Choice Set, Relative Income, and Inequity Aversion: Evidence from
an Artefactual Field Experiment
Haoran He† and Keyu Wu‡
Abstract Inequity aversion preference has been widely applied in interpretations of various
economic behaviors. A rapidly growing literature has been attempting to measure the strength of
inequity aversion preferences as accurately as possible. We vary two factors that might affect the
accuracy of the measurement of inequity aversion preference, i.e., choice sets with different
underlying inequity aversion strength ranges and with different relative income inequities in
which absolute income inequities remained fixed. We determine that unidirectional changes in
the choice sets for disadvantageous and advantageous inequity aversion preference significantly
bias the measured strength of both preferences in the same directions of the changes, and the
variance of inequity aversion increases with the range of choice sets. Moreover, a decrease in
relative income inequity raises the measured strength of advantageous inequity aversion but does
not affect disadvantageous inequity aversion preference. Our results suggest controlling for
choice sets and relative income inequity between players to improve the measurement accuracy
of inequity aversion preference.
Key words Inequity aversion; choice set; relative income; field experiment
JEL Classification C91, C93, D31
†
School of Economics and Business Administration, Beijing Normal University, Beijing 100875; E-mail address:
[email protected]; Tel.: 010-58807874.
‡
Department of Economics, University of Michigan, MI 48109, USA; Email address: [email protected].
Acknowledgments: We are grateful to Marie Claire Villeval, Qian Weng, and seminar participants at Beijing Normal University
for helpful discussions and comments on this paper. Financial support from the National Natural Science Fund (Project No.
71303022), the MOE (Ministry of Education in China) Project of Humanities and Social Sciences (Project No. 13YJC790039),
the Fundamental Research Funds for the Central Universities, and the Swedish International Development Cooperation Agency
(SIDA) to Environment for Development Initiative for supporting the project is gratefully acknowledged.
1
1. Introduction
A growing literature based on theoretical models and controlled experiments has provided
solid evidence regarding the deviations from rational behaviors that result from concerns about
fairness (see Fehr and Gächter, 2000 for a review). These studies find that fairness is one of the
key motivations besides self-regarding preference that drive people’s behaviors. Studies in
behavioral economics refer to people’s concern for fairness as “inequity aversion preference”,
which indicates that people are willing to relinquish their self-interests to promote fairness
(Bolton and Ockenfels, 2000). Some early studies employed empirical observations and
experimental tests to find preliminary evidence for how inequity aversion preference influences
people’s economic behaviors (e.g., Bewley, 1999; Camerer and Thaler, 1995; Kahneman et al.
1986). Since that time, inequity aversion has been gradually incorporated into traditional
economic models and has made various seemingly irrational behaviors more understandable
(e.g., Bolton and Ockenfels, 2000; Charness and Rabin, 2002; Dufwenberg and Kirchsteiger,
2004; Falk and Fischbacher, 2006; Fehr and Schmidt, 1999; Levine, 1998; Rabin, 1993). All this
theoretical work has attracted increasing attention and, importantly, laid the foundation for
subsequent studies. Among others, the F&S model developed by Enst Fehr and Klaus Schmidt
(1999) has become increasingly influential and frequently cited as one of the most important
contributions to the economics literature in recent decades.1
Given the success of the F&S model, it becomes important to accurately measure the
strength of the two types of inequity aversion preferences in the model, i.e., aversion to
advantageous inequity (advantageous inequity aversion) and aversion to disadvantageous
inequity (disadvantageous inequity aversion). Beginning with Fehr and Schmidt (1999)’s use of
a public goods game to measure the strength of inequity aversion at the aggregate level;
subsequent studies use various games in attempting to measure inequity aversion at the
individual level instead (Engelmann and Strobel, 2004; Bolton and Ockenfels, 2006; Güth et al.,
2009; Bartling, 2009; Dannenberg et al., 2007; Kerschbamer, 2010; Blanco et al., 2011; Yang et
al., 2012). Nevertheless, these studies found mixed evidence when they tried to use measured
preferences to explain and predict subjects’ economic behaviors using a within-subject design.
Dannenberg et al. (2007) find that advantageous inequity aversion was able to explain people’s
behaviors in the social dilemma game. Yang et al. (2012) also show that F&S model has fairly
strong explanatory power with respect to subjects’ behaviors in the production game, both in
terms of the irrational phenomena and the strength of the irrationality. However, using a simple
distribution experiment, Engelmann and Strobel (2004) find that models proposed by Fehr and
Schmidt (1999) or Bolton and Ockenfels (2000)2 are not able to interpret people’s distributive
behaviors. Blanco et al. (2011) conclude that the F&S model’s predictive power is limited at the
individual level although they demonstrate that inequity aversion motivates decision makers’
behavior.
Methodological differences in measuring inequity aversion preferences might be an
important contributing factor for the inconsistent explanatory power of these preferences across
studies. Moreover, different measurement methodologies can also result in variations in the
strength of inequity aversion preferences as measured individually across laboratory experiments
1
Figure A1a and A1b in appendix I present the total number of citations of Fehr and Schmidt (1999) across the years and
compare the citations of this paper to those of other influential papers by Nobel laureates in related fields, respectively.
2
Bolton and Ockenfels (2000) independently propose an inequity aversion model that is similar to Fehr and Schmidt (1999).
Bolton and Ockenfels (2000) have also been highly cited since published.
2
based on the F&S model. For instance, both α and β parameters measured by Dannenberg et al.
(2007) and Blanco et al. (2011) were larger than those in Yang et al. (2012). The discrepancies
in measurement may be partially driven by the choice menus used in the former papers, which
imply an upward-skewed distribution range for both parameters, and by the underlying
difference in relative income inequity associated with various choice menus used in the previous
literature. The first factor refers to the restrictions on the available choice set that might affect
behavior, and the second factor is linked to the essence of decision makers’ perception with
respect to fairness, which might also be driven by the proportion of one’s income compared to
others’ income. In this study, we investigate the possible influences of these two factors on
inequity aversion preference measurement by conducting an artefacture field experiment
(Harrison and List, 2004) with the general working population.
The remainder of this paper is organized as follows: Section 2 briefly reviews relative
studies. Next, our experimental design and results are presented in Sections 3 and 4, respectively.
We conclude in Section 5.
2. Previous literature and hypotheses
Our study is built on Fehr and Schmidt (1999)’s theory. There are two main assumptions
made in the F&S model: i) in addition to completely rational people, there is another group of
people whose utilities are affected by other people’s income; and ii) in general, humans do not
like “unequal” income distributions, i.e., they gain lower utility when there are gaps between
others’ income and their own income than when incomes are equally distributed. Moreover,
people in general suffer more from inequity that is to their material disadvantage than inequity
that is to their material advantage (Loewenstein, 1989). Based on these assumptions, the F&S
model is presented formally as:
U i ( x)  xi   i
1
1
max | x j  xi ,0 |   i

 max | xi  x j ,0 |
n  1 j 1
n  1 i1
,
(1)
where n denotes the total number of participants in the game. Each player is denoted as i (i=1,
2, …, n). xi = x1, …, xn refers to each player’s utility function. In that utility function, α is the
envy parameter, which captures the strength of utility loss from disadvantageous inequity,
whereas β is the guilt parameter, which captures the strength of utility loss from advantageous
inequity. When only two players participate in the game and if a decision-maker’s income is
surely no less or surely less than the counterpart player, equation (1) can be simplified as:
 xi   i max | x j  xi ,0 |, if xi  x j
U i ( x)  
 xi  i max | xi  x j ,0 |, if xi  x j
i j.
(2)
The first assumption of the F&S model means that αi and βi are not equal to 0, for at least some
players i; the second assumption means that αi≥0, βi ≥03, and βi≤αi.
A number of subsequent studies have attempted to develop inequity aversion theories along
the path of the F&S model. Rotemberg (2008) notes that predictions of equal distribution
behaviors in dictator games by the F&S model and the B&O model (Bolton and Ockenfels, 2000)
3
. It is notable that the fact that the F&S model assumes β will not be less than 0 means that people also do not like the
advantageous inequity. The reason for having this assumption is not that they do not believe that there are no people who favor
advantageous inequity, but they think that people who have β<0 would not have any effect on the experimental results (Fehr and
Schmidt, 1999). However, because it is widely found that a significant amount of subjects do favor advantageous inequity,
options of β<0 are always included in the choice menus.
3
are essentially consistent. Shaked (2006) argues that the behavioral predictions of F&S are based
on multiple parameter estimations, therefore behaviors in any games must depend on the
aggregate distributions of players’ inequity aversion preferences. Other studies show that the
F&S model fails to take reciprocity or intention into account (Falk et al., 2003; Kagel and Wolfe,
2001; Bereby-Meyer and Niederle, 2005; Xiao and Houser, 2005). Still other studies propose
more general criticisms of the models (Shaked, 2005; Engelmann and Strobel, 2006; Bergh,
2008; Binmore and Shaked, 2010). Thus, although the F&S model is not perfect, it indeed
stimulates a large body of follow-up literature4 because it develops a simple and direct way to
consider many anomalies in economics that classic game theories are not able to explain. We
will mainly introduce studies that used laboratory experiments to measure inequity aversion
preference at the individual level based on the F&S model.
Blanco et al. (2011) conduct an ultimatum game and a modified dictator game to measure
the α and β parameters in the F&S model. In the ultimatum game, the proposer must decide how
to allocate a total amount of 20 pounds between him-/herself and a responder, and the responder
must decide whether s/he is willing to accept the proposed allocations. In the modified dictator
game, the dictators must decide upon the amount of income they are willing to give up to
achieve an equal allocation of income between him-/herself and a recipient. Based on subjects’
decisions at every possible income distribution, α and β can be calculated for each subject.
Bartling et al. (2009) use four simple, binary distributional choices and categorize subjects into
prosociality, costly prosociality, envy, and costly envy. Güth et al. (2009) take a special form of
ultimatum game and dictator game in which they allow participants to choose the total payoff for
themselves and their paired player while fixing each decision maker’s share of the total payoff.5
Their results indicate that systematic differences in decisions are correlated with differences in
choice ranges. Dannenberg et al. (2007) adopt the ultimatum and modified dictator games
similar to Blanco et al. (2011), while eliminating possible strategic considerations. However, the
choice menus they used involve relatively complex numbers, and the total incomes of the two
matched players do not remain the same. Their design thus increases the cognitive burdens of
subjects. Kerschbamer (2010) develops a five-level choice menu that uses purely selfish options
located in the center and then includes inequity-aversion and inequity-seeking options
symmetrically. Given that this choice menu has only two categories in each direction, the
measured preferences for the inequity-aversion or inequity-seeking options are rough. Yang et al.
(2012) develop two simple choice menus that are not under the settings of ultimatum game or
modified dictator game and eliminate options of completely equal distribution; thus, they
emphasize subjects’ reactions to different levels of inequity.
From the comparisons, we find that the choice sets and relative income inequity differ
across all the studies that measure inequity aversion based on the F&S model. For instance, the
underlying value ranges of the choice menus for the α and β parameters used by Blanco et al.
(2011) are much higher compared with those in the menus used by Yang et al. (2012). Another
example is that the choice menu for the α parameter used in Blanco et al. (2011) has higher
relative income inequity than that of the menu in Dannenberg et al. (2007). Thus, differences in
choice sets and relative income inequity across choice menus make it more difficult to compare
4
Cooper and Kagel (2009) provide an excellent review of subsequent studies of Fehr and Schmidt (1999) after ten years have
passed from its being published.
5
Therefore, once the responder accepts the allocation, the decision does not involve any direct income cost or trade-off for
decision makers, no matter what decision is made.
4
measured parameters across studies. These differences can also be an important reason for the
variations in estimates of parameters and the variations in the predictive power of inequity
aversion across studies.
On the one hand, given that different studies have used menus with different choice sets
indicating different underlying inequity aversion parameter value ranges, essentially different
frames are used to measure the preferences6. Therefore, subjects may suffer from a “center-stage
effect” when making their decisions; in other words, people always tend to choose items in the
middle of a menu rather than on either of the two extreme sides (Valenzuela and Raghubir, 2009;
Dayan and Bar-Hillel, 2011; Rodway et al. 2012). Moreover, the change of choice sets may
increase the anchoring effect (Kahneman, 1992), which makes subjects unconsciously take the
first, the last, and the middle items as reference points, thereby affecting the measured strengths
of their other-regarding preferences. More generally, changes in choice sets per se can lead to
different revealed preferences and choices (DeShazo and Fermo, 2002; List, 2007; Bardsley,
2008). Thus, whether the strength of the inequity aversion parameters is sensitive to the choice
sets is the first question we investigate.
Hypothesis 1. Measured parameters of inequity aversion are subject to the systematic
influence of the choice set change. Specifically, a unidirectional extension of the choice set may
result in measurement bias in the same direction.
On the other hand, many studies offer evidence that people do care about relative income
inequity, as given by the proportion of the extra earning of one player to the other player (Agell
and Lundbrog, 1995; Clark and Oswald, 1996; Bewley, 1998) and the relative position of their
incomes within their respective comparison groups (Solnick and Hemenway, 1998; Pingle and
Mitchell, 2002; Akay et al. 2012), which is in addition to absolute income inequity. Plenty of
experimental evidence also shows that relative payoff has a strong influence on decisions
(Kahneman et al. 1986; Güth et al. 1982; Güth and Tietz, 1990; Fehr et al. 1993). However,
inequity aversion preference based on the F&S model only considers the absolute income
inequity between two players and does not take relative income inequity into account. Although
the model proposed by Bolton and Ockenfels (2000) considers relative inequity, no controlled
experiments or explicit analysis have been conducted to make comparisons between the
preferences for absolute and relative inequity aversion. This study attempts to answer the
following questions: Does relative income inequity affect people’s perception of “inequity” and
decisions related thereto? In addition, if there is such an effect, how do people’s decisions differ
from decisions made purely depending on absolute inequity, as in the F&S model?
Hypothesis 2. Changes of relative income inequity when absolute income inequity remains
the same affects the measured parameters of inequity aversion because people care about
relative inequity as well as absolute inequity.
3. Experimental design
To estimate the envy and guilt parameters as defined in the F&S model, we adopt the choice
menus developed by Yang et al. (2012) as our elicitation tool. We choose the menus mainly
6
A framing effect is an example of cognitive bias in which people react to a particular choice in different ways depending on
whether it is presented as a loss or as a gain (Plous, 1993). Levin et al. (1998) classify framing effects into three main types:
risky choice framing, attribute framing, and goal framing. The design of our experiment can be broadly classified as attribute
framing, in which we change only one attribute in each treatment that may trigger different decisions and outcomes.
5
based on three reasons. First, the choice menus are easily extendable and the extended choice
menus allow for a large choice set (i.e., wider interval of the possible value) of the α and β
parameters, and this extension is natural for subjects. Second, the choice menus eliminate
possible strategic consideration and the option of equal distribution, thereby decreasing the
influence of the explicit fairness concern that is implied by the equal distributed option on
subjects’ decisions. Finally, the structure of the menus is simple and readily understood, which
minimizes the cognitive burdens of subjects during the decision-making process.
Our experiment consists of a 2×2 between-subject experimental design with four treatments.
Table 1 presents our basic experimental design.
Table 1. Summary of experimental design
Large set
Small set
High relative inequity
Treatment 1
Treatment 3
Low relative inequity
Treatment 2
Treatment 4
The first dimension of our design involves small and large choice sets that imply small and
large value ranges of the inequity aversion parameters. In the “large set” treatment, the ranges of
values for the α and β parameters are -0.313≤α≤10 and -7≤β≤0.667, respectively, whereas in
the “small set” treatment, the value ranges of the same two parameters are -0.313≤α≤1 and
-0.143≤β≤0.667, respectively. Table 2 presents both the “large set” choice menus for α and β
(abbreviated as “large menu” hereafter). Subjects must choose one of two options in every
decision problem. From the first problem to the last problem, the incentive for choosing A is
decreasing, whereas the incentive for choosing B is increasing, such that decision makers are
expected to choose A in some of the earlier problems and B in some of the later problems.
Rational subjects should only switch once from A to B in each menu, or choose only A or only B
throughout the menu. The envy and guilt parameters are calculated as in Yang et al. by using
monotonic conversion.7 Then, the underlying α and β of the only switching point will be the
estimations of the decision maker’s envy and guilt parameters. It is notable that both the two
“large menus” reach the extension limits of menus used by Yang et al. (2012), and the
underlying parameters cover almost all the possible preference strengths.8
We construct the “small set” menus (abbreviated as “small menu” hereafter) by eliminating
several decision problems located in the extreme sides in the “large menus”. In other words,
small menus consist of Problems 1 to 22 of the large menu for α and Problems 7 to 24 of the
large menu for β, which means that extremely disadvantageous inequity aversion problems are
eliminated from the menu for α and extreme advantageous inequity aversion problems are
eliminated from the menu for β. The number of problems in the small menus is similar to the
number of choices in Yang et al. (2012), and the underlying parameter values in the small menus
cover the possible value ranges of most subjects’ revealed preferences, according to the data
from Yang et al. (2012).9
7
The calculation is based on the two-player version of the F&S model, i.e., equation (2). Take Problem 5 in the left panel of
Table 2 as an example, the utility is 130-α(150-130), with option A, and 100- α(260-100), with option B. If a subject is
indifferent between option A and B, i.e., 130-α(150-130) = 100- α(260-100), the underlying value of α will be -0.214. The
calculation method of the underlying value of β is similar.
8
Our large menus cover the value range of [-0.31, 10] and [-7, 0.67] for α and β, respectively. The extreme values of the envy
and guilt parameters thus cannot be reached by most decision makers.
9
Using Blanco et al. (2011)’s method, He and Villeval (2014) find that Chinese subjects’ inequity aversion preferences are
consistent with those of European subjects’ at the aggregate level. We thus use the results of Yang et al. (2012) from European
subjects to calibrate our choice of parameter ranges in “small menus”.
6
Table 2. “Large set” and “small set” choice menus for disadvantageous and advantageous inequity aversions
Disadvantageous inequity aversion (α)
Advantageous inequity aversion (β)
Option A
Option B
Option A
Option B
Decision
Choose B
Decision
Choose B
problem #
if:
problem # Yours
if:
Others’
Yours
Others’
Yours
Others’
Yours
Others’
1
205
90
170
50
1
150
150
100
260
β≤-7.000
α≤-0.313
2
200
90
170
50
2
145
150
100
260
β≤-3.000
α≤-0.290
3
140
150
100
260
3
195
90
170
50
α≤-0.267
β≤-1.667
4
135
150
100
260
4
190
90
170
50
α≤-0.241
β≤-1.000
5
130
150
100
260
5
185
90
170
50
α≤-0.214
β≤-0.600
6
125
150
100
260
6
180
90
170
50
α≤-0.185
β≤-0.333
7
120
150
100
260
7
175
90
170
50
α≤-0.154
β≤-0.143
8
115
150
100
260
8
170
90
170
50
α≤-0.120
β≤0.000
9
110
150
100
260
9
165
90
170
50
α≤-0.083
β≤0.111
10
105
150
100
260
10
160
90
170
50
α≤-0.043
β≤0.200
11
100
150
100
260
11
155
90
170
50
α≤0.000
β≤0.273
12
95
150
100
260
12
150
90
170
50
α≤0.048
β≤0.333
13
90
150
100
260
13
145
90
170
50
α≤0.100
β≤0.385
14
85
150
100
260
14
140
90
170
50
α≤0.158
β≤0.429
15
80
150
100
260
15
135
90
170
50
α≤0.222
β≤0.467
16
75
150
100
260
16
130
90
170
50
α≤0.294
β≤0.500
17
70
150
100
260
17
125
90
170
50
α≤0.375
β≤0.529
18
65
150
100
260
18
120
90
170
50
α≤0.467
β≤0.556
19
60
150
100
260
19
115
90
170
50
α≤0.571
β≤0.579
20
55
150
100
260
20
110
90
170
50
α≤0.692
β≤0.600
21
50
150
100
260
21
105
90
170
50
α≤0.833
β≤0.619
22
45
150
100
260
22
100
90
170
50
α≤1.000
β≤0.636
23
40
150
100
260
23
95
90
170
50
α≤1.200
β≤0.652
24
35
150
100
260
24
90
90
170
50
α≤1.444
β≤0.667
25
30
150
100
260
α≤1.750
26
25
150
100
260
α≤2.143
27
20
150
100
260
α≤2.667
28
15
150
100
260
α≤3.400
29
10
150
100
260
α≤4.500
30
5
150
100
260
α≤6.333
31
0
150
100
260
α≤10.000
Notes: 1. The underlined choices are those used by Yang et al. (2012); italicized choices are what we used in our “small set” menus. 2. The menus
used in our experimental instructions do not include the last column of underlying parameters.
7
We add an identical amount of 100 experimental points to both players that results in
changes in relative income inequity, whereas absolute inequity remains constant between the two
treatments. Thus, we construct “high relative inequity” and “low relative inequity” choice menus
(referred to as “high menu” and “low menu”, respectively, hereafter) in this manner as the
second dimension in our design. We construct the relative income inequity index for each option
by calculating the proportion of the extra earning of the counterpart player to the decision-maker
in this option.10 The results shown in Table A2 in the appendix indicate that the relative income
inequity of Option A surpasses that of Option B from Problem #20 forward in the high menu,
whereas it does so from Problem #24 in the low menu. In other words, the aversion to relative
income inequity should drive the switching point move downward from the high menu to the
low menu. Given that the utility in the F&S model is only the function of absolute inequity and
not relative inequity, envy and guilt parameters measured from the high and low menus should
be identical. In other words, individuals who make decisions according to the F&S model should
switch from A to B at the same problem in both the high and low menus. If relative inequity has
influence on individuals’ decisions, the utility gained from the corresponding problems in the
two menus should change. For instance, to reduce the relative inequity with the matched player,
a player who cares about relative income inequity should switch from A to B earlier in the high
menu than in the low menu.
The experiment was conducted at Beijing Normal University in Beijing, China. We
recruited 129 adult subjects in different majors from Spare-time College. These are people who
work in the daytime and attend classes at night or on the weekends to earn a junior college or a
bachelor’s degree. Most subjects already have several years’ working experience and are thus
more representative of the ordinary adult population than university students. Each subject can
only participate in one session. In the experiment, we control for the appearance order of the
menus and the appearance order of the problems in each menu to minimize possible anchoring
and order effects. Furthermore, we impose a single switching restriction between A and B in
each menu11. In addition, the subjects were informed that they could switch from the first
problem and that they were also allowed to not switch at all. After completion of the experiment,
subjects were asked to fill out questionnaires to collect demographic characteristics and the Big
Five as personality indicators.12 Subjects received no feedback on the outcome until the end of
the entire experiment. Sessions lasted approximately 40 minutes, and participants received an
average of 18.65 Yuan ($3.04 at the time of this experiment) in cash.
4. Results
The descriptive statistics on the demographic information of our adult subjects is reported in
10
In other words, we calculate this index, which is defined as “(others’ income-your income)/your income”.
Rational players with monotone preferences should switch only once from Option A to Option B. Imposing single switching
facilitates decision making and rules out inconsistent choices. The same procedure has been applied by Tanaka et al. (2010) and
Liu (2012) to elicit risk preferences and time consistency.
12
Borghans et al. (2008) review studies that combine economics and personality differences. The effects of personality
differences on various economic behavior have also been found in many laboratory experimental studies (Volk, Thoni, and
Ruigrok, 2011; Panaccio and Vandenberghe, 2012), but few papers have controlled personality traits when measuring inequity
aversion. The Big Five model is a widely accepted personality measure and interpretative dimension (Digman and
Takemoto-Chock, 1981; Fiske, 1949; Norman, 1963). The five dimensions in this model are as follows: neuroticism, which is a
tendency to experience negative emotions and sometimes called emotional instability; extraversion, which is characterized by
breadth of activities, surgency from external activity/situation and energy creation from external means; openness, which is a
general appreciation for art, emotion, adventure, unusual ideas, imagination, curiosity, and a variety of experience; agreeableness,
which reflects individual differences in general concern for social harmony; conscientiousness, which is a tendency to show
self-discipline, dutiful action, and aim for achievement against measures or outside expectations.
11
8
Table 3.13 These statistics show that 66% of the subjects are female, and the average age is 24.8
years. Slightly more than half originally come from rural areas and the average number of years
of schooling is 15. These socioeconomic characteristics are close to those of ordinary university
students but with larger variances. The length of time working full-time is up to 4.3 years with
average monthly income of 3,800 Chinese yuan. In addition, 32% of the participants are the only
child in their families, and the average family size is 2.78 persons. These characteristics,
however, differ significantly from those of students.
Table 3. Descriptive statistics of subjects’ demographic information (N=129)
Variable Name
Variable Definition
Mean
Std.Dev.
Min
Max
Female
= 1 if the subject is a female
0.66
0.48
0
1
Age
= age of subject (years)
24.77
4.94
18
57
Rural register
= 1 if the subject is registered as a rural resident
0.51
0.52
0
1
Education years
= subject’s years of schooling (years)
15.02
1.93
10
20
Working experience
= length of time working full-time (years)
4.27
4.32
0
37
3.80
2.73
0
20
0.32
0.47
0
1
2.78
1.32
0
6
Monthly income
Only child
Family size
= subject’s net monthly income divided by 1,000
(thousand yuan)
= 1 if the subject is the only child in his/her family
= number of family members living in the
subject’s household (persons)
We estimate the inequity aversion parameters for each subject as the interval between the
underlying parameters of the two decision problems at their switching points.14 Because the
choice menus used in treatment 3 (small set and high relative inequity choice menus) are similar
to the original menus used in Yang et al. (2012), it allows us to compare our data with their data.
Figure 2 shows that the distribution of α in our data is similar to that in Yang et al., whereas the
distribution of β in our data moves right and turns out to be closer to the distribution in Fehr and
Schmidt (1999) and Blanco et al. (2011). Our aggregate data show that 34.11% of the subjects
have estimated negative β15 compared with 56.94% negative β in Yang et al., which indicates
that a significant proportion of subjects are advantageous inequity seeking.
13
The descriptive statistics of treatment variables and other control variables are reported in Table A1 in Appendix I.
For example, if a subject choses A before Problem 16 and switches to B after Problem 16, the real α should fall between the
underlying α of Problem 15 (0.222) and the underlying α of Problem 16 (0.294). Following Blanco et al. (2011), we take the
mean value of the lower and upper bounds (0.222+0.294)/2=0.258 as the estimated α in our descriptive statistics. Blanco et al.
demonstrate that this simplification does not affect the results of the descriptive statistics, and we will use interval regressions to
consider the interval characteristics of the data.
15
29.5% of the aforementioned 34.11% subjects actually chose B before Problem 8 (the last decision problem with negative β),
and switched to A after Problem 8 (the first decision problem with positive β). These subjects might be slightly inequity-seeking
or completely selfish. Taking this into account, at least 24.0% of the entire subjects show advantageous inequity seeking.
14
9
β
100%
Frequency of choices in each treatment
Frequency of choices in each treatment
α
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
<0.25
0.25-0.75
0.75-1.25
>=1.25
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
<0.125
0.125-0.375
α Interval
>=0.375
β Interval
Treatment 3
Yang et al.
Figure 2. Aggregate inequity parameter distributions of our data compared with Yang et al.
Table 4 reports the descriptive statistics for α and β. Comparisons between Treatments 1
and 3 and Treatments 2 and 4 show that the mean α is larger in the large set treatment that allows
more decision problems with extreme high α values (p=0.043, Kolmogorov-Smimov Test),
whereas the mean β is smaller in the large set treatment that allows more decision problems with
extreme low β values (p=0.002, Kolmogorov-Smimov Test). In other words, the estimated α and
β change consistently in the unidirection of the choice set variation. Furthermore, comparisons
between Treatments 1 and 2 and Treatments 3 and 4 show that both the α and β parameters are
lower in high relative inequity treatments than in low inequity treatments (although the
difference is not significant with Kolmogorov-Smimov Tests), showing that relative income
inequity may change the estimated α and β parameters in the F&S model. The reason might be
that relative income inequity in Option A drops more quickly to the level in Option B in the
menus with high relative inequity menus, which leads to decision-makers switching from A to B
earlier in the high menus if they care about relative income inequity. In fact, if subjects only care
about relative income inequity (but do not care at all about absolute income inequity) when
addressing the α menus, they should switch to Option B beginning with Problems #20 and #24 in
the high and low relative inequity treatments, respectively. The standard deviations of both α and
β parameters are larger in Treatments 1 and 2, given that the possible range of their distribution
is wider in the two treatments.
Table 4. Descriptive statistics of α and β in various treatments
Treatment
Disadvantageous inequity
Advantageous inequity
aversion (α)
aversion (β)
T1
T2
T3
T4
T1
T2
T3
T4
Mean
0.30
1.05
0.02
0.05
-2.12
-1.18
0.26
0.31
Std. Dev.
1.73
2.82
0.29
0.22
3.44
2.97
0.30
0.29
Min
-0.31
-0.31 -0.31
-0.31
-7.00
-7.00
-0.14
-0.14
Max
10.00 10.00
1.00
0.92
0.67
0.67
0.67
0.67
31
29
34
35
31
29
No. of Obs.
34
35
10
Table 5 reports the regressions results of the determinants of the value of α (models (1) to
(2)) and the β (models (3) to (4)), as calculated from all 4 treatments. The dependent variables are
the values of the α or β parameters, whereas the independent variable vector X consists of several
components, i.e., X = (X0, Xi, Xj, Xm, Xn, Xr). Xi are the key treatment variables for the large set
and low relative inequity, whereas all the other variables take the role of controls in the tests: Xj
denotes the reversed appearance order of menus and decision problems; Xn denotes the
socioeconomic variables of the respondents and their families; Xm expresses various personality
indicators; and X0 is the constant term. The dependent variables α and β have an interval data
structure, i.e., some unknown values in certain intervals. Therefore, the interval regression model
(Stewart, 1983) is used.
Table 5. Interval regressions of the α and β parameters
Disadvantageous inequity
Advantageous inequity
aversion (α)
aversion (β)
Variable Name
Large set
Low relative inequity
Reversed problem order
Reversed menu order
Female
Age
Rural register
Years of education
Working experience
Monthly income
[1]
[2]
[3]
[4]
0.623*
0.628*
-1.597***
-1.456**
(0.342)
(0.346)
(0.548)
(0.566)
0.384
0.314
1.262**
1.271**
(0.342)
(0.348)
(0.550)
(0.566)
0.623*
0.784**
-0.258
-0.323
(0.334)
(0.345)
(0.535)
(0.557)
0.286
0.328
-0.0409
0.0497
(0.372)
(0.382)
(0.590)
(0.618)
0.227
0.283
0.970
0.983
(0.373)
(0.377)
(0.594)
(0.612)
0.0732
0.0659
-0.0331
-0.0319
(0.0756)
(0.0758)
(0.121)
(0.123)
0.365
0.224
-1.187*
-1.291*
(0.408)
(0.421)
(0.656)
(0.690)
0.0701
0.0950
0.488***
0.462***
(0.0960)
(0.0966)
(0.153)
(0.157)
-0.119
-0.116
0.00587
-0.00349
(0.0844)
(0.0845)
(0.134)
(0.136)
-0.0394
-0.0787
0.0248
0.0714
(0.0662)
(0.0708)
(0.107)
(0.118)
0.127
0.0998
0.341*
0.341
(0.128)
(0.129)
(0.206)
(0.209)
-0.665
-0.617
-0.322
-0.362
(0.448)
(0.448)
(0.708)
(0.721)
Having participated in an
0.355**
0.341**
-0.245
-0.230
experiment
(0.142)
(0.147)
(0.225)
(0.237)
-3.609*
0.628*
-7.906**
-1.456**
(1.913)
(0.346)
(3.136)
(0.566)
Big Five controlled
No
Yes
No
Yes
No. of Observations
126
124
126
124
Family size
Single child
Constant
11
Chi-square
23.28**
26.62*
31.43***
32.99**
Notes: Marginal effects are reported and standard errors are in parentheses. *** indicates
significance at the 0.01 level, ** at the 0.05 level, and * at the 0.10 level. Three and five
subjects who did not complete demographic and personality questionnaires are not included
in the sample, respectively.
The regression results confirm that the effects that we observe in the descriptive statistics
section are statistically significant. On the one hand, changes of choice set ranges significantly
affect the estimated disadvantageous and advantageous inequity aversion parameters.
Specifically, adding decision problems implying higher values in the α menu significantly
increases disadvantageous inequity aversion, whereas adding decision problems implying lower
values in the β menu significantly decreases advantageous inequity aversion. Our results show
that choice set variation across studies can explain at least some of the differences in the
estimated values of inequity aversion among the different studies. For example, compared with
Yang et al., the choice menus used by Blanco et al. allow larger values of α and β, which leads
the estimated values of α and β to be larger. On the other hand, the estimated value of the
advantageous inequity aversion parameter is significantly larger in the treatments with low
relative income inequity because relative income inequity in Option A drops more slowly to the
level in Option B in the low menus. However, relative income inequity does not affect
disadvantageous inequity aversion.
Our results also show that the reversed appearance order of decision problems, which leads
subjects to make decisions beginning with problems implying higher values of the parameters,
increases the value of the α parameter, but has no effect on the β parameters. As for the effects of
the demographic variables, those participants registered as rural residents and having fewer years
of schooling significantly reduce the degree of advantageous inequity aversion, which may be
due to the weak preference for advantageous inequity aversion in general (Loewenstein et al.,
1989; Fehr and Schmidt, 1999; Blanco et al., 2011). If we include multi-dimensional personality
indicators into the models, the constant term in the regression for the α parameter becomes
smaller and is no longer significant, which suggests that these personality indicators have
aggregate effects on the α parameter, although the effects are small in regard to specific
personality dimensions.
5. Conclusions
Accurate elicitation of the inequity aversion preference is the foundation for using it as the
important interpretation for many real world economic behaviors and consequences. We adopt a
2×2 experimental design to investigate how the elicitation of inequity aversion is affected by the
asymmetric variation in choice sets of the underling inequity aversion parameters and by the
change of relative income inequity when absolute income inequity remains fixed.
Our experimental results show that asymmetric variation in choice sets leads both
advantageous and disadvantageous inequity aversion to change in the same direction. The
variances of the estimated inequity aversion parameters also increase with the choice set ranges.
Therefore, it is important to standardize the experimental method of eliciting inequity aversion
preferences. In addition, if absolute income inequity remains constant, the measured
advantageous inequity aversion varies with relative income inequity, whereas disadvantageous
inequity aversion does not change with relative income inequity. This finding confirms that the
12
disadvantageous inequity aversion preference is more robust than the advantageous inequity
aversion preference (Fehr and Schmidt, 1999).
Our results suggest that the choice menus affect inequity aversion preferences through
choice set ranges and relative income inequity, implying that the α and β parameters elicited in
previous studies using menus with different choice sets and different levels of relative income
inequity are not particularly comparable, which might be a reason why previous studies have
found contradictory evidence regarding the explanatory power of the inequity aversion
parameters on related behaviors (e.g., Blanco et al. vs. Yang et al.). Hence, choice set ranges and
relative income inequity should be controlled when eliciting inequity aversion preferences.
Further research is needed to explore the effects of other potential influencing factors on inequity
aversion preferences, such as emotions, personal experiences, and reference points.
13
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16
900
The number of citations
The number of citations
Appendix I. Additional figures and tables
700
500
300
100
‐100
Google scholar
30000
25000
20000
15000
10000
5000
0
ISI web of science
Figure A1a. The number of papers that cited Fehr and Schmidt (1999) across the years (data
sources: Google scholar and ISI web of science; data collected in December, 2013).
Figure A1b. The total number of papers that have cited Fehr and Schmidt (1999) and various
important papers by Nobel laureates related to behavioral economics and game theory (data
sources: Google scholar and ISI web of science; data collected in May, 2014).
Table A1. Descriptive statistics for treatment variables and other control variables in the
regressions (N=129)
Variable
Definition
Mean
Large set menu
0=“small set” treatment, 1=“large set” treatment
Low relative
1=“low relative inequity” treatment, 0=“high
Inequity
relative inequity” treatment
Menu orders
Choices orders
1=menus shown in reverse order, 0=menus shown
in regular order
1=choices in menus shown in reverse order,
0=choices in menus shown in regular order
Std. Dev.
Min
Max
0.53
0.50
0
1
0.50
0.50
0
1
0.49
0.50
0
1
0.64
0.48
0
1
0.28
0.45
0
1
Experiment
1=has participated in experiments, 0=has not
Experience
participated in experiments
Neuroticism
Big Five personality dimension (5-25)
14.63
3.08
7
25
Extraversion
Big Five personality dimension (5-25)
17.60
2.84
9
25
Openness
Big Five personality dimension (5-25)
15.56
3.01
6
25
Agreeableness
Big Five personality dimension (5-25)
20.03
3.18
12
25
Conscientiousness
Big Five personality dimension (5-25)
19.11
2.81
12
25
Grit
grit scale (12-60)
42.22
8.46
16
60
Promotion
regulatory focus (1-5)
3.36
0.61
1.67
4.67
Prevention
regulatory focus (1-5)
3.42
0.67
1.4
5
17
Table A2. “High relative inequity” and “low relative inequity” choice menus for disadvantageous inequity aversion
Disadvantageous inequity aversion (α) – High Menu
Disadvantageous inequity aversion (α) – Low Menu
Decision
Option A
Option B
Relative
Relative
Decision
Option A
Option B
Relative
Relative
problem
inequity
inequity
problem
income
income
Yours
Others’
Yours
Others’
Yours
Others’
Yours
Others’
#
of A:
of B:
#
of A:
of B:
1
150
150
100
260
0.000
1.600
1
250
250
200
360
0.000
0.800
2
145
150
100
260
0.034
1.600
2
245
250
200
360
0.020
0.800
3
140
150
100
260
0.071
1.600
3
240
250
200
360
0.042
0.800
4
135
150
100
260
0.111
1.600
4
235
250
200
360
0.064
0.800
5
130
150
100
260
0.154
1.600
5
230
250
200
360
0.087
0.800
6
125
150
100
260
0.200
1.600
6
225
250
200
360
0.111
0.800
7
120
150
100
260
0.250
1.600
7
220
250
200
360
0.136
0.800
8
115
150
100
260
0.304
1.600
8
215
250
200
360
0.163
0.800
9
110
150
100
260
0.364
1.600
9
210
250
200
360
0.190
0.800
10
105
150
100
260
0.429
1.600
10
205
250
200
360
0.220
0.800
11
100
150
100
260
0.500
1.600
11
200
250
200
360
0.250
0.800
12
95
150
100
260
0.579
1.600
12
195
250
200
360
0.282
0.800
13
90
150
100
260
0.667
1.600
13
190
250
200
360
0.316
0.800
14
85
150
100
260
0.765
1.600
14
185
250
200
360
0.351
0.800
15
80
150
100
260
0.875
1.600
15
180
250
200
360
0.389
0.800
16
75
150
100
260
1.000
1.600
16
175
250
200
360
0.429
0.800
17
70
150
100
260
1.143
1.600
17
170
250
200
360
0.471
0.800
18
65
150
100
260
1.308
1.600
18
165
250
200
360
0.515
0.800
19
160
250
200
360
0.563
0.800
19
60
150
100
260
1.500
1.600
20
155
250
200
360
0.613
0.800
20
55
150
100
260
1.727
1.600
21
50
150
100
260
2.000
1.600
21
150
250
200
360
0.667
0.800
22
45
150
100
260
2.333
1.600
22
145
250
200
360
0.724
0.800
23
40
150
100
260
2.750
1.600
140
250
200
360
0.786
0.800
23
24
35
150
100
260
3.286
1.600
135
250
200
360
0.852
0.800
24
25
30
150
100
260
4.000
1.600
25
130
250
200
360
0.923
0.800
26
25
150
100
260
5.000
1.600
26
125
250
200
360
1.000
0.800
27
20
150
100
260
6.500
1.600
27
120
250
200
360
1.083
0.800
28
15
150
100
260
9.000
1.600
28
115
250
200
360
1.174
0.800
29
10
150
100
260
14.000
1.600
29
110
250
200
360
1.273
0.800
30
5
150
100
260
29.000
1.600
30
105
250
200
360
1.381
0.800
31
0
150
100
260
N/A
1.600
31
100
250
200
360
1.500
0.800
Notes: 1. Relative inequity is calculated as (income of the other person – income of oneself)/income of oneself; 2. The underlined choices are those used by Yang et al. (2012).
Italicized choices are what we used in our “small set” menus. Bold choices are where people who care only about relative income inequity should switch from option A to option
B. 3. The menus used in our experimental instructions do not include the last two columns of underlying relative income inequities.
18
Appendix II. Instructions for Treatment 1 (only for refereeing purpose, originally in
Chinese)
You will be randomly paired with another participant in this room. You will not be informed
about who you are paired with, and your paired participant will not be informed about who
he/she is paired with during and after the experiment. Your payoff will depend on the decisions
made by you and your paired participant.
You will make 55 decision problems: 31 in Menu 1 and 24 in Menu 2. There are two options in
each problem. You must make a decision between Option A and Option B.
Here is an example of how you make the decisions. Take Problem 1 in Menu 1 as an example:
Decision
Option A
problem
Option B
Yours
Others
Yours
Others
(player X)
(Player Y)
(Player X)
(Player Y)
In the role of Player A, you must choose either Option A or Option B in each problem. There are
two numbers in each option, one representing your payoff as player X, and the other representing
the payoff of your paired participant as player Y. For example, if you choose Option B in this
example, your payoff is 100 experimental points, and your paired participant gets 260
experimental points.
Below is Menu 1 with 31 decision problems:
Decision
Option A
problem
Option B
Yours
Others
Yours
Others
(player X)
(Player Y)
(player X)
(Player Y)
Below is Menu 2 with 24 choices:
Decision
problem
Option A
Option B
Yours
Others
Yours
Others
(player X)
(Player Y)
(player X)
(Player Y)
You must make decisions in the following manner:
You must decide the number of the decision problem until which you choose Option X and
after which you choose Option Y. You will have to fill in an integer number into one of the
two boxes on your decision sheet as indicated below, to specify your decision. In other words,
your decisions must be specified in the following format (please do not make decisions now or
fill in your decisions here):
In Menu 1, you choose A from Problem 1 to Problem
;
you choose B from Problem
to the last problem.
In Menu 2, you choose A from Problem 1 to Problem
;
19
you choose B from Problem
to the last problem.
Note that for each menu, the number you fill in the second box should be the number you fill in
the first box plus 1. For example:
Example 1: If you want to choose Option A for Problems 1-9 and Option B from Problem 10
forward in Menu 1, and choose Option A for Problems 1-13 and option B from choice 14
forward in Menu 2, you should fill in the number as follows:
In Menu 1, you choose A from Problem 1 to Problem
9
;
you choose B from Problem
10
to the last problem.
In Menu 2, you choose A from Problem 1 to Problem
13
;
you choose B from Problem
14
to the last problem.
Example 2: If you want to choose Option A for all problems in Menu 1, you should write “31” in
the first box, and do not write any number into the second box; if you want to choose Option
B for all problems in Menu 2, you should not write any number in the first box, and write “1”
in the second box as follows:
In Menu 1, you choose A from Problem 1 to Problem
31
;
you choose B from Problem
to the last problem.
In Menu 2, you choose A from Problem 1 to Problem
;
you choose B from Problem
1
to the last problem.
Payoff Determination
You must make decisions for 55 problems (31 in Menu 1 and 24 in Menu 2). At the end of the
experiment, one of the 55 problems will be randomly selected to determine payoff, and the
computer program will randomly assign you as the role of Player X or Player Y. If you are
assigned the role of Player X, your payoff will be determined as the amount you have chosen for
Player X. If you are assigned the role of Player Y, your payoff will be determined as the amount
your paired participant has chosen for Player Y.
For example, suppose the computer program randomly selects Problem 21 in Menu 1 to
determine the payoff, and you chose A and your paired participant chose B. If the program
randomly assigns you as the role of Player X, your payoff is 50 points and your paired
participant’s payoff is 150. If the program randomly assigns you to the role of Player Y, your
paired participant’s payoff is 100 and your payoff is 260 points.
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Decision Sheet
ID__________
Please fill in your ID in the upper left corner, and then fill in your decisions for the Menu 1
and Menu 2:
In Menu 1, you choose A from choice 1 to choice__________;
you choose B from choice__________ to the last choice.
In Menu 2, you choose A from choice 1 to choice__________;
you choose B from choice__________ to the last choice.
21