DP2016-13

Does Physical Exercise Affec t T ra deoffs
between Fixed Pa y and
Perform ance-related Pay for
Individ uals?
Weiyi ZHANG
Hiromasa TAKAHASHI
Junyi SHEN
March 24, 2016

Does physical exercise affect tradeoffs between fixed pay and performance-related pay
for individuals?

Weiyi Zhang
Graduate School of Economics, Kobe University
Hiromasa Takahashi
Faculty of International Studies, Hiroshima City University
Junyi Shen*
Research Institute for Economics and Business Administration, Kobe University
School of Economics, Shanghai University

Abstract
Much of the literature on performance-related pay has discussed the relationships withrisk attitude, job satisfaction, sorting effects, amongst other factors. This paper focuses on therelationship between individual preferences for physical exercise or sports and the tradeoff
between fixed and performance-related pay. First, a choice experiment is used to identify theindividual preference for payments, and the tradeoff between fixed and performance-related
pay. Next, OLS regression models are used to link the tradeoff with individual preference forphysical exercise or sports. The results show that such a preference has a positive andsignificant influence on individuals’ tradeoff of payments. For individuals who like physicalexercise or sports more, who are better at them, and who take part in them more frequently,
are more likely to prefer performance-related pay.
Keywords: physical exercise; sports; fixed pay; performance-related pay; tradeoff
JEL Classification: C35, J33, Z22* Corresponding author. Junyi Shen. Research Institute for Economics and Business
Administration, Kobe University, 2-1 Rokkodai, Nada, Kobe 657-8501, Japan. Tel/Fax: +8178-8037013. Email: shen@rieb.kobe-u.ac.jp

11. Introduction“Every man's work, whether it be literature or music or pictures or architecture ofanything else, is always a portrait of himself.”--Samuel Butler 1
The preference for payments can be seen as a portrait of oneself, showing people’s
potential taste.
Nowadays, flexible payment systems have become a central topic at firms. Generally,
there are three types of payment given to employees by firms: pure fixed, pure performancerelated, and mixed, combining fixed and performance-related, payments (Shen et al., 2014).
For the first, employees only receive fixed salaries without any flexible bonus. For the second,also called piece-rate payment, employees’ salaries are dependent on their outputs. The third
is a combination of the first two in that a part of employee salaries is fixed and the rest isdetermined by their outputs. These three kinds of payments each have advantages anddisadvantages. The fixed payment is stable, but too stable to make more money. The
performance-related payment can encourage employees to work more and obtain more:
however, it provides no stability and can be stressful to employees. Yeh et al. (2009) showedthat employees under a performance-based system have the longest working time, highest
level of job control, and highest percentage of employees who endured high stress at work.
The mixed payment has both the merit and demerit of the other two payments. Given that thepreferences for payment schemes differ between individuals, firms need to know whichscheme their employees prefer. A suitable scheme that can maximize each employee’s utility,
and consequently his/her output, is not only welcomed by employees but also profitable forfirms.
The individuals’ preference for payment schemes is usually unobservable and hard tomeasure. However, some aspects of individuals’ preference and/or behavior that might reveal
their preferred payment schemes are relatively easy to observe and measure. Therefore,
discovering these aspects is extremely important for both academics and practitioners
designing employee preferred payment schemes.
Much of the existing literature has discussed the relationship between payment schemes
and some individual attributes, such as risk preference, and job satisfaction, amongst otherthings. Performance-related pay is always the focus of this literature. Performance-related pay
has been proved to increase employees’ productivities and earning (Booth & Frank, 1999;
Lazear, 2000; Lemieux et al., 2009). Some studies have pointed out that besides increasing
the productivity of employees, performance-related pay can also create a sorting effect thathelps firms to attract more productive and high-ability employees (Lazear, 1999; Origo, 2009;
Stefanec, 2010).
1

Samuel Butler was a Victorian-era English author and novelist.

2Given that most people have different risk preferences, their preferences for the payment
system per se and the magnitude of the tradeoff between fixed pay and performance-related
pay should be different. It has been pointed out that risk lovers prefer performance-related
payment, and risk averse individuals value fixed payment more highly (Shen et al., 2014).
Further, Leonard et al. (2013) showed that greater tolerance of financial risk, and more patient
time preferences 2, among low-income ethnic minority population are linked with greater
physical fitness. Moreover, women are less risk loving than men, and women in permanent
jobs are more risk loving than women in temporary ones (Mauro & Musumeci, 2011).
People’s risk preferences are changeable according to the nature of the performance-related
payment. Kuhn & Yockey (2003) indicated that performance-related payment is more often
preferred by employees when the salary depends on individual rather than collective or teamperformance and employees are more optimistic about the likelihood of getting theperformance-related pay as individuals. 3
With respect to job satisfaction, Green (2004) pointed out that performance-related pay
may decrease job satisfaction for work intensification. However, Green & Heywood (2008)
found no evidence supporting Green’s point. Their result demonstrated that performancerelated pay tends to increase overall job satisfaction. In addition, Cornelissen et al., (2011)
found that before controlling for earnings, employees under the performance-related payment
scheme have higher job satisfaction than others, but after controlling for earnings, employees
in jobs with performance-related pay have the same job satisfaction as those not in such jobs.
In this study, we consider that physical exercise and sports may, to some extent, reveal
people’s preference for payment schemes. Physical activities are important for everybody’s
health. Physical inactivity has been proved to be a potential factor increasing premature
mortality and numerous adverse chronic health conditions. Increased blood pressure, coronary
heart disease, type-II diabetes, certain types of cancer, gallbladder disease, musculoskeletal
disorders, obesity, osteoporosis, and obstructive sleep apnea are just some consequences
frequently mentioned (Stamatakis et al., 2007). What’s more, the preference of doing physicalexercise not only affects one’s health, but also has an impact on employment and earnings.
Generally, the effects of doing physical activities may make people look fitter and attractive,
which have been shown to increase employment and earnings, and a healthy body can help toincrease individual efficiency (Lechner, 2009). Additionally, people may link someone who
likes exercise or sports with responsibility, discipline, competition, leadership, and teamwork
2 Time preference is the inclination of a consumer towards current consumption over future consumption. Having
a high time preference means that he or she prefer current consumption rather than future consumption, and viceversa.
3 There is one limitation on the application of the performance-related pay in firms despite its incentive andsorting effects. Eriksson & Villeval (2008) pointed out that the performance-related pay might expand the wage
difference among employees and increase team heterogeneity within firms, which would generate conflicts
between employees, destroy morale, kill teamwork, and hurt the output. As a result, it is less likely to be applied infirms reliant on a high level of.

3

(Pfeifer & Cornelissen, 2009). In a word, doing physical exercise could increase employment
opportunities and earnings, and the higher the frequency the greater the probability of
employment (Kavetsos, 2011). Regarding the relationship between the preference forpayments and exercise, Ewing (1998) provided related evidence using the 1990 wave of the
National Longitudinal Surveys of Youth (NLSY) data set. He found that former high school
athletes are more willing to be employed in jobs under a performance-related payment system.
More competitive individuals, as measured by their participation in sports, self-select to jobs
where they can be rewarded for the productivity of their competitive nature. However, thedata used in this study only focused on white males, and females and other races were notincluded.
Many people may think of someone who likes physical activity as more aggressive, selfconfident, and risk-loving, and consider that he or she may be more willing to choose
performance-related pay than other individuals. However, to the best of our knowledge, noattention has been paid to this issue in the literature. Therefore, we aim to address this gap by
providing new evidence.
The data used in this paper is from a questionnaire survey conducted at Hiroshima City
University, Japan. In the survey, a choice experiment is first applied to obtain the individual
tradeoff between fixed pay and performance-related pay. In the choice experiment,
respondents are asked to choose their preference from the three kinds of payments mentioned
above under a hypothetical situation. In the econometric analyses, the Random Parameter
Logit (RPL) model is used to estimate individual tradeoffs between fixed and performancerelated pay, and then the Ordinary Least Squares (OLS) regression is used to estimate theeffects of personal attributes including variables related to physical exercise and sports on theindividual tradeoff obtained from the RPL regression.
The rest of this paper is organized as follows. Section 2 introduces the methodologicalissues. Results are reported in Section 3, and discussions are provided in Section 4. Finally,
the last section draws a conclusion.
2. Methodology
2.1 Survey
The survey was conducted between July and November 2015 at Hiroshima City
University, Japan. All the respondents are undergraduates at Hiroshima City University. The
questionnaire follows Shen et al. (2014) and consists of two parts. The first part consists ofchoice experiment questions. In the choice experiment, respondents were asked to makerepeated choices among three payment schemes in different situations under a hypotheticalscenario. At first, a hypothetical scenario about a job description was presented to the
respondents. The main points of the scenario are as follows: (1) each respondent is presumed
to undertake a 5-hour part-time job of selling snacks at a local festival; (2) the price of each4

snack would be 150 JP yen; (3) there would be 500 participants in the festival; (4) there
would be no other shops selling snacks in the festival; (5) each respondent can choose thepayment system they preferred from alternatives we provided.
In each choice set, three alternatives, named payment A, payment B and payment C,
were presented to the respondents. A, B, and C represent a pure fixed payment, a pure
performance-related payment, and a mixed payment system with both fixed and performancerelated pay, respectively. Each payment contains two attributes: hourly pay and pay for eachsnack sold. The levels of these two attributes in each payment are presented in Table 1.
Twenty-seven choice sets were generated by adopting a full factorial design. Then, thesechoice sets were randomly divided into three different versions, and randomly allocated to the
respondents. Each respondent answered one version containing nine choice sets. An example
of a choice set is provided in Table 2.
The second part of the questionnaire contains several questions related to respondents’personal information, such as gender, height, risk attitude, questions related to physicalactivities, and so on. This part of the questionnaire is presented in the Appendix. In total, 211
respondents including 69 males and 141 females answered the questionnaire.4

Table 1. Attributes and Their Levels for Each Payment System
Levels of attributes
Attributes

Payment A

Payment B

Payment C

Hourly pay (JP yen)

800/900/1000

0

500

0

80/90/100

30/40/50

Pay for each snack sold (JP yen)

Table 2. An Example of a Choice Set
Payment A

Payment B

Payment C

Hourly pay (JP yen)

900

0

500

Pay for each snack sold (JP yen)

0

100

40

Please choose one most-desirable

□

□

□

payment plan by placing a √ in a □2.2 Econometric models
2.2.1 The Random Parameter Logit model
The method used to estimate the choice experiment data is the Random Parameter Logit(RPL) model (or mixed logit model). The RPL model is a very flexible model, which canapproximate any random utility model with different distributions of random parameters
4

One respondent did not report his or her gender.

5

(McFadden & Train, 2000). Compared to the standard Multinomial Logit model, the RPL
model overcomes the taste variation issues and does not exhibit the independence of
irrelevant alternatives (IIA) property. Thus, the RPL model can capture individual preference
clearly.
Random utility theory (Thurstone, 1927) is the basis of the choice model about decisionmaking. In the random utility theory about decision-making, the first basic assumption is thatdecision makers prefer the larger utility, and are more willing to choose the alternative thatmaximizes their utilities from a set of alternatives. The second is that the utility of analternative for an individual (U) consists of two parts, a deterministic component (V) and arandom error term (ε). Formally, individual q’s utility of choosing alternative i can bepresented as
𝑈𝑈𝑖𝑖𝑖𝑖=𝑉𝑉𝑖𝑖𝑖𝑖 +𝜀𝜀𝑖𝑖𝑖𝑖(1)

𝑉𝑉𝑖𝑖𝑖𝑖 = 𝛽𝛽 ′ 𝑋𝑋𝑖𝑖𝑖𝑖(2)

Then, the deterministic component of the utility 𝑉𝑉𝑖𝑖𝑖𝑖 also can be written as:
where 𝛽𝛽 ′ is the parameter vector associated with the vector of explanatory variables Xiq.

The probability that individual q will choose alternative i over alternative j is given by
𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃�𝑖𝑖‫ 𝑖𝑖𝑖𝑖𝑉𝑉�𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 = �𝐶𝐶׀‬+ 𝜀𝜀𝑖𝑖𝑖𝑖 > 𝑉𝑉𝑗𝑗𝑗𝑗 + 𝜀𝜀𝑗𝑗𝑗𝑗 , ∀ 𝑖𝑖 ≠ 𝑗𝑗𝑗𝑗𝑗𝑗�

(3)

where C is the complete choice set. By assuming the error terms in Equation (3) follow thetype I extreme value (EV1) distribution and be independently and identically distributed
across alternatives and cases, the standard Multinomial Logit model can be expressed as:exp(𝛽𝛽 ′ 𝑋𝑋𝑖𝑖𝑖𝑖 )𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖 = ∑𝐶𝐶(4)′
𝑐𝑐=1 exp(𝛽𝛽 𝑋𝑋𝑐𝑐𝑐𝑐 )In the RPL model, the choice probability that an individual q chooses alternative i isexpressed as:′
𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖= ∫ ∑𝐶𝐶

exp�𝛽𝛽 ′ 𝑋𝑋𝑖𝑖𝑖𝑖 �′
𝑐𝑐=1 exp�𝛽𝛽 𝑋𝑋𝑐𝑐𝑐𝑐 �𝑓𝑓(𝛽𝛽|𝜃𝜃)𝑑𝑑𝑑𝑑(5)

where f (β|θ) is the density function of β with θ referring to a vector of parameters of that′density function (mean and variance). Here, the RPL model probabilities 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖
are theweighted average of the standard Multinomial Logit probabilities 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖 and the weights
determined by the density function f (β|θ).

By using the RPL model, β can capture observation-specific variations of the effect of X

on outcome probabilities with the density function f (β|θ). In RPL models, some elements ofthe parameter vector β can be assumed to be fixed and others, to be random. However, it isnecessary to make a prior assumption about the distribution of random parameters in the RPL
6

model. Normal distribution, log-normal distribution, triangular distribution, and uniform
distribution are normally used.
Normal distribution is one of the most popular and commonly used distributions in the
RPL model. The assumption of normal distribution means the coefficient is estimated withouta strict sign, it could be either positive or negative. However, there is a limitation that normal
distribution has an infinite tail, which would present some unreasonable coefficient values inresults. Log-normal distribution is a continuous probability distribution of a random variable
whose logarithm is normally distributed. A random variable following lognormal distribution
only has one side of zero. A triangular distribution is a continuous probability distribution
with a lower limit, an upper limit, and a mode. There is a maximal value in the center,dropping off linearly on both sides. A uniform distribution has constant probability density on
an interval and zero probability density elsewhere. In this paper, all the above-mentioned
distributions are assumed and results based on these assumptions are compared.
As Hensher et al. (2005) showed, the RPL parameter estimates capture information on(1) the distributional form of the marginal utilities of each random parameter (specified by the
analyst), (2) the means of the distributions, and (3) the dispersion of the distributions provided
as the standard deviation. With this information, it is possible to obtain parameter estimatesfor each sampled individual. The individual tradeoff between fixed and performance-related
pay then can be calculated by dividing the latter parameter by the former.
2.2.2 The Ordinary Least Squares regression
The OLS regression was used to examine the effect of various personal attributes on theindividual tradeoff between fixed and performance-related pay obtained from the RPL model.
Table 3 provides the definition and descriptive statistics of all variables used in the OLS
regression. As shown in the table, there are four variables related to physical exercise andsports – Like, Proficiency, Frequency, and Minute. Since significant correlations wereobserved among these four variables (see Table 4), we ran the OLS regression separately as
follows:
Model 1: 𝑦𝑦1 = 𝛼𝛼0 + 𝛽𝛽1 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 + 𝛽𝛽2 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 + 𝛽𝛽3 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚_𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 + 𝛽𝛽4 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏ℎ𝑒𝑒𝑒𝑒𝑒𝑒 + 𝛽𝛽5 ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒ℎ +𝛽𝛽6 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 + 𝛽𝛽7 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝜀𝜀

Model 2: 𝑦𝑦2 = 𝛼𝛼0 + 𝛽𝛽1 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 + 𝛽𝛽2 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 + 𝛽𝛽3 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚_𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 + 𝛽𝛽4 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏ℎ𝑒𝑒𝑒𝑒𝑒𝑒 +𝛽𝛽5 ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒ℎ + 𝛽𝛽6 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 + 𝛽𝛽7 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝜀𝜀

Model 3: 𝑦𝑦3 = 𝛼𝛼0 + 𝛽𝛽1 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 + 𝛽𝛽2 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 + 𝛽𝛽3 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚_𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 + 𝛽𝛽4 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏ℎ𝑒𝑒𝑒𝑒𝑒𝑒 +𝛽𝛽5 ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒ℎ + 𝛽𝛽6 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 + 𝛽𝛽7 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝜀𝜀

Model 4: 𝑦𝑦4 = 𝛼𝛼0 + 𝛽𝛽1 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 + 𝛽𝛽2 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 + 𝛽𝛽3 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚_𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 + 𝛽𝛽4 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏ℎ𝑒𝑒𝑒𝑒𝑒𝑒 + 𝛽𝛽5 ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒ℎ +𝛽𝛽6 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑖𝑖𝑛𝑛𝑛𝑛 + 𝛽𝛽7 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝜀𝜀

In addition, we observed a significant positive correlation between male and height7(𝜌𝜌=0.7491, p<0.01), therefore, we did not put height directly into Models 1–4 to avoid themulticollinearity. Instead, we replaced male with height in Models 5–8 and ran the OLS
regressions again to check the robustness of our results obtained from Models 1–4.
Model 5: 𝑦𝑦5 = 𝛼𝛼0 + 𝛽𝛽1 ℎ𝑒𝑒𝑒𝑒𝑒𝑒ℎ𝑡𝑡 + 𝛽𝛽2 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 + 𝛽𝛽3 ℎ𝑒𝑒𝑒𝑒𝑒𝑒ℎ𝑡𝑡_𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 + 𝛽𝛽4 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏ℎ𝑒𝑒𝑒𝑒𝑒𝑒 + 𝛽𝛽5 ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒ℎ +𝛽𝛽6 𝑤𝑤𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 + 𝛽𝛽7 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝜀𝜀

Model 6: 𝑦𝑦6 = 𝛼𝛼0 + 𝛽𝛽1 ℎ𝑒𝑒𝑒𝑒𝑒𝑒ℎ𝑡𝑡 + 𝛽𝛽2 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 + 𝛽𝛽3 ℎ𝑒𝑒𝑒𝑒𝑒𝑒ℎ𝑡𝑡_𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 + 𝛽𝛽4 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏ℎ𝑒𝑒𝑒𝑒𝑒𝑒 +𝛽𝛽5 ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒ℎ + 𝛽𝛽6 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 + 𝛽𝛽7 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝜀𝜀

Model 7: 𝑦𝑦7 = 𝛼𝛼0 + 𝛽𝛽1 ℎ𝑒𝑒𝑒𝑒𝑔𝑔ℎ𝑡𝑡 + 𝛽𝛽2 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 + 𝛽𝛽3 ℎ𝑒𝑒𝑒𝑒𝑒𝑒ℎ𝑡𝑡_𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 + 𝛽𝛽4 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏ℎ𝑒𝑒𝑒𝑒𝑒𝑒 +𝛽𝛽5 ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒ℎ + 𝛽𝛽6 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 + 𝛽𝛽7 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝜀𝜀

Model 8: 𝑦𝑦8 = 𝛼𝛼0 + 𝛽𝛽1 ℎ𝑒𝑒𝑒𝑒𝑒𝑒ℎ𝑡𝑡 + 𝛽𝛽2 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 + 𝛽𝛽3 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚ℎ𝑒𝑒𝑒𝑒𝑒𝑒ℎ𝑡𝑡_𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 + 𝛽𝛽4 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏ℎ𝑒𝑒𝑟𝑟𝑠𝑠 +𝛽𝛽5 ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒ℎ + 𝛽𝛽6 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 + 𝛽𝛽7 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝜀𝜀

Table 3. Definition and descriptive statistics of variables used in the OLS regression
Variables

Definition

Obs

Mean

Min

Max

0

1

141

189

0

1

0.2

1

0

3

0

4

0

4

1

5

1

4

1

10

(S.D)
Male

Dichotomous variable = 1 if male and 0 if female.

210

0.3286(0.4708)

HeightHeight of the respondent210

162.2457(8.3979)

Brothers

Dichotomous variable = 1 if a respondent has

210

brothers or sisters and 0 otherwise
Risk

0.9
(0.3007)

Use Q5 in Appendix as risk attitude’s measure210

0.6514(0.1776)

Like

Do you like physical exercise or sports? Likert

208

scales from 0 (don’t like it.) to 3 (like it very

1.8125(0.9822)much)
Proficiency

Are you good at physical exercise or sports? Likert

208

scales from 0 (very week) to 4 (very good at)
Frequency

The frequency of respondents doing physical1.7885(1.0137)

208

exercise. Likert scales from 0 (almost not) to 4 ( 51.5577(1.1278)

times a week or more )MinuteTime spent on physical exercise once. Likert scales

128

from 1 (less than 30 minutes) to 5 ( more than 2

3.1016(1.2026)

hours)
HealthLikert scales from 0 (bad) to 4 (very good)

205

2.5854(0.8158)

Wellbeing

Likert scales from 1 (very unhappy) to 10 (veryhappy)

206

6.7718(1.8243)

8

Table 4. Correlation coefficients among variables related to physical exercise and sports
Like

Proficiency

Frequency

Like

1.000

Proficiency

0.7397 ***1.0000Frequency

0.4161 ***0.3192 ***1.0000

Minute0.4084 ***0.2328 ***0.0291 *Minute1.0000Note: * p < 0.1; ** p < 0.05; *** p < 0.01

3. Results
3.1 Sample description
As shown in Table 3, among all respondents, average height is 162 cm, the tallest is 189
cm, and the shortest is 141 cm. 189 respondents have brothers and sisters accounting for 90%of the total. Q5 in the Appendix is used as the standard measure of risk attitude. In thisquestion, mean is 0.65, max is 1 and min is 0.2. “Overall, how happy would you say you are
currently? Using a scale from 1 to 10 where “10” is “very happy” and “1” is “very unhappy,”
how would you rate you current level of happiness? ” is asked as a standard measure of
wellbeing, the average score of wellbeing is 6.772. Moreover, variables “like,” “proficiency,”“frequency,” and “minute” represent the questions relating to the individual preference forphysical exercise, which is the focus in this paper. Their Likert scale frequencies are listed inTable 5. The average score of “like” is 1.8125, and 141 respondents chose the options of “I
like very much” and “I like it,” accounting for 67.79% of the total. It means that most of the
respondents like physical exercise. The average score of “proficiency” is 1.7885, and only 53
respondents chose the options of “very good at” and “good at,” which accounts for 35% of thetotal. It indicates that most of the respondents are not good at physical exercise. Concerning
the frequency measure, it seems that the majority of respondents do physical exercise or
sports frequently. The average score of time spent is 3.1016, and 86 respondents taking up
68% of the total do physical exercise or sports for over an hour at a time.
Table 5. Likert scales frequency of variables related to physical exercise and sports
ScalesLike

Proficiency

Frequency

0

28

22

55

1

39

60

27

11

2

85

73

87

31

3

56

46

33

42

7

6

22

4
5
Total

Minute

22
208

208

208

9

128

3.2 The RPL results
Table 6 presents the estimated results of the Multinomial Logit (MNL) model andRandom Parameter Logit (RPL) model. The results presented were estimated by using
NLOGIT 5.0, a specialist discrete modeling package in LIMDEP (Econometric Software,Inc.). Compared to the MNL model, the goodness-of-fit measures (i.e., log-likelihood andPseudo R2) are significantly improved by applying the RPL model, which suggests theimportance of controlling for respondents’ heterogeneity.
In the RPL model, parameters of Hourly pay and Pay for each snack sold are assumed to
be randomly distributed, and those of alternative-specific constant terms, Payment A andPayment B, are assumed to be fixed.
Looking at the random parameters, Hourly pay and Pay for each snack sold havepositive and highly significant influences on the preference for payment schemes in normal,
triangular, and uniform distributions. This result indicates that the higher the pay, independentof whether it is fixed or performance-related pay, the happier the respondents are. In lognormal distribution, the mean coefficients of Hourly pay and Pay for each snack sold are
significantly negative, showing that the higher salary makes respondents unsatisfied.
Additionally, according to the results of nonrandom parameters, respondents favor thepayment B (i.e. the pure performance-related system) and do not prefer the payment A (i.e.
the pure fixed system), relative to the system C which mixes both fixed and performancerelated pay. The strong significance of the estimated standard deviations of assumed randomparameters in all the RPL models shows the existence of heterogeneity in respondents’preferences for payment schemes.
Furthermore, as mentioned in the previous section, it is possible to estimate the marginal
tradeoff between fixed and performance-related pay for each respondent by applying theresults of the RPL model and conditioning these on the individual choices. The tradeoff hereis the marginal rate of substitution between Pay for each snack sold and Hourly pay. This
tradeoff value gives necessary compensation for a one-unit decrease of an attribute tomaintain the same level of utility (Hiselius, 2003). For example, in order to maintain the same
utility, a decrease in Pay for each snack sold by one yen has to be compensated by an increaseof the Hourly pay. Therefore, the larger the tradeoff is, the respondent prefers the marginalincrease in Pay for each snack sold rather than Hourly pay.
Table 7 presents the results of the individual tradeoff in each distribution. As shown in
the table, the minimum and maximum values in a normal distribution are -1744.98 and71.0295, respectively. This is the same across all the distributions. Recalling the limitation of
normal distributions having an infinite tail mentioned in the previous section, which would
present some unreasonable coefficient values in results, therefore, we do not use individual
tradeoff estimates under the assumption of normal distribution in the OLS regressions. In
addition, the mean tradeoffs and their standard deviations are very similar in the other three10assumed distributions.
Table 6. Results of the MNL and RPL models
MNL

Random Parameter Logit model
NormalTriangular

Uniform

Log-normal

Random parameters in utility functions
Hourly pay

0.00837***

0.01866***

0.01848***0.01844***-3.98881***

Pay for eachsnack sold

0.05791***

0.09563***0.09453***0.10062***-2.38206***

Nonrandom parameters in utility functions
Payment A-0.51280-3.24782***-3.28937***-3.30459***-3.33553***

Payment B

0.68911*1.64076***

1.65902***

1.66264***1.76007***

Standard Deviation of random parameters
Hourly pay

0.00685***0.01510***0.01098***

0.37516***

Pay for each

0.04080***0.12697***

0.09391***0.43980***

Log likelihood-1760.22627-1250.02076-1244.16866-1244.36828-1248.16699

Pseudo R2

0.0866092

0.4005174

0.4033240

0.4032282

0.4014065

Note: * p < 0.1; ** p < 0.05; *** p < 0.01.

Table 7. The individual tradeoff in each distribution
Distribution

Mean

Std. Dev

Min

Max

Normal-2.24459

120.7171-1744.98

71.0295

Triangular5.616994

4.021813.948535

22.3638

Uniform

5.542571

3.624941

1.286418.3175

Log-normal

5.618518

3.35582.12565

20.4424

3.3 The OLS results
Figure 1 shows the mean individual tradeoff for different scales of the four questions
related to physical activities. As shown in the figure, it seems that the higher the scale is, thelarger the mean individual tradeoff, which suggests a possible positive effect from thepreference for physical exercise on the individual tradeoff between fixed and performancerelated pay.
Tables 8–10 present the OLS results in triangular, uniform, and log-normal distributions,
respectively. Models 1–4 are those using the variable of Male and Models 5–8 are those using
the variable of Height instead of Male.
With respect to the results of Models 1–4, as shown in Table 8 for a triangular11

distribution, Male is consistently positive and statistically significant in Models 1 – 4,
suggesting that males prefer the marginal increase in the performance-related pay overfemales. Like is positive in Model 1 and statistically significant at the level of 1%, while theinteraction term Male_like is not significant. This result indicates that respondents who like
physical exercise or sports value marginal increases in performance-related pay more highly
than in fixed pay. In Model 2, Proficiency and the interaction term Male_proficiency are
positive and statistically significant, suggesting that respondents who are relatively better at
physical exercise or sports prefer performance-related pay to fixed pay, and this preference isespecially strong in males. In Model 3, Frequency is statistically significant and has a positive
impact on the individual tradeoff. This means that respondents who do physical exercise or
sports more frequently favor the marginal increase in the performance-related pay more. Inmodel 4, Minute is statistically insignificant, implying that the time spent on physicalactivities has no significant impact on the individual tradeoff. Other variables such as
Brothers, Health, Risk, and wellbeing are not significant in all the models. The estimatedresults of Models 1–4 under the assumptions of uniform distribution and log-normal
distribution are similar to that in the triangular distribution (see Tables 9–10).
Turning to Models 5–8, as shown in Table 8 for a triangular distribution, Height ispositive and statistically significant in all the four models, suggesting that respondents’ height
has a positive impact on the individual tradeoff. The taller a respondent is, the more he or she
prefers performance-related pay. Similar to those estimates in Models 1–4, Like, Proficiency,
Frequency, and the interaction term Height_proficiency are positive and statisticallysignificant, and Minute and its interaction term with height (Height_minute) are notsignificant. However, the interaction terms Height_like and Height_frequency are estimated to
be positively significant, which is different from those in Models 1– 4. It implies the influenceof individual preference and frequency of physical exercise or sports on the tradeoff isdependent on height. Again, other variables such as Brothers, Health, Risk and wellbeing are
not significant in all the models, and the estimated results of Models 5–8 under theassumptions of uniform distribution and log-normal distribution are similar to that intriangular distribution (see Tables 9–10).

12Figure 1. Mean individual tradeoff for different scales of physical exercise or sports

13

Table 8. Estimated results of OLS model in triangular distribution
Gender models

Height models

Model 1Model 2Model 3Model 4Model 5Model 6

Model 7

Model 8Constant
Brothers

5.534***(1.841)-0.150 (0.911)

4.802***(1.811)
0.167 (0.882)

4.402** (1.901)
0.559 (0.905)

6.971**(2.932)-0.016 (1.375)-6.932 (5.774)-0.023 (0.898)-6.084 (5.690)
0.240 (0.883)-10.950**(5.527)
0.634 (0.893)-13.688 (8.789)
0.001 (1.342)

Health

0.010 (0.374)-0.157(0.370)0.198 (0.369)-0.043 (0.557)-0.037 (0.371)-0.104(0.368)0.223(0.364)0.014 (0.549)

Wellbeing-0.107(0.164)-0.043(0.159)-0.097 (0.163)-0.350 (0.273)-0.096 (0.162)-0.069(0.158)-0.098(0.161)-0.327(0.269)Risk-1.860(1.551)-1.449(1.531)-0.993 (1.560)-1.258 (2.316)-2.006 (1.526)-1.802(1.513)-1.206(1.535)-1.569(2.273)Male

1.270* (0.604)

1.262** (0.576)

1.459** (0.587)

2.012**(0.873)

Like

0.863***(0.293)

Male_like

0.328

0.843***(0.293)(0.593)Height0.079** (0.034)

Height_like

0.0568* (0.033)

Proficiency

0.929***(0.273)

Male_proficiency

1.289** (0.568)

0.071** (0.033)

0.098***(0.032)

0.132***(0.0499)

0.849***(0.280)

Height_proficiency

0.073** (0.032)

Frequency

0.532** (0.246)

Male_frequency

0.844 (0.525)

0.517** (0.242)

Height_frequency

0.062** (0.030)

Minute0.532 (0.348)

Male_minute-0.095 (0.693)

Height_minute

0.465 (0.345)
0.011 (0.039)

Note: * p<0.1, ** p<0.05, *** p<0.01; Standard Error in parentheses.

14

Table 9. Estimated results of OLS model in uniform distribution
Gender models

Height models

Model 1Model 2Model 3Model 4Model 5Model 6

Model 7

Model 8Constant

5.318***(1.647)

4.640***(1.615)

4.338**(1.706)

6.652** (2.584)-6.602(5.150)-5.744(5.064)-10.562**(4.954)-12.523(7.724)

Brothers-0.158(0.814)0.132(0.787)0.496 (0.812)-0.129 (1.212)-0.031(0.801)0.222(0.786)0.558(0.800)-0.091(1.179)Health-0.013(0.334)-0.172 (0.330)

0.173 (0.331)-0.040 (0.491)-0.060(0.331)-0.124(0.328)0.195 (0.326)

0.024(0.483)Wellbeing-0.074(0.147)-0.015 (0.142)-0.062 (0.146)-0.296 (0.241)-0.065(0.144)-0.041(0.141)-0.063(0.144)-0.281(0.236)Risk-1.663(1.387)-1.281 (1.366)-0.904 (1.400)-1.075 (2.041)-1.810(1.361)-1.599(1.347)-1.119(1.376)-1.373(1.998)Male

1.201** (0.540)

1.199** (0.514)

1.414***(0.527)

1.898** (0.770)

Like

0.799***(0.262)

Male_like

0.377

0.781***(0.261)(0.530)Height

0.076** (0.030)

Height_like

0.057*(0.029)

Proficiency

0.865***(0.244)

Male_proficiency

1.245** (0.507)

0.068** (0.030)

0.095*** (0.029)

0.122*** (0.043)

0.787***(0.249)

Height_proficiency

0.073** (0.028)

Frequency

0.431* (0.220)

Male_frequency

0.793* (0.471)

0.418* (0.217)

Height_frequency

0.057**(0.027)

Minute0.475 (0.307)

Male_minute

0.082 (0.611)

Height_minute

0.412 (0.303)
0.020 (0.035)

Note: * p<0.1, ** p<0.05, *** p<0.01; Standard Error in parentheses.

15

Table 10. Estimated results of OLS model in log-normal distribution
Gender models

Height models

Model 1Model 2Model 3Model 4Model 5Model 6

Model 7

Model 8Constant

5.277***(1.463)

4.667***(1.433)

4.411***(1.516)

6.133***(2.311)-5.096(4.578)-4.355(4.503)-8.667*(4.404)-11.169 (6.908)

Brothers-0.116(0.723)0.148 (0.698)

0.461(0.721)-0.100 (1.084)-0.017(0.712)

0.219(0.699)

0.514 (0.712)-0.041

Health

0.189 (0.297)

0.050 (0.293)

0.365(0.294)0.188 (0.439)

0.149(0.294)

0.097(0.291)

0.384 (0.290)

0.252 (0.432)

Wellbeing-0.103(0.130)-0.051(0.126)-0.095 (0.130)-0.238 (0.215)-0.098(0.128)-0.078(0.125)-0.097(0.128)-0.228Risk-1.769(1.232)-1.395 (1.212)-1.102 (1.244)-1.383 (1.825)-1.929(1.209)-1.717(1.197)-1.299(1.223)-1.671 (1.787)

Male

1.047** (0.480)

1.059** (0.456)

1.253*** (0.468)

1.674** (0.688)

Like

0.704***(0.233)

Male_like

0.506 (0.471)
0.059**(0.027)

0.083***(0.026)

0.110***(0.038)(1.055)(0.211)0.695***(0.232)

Height

0.066** (0.027)

Height-like

0.054** (0.026)

Proficiency

0.757***(0.216)

Male_proficiency

1.238***(0.449)

0.688***(0.221)

Height_proficiency

0.069***(0.025)

Frequency

0.381* (0.196)

Male_frequency

0.760* (0.419)

0.369* (0.193)

Height_frequency

0.054** (0.024)

Minute0.393 (0.274)

Male_minute

0.160 (0.546)

Height_minute

0.343 (0.271)
0.015 (0.031)

Note: * p<0.1, ** p<0.05, *** p<0.01; Standard Error in parentheses.

16

4. Discussion
This paper focuses on the relationship between the individual preference for physicalexercise or sports, and the tradeoff of different payment schemes. The results support the
hypothesis that people who prefers physical activities more value the marginal increase in theperformance-related pay more highly than in the fixed pay. It can be shown that people who
like exercise or sports tends to be more aggressive and competitive in general. Ewing (1998)
supports this viewpoint by pointing out that athletic participation may be a signal of anindividual who is less likely to shirk. Those people devote more time to athletics than others,
and their competitive and hardworking nature makes them more likely to be productive
employees. Because of this, the job under the performance-related payment system seems anappropriate one for them. More competitive people, as measured by their preferences forphysical exercise or sports, prefer jobs with a performance-related payment system where
they can be rewarded for their higher productivity.
The result that amount of time spent on physical exercise at once does not have asignificant influence on the preference for payment schemes is somewhat interesting. Thisevidence is probably reasonable because spending too much time doing physical exercise or
sports is harmful to health due to sports fatigue and injury. Therefore, most people would
avoid this happening. Therefore, time spent should not be measured as a signal of thepreference for physical exercise or sports.
In addition, gender and height have positive and significant influences on the preference
for payments. Male or taller individuals prefer the marginal increase in the performancerelated pay rather than in the fixed pay. According to evidence from Mauro & Musumeci(2011), males tend to be more risk loving than females and are usually willing to sacrificeassured pay in order to pursue a better reward. As a result, males are more willing to receive amarginal increase in the performance-related pay than females who are usually more risk
averse. With respect to height, people may regard taller people as being more persuasive(Young & French, 1996), more attractive (Freedman, 1979; Harrison & Saeed, 1977; Lerner& Moore, 1974), and more likely to work as a leader of other people (Higham & Carment,
1992; Stogdill, 1948). Moreover, height also has a great influence on how people regard
themselves. Because taller individuals are always viewed and treated with respect by others,
they may develop greater self-worth and self-confidence (Roberts& Herman, 1986). Judge &Cable (2004) analyzed the relationship of physical height to career success, and proved that tallindividuals have advantages in their careers. As a result, taller individuals would be more
confident about themselves to receive the performance-related pay. Hence, it is plausible thattaller individuals prefer the marginal increase in the performance-related pay rather than in
the fixed pay.
Yet contrary to the previous literature, the coefficients of risk in this paper are
insignificant in all models, showing risk attitude does not have a significant impact on
17

individual tradeoff between fixed and performance-related pay. 5 This may be because among
all respondents there are 141 females who tend to be risk averse, and only 69 males. Including
too many female respondents in the sample may dilute the effect of risk attitude on individual
tradeoffs between different payments.
Finally, this study has several limitations. First, some other socio-demographic variables
such as age, education level, and household income are considered to have possible impacts
on the preference for payment schemes and should be used in the analysis. However, due tothe limitations of the survey that all the respondents are university undergraduates, thesevariables could not be analyzed. Second, this paper uses self-reported height and thepreference for physical activities. Respondents might overestimate their height and might
misidentify their preferences, which would jeopardize the validity of the results. Finally, theimbalance between male and female respondents in the sample might be seen as anothershortcoming of this study.
5. Conclusion
In this paper, by using the survey data collected at Hiroshima City University, we
empirically examined the relationship between individual tradeoff of payment schemes andtheir preference for physical exercise or sports. The results indicate that respondents who like
physical exercise or sports more, who are better at them, and who do them more frequently,
are more likely to prefer the performance-related rather than the fixed pay. In addition, males
or taller individuals are also found to favor the performance-related pay.
It is a win-win situation for both employers and employees to have an employee
preferred payment scheme. Though it is extremely difficult for employers to observe
employees’ preferences for payment schemes, the results of this study might be able to give
employers a new method to elicit employees’ preference for payments.
Finally, the limitations mentioned in the previous section suggest a need for morecomprehensive studies, with fewer student respondents participating in the survey. Doing so
will allow for more socio-economic attributes that might influence individuals’ preferences
for payment schemes to be investigated.
Acknowledgments
Financial support from the Japanese Ministry of Education, Culture, Sports, Science andTechnology through Grants-in-aid for Scientific Research (C) 25380234 and 15K03353 is
gratefully acknowledged. All the views expressed in this paper and any errors are the sole

responsibility of the authors.

5

The answers of Q6 and Q7 presented in the Appendix were also used as risk attitudes in the OLS models.
However, they are not significant.

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Appendix. The second part of the questionnaireQ2. Your sex?
A. maleB. femaleQ3. Your height: ____________cm
Your weight: ____________kg
Q4. Do you have brothers or sisters?
A. Yes

B. No

Q5. There are two alternatives. Alternative 1 is that you will obtain 100 thousand JP yen witha probability of 100%. Alternative 2 is that you will obtain 200 thousand JP yen with aprobability of ( ) %. Please fill in the parenthesis with a numeral so that these twoalternatives have the same value to you.
Q6. There are two alternatives. Alternative 1 is that you will obtain 100 thousand JP yen witha probability of 50%. Alternative 2 is that you will obtain 200 thousand JP yen with aprobability of ( ) %. Please fill in the parenthesis with a numeral so that these twoalternatives have the same value to you.
Q7. When you go out, you will bring the umbrella if a () % chance of rain is announced as

the weather forecast. Please fill in the parenthesis with a numeral.
Q8. Do you like physical exercise or sports?
A. I like it very much B. I like it

C. Neither like nor dislike

D. No, I don’t like it

Q9. What’s your favorite physical exercise or sports?
First: _______________
Second: _______________
Third:_______________

Q10. Are you good at physical exercise or sports?
A. Very good

B. Good

C. Ordinary

D. Not very good

E. Very weakQ11. How often did you do physical exercise or sports?
A. 5 times a week or more
C. 1 to 2 times a week

B. 3 to 4 times a week
D. 1 to 3 times a month21

E. Almost notIf you chose A, B or C in Q11, please continue with Q12.
If you chose D or E in Q11, please go to Q14.
Q12. You said you did physical exercise or sports frequently in Q11, why was that? Multiple
selections are allowed.
A. I like it

B. To improve your healthD. To make friends

C. To control your weight

E. I have spare time

F. Others

Q13. How many minutes do you usually spend doing physical exercise or sports at a time?
A. Less than 30 minutes

B. 30 minutes to 60 minutes

D. 90 minutes to 120 minutes

C. 60 minutes to 90 minutes

E. More than 2 hours

Please go to Q15
Q14. From the following reasons, what is preventing you from doing physical exercise or
sports? Multiple selections are allowed.
A. I don’t like physical exercise or sports
C. Physical disability

B. I do not have the time

D. The sports facilities are not available

E. I do not have friends to do sports with

F. Others

Q15. How about your health currently?
A. Very good

B. Good

C. Ordinary D. Not very good

E. BadQ16. Overall, how happy would you say you are currently? Using a scale from 0 - 10 where“10” is “very happy” and “1” is “very unhappy,” how would you rate you current level ofhappiness?
1

2

3

4

5

6

22

7

8

9

10