and volume resources, across products. Thus, we can model most re-

sources as consumed in proportion to volume. A negative value for COR implies significant dis-

parity between the consumption patterns of batch and volume resources, across products.

Within each combination of a unique environment (i.e., a specific value for RC_DISP,

DENS and COR), we simulate 20 benchmark cost systems. For each such draw, as in Datar and

Gupta (1994, 571) we assume that the firm knows total resource cost without error and set this

value at $1,000,000.7 We distribute this total cost among 50 resources, with the variance in the

distribution governed by the parameter RC_DISP. This distribution yields a vector of resource

costs. We next simulate the resource consumption matrix to conform to the parameters DENS

and COR, which influence the density of the consumption matrix and the correlation in con-

sumption patterns respectively. Finally, we compute the vector of benchmark costs as the prod-

uct of resource cost vector and the resource consumption matrix. Thus, we have 20 benchmark

data for each combination of the three environmental parameters.

                                                            7 We hold total resource cost constant and employ a tidy allocation scheme in order to maintain compara-bility of the simulated data. However, as in Hwang et al (1993), our method can accommodate partial al-location of resources by interpreting the last cost object as idle or unused capacity. In robustness tests, we vary the number of resources considered and find no qualitative change in our inferences.

12  

Step 2: Generating “Noisy” Systems

For each benchmark cost system, we construct many noisy approximations. We visualize each

noisy system as containing a specified number of activity cost pools and a corresponding matrix

of activity consumption patterns. We construct many noisy systems by varying the following pa-

rameters, which reflect potential heuristics used by a system designer:

• We vary the number of activity cost pools. The smaller the number of activity pools, the

greater the extent to which the vector of resource costs is compressed and the greater the ex-

tent of aggregation in the cost system.

• We vary the heuristic we use to assign resources to activity pools. We use a random assign-

ment as a baseline. We consider two possible implementations of size-based assignments that

follow the Willie Sutton rule, and term them Willie Sutton I and Willie Sutton II. Finally, we

consider two correlation-based rules. At the end of this step, we have therefore compressed

the vector of resource costs to generate a set of activity pools and have assigned resources to

individual pools. This process, of course, corresponds to the first stage in a two-stage alloca-

tion process.8 (The next section details the heuristics.)

• We vary the rule by which we select the driver and construct the activity driver percentages

used to allocate costs in an activity pool to products. As a baseline, we use the driver pattern

for the largest resource contained in the cost pool. We generate allocation indices by progres-

sively increase the number of resources averaged to obtain the consumption patterns. (See

next section for detail on the rules.)

• Finally, we vary the extent of measurement error in measuring driver quantities. Low mea-

surement error corresponds to system as might be found in settings with a time clocking sys-

tem for worker and staff time and where estimates on driver consumption are regularly revi-

sited. A high value represents a setting where there is no system to keep track of staff’s time

allocation and the system uses out-dated estimates. These two last steps generate the matrix

activity consumption patterns that maps how products consume individual activities

We compute the reported cost by multiplying the activity cost vector and the activity consump-

tion matrix. This computation is the same as is done in the second-stage of a standard two-stage

allocation system.

                                                            8 Our method implies that each resource indivisibly maps to at most one activity cost pool. If a given re-source maps to 2 or more pools, we can view each portion as a separate resource.

13  

Step 3: Measuring the Error in Reported Costs

Even within the context of decision making, costing systems serve many different needs, such as

helping to set product prices, selecting product portfolios, and planning capacity. These diverse

objectives might impose a different loss function when decisions are made based on reported

costs. Thus, we might need different measures of accuracy in different decision contexts. Hence,

we include a variety of error measures as the dependent variable in our simulation experiments.

The main error metric we report in tables and plots follows Babad and Balachandran (1993),

Homburg (2001) and Labro and Vanhoucke (2007, 2008). This metric is the distance or 2-norm,

( )∑=

−=CO

kkk fctcEUCD

1

2 where k indexes the number of cost objects (1, …, CO), tck is the

benchmark cost accruing to cost object k , and fck is the (false or noisy) cost allocated to cost ob-

ject k by the costing system approximation. This measure is appealing because we can interpret it

as the Euclidian distance between the two vectors.9 Moreover, this measure is symmetric and,

given we keep total resource cost constant at $1 million, captures the magnitude of the overall

error in the costing system in dollar terms. Finally, the square of this metric (i.e., the mean

squared error) is a measure of the loss from incorrect pricing decisions in monopolistic and oli-

gopolistic markets (Vives 1990; Banker and Potter 1993; Alles and Datar 1998; Datar and Gupta

1994; Hwang et al. 1993).

We also calculate a “materiality” measure, %ACC, the percent of products costed accu-

rately. This measure tracks the percent of cost objects measured without substantial error (Labro

and Vanhoucke 2007, 2008). Following Kaplan and Atkinson (1998, 111), we define immaterial

costing errors as within a 10% symmetric interval around the benchmark cost and

late % ∑ 1|0.95 1.05 ; 0 . Dopuch (1993) argues

that a necessary condition for potential improvements in managerial decisions from new account-

ing systems is that the new system generates estimates that are materially different from those

obtained from the existing system. Hence, this metric is valid in decision contexts where small

errors are not important, but large errors are costly.

                                                            9 The correspondence is inexact because each vector is constrained to add to the same total, which means that the dimensions are not independent.

14  

The final metric we consider is a mean percent error metric, MPE = . This

choice follows Christensen and Demski (1997) who take percent errors per product and mean

percent error for the whole costing system (MPE) as their dependent variables; and Gupta (1993)

who uses percent errors at the product level. In some contexts, management may be more inter-

ested in these relative measures, since a $10 cost difference for a $10 product has a greater

chance of inducing an incorrect decision than a $10 cost difference for a $1,000 product. This

measure also has the advantage of being independent of the number of cost objects in the system.

Not surprisingly, all of our error metrics are highly correlated.

Methods for Assigning Resources to Activity Pools

We consider five different methods for assigning resources to cost pools.

• Random Assignment. As a baseline, we randomly assign resources to activity cost pools.

We also view this assignment as a system that has grown organically over time.

The next two size-based methods examine the intuitive prescription of the Willie Sutton rule

that cost system designers should focus on the largest resources (Cooper and Kaplan, 1998b).10

This guidance is however vague and we were unable to find a consistent definition or interpreta-

tion of this rule in our literature search. Hence, we model two different interpretations of the rule,

and term these methods Willie Sutton I and II.

• Willie Sutton I. The Willie Sutton I rule assigns the largest resources systematically, by

size, to activity pools. In particular, if the firm has decided to form six activity cost pools, we

assign the six largest resources to individual activity pools. We randomly assign the remain-

ing resources among the six pools. This approach reflects the practice of adding smaller

pools like labor supervision to a bigger pool like labor, or machine maintenance to a bigger

pool like machining cost.

• Willie Sutton II. The Willie Sutton II method also assigns the largest resources to individ-

ual pools, but differs in its treatment of the remaining resources. Instead of randomly distri-

buting these resources among activity pools, we lump them into one residual separate pool.

                                                            10 Cooper and Kaplan (1998b, 100) describe the focus on the largest resources as follows “[T]he Willie Sutton rule: Look for areas with large expenses in indirect and support resources, especially when these expenses have been growing.” They go on to state that, “when developing ABC systems, we should fol-low Willie’s sage advance (but not his particular application of the insight) to focus on high-cost areas where improvements in visibility and action could produce major benefits to the organization.”  

∑=

−CO

k k

kk

tcfctc

CO 1

1

15  

This approach reflects the use of an aggregate “miscellaneous” cost pool for resources not

large enough to warrant an individual cost driver but that need to be allocated to products.

The last two methods follow the prescription to group like resources together. We define “like”

resources by the correlations among consumption patterns. Again, we can implement this rule in

several ways.

• Correlation Random. For the fourth method we consider (CORREL with random seed-

ing), we seed the desired number of activity pools with a random choice of resources. We

then pick “like” resources to add to the base resource in an activity pool. We restrict the

number of resources added to a pool so that each activity pool contains approximately the

same number of resources.

• Correlation Size. The final method (CORREL with size based seeding) is similar except

that we seed the desired number of activity pools with the largest resources rather than ran-

domly. This method reflects a convex combination of the Willie Sutton rule for focusing on

size and the prescription of using correlations to group like resources together. This method

also follows the prescriptions to use multiple criteria when grouping resources into activities

(Cokins 2001; Fregman and Liao 1981).

Methods for Calculating Driver Quantities

As in assigning resources to activity pools, we have a wide range of choices when choosing con-

sumption drivers to use for allocating costs from activity pools to products. Perhaps the simplest

approach (the “big pool” method) is to use the driver for the largest resource in an activity cost

pool as the driver for that pool.11 The big pool method does not employ data concerning con-

sumption patterns for the other resources in the activity cost pool. For example, we might pool

many labor-related costs (e.g., supervision) into an aggregate pool and use labor hours to allocate

the cost. A one-pool system based on labor hours or labor cost is an extreme example of a big

pool allocation. At the other end of the spectrum, we can consider a consumption driver that is

the average the individual drivers for each and all of the resources in the cost pool (“average”

method). For example, we could use the time spent on any machine in the whole of a production

cell as an allocation basis for the machining cost pool. While not uncommon, we note that this

approach requires a large amount of data to implement.

                                                            11 Hwang et al. (1993) refers to a similar method as the “high cost” method.

16  

While the big pool and average methods anchor two ends of a spectrum, intermediate me-

thods might average only a sub-set of the largest resources in a pool. For example, a firm might

use only a combination of labor hours and machine hours to develop an indexed driver. Use of an

indexed rate, whereby an average of the driver patterns for the few largest resources in a pool is

used as allocation base, is widespread. Fregman and Liao (1981) show that firms used indexed

rates to allocate about 10% of activity cost pools, with the proportion being significantly higher

in areas with low cost traceability. They also report that firms used index rates to allocated 44%

of G&A expense pools, 31% of R& D pools and 45% of the Marketing cost pools. In a meta-

analysis, Shields et al (1991) report a range of 8.9% to 46.3% for the use of multiple bases in the

US; the rate in Japan is 18.4%. Finally, Sakurai (1996, 100-101) extensively discusses the con-

struction and use of composite rates by Japanese manufacturers. Given the evidence demonstrat-

ing the widespread use of indices, we examine indexed rates that consider the largest two, three,

four or five resources assigned to a cost pool.12

IV. DATA AND DESCRIPTIVE STATISTICS Our main results relate to environments with fifty resources and fifty cost objects. Ro-

bustness checks for different combinations yield identical inferences.13 Table 1 provides descrip-

tive statistics concerning our simulated benchmark cost systems. We have 960 benchmark sys-

tems as we have 48 economic environments (comprising of three levels of resource dispersion,

and four levels each of the extent of resource sharing and correlation in consumption patterns; 48

= 3 * 4 * 4) and draw 20 samples for each environment. The top section of panel A shows the

effect of varying the dispersion of costs among resources (RC_DISP). As we increase RC_DISP,

the ratio of percentage costs in the largest to the smallest resource cost pool increases monotoni-

cally from 3.20 to 11.39. Alternate measures such as the standard deviation in resource costs and

a Herfindhal index show similar variation (results untabulated).                                                             12Weighting the drivers for different resources is an obvious improvement. However, the weights to use are unclear. Because of our linear structure, weighting by resource costs undoes the aggregation of re-sources into cost pools and it can be analytically shown that this results in reported costs equalling benchmark costs. Sakurai’s (1996) illustrations show equal and unequal weighting of resource drivers to compute an indexed or composite rate. 13 Because our interest relates to the ratio of the number of resources to the number of cost objects, our robustness tests hold the number of cost objects, CO, at 50 and vary the number of resource cost pools. We do not vary the number of cost objects since changing CO would systematically affect our error measures, thereby hindering comparability across simulated environments. Untabulated checks show that our inferences are robust.

17  

The parameter DENS controls the density of the benchmark consumption pattern matrix.

As we increase the value of DENS, the percent of zeros in the consumption matrix decreases

from 71% to 6%. As shown in the next line, this decrease in the traceability of resources means

that the number of products sharing any given resource increases from 14.52 to 46.88 or from 29

to 94% of all products. As resources become less traceable to specific products, more products

share the resources. We also find more dispersion in consumption of resources across products as

we increase resource sharing. The average range of consumption (i.e., range in percent of re-

source cost consumed by products for a resource, averaged across resources) decreases from 23

percent to 5 percent. That is, the fewer products that consume a resource, the more unequal their

relative consumption.

The third section of Panel A shows the impact of changing the correlation pattern (COR)

we induce on the drivers that describe resources usage by products. We find that the average cor-

relation between the consumption pattern for the largest pool and all other pools drops from

0.376 to 0.149 as we decrease the value for COR. In addition, a similar correlation with batch

resources by themselves turns negative. We would expect such a negative correlation when the

ratio of the number of batches to the number of units varies across products. Such variance oc-

curs when, for example, when a firm makes large volume products in a few large batches and but

uses many small batches to make low volume products. In either case, big differences in con-

sumption patterns exist between unit-level activities and batch-level activities in an ABC hie-

rarchy.14

Finally, for several other elements of the economic environments, we set bounds and vary

them randomly for each benchmark system. Specifically, we simulate the average percent of

costs devoted to batch resources randomly to be between 20 percent and 50 percent.15 Similarly,

                                                            14 We could obtain this variance also when batch size is the same even though production volume varies considerably or when batch size varies for products with similar volumes. 15Survey research (e.g. Foster and Gupta, 1990) has shown that resources devoted to volume-level activi-ties represent a significant portion of total costs. Ittner et al. (1997, Table 4) show that unit cost make up 65% of the cost hierarchy in a maker of outdoor backpacks, or 35% non-unit costs. Goddard and Ooi (1998) describe the ABC system for the Library at the University of Manchester. This system has 38% in indirect costs. Therefore, our main results are derived from simulations where between 50 to 80% of the resources are volume resources and hence show a positive correlation pattern in the consumption matrix. We vary the remaining resources between positive (additional volume resources), zero, and negative (batch resources) correlation. As shown in Table 1 Panel A, our final set of simulations contains approxi-mately 35% batch costs. We run robustness checks for the percentage of resources denoted as batch costs and obtain similar results.

18  

we generate the unadjusted consumption pattern for volume resources by randomly inducing a

positive correlation with the baseline resource. The average correlation of the consumption pat-

tern of the largest volume resource with other volume resources, weighted by the percent costs in

each resource pool, is reliably positive at 29.3 percent.16

We next turn to the noisy systems associated with the benchmark systems. For clarity, we

present descriptive data for one method for assigning resources to activity pools (Willie Sutton I)

and one method for choosing drivers (average method). (As we see later, the error values change

considerably based on the methods chosen.) We aggregate data over 3 levels for measurement

error (10, 30 and 50% error in measuring driver percentages) and over 6 values for the number of

activity pools (1, 2, 4, 6, 8 and 10).17 Thus, we have 18 associated observations for each of the

960 benchmark systems giving us 17,280 observations. (The total number of observations is

518,400 = 17,280 * 30 because we consider 5 methods for assigning resources and 6 methods for

calculating consumption patterns.)

Panel B shows univariate statistics concerning the error metrics we consider for the Wil-

lie Sutton I assignment with the average method for driver selection. The %ACC metric shows

that, on average, 25.84% of products have reported costs that are within 10% of their benchmark

costs; the average mean percentage error (MPE) is 16.8%. However, there is wide variation

across systems. The percent of products with accurate costs (%ACC) ranges from 0 to 100%, and

the mean percentage error (MPE) goes from 1.47% to 62.59%, suggesting that system design

exerts considerable influence on the error relative to benchmark costs. The data also show that

for all error metrics the mean value exceeds the median, indicating that all of the error distribu-

tions are right skewed. Panel C shows that the metrics are highly correlated (note that the percen-

tage accurate products [%ACC] is inversely related to error). This correlation, which is robust to

the choice of methods, provides a preliminary indication that our inferences are not sensitive to                                                             16Intuition suggests that the consumption pattern of volume-based resources should be positively corre-lated. However, we have no theory or field-based evidence to judge the magnitude of the value. In terms of cumulative effects, the ratio of the costs of the products with the five highest to the five lowest bench-mark costs has a mean of 4.55 with a minimum of 1.5 and a maximum of 16.27. The average ratio of the costs of the highest and lowest cost products, across benchmark systems, is 14.3. 17Cardinaels and Labro (2008) find in a lab experiment that people overestimate the time they spend on all activities that constitute their job description (a form of measurement error) by on average 37%. The range for the number of activity pools is consistent with the Drury and Tayles (2005) survey of 187 firms about their management accounting systems. Their Table 3 shows that the median number of cost pools was between 6 and 10. The minimum was one and eighty-five percent of the organizations had fifty or fewer cost pools.

19  

the choice of an error metric. Untabulated checks indicate that our results are robust to changing

the dependent variable, so in what follows we will only report EUCD as dependent variable in

the interest of brevity. We picked EUCD over other measure because the square of this metric

(mean squared error) has been shown theoretically to be the relevant loss function in various

pricing decisions. Further, it is possible to interpret this metric as a percentage error as we keep

total resources constant across all scenarios.

V. RESULTS

Heuristics for Assigning Resources to Cost Pools

Our first set of results pertains to the performance of the five methods or heuristics for as-

signing resources to activity cost pools. Figure 2 indicates that correlation-based methods domi-

nate other approaches in terms of reducing the error in reported costs. More surprising, the base-

line random allocation is indistinguishable from one size-based method (Willie Sutton I with

random assignment of small resources) and beats the other size-based method (Willie Sutton II

with grouping small resources in a miscellaneous overhead pool) handily. Further, within corre-

lation-based methods, a size based seeding shows limited improvement over a random seeding.

Intuitively, because a correlation based method pools resources with similar resource consump-

tion patterns most costs would be allocated with low specification error. However, size-based

methods suffer either because they pool smaller costs with larger resources (WS I method) or

group a large amount of costs into a misc pool (WS II method).18 We conclude that size-based

rules for allocating resources to activity pools might hurt rather than help.19

Figure 2 also shows that the number of activity pools matters greatly. The average error

(EUCD value) reduces from 37,657 for one pool to 23,675 with 10 pools when we use the Willie

Sutton I method. (The decrease is from 37,929 to 16,603 with Correlation - Random.) As ex-                                                            18 This assertion holds for the usual case. However, it is easy to construct extreme examples where a size-based method coupled with a big pool allocation delivers lower error than a correlation based method. For example, construct a setting where 2 resources account for 99% of the cost and have a high correlation in their consumption patterns. With a 2-pool system, a size-based method will form separate pools for these two resources, allocated using the appropriate drivers. A correlation-based method can pool these two resources into one pool, and result in one of the two costs being allocated with error. 19Because the guidance re the Willie Sutton rule is vague, we also implemented a system in which we measured correctly the driver pattern for the largest cost pools. Our results stand. We also note that the number of resources per activity pool is similar between the Willie Sutton I method and the correlation based method. Thus, the difference is not driven by this possible source of variation. (We thank Romana Autrey for suggesting this test.)

20  

pected, the error is decreasing and concave in the number of pools. 20 Untabulated data show that

we continue to obtain statistically significant (but economically small) gains of adding activity

cost pools even when the ratio of the number of activity pools to the number of resources is as

high as 80% (40 pools for 50 resources).

Table 2 presents data that provides insight into how measurement error and characteris-

tics of the production environment affect the error in reported costs for different assignment me-

thods. We do this only for two assignment methods that either dominate or perform as well as

comparable heuristics: Willie Sutton I and Correlation Random. First, the top rows in Table 2,

Panel B and the ANOVA results in panel C show that measurement error has a greater effect

with a correlation based assignment. The gain from using a correlation-based method declines

from 37% to 10% as the measurement error increases. Intuitively, with size-based methods, re-

sources in any given pool might have different allocation patterns. In contrast, a correlation

based assignment method generates resources in a pool with similar consumption pattern. The

impact of adding error to an average of dissimilar patterns is smaller because while the error

moves the average patterns away from the patterns for some resources, the error also moves the

patterns toward the consumption patterns for other resources in the pool and the probability of

offsetting increases.21

We now turn to the effect of aspects of the production environments. In panel A, we view

the ratio of the number of activity pools to the number of resources as the extent to which a cost

model compresses the information in the underlying economic environment. When this ratio

ranges from 4% (1 pool) to 20% (10 pools) of resources, we find about a 30% relative gain from

using the correlation method, relative to the size-based method. (The gain begins to taper off

once the ratio of the number of activity pools to the number of resources gets to about 40%).

                                                            20 For additional insight, consider the correlation method with size based seeding and the average method for selecting a driver. In this case, analysis of the percentage error shows that with 8-10 pools, slightly more than 50% of products have reported costs that lie within 10% of the true cost. Further, there are few products with more than 50% error in reported costs. This accuracy rate decreases rapidly as the number of pools decreases. We also find instances of extremely large (both positive and negative) errors. Finally, the median error is a over-costing of 18% for the correlation method with random seeding and using the average method for driver selection. Comparison of these data with the data from other methods leads to inferences similar to those reported in the text. 21 As expected, the effect of measurement error on accuracy of product costs is convex under all assign-ment methods. Untabulated data also show a significant interaction with the number of cost pools. The incremental effect of higher measurement error decreases as the number of cost pools increases. Intuitive-ly, the measurement errors in the different pools cancel out as we increase the number of activity pools. 

21  

Thus, the relation is better described as an inverted U because the gain is zero both when the

number of resources is small (1 pool) or is very large (when each resource has its own pool.)

Next, over the ranges that we consider, resource dispersion increases the error in a cost

system (see also Labro and Vanhoucke, 2008). Intuition suggests that resource dispersion should

increase the performance of a size-based allocation more than the performance of other assign-

ment methods because increased dispersion improves the chances for a few large resources and

many small ones. However, data do not support this assertion. The gain is relatively flat, and an

ANOVA of the percent gain of moving from Willie Sutton I assignment to an assignment based

on correlation with random seeding (see panels B and C of table 2) shows that other environmen-

tal factors matter more. (Our large sample size results in statistical significance, however.)22

Intuitively, we expect that a greater degree of resource sharing by products would make it

harder for an allocation to capture true resource consumption. However, we find that a greater

degree of resource sharing (density) reduces error in reported costs. We observe this effect re-

gardless of the method used to assign resources to pools. One explanation is that a job shop with

little sharing of resources across products might need a more sophisticated system (e.g., more

pools) to accomplish the same level of accuracy as a process shop where all products make use

of the same set of resources (even if the pattern of consumption varies across products). Howev-

er, the relative effect of resource sharing on the difference between the effectiveness of the corre-

lation-based method and the size-based method is not large. The change in the gain from using

the correlation-based method over the Willie Sutton I method is small (the percent gain decreases

from 23% to 15%) over the range of densities that we consider.

Not surprisingly, the extent of correlations in consumption patterns matters a great deal in

determining the absolute and relative performance of the assignment rules. At an absolute level,

the accuracy of any assignment method worsens as consumption patterns become increasingly

dissimilar (COR moves from 0.33 to -0.66). The relative decline with the correlation-based me-

thod is only 20%, whereas the performance of the size-based assignment method worsens consi-

derably (by about 55%). It becomes increasingly important to consider correlation based me-

                                                            22This assertion is not valid when we employ the big pool method for selecting drivers. Increasing re-source dispersion decreases error when we employ the big pool method in combination with a Willie Sut-ton I assignment where several small resources combine with a single large one. High dispersion disad-vantages the average method here because it gives equal importance to the consumption patterns of both large and small resources.

22  

thods when the system designer has grounds to believe that resource consumption patterns vary

considerably.

The Performance of an Implementable Blended Method

Implementing a correlation-based method needs more data than is required to execute a

size-based rule. Size, in dollars, is already available from accounting records, but correlation

based data are not. We therefore investigate if a coarse partition of resources based on rough es-

timates of correlation is enough to capture much of the advantage of a method that employs ac-

tual correlations. This variation, spurred by the rankings of the five heuristics we examined, is

the sixth method we consider and is designed to be implementable without demanding detailed

information on correlation patterns. In particular, we first partition resources into batch and vo-

lume based resources because these resource groups are likely to have dissimilar consumption

patterns. (Recall that the COR parameter influences the average correlation between the baseline

volume resource and all batch resources.) We then implement a size based allocation (a la the

Willie Sutton I method) separately for these two groups. That is, we partition by a rough estimate

of correlation to form resource tiers and then use a size-driven method within tiers.

Figure 3 presents the results. We find that the performance of the blended method is often

superior to the performance of the correlation-based allocation method (with random seeding)

even though it uses less information. Naturally, as seen in table 3, environmental parameters in-

fluence the relative gain from using the blended method over the pure size-based method (Willie

Sutton I).23 For example, the gain from the blended method is decreasing in COR. That is, even

using a gross guess about correlation structure is useful in reducing error when assigning re-

sources to activities, particularly when we have an ex ante reason to suspect dissimilar consump-

tion patterns. (A large negative value for COR would be consistent with the view that batch re-

sources are consumed in patterns that differ from the patterns for volume based resources.) These

conclusions provide strong support to the ABC prescription of classifying resources as per the

activity hierarchy and constructing separate pools for each tier of resources. The results also sup-

port the use of multiple criteria for assigning resources to pools, and suggest that size might be a

good candidate for a secondary primary criterion for grouping resources.

                                                            23 In untabulated results, we find that the gain tapers off as we increase the number of activity pools. This finding obtains because the separation of resources occurs naturally as the number of activity pools ap-proaches the number of resources to be assigned.

23  

Improved Guidance for Resource Assignment

Our finding that correlation based assignment rules work well for grouping resources into

activity pools motivates a modified experiment, designed at offering improved guidance to sup-

port correlation-based resource assignments. Specifically, we allow the number of activity pools

to vary endogenously rather than fixing it exogenously. We consider a simple assignment rule in

which we seed the first pool with the largest resource. We then add to this pool all those re-

sources whose consumption patterns have a correlation with the consumption pattern for the base

resource is higher than a specified cut-off value. We then seed the second pool with the largest

among the remaining resources. We again consider correlations to decide the resources to group

into the second activity pool. We continue this process until the number of remaining resources

is less than a specified number of resources (all remaining resources put into a miscellaneous

cost pool). We vary both the cut-off correlation value and the number of resources to pool into

the miscellaneous pool. As before, we vary characteristics of the production environments that

we consider.

Table 4 provides the core results. Consider the column for the cut-off correlation of 0.4.

Here, our measure of the error in reported costs (EUCD) has a value of 17,018 when we allow

only five of the 50 resources to be in the miscellaneous cost pool. At this level, the average sys-

tem has 19 activity pools. When 50% of the available resources (25 of 50 resources, containing

as much as 31% of total costs) are grouped as miscellaneous costs (last row of Table 6), the error

metric only registers a marginal increase to 19,609, while the number of activity pools drops to

6.35. Data reported in the other columns show a similar pattern. We conclude that firms can

group a large portion of their costs as “miscellaneous” without significantly degrading system

accuracy when an assignment rule based on a cutoff level for correlation is used.

Now, consider the row that reports data for the setting in which we group as many as 15

resources into the miscellaneous cost pool. Not surprisingly, as we increase the cut-off correla-

tion value we find a steady increase in system accuracy as well as a steeper increase in the num-

ber of cost pools formed. The tradeoff here has to depend on the perceived benefits of increased

accuracy versus the costs of adding more pools.24 Figure 4 shows that the number of cost pools

                                                            24 The grey shaded areas in Table 4 indicate experiments where the number of endogenously created activity pools almost always hits the maximum number possible (=number of RCP – number of resources in miscellaneous cost pool) or is at a minimum value (e.g., 2). Thus, the data suggest that this cost/benefit tradeoff is negatively affected when high cut off correlations are used.

24  

for this setting clusters between 10 and 17, and provides additional support for the assertion that

a firm might be able to devise a “good enough” system with a relatively small number of activity

pools.25 Moreover, we find it striking that even a value of 0.4 for the cut-off correlation leads to

system accuracy that is comparable to the information-intensive method (correlation-with size

based seeding) we employed in the first experiment (See figure 2). We conclude that correlation-

based methods that employ crude and/or noisy measures of the underlying correlation might be a

practical way for grouping resources into activity pools.

Panel B of Table 4 explores the effect of environmental parameters. We find that re-

source dispersion has a negligible effect on both the error in reported costs and on the number of

activity pools formed. Next, we find that the correlation pattern between batch and volume re-

sources matters greatly. The rules perform well either when these two groups of resources have

distinctly similar or distinctly dissimilar consumption patterns. However, the system has the most

error when the consumption patterns are orthogonal to each other. Intuitively, with dissimilar

consumption patterns, batch and volume resources form separate activity pools, each of which is

allocated well to products. However, a correlation near zero reduces the ability of the heuristic to

separate out batch and volume resources, degrading performance and generating systems with

many cost pools. Finally, consistent with earlier findings, we find a monotonic decline in error in

reported costs as the extent of sharing of resources by products increases. This pattern obtains

even though we find an accompanying reduction in the number of activity pools as the density of

consumption matrix increases. Overall, we again find that the density of consumption matrix is

perhaps the most important feature of the production environment to consider when making

choices about parameters of the cost system.

Heuristics for Choosing the Cost Driver

Our final set of results pertain to the choice of a driver used to allocate costs from a given

cost pool to products. We parameterize the rules by the number of resources within an activity

pool whose consumption patterns we average to obtain the allocation rate. At one end, the big

pool method only considers the pattern for the largest resource in the pool. At the other extreme,

the average method equally weights all the resources in an activity pool. Intermediate indexing

methods consider the two, three, four or five largest resources in a pool to calculate the allocation

base at a cost pool.

                                                            25 Untabulated results show that the inference holds even when we increase the number of resources we consider.

25  

As Figure 5 shows, there is a significant gain to using the average method relative to the

big pool method. As shown in panel A of table 5, the change eliminates about 50% of the error

resulting from use of the big pool method. However, the average method is information inten-

sive. Thus, we also consider intermediate composite rates that consider fewer resources. Consid-

er the data for NUM = 3 (i.e., we consider the top three resources in a pool to calculate driver

percentages). Relative to the big pool method, the gain is only 5.71% when we have a one-pool

system. However, the gain rapidly increases and reaches 52% when we consider a 10-pool sys-

tem, because the number of resources per pool declines as we increase the number of activity

pools, while the number of resources averaged is the same. Nevertheless, we find a gain of

30.7% even with six activity pools, meaning that each pool has 8.33 resources, on average. The

data in Panel A also show that a system designer might be better off with an index of a limited

number of resources in the pool relative to a simple averaging of all resources when selecting an

allocation base. We find that a driver that only considers four or five resources beats the average

method (in terms of errors in reported costs) when the number of activity pools is at a medium

level (8 - 10 pools). Intuitively, with 7 to 10 resources pooled into an activity pool, the average

method starts to weigh the consumption pattern of the smaller resources in the pool too heavily,

moving away from the weighted average that is the accurate consumption pattern given our li-

near setup.

As shown in Table 5, Panel B, we find that our general conclusion holds if we use a cor-

relation-based method to assign resources to activity pools. The potential gains from averaging

are larger (about 65% relative to 55% for the WS I method) because the assignment method re-

duces the probability that we will average dissimilar consumption patterns. However, while in-

dexing continues to yield significant gains, the performance never beats that with the average

method.

Table 6 reports how the gain from indexing (NUM = 3 versus the big pool method) fares

in different production environments. The descriptive data in panel A and the ANOVA in panel

B both indicate that the gain is general in nature. We continue to average about a 30% gain from

indexing, relative to the big pool method, across a wide range of environmental parameters. We

note that the less resource sharing there is in the production environment (low density of the con-

sumption matrix), the higher the gain is from indexing. Of course, consistent with the data in ta-

ble 5, the ANOVA in panel B indicates a significant effect due to the number of activity pools

26  

(mechanically, the number of resources per pool declines, leading to greater accuracy for index-

ing). This result suggests that such indexing or use of composite drivers for the same activity

pool may be particularly important in job shop environments. Overall, our findings indicate that

while it is useful to consider the consumption patterns of all resources in an activity pool, it

might be economically enough to calculate drivers using only the largest few resources in a pool.

VI. CONCLUDING REMARKS

Our paper uses extensive simulation data to rank alternate rules / heuristics for grouping

resources into cost pools and for generating cost drivers (allocation bases) for the resulting cost

pools.. To our knowledge, this paper is the first to compare the alternate heuristics employed by

system designers. 

Our results offer some unique insights.

• We find that, contrary to common recommendation, various implementations of the Willie

Sutton rule (using resource size) do not work well for assigning resources to activity pools.

Assigning costs to cost pools using resource correlations dominates using resource size. Be-

cause a full correlation based approach is data intensive, we investigate a blended method,

whereby resources are roughly grouped by gross correlations in their consumption pattern

(e.g. batch and volume resource groups), followed by a size-based assignment to activity

pools. This blended method performs almost as well as the full-information correlation ap-

proach. Among the environmental parameters we consider, the density of the consumption

matrix (i.e., the extent of resource sharing by products) is the key driver of error in a system,

followed by the extent of similarity in consumption patterns. Surprisingly, the dispersion of

resource costs does not significantly affect system error, for the ranges that we consider.

• Our second set of results give normative guidance on how to implement crude or coarse cor-

relation-based assignment rules that capture much of the gains from a correlation based as-

signment rule, without being information intensive. This experiment endogenously deter-

mines the number of cost pools. We explore how the cut-off correlation used to pool re-

sources and the percent of total cost of resources pool in a miscellaneous cost pool affect ac-

curacy. We find surprisingly low system error using a relatively small value for the cut-off

correlation (e.g. correlation .40) to determine whether to pool a resources into an activity

pool. Moreover, we find that a firm can group nearly 25% of its costs into a miscellaneous

27  

cost pool without significantly degrading system accuracy. We again find that these choices

matter more in environments with greater resource sharing by products.

• Our final set of results pertains to selecting the consumption driver for allocating costs con-

tained in activity pools to products. We find that using the largest resource in a pool as the

cost driver (big pool method) is not very effective. We find that there are significant gains

from considering a composite driver that combines the consumption patterns for a few of the

largest resources into an allocation index. Indeed, with a medium number of cost pools, we

find that an index driver can perform better than an information-intensive method that con-

siders all resources in the cost pool. Finally, the gain from using an index (relative to the big

pool method) increases in the extent of resource sharing by products and the number of cost

pools. These findings underscore that driver selection might be particularly important in job

shop type environments in which products exhibit diversity in both the sets of resources they

consume and in the proportion of consumption.

Our work is subject to at least three caveats. First, our simulation manipulates measure-

ment error as an exogenous construct in order not to build in particular results on trade-offs in

our experimental design. However, Cardinaels and Labro (2008) show in a laboratory experi-

ment that the extent of measurement error increases endogenously with the number of activity

pools. Such endogenously increasing measurement error will reduce the positive effect on accu-

racy of adding cost pools. Second, our analysis only investigates the decrease in costing error

and does not consider the costs of designing and maintaining the cost system. This cost has to be

weighed off against the increase in accuracy obtained. Since cognitive, behavioral, and system

development costs vary across organizations and users, we expect that the optimal tradeoff is

likely case-specific. Finally, decisions about error tolerance and accuracy levels depend on the

specific use of the cost system. Costing systems serve many different needs, such as pricing and

product mix decisions, capacity planning, capacity allocation, control, benchmarking, and project

selection. These diverse objectives may require different levels of accuracy (or bias), a topic

which is outside the scope of our study.

Our results offer several interesting avenues for future research. Of particular interest is

the modeling of a richer setting that can accommodate the identification of unused capacity, par-

ticularly as an outcome of changing volumes and product mixes. This extension, which explicitly

considers a “dynamic” setting, can then be useful when considering alternate uses for ABC sys-

28  

tems.26 We also could examine cost system robustness to changes in the production processes.

Firms identify where to improve their production processes using data supplied by their costing

systems. Such improvements often occur at a faster rate than the rate at which firms update their

costing systems. How robust is a system (either from a product costing or cost management

perspective) when it sows the seeds of its own destruction? A second and potentially very in-

sightful avenue is to extend this methodology to study recent practices such as lean accounting

and time-based ABC. The latter seems a particularly interesting avenue to explore because it

moves away from the percentage allocations of costs from activity pools and toward a direct

charge out from individual resources. In our framework, we could model the change toward

time-based ABC as an increase in the number of activity pools but at the cost of increasing mea-

surement error. Lastly, this stream of research can also be of interest to researchers who examine

the antecedents and/or consequences of the provision in organizations of more (or less precise)

information in continuous settings [finer (coarser) information in discrete settings]. For example,

in accounting an important literature on the link between precision of information and properties

of disclosure has developed (see Verrecchia 1990, Dye and Sridhar 2007, Langberg and Sivara-

makrishnan 2008). Empirical testing of these hypotheses requires that we understand how infor-

mation fineness/preciseness might translate into properties of observable data, such as the prop-

erties of costing systems studied here. Many of the rules, heuristics, and system design parame-

ters studied here are observable to the empiricist. Further research could combine these observa-

ble properties into a composite index that might serve as an empirical proxy of the theoretical

construct of precision. Our hope is that such translation will help ground the often normative lite-

rature on product costing in information economics, providing it with a solid theoretical base.

                                                            26 The extension is important because Nair (2000) reports that only 58% of firms list product/service cost-

ing as a primary goal of activity-based costing. He also reports that 51% of respondents identify process analysis and 49% identify performance management as key goals. Further, most firms update their ABC systems at least once a year. 

29  

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32  

Figure 1 Overview of Experiment

Model various production envi-ronments by varying resource dis-persion, extent of resource sharing and similarity in resource con-sumption patterns

For each environment, generate many benchmark systems that provide benchmark or “true” costs

For each noisy system, compute the vector of re-ported or “noisy” product costs

Calculate error metric by comparing bench-mark and noisy costs

For each benchmark system, con-struct many noisy approximations by varying system features such as the number of pools, how to assign resources to pools, how to pick drivers and so on

Analyze how the features of the noisy system affect error. Consider interactions with environmental parameters

33  

Figure 2 Effect of the Method for Assigning Resources to Activity Pools

Notes: 1. Individual series relate to various methods for assigning resources to activity pools. RANDOM ASSIGNMENT: Resources assigned randomly to activity pools. WILLIE SUTTON I: Largest ACP resources assigned to number of activity pools chosen by system

designer (i.e., ACP). The costs of remaining resources are assigned randomly to the activity pools. WILLIE SUTTON II: Largest ACP-1 resources assigned to number of activity pools chosen by sys-

tem designer, with one pool left open. The costs of remaining resources are assigned to the last open pool (miscellaneous costs).

CORRELATION (SIZE BASED SEEDING): Largest ACP resources assigned to the number of activity pools chosen for by system designer (ACP). For the first activity pool, select those resources with the highest correlation with the resource in the pool. Assign a total of INT(RCP/ACP) resources to this pool. Repeat for second activity pool and so on.

CORRELATION (RANDOM SEEDING): Pick ACP resources randomly and allocate one each to the number of activity pools chosen for by system designer (ACP). For the first activity pool, select those resources with the highest correlation with the resource in the pool. Assign a total of INT(RCP/ACP) resources to this pool. Repeat for the second activity pool and so on.

EUCD: Metric of error between benchmark and reported costs, calculated as the 2-norm between the vectors of benchmark and reported costs.

2. Used the average method for selecting driver used for allocating costs from activity pools to cost objects. Under this method, consumption percentages are calculated as the average of the consump-tion percentage for all resources in the activity pool. Inferences are unaltered with other choices for calculating consumption percentages.

10,000

15,000

20,000

25,000

30,000

35,000

40,000

1 2 4 6 8 10

Err

or in

Rep

orte

d C

osts

(EU

CD

)

Number of Activity Cost Pools

Random assignment

Correlation (random seeding)Correlation (size based seeding)Willie Sutton I

Willie Sutton II

34  

Figure 3 The Performance of the Blended Method for Assigning Resources to Activity Pools

Notes: 1. Individual series relate to various methods for assigning resources to activity pools.

BLENDED METHOD: Resources are first separated as per whether they are batch or volume re-sources. The size-based Willie Sutton I method is used for each group, with each category having ½ the number of available cost pools.

WILLIE SUTTON I: Largest ACP resources assigned to number of activity pools chosen by system designer (i.e., ACP). The costs of remaining resources are assigned randomly to the activity pools.

CORRELATION (RANDOM SEEDING): Pick ACP resources randomly and allocate one each to the number of activity pools chosen for by system designer (ACP). For the first activity pool, select those resources with the highest correlation with the resource in the pool. Assign a total of INT(RCP/ACP) resources to this pool. Repeat for the second activity pool and so on.

EUCD: Metric of error between benchmark and reported costs, calculated as the 2-norm between the vectors of benchmark and reported costs.

2. Used the average method for selecting driver used for allocating costs from activity pools to cost objects. Under this method, consumption percentages are calculated as the average of the consump-tion percentage for all resources in the activity pool. Inferences are unaltered with other choices for calculating consumption percentages.

-

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

1 2 4 6 8 10

Err

or in

Rep

orte

d C

osts

(EU

CD

)

Number of Activity Pools

Blended Method

Willie Sutton I

Correlation with random seed

35  

Figure 4

Distribution of the Number of Endogenously Formed Activity Pools  

Notes: 1. The assignment method is as follows. The fist pool seeded with the largest resource. Additional re-

sources that satisfy the correlation cut-off (relative to the first resource in the pool) added to pool. Second pool seeded with largest among remaining resources. Additional resources satisfying correla-tion cut-off added. Continue process until number of remaining resources is less than specified (all remaining resources put into misc cost pool). Also grouped all remaining resources into the last pool if the number of activity pools became 30 (the maximum number of possible activity pools).

2. Data represent a setting in which the cut-off correlation is 0.4 and the number of resources in the misc cost pool can be as high as 15 resources.

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Perc

ent o

f obs

erva

tions

Number of Activity Pools Formed

36  

Figure 5 Effect of Method for Selecting Cost Driver (Indexing)

Panel A: Use Willie Sutton I to Assign Resources to Activity Pools

Panel B: Use Correlation (Random Seeding) to Assign Resources to Activity Pools

Notes:

1. Individual series relate to various methods for calculating driver percentages used to allocate costs from activity pools to cost objects. Data pertain to 50 resources.

2. Variable definitions: BIG POOL: The allocation percentages are those of the largest resource in the activity cost pool. NUM: Calculated driver percentages as the average of the largest NUM resources in the activity cost pool. AVG: Calculated driver percentages as the average of the driver percentages for all resources in the activity cost pool. EUCD: Metric of error between benchmark and reported costs, calculated as the 2-norm be-tween the vectors of benchmark and reported costs.

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

1 2 4 6 8 10Err

ror

in R

epor

ted

Cos

ts (E

UC

D)

Number of Activity Pools

Big pool

Num=2

Num=4

Num=5Average

010,00020,00030,00040,00050,00060,00070,00080,000

1 2 4 6 8 10

Err

or M

etri

c (E

UC

D)

Number of Activity Pools

Big pool

Num=2

Num=4Num=5

Average

37  

Table 1 Descriptive Statistics

Panel A: Benchmark Cost Systems

Units Average values Variation in resource costs (using parameter RC_DISP)

Global average

Low dispersion (RC_DISP= 0.25)

Med dispersion (RC_DISP = 0.50)

High dispersion(RC_DISP = 0.75)

N = 960 N=320 N=320 N=320 % cost in largest pool / % cost in smallest pool (COST_RATIO_T)

Ratio 6.78 3.20 5.75 11.39

Density of consumption matrix (us-ing parameter DENS)

Global average

Little sharing of resources

(DENS = -0.75)

Medium sharing of resources (DENS = 0)

High sharing of resources

(DENS = 0.75)

Very high sharing of resources (DENS = 1.50)

N = 960 N=240 N=240 N=240 N=240 Percent of zero entries in consump-tion matrix

% 36.04 70.95 46.11 20.87 6.22

Average number of products con-suming a resource (out of 50 prod-ucts)

Number 31.97 14.52 26.94 39.56 46.88

Average range in consumption of a resource across products (given pos-itive use)

% 11.43 23.22 11.08 6.61 4.79

Importance of resources devoted to batch activities (using parameter COR)

Global average

Similar consumption patterns (COR = 0.33)

Intermediate consumption patterns (COR = 0.0)

Intermediate consumption patterns (COR =-0.33)

Dissimilar consumption patterns (COR =-0.66)

N = 960 N=240 N=240 N=240 N=240 Correlation between largest pool and all resources

Number 0.264 0.376 0.298 0.232 0.149

Correlation between largest pool and batch resources

Number -0.029 0.300 0.000 -0.061 -0.125

38  

Table 1 (continued) Descriptive Statistics

Panel A (cont’d): Benchmark Cost Systems Characteristics not varied systematically across cells

Average Median Inter-quartile range

% resources in pools devoted to batch activities

% 35.07 34.87 14.14

Correlation between largest pool and volume resources

Number 29.36 29.60 15.60

Panel B: Error metrics: Univariate statistics (N =17,280)

Mean Min Q1 Q2 Q3 Max EUCD 28,448 2514 16,237 24,882 36,919 124,155 %ACC 25.84 0 14 22 34 100 MPE 16.8 1.47 9.66 14.92 21.82 62.59

Panel C: Correlation among error metrics (N = 17,280)

EUCD %ACC MPE EUCD 1.00 -0.745 0.955 %ACC 1.000 -0.769 MPE 1.000

Notes: 1. Willie Sutton I method used for assigning resources to activity pools: largest resources assigned to

number of activity pools chosen for by system designer (ACP). The costs of the remaining resources are assigned randomly to the activity pools. Average method for selecting driver used to allocate costs from activity pools to cost objects: Calculated driver percentages as the average of the driver percen-tages for all resources in the activity cost pool. Inferences in panels B and C unaltered with other me-thods for assigning resources to activity pools or selection of driver pattern.

2. Average method for selecting driver was used to allocate costs from activity pools to cost objects. Consumption percentages are calculated as the average of the consumption percentages for every re-source in the activity pool. Inferences are unaltered with other choices for drivers.

3. Variable definitions: RC_DISP: Dispersion in the size of resource cost pools. Higher values correspond to greater disper-sion.

COR: Magnitude of the (average) correlation in resource consumption patterns between the baseline volume resource and batch resources.

DENS: Measure of the extent of resource sharing by products. Greater values correspond to a greater degree of resource sharing and lower traceability of resources to cost objects.

EUCD: Metric of error between benchmark and reported costs, calculated as the 2-norm between the vectors of benchmark and reported costs

%ACC: Percent of products whose reported cost is within 10% of their benchmark costs. MPE: Mean percentage error, which is the average of the relative error in reported costs.  

39  

Table 2 Effect of Environmental Parameters on Assignment Heuristics

Panel A: Effect of number of activity cost pool on the reduction in the error in reported costs

(correlation with random seeding versus Willie Sutton I assignment)

Number of ac-tivity pools (ACP)

EUCD with Size-based allocation (Willie Sutton I Method)

EUCD with Correlation based allocation (ran-dom seeding)

Percent gain

1 37,657 37,929 -0.72% 2 31,537 25,181 20.15% 4 27,676 20,404 26.27% 6 25,566 18,563 27.39% 8 24,576 17,188 30.06% 10 23,675 16,603 29.87%

Panel B: Effect of environmental parameters and other system design choices on the reduc-

tion in the error in reported costs (correlation with random seeding versus Willie Sutton I assignment)

Extent of Measurement Error Value of construct MSMT_ERR = 0.1 MSMT_ERR = 0.3 MSMT_ERR = 0.5 Difference in EUCD 8,111 5,892 3,406 Percent gain 36.54% 21.19% 9.64% Resource dispersion Value of construct RC_DISP= 0.25 RC_DISP= 0.5 RC_DISP= 0.75 EUCD (WS I) 27,381 28,860 29,101 EUCD (Corr – Rand) 22,044 22,275 23,616 Percent gain 19.49% 22.82% 18.85% Correlation in consumption pattern between volume and batch resources Value of construct COR = -0.66 COR = -0.33 COR = 0 COR = 0.33 EUCD (WS I) 35,162 29,837 26,201 22,591 EUCD (Corr – Rand) 25,050 22,701 22,004 20,824 Percent gain 28.76% 23.92% 16.02% 7.82% Extent of resource sharing by Products Value of construct DENS = -0.75 DENS = 0.0 DENS = 0.75 DENS = 1.50 EUCD (WS I) 41,610 29,549 23,029 19,602 EUCD (Corr – Rand) 32,014 23,176 18,767 16,622 Percent gain 23.06% 21.56% 18.51% 15.20%  

40  

Table 2 (continued) Effect of Environmental Parameters on Assignment Heuristics

Panel C: ANOVA of percent gain in EUCD (= EUCD with Willie Sutton I method - EUCD with correlation with random seeding)

Source of Variation d.f. F p > F Number of Activity Pools (ACP) 5 193.81 < 0.0001 Measurement Error (MSMT_ERR) 3 470.26 < 0.0001 Resource dispersion (RC_DISP) 2 12.35 < 0.0001 Extent of resource sharing (DENS) 3 11.49 < 0.0001 Correlation between batch and vo-lume driven resources (COR) 3 183.02 < 0.0001 Residual < 0.0001 Adjusted R-Square 74.80%

Notes: 1. The first row in each panel reports EUCD using Willie Sutton I method for assigning resources to

activity pools. The second row reports EUCD using the correlation structure (with random initial seeding) for assigning resources.

2. Average method for selecting driver used to allocate costs from activity pools to cost objects: Calcu-lated driver percentages as the average of the driver percentages for all resources in the activity cost pool.

3. Variable definitions: RC_DISP: Dispersion in the size of resource cost pools. Higher values correspond to greater disper-sion.

COR: Magnitude of the (average) correlation in resource consumption patterns between the baseline volume resource and batch resources.

DENS: Measure of the extent of resource sharing by products. Greater values correspond to a greater degree of resource sharing and lower traceability of resources to cost objects.

EUCD: Metric of error between benchmark and reported costs, calculated as the 2-norm between the vectors of benchmark and reported costs

 

41  

Table 3 Error in Reported Costs: Blended Method for Assigning Resources

Panel A: Effect of number of activity cost pool on the reduction in the error in reported costs

(blended method versus Willie Sutton I assignment) Number of activity pools (ACP)

EUCD with blended method

Percent gain relative to Willie Sutton I method

Percent gain relative to correlation based method with random seeding

1 37,519 0.37% 1.08% 2 24,521 22.25% 2.62% 4 18,651 32.61% 8.59% 6 16,139 36.87% 13.06% 8 14,596 40.61% 15.08% 10 13,697 42.15% 17.51%

Panel B: Effect of environmental parameters on the reduction in the error in reported costs

(Blended method versus Willie Sutton I assignment) Resource dispersion Value of construct RC_DISP= 0.25 RC_DISP= 0.5 RC_DISP= 0.75 EUCD (Blended method) 16,873 18,488 20,133 Percent gain 38.38% 35.94% 30.82% Correlation in consumption pattern between volume and batch resources Value of construct COR = -0.66 COR = -0.33 COR = 0 COR = 0.33 EUCD (Blended method) 19,574 18,350 18,098 17,968 Percent gain 44.33% 38.50% 30.93% 20.46% Extent of resource sharing by Products Value of construct DENS = -0.75 DENS = 0.0 DENS = 0.75 DENS = 1.50 EUCD (Blended method) 25,994 18,755 15,350 13,891 Percent gain 37.53% 36.53% 33.35% 29.13% Notes: 1. The first row in each panel reports EUCD using blended method assigning resources to activity pools.

The second row reports percent gain in EUCD relative to using the Willie Sutton I method. 2. Average method for selecting driver used to allocate costs from activity pools to cost objects: Calcu-

lated driver percentages as the average of the driver percentages for all resources in the activity cost pool.

3. Variable definitions: RC_DISP: Dispersion in the size of resource cost pools. Higher values corres-pond to greater dispersion.

COR: Magnitude of the (average) correlation in resource consumption patterns between the baseline volume resource and batch resources.

DENS: Measure of the extent of resource sharing by products. Greater values correspond to a greater degree of resource sharing and lower traceability of resources to cost objects.

EUCD: Metric of error between benchmark and reported costs, calculated as the 2-norm between the vectors of benchmark and reported costs.

42  

Table 4 Endogenously Determined Number of Activity Pools

Panel A: Descriptive Statistics

Cut-off correlation value for grouping resources into the same activity pool

Number of resources in Misc cost pool (% of resources)

Average of cost in the miscellaneous cost pool (in %)

0.2 0.4 0.6 0.8

5 (10%)

5.24% 22,823 [7.13] (2, 16)

17,018 [19.17] (3, 25)

12,173 [29.11] (14,30)

10 (20%)

9.53% 22,742 [5.47] (1, 12)

17,408 [15.79] (3, 25)

12,263 [26.93] (7, 30)

Max # ACP

reached

15 (30%)

15.81% 22,842 [4.39] (1, 10)

17,761 [12.25] (2, 23)

12,620 [22.96] (7, 30)

20 (40%)

23.04% 23,216 [3.58] (1, 8)

18,176 [9.33] (2, 19)

13,647 [18.33] (5, 29)

10,508 [25.65] (16, 30)

25 (50%)

31.08% Min # ACP

reached

19,610 [6.35] (2, 16)

15,041 [13.89] (4, 24)

12,089 [20.68] (9, 26)

 

43  

Panel B: Determining the number of activity pools endogenously: Interaction with environ-mental parameters.

Resource dispersion Value of construct RC_DISP= 0.25 RC_DISP= 0.5 RC_DISP= 0.75 EUCD 17,088 17,557 18,636 Average # of ACP 12.23 12.31 12.21 Correlation in consumption pattern between volume and batch resources Value of construct COR = -0.66 COR = -0.33 COR = 0 COR = 0.33 EUCD 18,171 17,303 16,999 18,570 Average # of ACP 7.75 14.62 15.69 10.95 Extent of resource sharing by Products Value of construct DENS = -0.75 DENS = 0 DENS = 0.75 DENS = 1.50 EUCD 21,841 18,294 16,069 14,838 Average # of ACP 13.10 12.54 11.74 11.63 Notes: 1. In panel A are respectively reported: the average value for EUCD, [average number of activity cost

pools formed], and (the range for the number of activity pools formed). Values in italics indicate that the value is at the exogenously specified maximum for the number of activity pools (30). The grey shaded areas indicate experiments where the number of endogenously created ACP hits the maximum number of ACP possible (=number of RCP – number of resources in miscellaneous cost pool) or the number of pools is very small (e.g., 2).

2. The first pool seeded with the largest resource. Additional resources that satisfy the correlation cut-off (relative to the first resource in the pool) added to pool. Second pool seeded with largest among re-maining resources. Additional resources satisfying correlation cut-off added. Continue process until number of remaining resources is less than specified (all remaining resources put into misc cost pool). Also grouped all remaining resources into the last pool if the number of activity pools became 30 (the maximum number of possible activity pools).

3. Used the average method for calculating driver percentages for an activity cost pool. 4. Data for panel B pertain to a setting with cut-off correlation = 0.4 and with as many as 15 resources in

the miscellaneous cost pool. 5. Variable definitions:

RC_DISP: Dispersion in the size of resource cost pools. Higher values correspond to greater disper-sion.

COR: Magnitude of the (average) correlation in resource consumption patterns between the baseline volume resource and batch resources.

DENS: Measure of the extent of resource sharing by products. Greater values correspond to a greater degree of resource sharing and lower traceability of resources to cost objects.

EUCD: Metric of error between benchmark and reported costs, calculated as the 2-norm between the vectors of benchmark and reported costs.

 

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Table 5 Gain from Using an Indexed Cost Driver

Panel A: Resources assigned to activity pools using Willie Sutton I method

% gain relative to error from using the Big Pool method for selecting driver pattern

ACP NUM = 2 NUM = 3 NUM = 4 NUM = 5 Average of all resources in activity pool

(AVG) 1 6.28% 5.71% 7.91% 8.53% 47.99% 2 1.61% 5.21% 10.30% 13.86% 51.38% 4 10.23% 18.84% 28.14% 36.23% 55.96% 6 16.85% 30.69% 44.46% 56.08% 57.09% 8 22.46% 42.09% 58.20% 64.72% 55.99% 10 30.81% 52.82% 63.85% 63.26% 55.49%

Panel B: Resources assigned to activity pools using correlation among resource consumption

patterns (random seeding)

% gain relative to error from using the Big Pool method for selecting driver pattern

ACP NUM = 2 NUM = 3 NUM = 4 NUM = 5 Average of all resources in activity pool

(AVG) 1 6.34% 5.78% 7.82% 10.03% 48.20% 2 14.40% 24.08% 32.06% 37.45% 65.68% 4 24.20% 37.25% 46.30% 53.31% 67.24% 6 29.49% 44.51% 53.84% 60.08% 66.12% 8 34.20% 50.34% 59.19% 64.68% 66.33% 10 37.76% 54.17% 62.07% 65.20% 65.45%

Notes:

1. Data pertain to 50 resources. 2. Variable definitions:

BIG POOL: The allocation percentages are those of the largest resource in the activity cost pool. NUM: Calculated driver percentages as the average of the largest NUM resources in the activity cost pool. AVG: Calculated driver percentages as the average of the driver percentages for all resources in the activity cost pool. EUCD: Metric of error between benchmark and reported costs, calculated as the 2-norm be-tween the vectors of benchmark and reported costs.

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Table 6 Interaction between the Method for Choosing Driver and

Environmental Parameters and Other System Design Choices

Panel A: Effect of environmental parameters and other system design choices on the reduc-tion in the error in reported costs (big pool versus using index of top three re-sources).

Resource dispersion Value of construct RC_DISP= 0.25 RC_DISP= 0.5 RC_DISP= 0.75 Difference in EUCD 21,084 20,112 19,408 Percent gain 33.53% 33.65% 33.05% Correlation in consumption pattern between volume and batch resources Value of construct COR = -0.66 COR = -0.33 COR = 0 COR = 0.33 Difference in EUCD 22,860 17,719 18,200 22,027 Percent gain 35.32% 30.97% 31.27% 35.77% Extent of resource sharing by Products Value of construct DENS = -0.75 DENS = 0 DENS = 0.75 DENS = 1.50 Difference in EUCD 36,332 22,755 12,344 9,376 Percent gain 33.93% 36.01% 30.71% 29.88% Panel B: ANOVA of percent difference in EUCD (= EUCD with big pool method - EUCD with

index of largest 3 resources) Source of Variation d.f. F p > F Number of Activity Pools (ACP) 5 867.39 < 0.0001 Measurement Error (MSMT_ERR) 3 205.29 < 0.0001 Resource dispersion (RC_DISP) 2 0.22 0.8050 Extent of resource sharing (DENS) 3 21.19 < 0.0001 Correlation between batch and vo-lume driven resources (COR)

3 25.52 < 0.0001

Residual < 0.0001 Adjusted R-Square 85.21%

Notes: 1. Correlation with random initial seeding was used for assigning resources to activity cost pools. 2. Variable definitions: RC_DISP: Dispersion in the size of resource cost pools. Higher values corres-

pond to greater dispersion. COR: Magnitude of the (average) correlation in resource consumption patterns between the baseline

volume resource and batch resources. DENS: Measure of the extent of resource sharing by products. Greater values correspond to a greater

degree of resource sharing and lower traceability of resources to cost objects. EUCD: Metric of error between benchmark and reported costs, calculated as the 2-norm between the

vectors of benchmark and reported costs.

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Appendix A Notation for Key Constructs

Modeling Production Environment RC_DISP Dispersion in the size of resource cost pools DENS Traceability of resource costs COR Correlation in consumption patterns PER_BATCH Percentage of batch resources CO Number of cost objects Parameters of the noisy system ACP Number of activity cost pools MSMT_ERR Measurement error in mapping activities to cost objects Errors in cost system EUCD Metric for average error in cost system %ACC The percent of cost objects with reported costs within 10% of

their benchmark cost MPE Mean percent error metric Matrices and Vectors RCP The 1 x RCP vector of resource costs RES_CONS_PAT The RCP x CO matrix of benchmark consumption of resources

by cost objects BMARK_COST The 1 x CO vector of benchmark costs ACP The 1 x ACP vector of costs in activity pools ACT_CONS_PAT The ACP x CO consumption matrix implied by the observed cost

system REP_COST The 1 x CO vector of reported costs

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Appendix B Detailed Algorithm of the Simulation Model

Algorithm for Simulating a Benchmark costing System

1. Populating the vector RCP of dimension [1 x RCP]. We set RCP = 50. a. Draw PER_BATCH (=monetary value of batch resources) from a uniform distribution

with bounds [0.2, 0.5]. b. For the first Gsize (= number of volume resources) columns, generate a number from a

uniform distribution with bounds constant ± RC_DISP. Recalculate these values to represent the proportion of total resources TR in the various resource cost pools by divid-ing each element in the vector with the sum of all elements. Multiply these proportions with (1-PER_BATCH) × TR to obtain the monetary value of each rcpi. Assure a mini-mum level is assigned to each rcpi; to ensure that no resource pools are empty. Gsize was set to approximately 50 percent of RCP.

c. Repeat the procedure under b. for the remaining columns in RCP. These represent the batch resources.

2. Simulate the elements altik of RES_CONS_PAT. These elements represent the percentage allocations from rcpi to cok. a. Generate a random normally distributed vector of a baseline resource(s) X of dimension

[1 x CO], used by all cok. Generate additional (gsize) randomly distributed vectors Yi. Define ̃ √1 ̃ with ̃ random between 0.2 and 0.8. By multivariate normality, X and Zi have a correlation of ̃ .

b. Draw d from a uniform distribution with mean DENS + U(-0.25, 0.25). DENS is a para-meter that is varied systematically from negative (-0.75), over zero, to positive (0.75 and 1.5). Add d to each row Zi (except for the baseline resources) to shift the mean. In all rows, truncate elements to set all negative values to zero. This step ensures that, if DENS is negative many elements in each row will be zero and hence the row will be sparse. Re-calculate the values in each row to represent the proportion of the resource used by the various cost objects, by dividing each element (for a given row) by the sum of all the elements in that row. This creates a vector with elements altik, the resource consumption pattern for the first gsize resources. (We add a large positive value to the baseline re-source(s) to ensure that all resources consume the baseline resources.)

c. Generate further (rcp – gsize) randomly distributed vectors Yi. Here, define

ii YCORXCORZ 21−+∗= with COR the correlation that is varied in a controlled way to simulate the differences between volume and batch resources. By multivariate normali-ty, X and Zi have a correlation of COR. With COR negative, this procedure results in batch resources that account for PER_BATCH % of costs; with COR positive (0.5), this PER_BATCH% represents additional volume resources. As under b., apply DENS, trun-cate and recalculate the values to obtain the altik elements for these resources.

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3. Multiply the vector RCP of dimension [1 x RCP] of rcpi elements with the RES_CONS_PAT matrix of allocation patterns altik of dimension [RCP x CO] to obtain the BMARK_COST vector of benchmark costs tck of dimension [1 x CO].

Algorithm for Simulating a Noisy Costing System

1. Pooling of RCP into a set number of ACP a. If the assignment of RCP to ACP is random, generate a random number xi between 0

and 1 for every rcpi. Allocate rcpi to acpj according to the bucket in which xi falls, i.e. for which with j = 1, …, ACP. Define set Bj = {rcpi allocated to

acpj}. Other assignment heuristics follow similar rules. b. For all such generated sets Bj and for all i for which rcpi belongs to set Bj, calculate

and place this in the jth column of the ACP vector with the activity pool costs of

dimension [1 x ACP]. For the random assignment, check that such generated vector does not contain any zeros; if so, throw observation out and start again at 1a.

2. Pooling of the resource consumption matrix RES_CONS_PAT of dimension [RCP x CO] into the aggregated consumption matrix ACT_CONS_PAT of dimension [ACP x CO].

a. If the aggregation method is average, then for each set Bj and for all i for which rcpi belongs to set Bj, calculate the average of the rows altik of [RCP x CO]. Place this row in row j of the aggregated consumption matrix ACT_CONS_PAT. This procedure ensures that the costs in the aggregated cost pool are allocated to prod-ucts based on the average consumption pattern of all resources contributing to the pool. Other indexing methods are similar except they vary the number of re-sources averaged.

b. If the aggregation method is Big Pool, then for each set Bj, find the largest rcpi contributing to this set. Place the row altik RES_CONS_PAT that corresponds to this largest rcpi in row j of the aggregated consumption matrix ACT_CONS_PAT. Thus, the costs in the aggregated activity cost pool will be allocated to products based on the consumption pattern of the largest contributing resource cost pool.

3. Applying measurement error to the elements of the consumption matrix ACT_CONS_PAT of dimension [ACP x CO] by multiplying every cell in this matrix with 1 + a percentage drawn from a uniform distribution with mean 0 and supports -MSMT_ERR and +MSMT_ERR. We vary MSMT_ERR from low (0.1 or 10%), over me-dium (0.3), to high (0.5 or 50%).

4. Multiply the ACP vector with activity pool costs of dimension [1 x ACP] thus generated with the ACT_CONS_PAT matrix of consumption patterns of dimension [ACP x CO] from (3) to calculate the cost that the noisy costing system allocates to each cost object (fck) and store this in the REP_COST vector of dimension [1 x CO].

5. The main dependent variable (and the dependents used as robustness checks) and the va-riables used as covariates can all be calculated from the thus generated data.

1 ,ij jx

A C P A C P−⎡ ⎤∈ ⎢ ⎥⎣ ⎦

∑i

ircp