Online First Version

Does a Leading Indicator Related to a Customer Improve a Firm’s Profit?
Jumpei Hamamura
Faculty of Business Administration, Momoyama Gakuin University

Accepted Paper
Received November 2, 2022
Accepted January 24, 2024
Available Online January 29, 2024

This article has been accepted for publication and undergone full peer review but has not been
through the copyediting, typesetting, pagination and proof-reading process which may lead todifference between this version and its final form.

Accepted Article
Does a leading indicator related to a customer improve a firm’s profit?

Jumpei Hamamura
Momoyama Gakuin University, Japan
Faculty of Business Administration

Jumpei Hamamura,
Corresponding author. Momoyama Gakuin University, Japan, 1-1, Manabino, Izumi-city,
Osaka 594-1198, Japan. Phone: +81 725 54 3131. Fax: +81 725 54 3202. Email id:
jhama0129@gmail.com
Acknowledgements: I would like to express a special thank you to my anonymous reviewer, Laixun
Zhao, and Masahiro Enomoto (Editors), for the very helpful and constructive comments. Earlier
versions of this research were presented in the 70th Kansai regional meeting on Japanese Accounting
Association in Kwansei Gakuin University, 2020, seminars at Kyushu University and Osaka University.
The author would like to thank participants in the conferences and seminars for their helpful suggestions.
The author is thankful to Keisuke Hattori, Tatsuo Inoue, Takaharu Kawai, Katsuhiko Muramiya, andAtsushi Shiiba for their helpful comments. This work was partially supported by JSPS KAKENHI(Grant Numbers JP18K12909 and JP21K13409), and The Japanese Association of Management
Accounting (Study Group in 2022). The usual disclaimers apply.

Accepted Article
Does a leading indicator related to a customer improve a firm’s profit?

Abstract: This study demonstrates that, in two periods, the total profit of a firm in productmarket competition decreases with a leading indicator that emphasizes consumers. Whileprevious studies in the management accounting literature have suggested that leading
indicators are useful for predicting firms’ future profits, few studies have theoreticallyinvestigated this topic. Therefore, we explore the usefulness of leading indicators to
improve firms’ long-term profit using a game theoretical approach. Consistent with
empirical evidences, our model analysis demonstrates that a leading indicator improves
firms’ profits in the second period, while it harms first-period profit and total profit due toexcessive supply in a specific economic environment.
Keywords: performance evaluation; delegation game; leading indicator; non-financial
indicator; duopoly competition

Accepted Article
1. Introduction
The choice of performance indicators is an important problem when designingperformance evaluation systems in companies. In management accounting, theperformance evaluations of internal employees are important, and furthermore, themanagers of the company are recognized in the proxy statement. Recently, stakeholders
can easily access information about performance evaluation systems of a company’s
managers via the disclosure of the integrated report. This report does not reveal theperformance indicators or their weights but discloses information about goal achievement
and managerial compensation. For example, Coca Cola Ltd. uses short-term performanceindicators (net operating revenue and operating income) and long-term incentive plans(net operating revenue, earnings per share, free cash flow, and total shareowner return
modifier) to evaluate managers.1
From the example of Coca Cola Ltd., it is evident that company owners attempt
to control managers’ behavior by using performance indicators in practice. Decisions
about performance indicators and the weights placed on them are important as thesedecisions affect the behavior of managers through compensation contracts. For example,
when a manager is evaluated only in periods of corporate social responsibility (CSR)
activities, the manager will not focus on the firm’s profit and perform in such a way as toenhance CSR via social activities. Additionally, when managers are evaluated only byfinancial performance, they will not focus on customers and instead pursue short-term
profits.
In management accounting, considering the balance between short-term and longterm decisions, it is important to manage the firm-wide performance. A Balanced Score

1

We obtained this information from Coca Cola’s Proxy Statement for 2019, p. 11 (Last accessed,
November 5, 2021) https://www.sec.gov/Archives/edgar/data/21344/000120677419000735/ko_courtesypdf.pdf

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Accepted Article
Card (BSC) with multi-level performance indicators is a typical way that companies
incorporate short-term and long-term decisions into company strategy. Additionally,
manager performance evaluations based on multi-indicators (except for BSCs) are usedin many companies to maintain a balance between short-term and long-term decisions, as
an example of a proxy statement. When a company improves the stability of long-term
profits, the value and reputation of the company will also improve in the long-term, which
promotes company sustainability.
Thus, leading indicators are frequently adopted as long-term performanceindicators in practice. For example, customer satisfaction or complaints affect theretention rates of products or services and are important for improving companies’ futurefinancial performance. Empirical management accounting research has emphasized on
the importance of these non-financial, consumer-oriented performance indicators. For
example, Ittner and Larcker (1998) finds that customer satisfaction does not only predict
future profits at the business-unit level, but it also leads to the future performance at thefirm level. Banker et al. (2000) demonstrates similar evidence in hospitality firms byanalyzing archival time-series data. In Banker et al. (2000), customer complaints provide
meaningful information about a company’s future profits. This empirical evidence
suggests that non-financial customer-oriented indicators can predict firms’ future profits.
Ittner and Larcker’s (1998) findings have important implications about the choiceof managers’ performance indicators. If performance indicators related to customers or
consumers can predict future profits at the firm level, establishing customer-oriented
performance indicators for managers can lead firms’ future profits and help managers
avoid myopic behavior. Therefore, indicators related to customers are effective forcontrolling the behavior of firm managers by encouraging them to take a longer-term
approach.

2

Accepted Article
In prior management accounting research, Ittner and Larcker (1998) and Banker
et al. (2000) empirically indicate improvements in future short-term profits byconsidering indicators related to customers. Therefore, prior literature has found thatindicators related to customers lead firms’ short-term future profits rather than long-term
total profits. Certainly, one may infer that improvements in a firm’s profits enhances
future firm value and the firm can then return this profit to shareholders. However, whena shareholder elects to hold onto stocks, they are interested in the firm’s long-term total
profit. A shareholder would prefer that a firm maintains stable profits to maximize thetotal profit in holding stocks, and therefore, this study focuses on firms’ total profit in thelong-term and analyzes the usefulness of the leading indicator. Based on the above
discussion, this study considers the following research question (RQ):

RQ: Does a non-financial leading indicator related to a customer theoretically improve
the total profit of a firm with product market competition?

This study considers the RQ using a game theoretical approach, which assumes
product market competition. In this case, one can infer that contract theory provides
useful insights to study performance evaluation, as it considers internal control byassuming a principal-agent problem. Dutta and Reichelstein (2003) employes contract
theory to analyze the effectiveness of non-financial indicators as leading indicators,
assuming a two-term contract. However, many firms face product market competition inpractice, and this factor tends to be overlooked in the management accounting research.
For example, assuming a BSC approach, when a firm incorporates multi-indicatorperformance evaluation into its strategy, a game theoretical approach that assumes
product market competition is compatible, as strategies are affected by competitor

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Accepted Article
decisions in a product market. To reinforce this fact, prior studies have analyzed managers’
performance evaluations, assuming product market competition. For example, Vickers(1985) and Fershtman and Judd (1987) used a delegation game in their analyses from amanagerial viewpoint. Furthermore, some studies examined managers’ optimal
performance indicators under product market competition (e.g., Hino and Zennyo 2017;
Hirose et al. 2020; Matsumura and Ogawa 2014; Miller and Pazgal 2005; Ritz 2008).
Additionally, based on a delegation game, several studies have analyzed relative
performance evaluation, which is a significant performance evaluation topic inmanagement accounting studies (e.g., Aggarwal and Samwick 1999; Fumas 1992;
Hamamura 2021, 2022, 2024; Hamamura and Ramani 2023; Jansen et al. 2009; Miller
and Pazgal 2001, 2002). The above studies have explored the optimal performance
evaluation system to include competitor profit in managers’ objective functions. The
improvement of competitor profit directly affects managerial performance in thesestudies. However, this study assumes a customer indicator as the performance indicator,
which is different from their approach.
In accounting studies, Hamamura (2019) considers competitor’s profit as anadditional performance indicator. When a positive weight is placed on a competitor’s
profit, it is related to firms tacitly cooperating to enhance the product market byconsidering overall industry profits. Hamamura (2019) interprets a case in which amanager is evaluated using a BSC and can affect the future profits of an industry and theirown firm by considering industry profits. It is obvious that enhancing industry profits will
have a positive effect on the future profit of the industry and on one’s own firm. Increased
industry profits lead to increased market size, and firms can obtain higher profits in alarger market. Hence, Hamamura (2019) explores the long-term behavior of managers.

4

Accepted Article
Moreover, several studies have analyzed objective functions, including consumer
surplus; these studies are different from the relative performance evaluation research.
Arya et al. (2019) conducts pioneering research in accounting, exploring disclosure
decisions in cases where managers emphasized consumer surplus. Considering consumer
surplus means emphasizing performance indicators related to the customer. Therefore,
this study examines manager contracts with owners who use consumer surplus as aleading indicator and compares those cases to non-leading indicator cases, assuming thesame performance indicators as in Arya et al. (2019).2 When the profit in the consumer
surplus case is less than the profit in another case, the adoption of a leading indicator does
not improve the total profit of a firm in this model.
We assess the usefulness of including consumer surplus in the objective functions,assuming quantity competition and a two-period game. Consequently, in equilibrium, themain model demonstrates that each firm includes consumer surplus in the objectivefunctions as a leading indicator in a specific economic environment. However, thisequilibrium is not Pareto efficient in the specific economic condition. As the adoption ofa leading indicator enhances demand-enhancing investment in the first period andremains in effect in the second period, the profit in the second period will improve.
However, the profit in the first period will decline because the manager has an incentive
to exceed supply and investment by emphasizing consumer surplus in a specific economic
environment. As the balance of these trade-off effects is altered by exogenous variables,
the total profits of firms in two periods decline in a specific economic environment.
A crucial factor in this outcome is excessive supply, which arises from productmarket competition because firms attempt to obtain large market shares by a credible

2

This objective function, which is considered by Arya et al. (2019), has been analyzed in the economic
research as a delegation game (e.g., Chen et al. 2016; Hino and Zennyo 2017; Kim et al. 2019).

5

Accepted Article
threat. Certainly, while excessive supply increases the total cost of production andinvestment, the reduction in price from excessive supply has a serious effect on firm profit
in our model. Hence, the adoption of a leading indicator has an impact on product market
competition and an owner chooses a performance indicator by considering competition.
While managers ordinarily exercise customer-friendly management techniques toimprove customer-oriented performance indicators through costly investments, our result
is obtained from the impact of excessive supply. This study considers that investmentsthat continue to have demand-enhancing effects in the next period represent long-term
benefits from the investment. When the investment does not have an impact on future
demand functions, we can demonstrate our important result. Without an investment that
continues to have this demand-enhancing effect, the model of this study is the choice ofperformance indicator, which is not related to long-term benefits. Hence, this study
considers investment that continues its demand-enhancing effect in the next period.
This result has some implications for the choice of performance evaluation in
management accounting research. Obviously, future profit is improved by a leading
indicator, as shown by Ittner and Larcker (1998) and Banker et al. (2000). However,excessive competition may arise if a leading indicator is adopted in the first period.
Consequently, the profit in the first period with the leading indicator will decline, andtherefore, owners should carefully adopt a leading indicator depending on the economic
environment.

2. Basic model
We consider a two-period model. There are two firms, Firms 1 and 2, in a final productmarket, and they engage in quantity competition. In the first period, both firms decide on

6

Accepted Article
costly investments, which have the effect of enhancing demand (e.g., advertising). The
demand function of firm 𝑖 in the first period is as follows:
𝑝

𝑎

𝐼

𝛾𝐼

𝑞

𝑞 ,

(1)

is the market price of firm 𝑖 in period 𝑡 ∈ 1, 2 , 𝑞 is quantity, 𝐼 iswhere 𝑝demand-enhancing investment, and 𝑎 is positive constant. Hereafter, we represent
𝑖, 𝑗

1,2 , 2,1 . Additionally, 𝛾 ∈ 0,1 represents the spillover effect, which is thecompetitor’s demand-enhancing investment. Advertising does not have a perfectspillover effect on the competitor’s product. Hence, this study assumes imperfectspillover.
In the second period, investments in the first period remain at the discount rate𝑟 ∈ 0,1 , as follows:
𝑝

𝑎

𝑟 𝐼

𝛾𝐼

𝑞

(2)

𝑞 .

It is important that the investment effects of the first period remain in the second period
because the demand-enhancing effect of advertising remains even after the investment.
Hence, we assume the demand-enhancing effect imperfectly remains in the next period.
If this study does not assume a remaining effect, decision-making in the second period
does not involve a relationship between periods. Without the remaining effect, it does notmake sense to analyze the long-term model; this study assumes this effect.
Both firms produce and sell the final product with marginal cost 𝑐. This study
assumes marginal cost 𝑐 to be 0 for simplicity. The profit function of firm 𝑖 in the first
period is as follows:
𝜋

𝑝 𝑞

1
𝑘𝐼 ,
2

(3)

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Accepted Article
where 𝑘𝐼 /2 is the investment cost and 𝑘

0 is efficiency of the investment. In thesecond period, both firms do not invest to enhance demand. Hence, the profit function offirm 𝑖 in the second period is as follows:
𝜋

𝑝 𝑞 .

(4)

This study assumes that owners delegate decision rights of the quantity in the productmarket to managers.
While the owners aim to maximize total profit Π𝜋

𝜋 , manager

performance is evaluated by owners using other performance indicators. Based on
previous delegation game studies, the manager is evaluated by the objective function 𝑂 ,which is chosen by the owner. This study assumes that the contract between the ownerand manager is renewed in every period. Hence, the manager is a short-run player who
maximizes objective functions in every period to obtain high compensation. Here, we
assume the objective function of firm 𝑖’s manager in the first period is as follows:𝑂𝜋𝛼 𝐶𝑆 ,(5)

where 𝐶𝑆 is the consumer surplus in period 𝑡 and the weight placed on the consumer
surplus, 𝛼 ∈ 0,1 , is the exogenous variable. This study assumes 𝐶𝑆
2𝑞 𝑞𝑞/2 in period 𝑡, based on Dixit (1979) and Singh and Vives (1984).

𝑞

Therefore, the owner evaluates the manager considering consumer surplus in the first
period. The weight placed on the consumer surplus is an exogenous variable as it is notimportant to choose the level of 𝛼, while it is important whether 𝛼

0 in this study.

Hence, this study assumes the level of 𝛼 to be an exogenous variable and chosen by𝛼

0 or 𝛼0.

Prior literature proposed that when the emphasis is on the consumer or customer,
it enhances firms’ future profits (e.g., Ittner and Larcker 1998). This study analyzes
8Accepted Article
whether the profit of the second period and the total profit are improved by emphasizing
consumer surplus (𝛼0) in the first period. In the second period, the owner would wantto maximize the profit after adoption of the leading indicator and prior literature considers
only financial performance as an independent variable (Banker et al. 2000; Ittner andLarcker 1998), this study assumes that the manager is evaluated only by profit in thesecond period. Hence, the manager of firm 𝑖 in the second period is evaluated by thefollowing objective function:
𝑂

𝑝 𝑞 .

(6)

The timeline of this model is as follows: in the first period, the owners decide
whether 𝛼

0 or 𝛼0 on date 1. Next, on date 2 in the first period, managers decideon the demand-enhancing investment and quantity in a product market. On date 3 in thefirst period, managers are rewarded by the owner. In the second period, managers decideon the quantity of the product on date 1. On date 2 in the second period, managers are
rewarded by the owner. This study assumes all the endogenous variables are observable
after the decision. The notations are presented in Table 1.
Here, with exception of the analysis in the monopoly case, this study specifies
𝛼, 𝑘, 𝑎, as 𝛼

𝛼

𝛼, 𝑘

1, and 𝑎

1 for simplicity in our main analysis. These

specifications do not seriously impact the outcome of this study, and it is difficult toanalyze and interpret the outcome without these specifications. Additionally, when 𝛼
𝛼

𝛼, 𝑘

1, 𝑎

1, 0

𝛼

1/4, and 0𝛼𝛾 are satisfied, all outcomes are

positive in our model. In this study, we consider our model under the following
assumptions.

9Accepted Article
Table 1. Notations
𝜋
Π
O
i
j
t
p
q
I
CS
𝛼
k
r
a
𝛾
L
NL
PI

Short-term profit
Total profit for a firm in two periods
Objective function of managers
Subscript that indexes a player
Subscript that indexes a firm other than player i
Subscript that indexes period (𝑡 ∈ 1,2 )Retail price
Quantity
Demand-enhancing investment
Consumer surplus
Weight placed on consumer surplus (𝛼 ∈ 0,1 )Efficiency of investment greater than 0
Discount rate of investment in the second period (𝑟 ∈ 0,1 )Positive constant greater than 0
Spillover effect, which is the competitor’s demand-enhancing investment (𝛾 ∈0,1 )Leading indicator caseNo leading indicator case
Performance indicator chosen by the owner (𝑃𝐼 ∈ 𝐿, 𝑁𝐿 )Parametric Assumption. This study specifies 𝛼, 𝑘, 𝑎, as 𝛼𝛼𝑎𝛾 to ensure positive

1 . In addition, we assume that 0𝛼

1/4 , and 𝛼𝛼, 𝑘1, andoutcomes in our model.

We present the reason for this assumption in the Online Appendix.
The leading indicator in this study may not correspond to that in prior studies
because prior empirical studies do not analyze consumer surplus as a leading indicator(e.g., Ittenr and Larcker 1998; Banker et al. 2000). However, we consider the consumerrelated indicator (one of the leading indicators) as prior studies considered it, andconsumer surplus is a consumer indicator because improving consumer surplus increases
the utility for consumers. Prior studies have interpreted a firm that emphasizes consumer

10

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surplus as a customer-friendly firm (e.g., Ying, Li, and Xuemei 2015). Therefore, thisstudy assumes that consumer surplus is an indicator related to customers.

3. Monopoly caseFirst, before analyzing the basic model, we explore the impact of the leading indicator on
total profit in the monopoly case. It is important to analyze the monopoly case, because
it is one of the benchmark cases of our model. In this case, we consider the demand
function in the first period as follows:
𝑝

𝑎

𝐼

𝑞 .

(7)

In addition, the demand function of the second period is as follows:
𝑝

𝑎

𝑟𝐼

𝑞 .

(8)

In this case, consumer surplus that is included varies as 𝐶𝑆𝑞/2, because

this firm does not have competitors and the quantities of this firm directly impact
consumer surplus. In the monopoly case, we consider the endogenous decision of 𝛼
before the decision of 𝐼.
By backward induction, we obtain the following outcomes:
𝐼

𝑞

1
1

𝛼

,

1
1

𝛼

,

𝑞

1 𝑟 𝛼
,
2 1 𝛼

𝑝

1,

𝑝

1 𝑟 𝛼
,
2 1 𝛼

(9)

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Accepted Article
𝜋

1 2𝛼
,
2 𝛼 1

𝜋

1 𝑟 𝛼
.
4 1 𝛼

Because when 𝛼

1/2 is satisfied, all outcomes are positive, the Parametric

Assumption ensures the positive outcome in this case.
In this case, we consider Πanalysis, Π
1

2𝛼

Π ∣
𝛼 / 2

𝜋

𝜋

is satisfied under 0𝛼𝑟

and analyze ΠΠ ∣. From the

𝛼

1

𝛼

1/2 and

𝛼 / 2

1 . This outcome implies that the monopoly firm

adopts the leading indicator when the remain effect of the investment is large. We
summarize this outcome as a following lemma.

Lemma 1. In the monopoly case, under 0
1

2𝛼

𝛼 / 2

𝛼

𝑟

𝛼

1/2 and

1

𝛼 / 2

𝛼

1 the leading indicator is adopted by the owner.

This section confirms that the positive effect of the leading indicator is importantand the usefulness of the long-term behavior coincides with prior management accounting
studies (e.g., Banker et al. 2000; Ittner and Larcker 1998). The next section considers theimpact of competition on a firm’s total profit in two periods with the leading indicator.

4. Leading indicator harms total profit under duopoly competition
In this section, we analyze the basic model that was constructed in Section 2. First, weconsider the case in which both firms choose 𝛼

0 case as Case 1 and 𝛼

0 case as

Case 2. After that, we compare the total profit of Case 1 to that of Case 2 and demonstrate12

Accepted Article
the combinations of payoff in these cases. In addition, endogenously chosen 𝛼 (𝛼or 𝛼00) is analyzed in the next section.

4.1. Case 1: Each firm is evaluated only by profit
First, by backward induction, we identify the equilibrium strategies and profit as follows.
𝐼

1

,

2

𝑞

,

𝑞

,

𝑝

,

𝑝

,

𝜋

,

𝜋

,

𝛾

,

1

,

2

𝛾

2

𝛾 𝑟 1
3 2 𝛾
1

𝛾

,

(10)

,

2

𝛾

2

𝛾 𝑟 1
3 2 𝛾
1

𝛾

.

,

2 2

𝛾

2

𝛾 𝑟 1
9 2 𝛾

𝛾

,

where superscript 𝑁𝐿, 𝑁𝐿 represent the case in which both firms do not use the leading
indicator in the performance evaluation of managers. Hereafter, combinations of theperformance indicator, 𝑃𝐼, of firm 𝑖 and 𝑗 are denoted as 𝑃𝐼 , 𝑃𝐼 . Representing thecase with the leading indicator as 𝑃𝐼
Additionally, Π,𝐿 and without the leading indicator as 𝑃𝐼

is defined as Π

,

𝜋

,

𝜋

,

. Here, when the

Parametric Assumption is satisfied, all outcomes in this section are positive.

13

𝑁𝐿.

Accepted Article

4.2. Case 2: Both firms are evaluated by the leading indicator
We solve the model with the 𝛼 ∈ 0,1 case. By backward induction, we consider thequantity decision in the second period. Differentiating the objective function of firm 𝑖 in
the second period, we obtain the first order condition as follows:

𝑞

1

𝑞

𝑞

𝑟 𝐼
2

𝛾𝐼

(11)

.

From this outcome, we obtain the optimal strategy of firm 𝑖 in the second period.
1

𝑞

𝑟

2

𝛾 𝐼

1

2𝛾 𝐼

3

From Eq. (12), when 𝛾 satisfies 0

𝛾

(12)

.

1/2, the quantity of firm 𝑖 decreases as thecompetitor’s investment increases.
Next, firms decide the level of investment and sales quantities in a product market.
Hence, considering the quantity and investment decision in the first period and obtaining
the best response function of firm 𝑖 toward the competitor’s strategy is as follows.
1

𝑞 ,𝐼 ,𝐼

𝑞
𝐼 𝑞

1

𝛼 𝑞
2 𝛼

𝐼

𝛾𝐼

(13)

𝑞 .

From this outcome, we obtain
𝑞

,

𝑞

,

2
2

1
2𝛼

𝛾

,

2𝛼 𝛾 𝑟 1
3 2 2𝛼 𝛾

𝛾

,

,

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𝐼

1
2𝛼

,

2

𝛾

,
(14)

1

,

𝑝

2

𝑝

,

𝜋

,

𝜋

,

2

2𝛼
,
2𝛼 𝛾
2𝛼 𝛾 𝑟 1
3 2 2𝛼 𝛾
1

2 2
2

𝛾

,

4𝛼
,
2𝛼 𝛾

2𝛼 𝛾 𝑟 1
9 2 2𝛼 𝛾𝛾,where superscript 𝐿, 𝐿 represents that both firms adopt the leading indicator. Because
when 𝛼 satisfies 0𝛼

1/4 , all outcomes of this model are positive, under theParametric Assumption, we obtain the positive outcomes. Additionally, we define
Π

,

≡𝜋

,

𝜋

,

.

4.3. Comparing Case 2 with Case 1
Here, we compare the total profits of Cases 1 and 2. First, consider 𝜋 ,
𝜋,

,

𝜋,

4𝑟𝛼 1

,

𝜋,

,

.

,

𝛾 𝑟 1

From Eq. (15), 𝜋 ,,𝛾 2 𝛼 𝛾2 𝛾 2
9 2 𝛾 2 2𝛼 𝛾
𝜋,

,

2𝛼

𝛾

0.

(15)

is obtained. Therefore, the leading indicator improves

the future profit of firms in our model and we obtain the following lemma:15

Accepted Article
Lemma 2. In product market competition, the profit of the second period improves fromthe leading indicator in the first period.

Additionally, under the Parametric Assumption, we consider 𝜋 ,

,

𝜋,

,

as follows.
,

𝜋,

𝜋,

,

2𝛼 2 𝛼 3𝛾 𝛾
2 𝛾 2 2𝛼 𝛾

(16)

0.

We obtain the following lemma from this outcome.

Lemma 3. In product market competition, the profit of the first period decreases from theleading indicator in the first period.

The economic intuition behind this outcome is as follows. First, Lemma 3 is obtained byexcessive supply from the leading indicator related to the customer for the same reason
as in the monopoly case. In the competitive case, the effect of a decreasing price is larger
than that in the monopoly case because the market price also decreases from thecompetitor’s excessive supply. With this negative effect, the profit intensity of the first
period decreases. In addition, the difference between 𝛼

0 and 𝛼0 is represented

as the level of investment. When the level of investment in the first period is large, firms
can enhance the demand in the next period, thereby improving the profit in the second
period. Therefore, the comparison of levels of investment in the first period is as follows:
𝐼

,

𝐼

,

2

2𝛼
𝛾 2 2𝛼,Under the Parametric Assumption, 𝐼
Next, we consider Π

,

Π

(17)

.

𝛾

𝐼
,

,

is obtained in this outcome.

and obtain the following outcome.
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Accepted Article
Π

where
𝛼

,

Π

Φ≡9 2

𝛾 . From Φ
9𝛾 3

𝛼

,

𝛾

9 2
𝛼

𝛾

2𝛼

3𝛾

2𝑟 2

2𝑟 2 𝛾 2 𝛾 𝛾
9 4𝑟 2 𝛾 𝛾,

Π,1/4. For example, under 𝑟because we assume 𝛼
𝛾

𝛾

(18)

,

𝛾 2

𝛾

𝛾

2𝑟 1

2𝑟 2 𝛾 1
2𝑟 1 𝛾

𝛾

18

𝛾

2

0, whenis satisfied, we obtain Π
obtain 𝛼2𝛼Φ
𝛾 2 2𝛼

0, 𝛼

≡ 𝛼,

(19)

straightforwardly. Depending on 𝛾 and 𝑟, we
0.1 and 𝛾

0.2, 𝛼 ≃1.23 (in this case,

0 is obtained). This implies that, under 𝑟

0.1 and0.2, we can ensure the existence of 𝛼 ∈ 𝛼, 1/4 . Therefore, the leading indicatordoes not improve firms’ total profit under the specific condition. Based on this outcome,we propose the following proposition.

Proposition 1. Under the Parametric Assumption, there exists the case in which
Π

,

Π

,

is obtained.

Note that one can obtain the case in which 0𝛼

1/4 is satisfied, depending on the

combinations of 𝑟 and 𝛾. In this case, for 0

𝛼

𝛼, Π

,

Π

,

is obtained.

This proposition implies that the leading indicator harms the total profits in a
specific case. This outcome is obtained from the trade-off between the positive andnegative effects of the leading indicator. The leading indicator improves the profit in thesecond period by increasing the level of demand-enhancing investments but decreases the
profit in the first period as a result of excessive supply. The balance between effects is
decided by the combination of parameters. When the spillover effect is small, the positive17

Accepted Article
effect is weakened because the competitor’s investment does not impact demand
seriously. This weakened spillover effect does not enhance the positive effect of the costly
investment. For this reason, when 𝛾 is small, the positive effect of enhancing profit in
the second period cannot exceed the negative effect of decreasing profit in the first period.
Consequently, the total profit will decline.
Regarding the numerical example, this study considers the impact of exogenous
variables. In this analysis, we fix 𝑟Π,

0.65, 0.72, 0.78 and draw a region of Π,in Figure 1.

𝒓

Figure 1. Plot region Π

,

𝟎. 𝟔𝟓

𝟎. 𝟕𝟐

𝒓

,

decreases as 𝑟 increases because theFrom this figure, the region of Π

𝒓

,

Π

Π

,

as 𝑟 chenges.

𝟎. 𝟕𝟖

impact of the positive effect in the second period increases by the remaining effect ofinvestment. In addition, when 𝛾 is large, the spillover effect, which has a positive impact
on each firm’s demand, improves. Therefore, a large 𝛾 improves the positive effect of
the leading indicator.
We demonstrate the case in which the total profit of the firm in the delegation
game suffers as a result of the leading indicator. However, this outcome is not the18

Accepted Article
equilibrium case of endogenous 𝛼. Therefore, we consider the choice of 𝛼

0 or 𝛼0 in the next section.

4.4. Endogenous choice of whether firms use the leading indicator
We demonstrate that both firms choose the adoption of the leading indicator and it
negatively affects firms’ profit. Consider the asymmetric case where one of the firms
adopts the leading indicator as the equilibrium strategy and the other firm does not. In
𝑃𝐼 , 𝑃𝐼

this subsection, we analyze the case where

𝑁𝐿, 𝐿

and obtain thefollowing outcome.
𝑞

,

𝑞

,

𝑞

,

𝑞

,

𝛾

𝛼
,
𝛼 𝛾

𝛾
𝛾 2

𝛼
,
𝛼 𝛾

1
3

𝑟 𝛾 1 𝛾
3𝛾 2

𝛾 2

𝐼

,

𝐼

,

3𝑟𝛼 1

𝛾

𝛼
,
𝛼 𝛾

𝛾

𝛼
,
𝛼 𝛾

𝛾 2

𝛾

,

𝑟𝛾 1 𝛾𝛾 2
3𝛾 2 𝛼 𝛾

𝛾
𝛾 2

3𝛼 1
𝛼 𝛾

𝛼

𝛾

,

(20)

𝑝

𝛾

,

𝑝

𝛾 2
,

𝛼
,
𝛼 𝛾

𝛾 1 2𝛼𝛼,
𝛾 2 𝛼 𝛾19

Accepted Article𝑟 𝛾 1 𝛾
3𝛾 2

1
3

𝑝

,

𝑝

,

𝜋

,

𝜋

,

𝛾

𝜋

,

3𝑟𝛼 1

𝜋

,

3𝑟𝛼 1

𝛾

𝛾
2𝛾 2

𝛼
𝛼

3𝛼 1
𝛼 𝛾

,

𝑟𝛾 1 𝛾𝛾 2
3𝛾 2 𝛼 𝛾

𝛾

𝛾

𝛼

𝛾

𝛾 2

𝛼

𝛾

𝛾 2

𝛼

𝛾

,

,

𝑟𝛾 1 𝛾
9𝛾 2 𝛼𝛾

𝛼,𝛼 𝛾 1 4𝛼2𝛾 2 𝛼 𝛾

3𝑟𝛼 1

𝛾

,

𝛾

𝑟𝛾 1 𝛾
9𝛾 2 𝛼.

𝛾

All outcomes are positive under the Parametric Assumption. From this outcome, we
obtain the Parametric Assumption.
,

From this outcome, Π
,

Π

,

is

2𝛼Ψ
𝛾 𝛾 2

,

Π

Π

9 2

𝛼

(21)

,

𝛾

where

Ψ≡ 2

𝛾 𝛾 9 1

𝛾

2𝑟 6

11𝛾

8𝛾

2𝛾

𝑟 6

4𝛾

𝛼 9 1

5𝛾

𝛾

2𝑟𝛾 6

11𝛾

8𝛾

2𝛾

2𝑟 9

29𝛾

14𝛾

2𝛾

4𝛾

. When Ψ

0 is satisfied, we obtain Πother words, when 𝛼2𝛾 𝛾 9 1

2𝛾

4𝛾

5𝛾

4𝛾

27𝛾

29𝛾

Π

,

4𝛾

/ 9 1
14𝛾

2𝛾

𝛾

𝛾

2𝑟 6
2𝑟𝛾 6

is satisfied under 𝛼

11𝛾
11𝛾

,

8𝛾
8𝛾

20

Π

2𝛾

4𝛾

27𝛾

2𝛾

,

. In
𝑟 6

2𝑟 9

1/4 , we obtain Π. Hence, when the competitor adopts the leading indicator, 𝑃𝐼

response strategy.

2𝛾,

𝐿 is the best-

Accepted Article,

In addition, Π
Π

,

8𝛾

35𝛾

13𝛾

2𝛾

2𝑟𝛾 10

2𝛼X
𝛾 2

19𝛾

6𝑟 1

𝛾

4𝑟 1

4𝛾

4𝛾

𝛼 9 2

5𝛾

3𝛼 3

2𝛾

6𝑟 6

13𝛾

12𝛾

13𝛾

3𝛾

2𝑟 3

satisfied, we obtain Π

(22)

𝛼

𝑟 6

,

,

Π

2𝛼

,

9𝛾 2

X ≡ 3𝛼 3

11𝛾

is

,

Π

where

,

Π

𝛾

𝛾 𝛾

5𝛾

2

8𝛾

, and 𝑃𝐼𝛾 𝛾 9 1𝛾𝛾

2𝑟𝛾 24

9𝛾
8𝛾

𝛾
15𝛾

3𝛾

2𝑟 6

6𝛾
. When Χ

0 is

𝐿𝐼 is the best response strategy. We candemonstrate the existence of the case in which Χ

0 is satisfied.

Based on the above discussion, under the Parametric Assumption, when Ψand Χ

0 are satisfied,

𝑃𝐼 , 𝑃𝐼𝐿, 𝐿

0is chosen in equilibrium. However,

because it is difficult to obtain the explicit outcome about the comparison among profits,
we numerically highlight the case in which leading indicators harm the firm’s profit under
the specific economic environment.
We consider the condition of Ψ ≡ 2

𝛾 𝛾 9 1

𝛾

2𝑟 6

11𝛾

2𝛾

𝑟 6

2𝛾

𝛼 9 1

5𝛾

𝛾

2𝑟𝛾 6

11𝛾

8𝛾

2𝛾

2𝑟 9

27𝛾

29𝛾

14𝛾

2𝛾

𝛼

2

𝛾 𝛾 9 1

𝛾

2𝑟 6

11𝛾

8𝛾

2𝛾

2𝑟𝛾 6

11𝛾

4𝛾

𝑟 6

2𝛾

4𝛾

4𝛾

/ 9 1

5𝛾

4𝛾

𝛾

2𝑟 9
In this case, showing 𝛼
Π

,

Π

,

4𝛾

27𝛾

29𝛾

14𝛾

4𝛾

0 under 𝛼

2𝛾

8𝛾
≡𝛼

8𝛾

1/4.

2𝛾
.

(23)

1/4, we can confirm that there exists the case in which. To demonstrate the case wherein 𝛼

210, we specify the numericalAccepted Article
example as 𝑟

0.1 and 𝛾

outcome satisfies 𝛼

0.2 . In this case, we obtain 𝛼≃

1.84197 . This𝛾; therefore, there exists the case in which Ψ

0. Additionally,

from the coefficient of 𝛾, when 𝛾 is sufficiently large, we obtain a positive 𝛼 , which
may exceed 1/4. Even if we organize by 𝛾, we can obtain 𝛼

1/4. We do not

specify the condition of 𝛾 because it leads to complex conditions. However, we canobtain important outcomes numerically. Under 𝑟
1.71468𝛼 2.388787
in 𝛼

1.29686𝛼 / 1.8

0.1 and 𝛾

𝛼 , and Ψ|

0.2, we obtain Ψ. ,.

0 is satisfied

1/6.
Next, we demonstrate the existence of the case in which Χvariables as 𝑟
2.388787

0.1 and 𝛾

13.683168𝛼

negative under 𝛼0.2 . In this case, we obtain Χ|

20.3712𝛼

. ,

.

≃

9.3072𝛼 , and this outcome is always

1/4.

From above discussions, when we specify 𝑟 and 𝛾 as 𝑟
we obtain Π

0, specifying the

,

Π

,

and Π

,

Π

,

0.1 and 𝛾

0.2,. This outcome implies that an

equilibrium exists in which both firms adopt leading indicators under the specificeconomic environment. We summarize our analysis as a following observation.

Observation 1. Under the specific economic environment, there exists a case in which
both firms adopt the leading indicator in equilibrium.

𝑃𝐼 , 𝑃𝐼

Additionally, in theenvironment of Π

,

Π

𝐿, 𝐿
,

case, we can obtain the specific economic. Therefore, the combination of payoffs in equilibriumis the same as in the prisoner’s dilemma and is not a Pareto-efficient outcome. We focus
on this case based on the numerical analysis.

22

Accepted Article
Using Eq. (19), we demonstrate that both firms adopting the leading indicator
leads to a Pareto-optimal outcome. Considering the same specification of the variables in
Observation 1 ( 𝑟

0.1 and 𝛾

0.2 ), we obtain that Π

,

Π

,

under thefollowing case.
Π

,

Π

,

≃

𝛼 0.208 0.1696𝛼
0.9 𝛼This outcome implies that Π

,

Π

(24)

0
,

is obtained in a specific economic

environment. Consequently, we obtain the following observation.

Observation 2. Under the specific economic environment, there exists a case in which
both firms are not a Pareto-efficient combination of payoffs in equilibrium.

This study demonstrates that when the owner can decide whether to adopt theleading indicator and both firms adopt it, it does not improve the long-term profit of thefirm in specific economic environments. The driving force of this outcome is that theleading indicator can act as a commitment device. When the firm emphasizes consumer
surplus by the leading indicator, the firm will supply excessively in a product market.
Because this study considers quantity competition, the same as in Arya et al. (2019), eachfirm wants to obtain the first mover advantage. In this case, emphasizing consumer
surplus is a commitment device to choose an aggressive strategy in a quantity competition
because it enhances quantity in a market. As a result, each firm chooses adoption of theleading indicator to threaten the competitor by excessive competition.
Ittner and Larcker (1998) and Banker et al. (2000) empirically demonstrated that
non-financial indicators as leading indicators improve the future profit of firms. In
management accounting, firms use leading indicators to achieve financial performance23

Accepted Article(e.g., BSC). However, the main result of this study suggests that while short-term profit
improves, long-term profit does not improve from the leading indicator when the firm
faces competition in a product market. The main result of this study implies that adoptionof the leading indicator does not always improve the long-term total profit of the firm,
which is important for firms interested in long-term sustainability and in returning profits
to shareholders. The implication of this is that the owner must heed the economic
environment and choose the appropriate performance indicator.
In addition, it is interesting that while the adoption of the leading indicator is
explained as a long-term concern, this study demonstrates the case in which the long-term
profit decreases from the leading indicator. Therefore, the leading indicator is not always
linked to future financial performance. Obviously, the firm loses profit from excessively
emphasizing long-term decisions and the firm’s profit will suffer in the long-term fromthis negative effect.
Additionally, our results explain the decline in profit for Japanese companies. In
the 1990s, management accounting research explored long-term incentives in Japanesecompanies (e.g., Cooper and Slugmulder 1999; Gietzmann 1996). However, in the 2010s,
Japanese companies did not symbolize good business because they did not sustain highprofits due to market competition from foreign companies. Our model captures therelationship between time for patience and benefit of success, which is emphasized by
Japanese firms that provide long-term profits.
Nowadays, these managerial performance indicators are disclosed in proxystatements, indicating that many managers are evaluated by non-financial indicators as
leading indicators. The adoption of these leading indicators is an area of keen interest in
management accounting practice and management accounting research should examine
this topic further in future research.

24

Accepted Article
5. Additional analysis: Managers also emphasize consumer surplus in the second
period under leading indicator

In this analysis, we assume 𝑂𝜋𝛼 𝐶𝑆 under the leading indicator case. In thissubsection, we assume Parametric Assumption to solve our model explicitly. We can use
the outcome in Section 4.1 to consider the non-leading indicator case. Therefore, in thissection, we analyze the cases of 𝐿, 𝐿

and 𝑁𝐿, 𝐿

for the symmetry of objectivefunctions. Thus, using Parametric Assumption, we obtain following observations basedon the numerical analysis.

Observation 3. When the Parametric Assumption is satisfied, firms adopt the leading
indicator in equilibrium in a specific economic environment.

Observation 4. When both firms adopt a leading indicator, there exists the case in which
the combined payoff is not Pareto optimal in this equilibrium.

Proof. See Online Appendix.

This additional analysis indicates that our outcome is robust when managers emphasize
consumer surplus in the second period under the leading indicator. Compared to previous
outcomes, this observation implies that the additional leading indicator leads to more
excessive surplus and investment in the second period. Therefore, assuming the leading
indicator in the first period, we can analyze its impact. In particular, in this case, the casewhere the leading indicator harms firms’ total profit is expanded. The profit of the second25

Accepted Article
period decreases as 𝛼 increases, because firms commit to aggressive strategies in thesecond period as a result of the leading indicator. Therefore, our main result is robust.

6. Discussion and conclusion
Assuming the effect of demand-enhancing investment in the first period remains in thesecond period in the context of product market competition, this study considers whether
leading indicators contribute to total profit. The results of the model demonstrate that theleading indicator does not improve total profit in a specific economic environment. Whilethe leading indicator improves profit in the second period, it lowers profit in the first
period because of excessive supply. The balance of this trade-off affects total profit.
This result has important implications in management accounting research. For
example, Ittner and Larcker (1998) and Banker et al. (2000) find empirical evidence thatthe leading indicator has an important impact on the future profit of a firm. Our result
theoretically supports this empirical evidence using a game theoretical approach,assuming product market competition. Hence, this study contributes theoretical evidence
to the empirical findings in leading indicator investigations. In addition, this study
considers total profit in the long period, discussing the usefulness of the leading indicatorin product market competition.
This study has several limitations. First, we identify some exogenous variables tothe numerical variables in the equilibrium strategy. While these variables should be
generalized in future studies, this study demonstrates an important specific case. Second,
this study assumes that the competitor’s performance indicators are observable. While itis generally difficult to observe a competitor’s internal strategies, this study refers toproxy statements in the United States, which affect the observability of performance26

Accepted Article
indicators. Hence, it may be reasonable to assume that in the presence of proxy statements,
firms would know their competitor’s performance indicators. It would be promising,
however, to identify strategic alternatives for when performance indicators are notcommon knowledge, as establishing leading indicators would be beneficial for both firms.
Third, we consider the exogenous weight placed on the leading indicator. Therefore,
future research should consider endogenous weight. In particular, uncommon weight inboth firms and during two periods needs to be considered. This analysis will be useful inunderstanding the leading indicator. Lastly, one may infer that while we refer to consumer
surplus as a leading indicator, it does not correspond to the definition in empirical studies.
Therefore, we need to consider other performance indicators in future research.

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