Skewness-adjusted social preferences: Experimental evidence on the relation between inequality, elite behavior, and economic efficiency

Accepted Manuscript

Skewness-adjusted Social Preferences: Experimental Evidence on the Relation between Inequality, Elite Behavior, and Economic Efficiency Fabian Paetzel, Stefan Traub PII: DOI: Reference:

S2214-8043(17)30043-5 10.1016/j.socec.2017.05.001 JBEE 275

To appear in:

Journal of Behavioral and Experimental Economics

Received date: Revised date: Accepted date:

20 February 2016 2 May 2017 2 May 2017

Please cite this article as: Fabian Paetzel, Stefan Traub, Skewness-adjusted Social Preferences: Experimental Evidence on the Relation between Inequality, Elite Behavior, and Economic Efficiency, Journal of Behavioral and Experimental Economics (2017), doi: 10.1016/j.socec.2017.05.001

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Highlights • We model social preferences as a function of the skewness of the distribution of initial endowments. Skewness is a measure of the asymmetry of the distribution of endowments around the mean. We argue that skewness reflects the social distance between ‘elite’ players with high initial endowments and other players with lower endowments, better than variance and concentration measures like the Gini-coefficient.

CR IP T

• We hypothesize that elite players become more selfish with increasing skewness and therefore contribute less to a public good in the framework of a one-shot non-linear public good game. • The results of an experimental test, in which we systematically vary the distribution of endowments between treatments, confirm that the model is able to correctly explain the observed pattern of contribution behavior.

AN US

• We find that cooperation and efficiency are lowest with right-skewed distribution of endowments.

AC

CE

PT

ED

M

• Our paper therefore improves the understanding of the behavioral link between inequality and efficiency.

1

ACCEPTED MANUSCRIPT

Skewness-adjusted Social Preferences: Experimental Evidence on the Relation between Inequality, Elite Behavior, and Economic Efficiency Fabian Paetzel∗ and Stefan Traub

AN US

Revised Version, May 2017

CR IP T

Department of Economics & FOR 2104, Helmut-Schmidt-University, Hamburg, Germany

M

Abstract

AC

CE

PT

ED

In this paper, we model social preferences as a function of the skewness of the distribution of initial endowments. Skewness is a measure of the asymmetry of the distribution of endowments around the mean. We argue that skewness reflects the social distance between ‘elite’ players with high initial endowments and other players with lower endowments, better than variance and concentration measures like the Gini-coefficient. We hypothesize that elite players become more selfish with increasing skewness and therefore contribute less to a public good in the framework of a one-shot non-linear public good game. The results of an experimental test, in which we systematically vary the distribution of endowments between treatments, confirm that the model is able to correctly explain the observed pattern of contribution behavior. We find that cooperation and efficiency are lowest with right-skewed distribution of endowments. Our paper therefore improves the understanding of the behavioral link between inequality and efficiency.

JEL classification: C91, D31, H41 Keywords: Experiment, Inequality, Social Preferences, Elites, Non-linear public good game ∗

Corresponding author. Department of Economics & DFG Research Group FOR 2104, HelmutSchmidt-University, Hamburg, Germany, [email protected]. We thank Matthias Greiff, Bernhard Kittel, James Konow, Roland Menges, Martin Missong, Joe Oppenheimer, Valentin Schr¨ oder, Rupert Sausgruber, Henning Schwardt, Bj¨ orn Vollan for helpful comments. All remaining errors are our own.

ACCEPTED MANUSCRIPT

1

Introduction

AC

CE

PT

ED

M

AN US

CR IP T

The questions of how (rising) inequality influences people’s behavior, the selfishness of their actions, and economic efficiency is a hotly debated issue both in many academic disciplines and in the public.1 Recent work in psychology and economics suggests that upper-class individuals act less ethically than lower-class individuals (e.g. Piff et al. 2012). Trautmann et al. (2013) give an overview of how different dimensions of being upper class (wealth, income, education) are associated with different ethical and unethical behaviors. Even though there is no clear-cut evidence that members of the elite are more selfish in general, it seems to be an empirical regularity that their behavior differs from non-elite people in some dimensions. In this paper, we neither attribute behavioral differences between the ‘elite’ and the rest of society to endowment differences nor to self selection (a positive correlation between selfishness and endowment); rather we hypothesize in line with Cote et al. (2015) and Heap et al. (2016) that the inequality in the society itself makes elite members more selfish and less generous. Thus, we offer a new perspective on the relation between inequality, elite behavior, and economic efficiency. Inequality, however, is an imprecise term that has many facets. To be more precise, we believe the shape of the endowment distribution in terms of its skewness to cause individual behavioral responses of elite members. Skewness is a measure of the asymmetry of the distribution of endowments around the mean. At the societal level, these responses then affect economic efficiency (in the Kaldor-Hicks sense). In our opinion it is self-evident to focus on skewness as it reflects the social distance between elite players with high initial endowments and other players with lower endowments, better than variance and concentration measures like the Gini coefficient. In a group with a right-skewed endowment distribution, a small high-endowment elite is contrasted with a large number of low-endowment players; in a group with a symmetric endowment distribution equally sized groups of high- and low-endowment players interact. Certainly, an elite player’s perception of her social position in relation to low-endowment players will differ between these two groups. We formalize these consideration by means of a skewness-adjusted model of social preferences, a modification of Charness and Rabin (2002). In the framework of this model, we are able to test the hypothesis that the more skewed the endowment distribution is, the greater is the weight that a high-endowment player assigns to her own payoff (the terms ‘more skewed’ and ‘increasing skewness’ mean that probability mass is shifted from the upper to the lower tail of the endowment distribution, that is, it becomes more right-skewed). The experimental test is done by means of a three person non-linear public good game. We systematically vary the variance, the skewness and also the Gini-coefficient of the endowment distribution in order to compare their influence on social preferences and individual contributions to the public good. Due to the non-linearity of the payoff function, the social optimum in terms of highest group payoffs is achieved with moderate contributions. As a consequence of increasing selfishness in high-income players treated with more skewed endowment distributions, we expect to observe group efficiency to be suboptimal and 1

For example, Piketty (2015) calls for putting distribution back at the center of economics. A recent special report of the OECD (2015) was titled “In It Together: Why Less Inequality Benefits all”.

3

ACCEPTED MANUSCRIPT

2

Literature Review

AN US

CR IP T

to decrease in skewness. The experimental results show that the skewness-adjusted social-preference model is able to explain both individual contributions and the level of group efficiency. Selfishness is smallest and group contributions are largest in groups with left-skewed endowment distribution; selfishness is highest and contributions are lowest in groups with right-skewed endowments distribution. This effect is shown to be primarily due to the fact that the selfishness of high-endowment players is positively correlated with the skewness of the initial distribution of endowments. Together with the finding that group contributions are higher than the purely selfish and lower than grouppayoff maximizing utilitarian prediction in all treatments, we draw the conclusion that efficiency is lowest if inequality in terms of skewness is highest, that is, if the endowment distribution is right-skewed. The rest of the paper is organized as follows. Section 2 reviews the relevant literature. Section 3 presents the skewness-adjusted social-preference model and derives hypotheses. In Section 4, we give a description of the experimental design. Section 5 presents the results of the experiment. Section 6 concludes.

AC

CE

PT

ED

M

Our work touches several branches of the literature, which are briefly summarized here. The next two paragraphs link our work to previous work on elites in psychology and economics. Recent work in psychology suggests that upper-class individuals behave less ethically than lower-class individuals. Grossmann and Varnum (2011), Kraus and Keltner (2009), Kraus et al. (2011) and Lammers et al. (2012) find that upper class individuals show more dispositional attributions, less empathic accuracy, more selfinterest and less engagement in social interactions. For instance, Piff et al. (2012) show that the less-ethical behavior of upper-class individuals can also be observed in real-life situations such as breaking the law of the road more frequently. Trautmann et al. (2013) give an overview of how different dimensions of being upper class (wealth, income, education) are associated with different ethical and unethical behavior. For example, they show that only wealthy people (not people with high income or high education) judge ‘cheating on taxes’ more often as not being ‘unethical’. Even though there is no clear-cut evidence that members of the elite behave always more selfish, it seems to be an empirical fact that members of elites behave in some dimensions differently from non-elite members. The basic idea that the behavior of the elite is important to consider in the politico-economic system is not new. Sokoloff and Engerman (2000), Acemoglu et al. (2005), and Glaeser et al. (2003) highlighted the importance of elites in the process of development of countries. For example, Glaeser et al. (2003) stress the probability of having efficient institutions, which induce positive effects for development of a society, to be reduced in the presence of high inequality. The rationale behind this argument is that if inequality is high, the elite has an interest in securing their own stakes. We do not want to overemphasize the link between this work and experimental work, but it seems to us that understanding how members of the elite are affected by the shape of the distribution is also essential for understanding how inequality has an 4

ACCEPTED MANUSCRIPT

AC

CE

PT

ED

M

AN US

CR IP T

effect on development. The literature offers a broad variety of concepts for modeling social preferences. Depending on the relative weights given to own and other persons’ payoff or utility, one can allow for altruism, envy, inequality aversion, efficiency preferences, competitive preferences and so on (for an overview, see Fehr and Schmidt, 2006; Erlei, 2008). Different formal models of social preferences have been introduced, for example, by Fehr and Schmidt (1999), Bolton and Ockenfels (2000) and Charness and Rabin (2002). Our social preference functional is a modification of the Charness and Rabin (2002) model, adjusted for skewness in the three-person case (for details see the next section). We test our skewness-adjusted social preference model within the framework of a non-linear public good game. See Laury and Holt (2008) for a general overview of non-linear public good experiments. Prominent examples of non-linear public good experiments are Isaac and Walker (1998) and Vesterlund (2012). We decided to use a non-linear game, because they have interior Nash-equilibria and group efficiency is not necessarily highest where the sum of individual contributions is highest, that is, over-contribution is possible. A bunch of papers analyze the effect of inequality in terms of endowment heterogeneity on contributions using linear public good experiments, comparing treatments with equal and unequal endowments (Issac and Walker, 1988; Sutter and Weck-Hannemann, 2003; Cherry et al., 2005; Buckley & Croson 2006; Anderson et al., 2008; Keser et al., 2011; Reuben and Riedl, 2013). Bergstrom et al. (1986), Chan et al. (1996) and Chan et al. (1999) analyze the effect from endowment heterogeneity on contributions in a non-linear pubic good experiment. See Zelmer (2003) for a meta-analysis. Their findings are mixed, but the overall effect of inequality on contributions seems to be negative. Put differently, endowment heterogeneity seems to stimulate selfish behavior in subjects playing public-goods games. The following two recently published papers are most closely related to our work. Heap et al. (2016) find that endowment inequality has an effect only on public good contributions of the ‘rich’ players, while the contributions of the ‘poor’ players are not affected by inequality. The paper carefully shows that the lower contributions on part of the rich are not caused by their higher endowments but by inequality. However, the authors do neither provide a theoretical foundation of their observations nor focus on the shape of the endowment distribution. Cote et al. (2015) propose a similar causality running from inequality to selfishness of high-income individuals. They find evidence in a nationally representative survey that only in the most unequal US states, higher-income individuals are less generous than lower income individuals. They add supporting experimental evidence from a dictator game: high-income individuals give less than low-income individuals only if inequality is high. In contrast to Cote at al. (2015), we use a three-player public good game instead of a dictator game and systematically vary the shape of the endowment distribution. We make four contributions to these literatures: First, we present a new socialpreference functional, which models social preferences as a function of the skewness of the endowment distribution. Second, we show how such preferences can affect the contribution behavior of the better-off in a public good game. Third, we present experimental evidence that better-off subjects react to skewness in the way hypothesized and show that relative utility-weighting is neither a function of the Gini5

ACCEPTED MANUSCRIPT

coefficient (the concentration of endowments) nor of the variance (dispersion) of the endowment distribution. Fourth, our experimental results suggest that inequality in terms of skewness, once it is channelled into ‘elite’ behavior by means of the public good game, has a detrimental effect on group efficiency.

3

Model and Hypotheses

Contributions in a non-linear public good game

CR IP T

In this section, we present our theoretical model. We modify the social-preferences model by Charness and Rabin (2002), henceforth quoted as CR, as to two aspects. First, we extend CR to the three-person case.2 Second, we let the weight that players give to the payoff of worse-off players depend on the skewness of the initial endowment distribution. These extensions enable us to formalize and experimentally test the behavior of ‘elites’.

M

AN US

Three players i, i ∈ {1, 2, 3}, form a group. Each player is initially endowed with an individual-specific endowment e1i . The endowment is assumed to be perfectly convertible into a private consumption good c and the contribution to a public good s1i , respectively. Subjects maximize the product of private consumption c1i and returns from the public good (c2i ). Players individually decide on the contribution to the public good. Individual contributions s1i are restricted to the closed interval [0, e1i − 1], guaranteeing that utility is always positive: c1i ≡ e1i − s1i ≥ 1 .

(1)

CE

PT

ED

Individual contributions carry an individual return of α > 0. Furthermore, they cause a positive externality augmenting the other players’ payoff. The marginal effect from the externality is denoted by ζ, where 0 < ζ < α. Note that the latter assumption implies the social return on contributions to be higher than the private return because ζ + α > α as it is usually assumed in public-good games. The immanent free-rider problem is apparent. Totalling, player i’s return from the public good is given by e2i = α · s1i + ζ · (s1j + s1k ),

i 6= j 6= k .

(2)

AC

Obviously, equation (2) satisfies the usual condition that the marginal returns on contribution to the public good are constant, that is, ∂e2i /∂s1i = α and ∂ 2 e2i /∂(s1i )2 = 0. The return from the public good is given by c2i ≡ e2i ≥ 0 .

(3)

2 In their appendix, CR extend their basic two person model to a n-player model, which, however, does not allow for inter-subjects comparisons. In contrast, our three-person model accounts for individual inter-subject comparisons, meaning that each player assigns utility weights to all three players.

6

ACCEPTED MANUSCRIPT

Preferences and Utility

ui (c1i , c2i ) = c1i · c2i .

CR IP T

The original CR model takes into account both distributional preferences and reciprocity. In our one-shot public-good game with simultaneous contribution choices, we can omit the reciprocity parameter. Moreover, as CR has been formulated in terms of two-person games, we adapt it to three individuals to allow for inequality in terms of skewness. Instead of using an additive payoff function (c1i + c2i ), we decided to use the following multiplicative payoff function of player i (4)

AN US

Using this payoff function makes the game non-linear in payoffs and it therefore can have an inner equilibrium, depending on the parametrization. After plugging (1) and (3) into (4), we obtain   ui = (e1i − s1i ) · α · s1i + ζ · (s1j + s1k ) . (5) Let I denote an indicator function, defined as follows:  1 if ui ∈ A I{A} (ui ) = 0 otherwise ,

(6)

ED

M

where A indicates subsets of the real line. Player i’s preferences are then represented by (7) as follows    vi = 1 − ρ(ν) I{(uj ,∞)} (ui ) + I{(uk ,∞)} (ui ) −   σ I{(−∞,uj ]} (ui ) + I{(−∞,uk ]} (ui ) ui +   ρ(ν)I{(uj ,∞)} (ui ) + σI{(−∞,uj ]} (ui ) uj +   ρ(ν)I{(uk ,∞)} (ui ) + σI{(−∞,uk ]} (ui ) uk . (7)

AC

CE

PT

The parameters ρ and σ represent weights of a player’s own payoff and the other players’ payoffs, depending on the position in the (ex post) payoff distribution. ρ(·) is the ‘better-off’ weight, that is, the player weights her own payoff and the payoffs of all players that are worse-off than her by (1 − ρ(·)) and ρ(·), respectively. In accordance with our working hypothesis that the self-interest of ‘elites’ increases with increasing skewness of the distribution of initial endowments ν, we assume that ∂ρ(ν)/∂ν < 0. Parameter σ is the ‘worse-off or equal to’ weight, that is, she weights her own payoff and the payoffs of all players that are at least even with her by (1 − σ) and σ, respectively. Here, we assume that the parameter is independent of the distribution of initial endowments. This is in line with Heap et al. (2016) who find that endowment inequality only affects the contribution behavior of ‘rich’ players. Whether or not this assumption applies also to our game is an empirical question. The purpose of our experiment is to answer this question by comparing our data with the behavioral predictions of the model. Note that the general representation of social preferences (7) allows for several special cases with regard to the parametrization by σ and ρ(·). Purely selfish preferences, vi = ui , are obtained by setting σ = ρ(·) = 0. Utilitarian preferences, vi = 1/3·(u1 +u2 +u3 ), result from setting σ = ρ(·) = 1/3. More general social-welfare 7

ACCEPTED MANUSCRIPT

CR IP T

preferences (Andreoni and Miller, 2002) would result if setting 0 < σ ≤ ρ(·) < 1/2, that is, everyone gets a positive weight, but not necessarily the same.3 Inequity aversion (Fehr and Schmidt, 1999) requires σ < 0 < ρ(·) < 1/2, that is, the weight that a player gives to other players that excel her is negative. Competitive preference mean that a player aims at excelling other players even at the cost of efficiency losses. Hence, we would have negative weights for all other players σ ≤ ρ(·) < 0. The experiment does not explicitly aim at testing whether one of these parametrizations outperforms the other; we rather see them as benchmarks in order to classify our subjects. The crucial difference between these specifications of social preferences and our extended social preference functional is in the ‘better-off’ weight ρ that is assumed to be constant in the former cases and a function of skewness in the latter case. Nash Equilibrium

AN US

Players maximize their utilities (7) with respect to their contribution s1i , i = 1, 2, 3, given the contributions of the other players s1j and s1k , k 6= j 6= i. Let s1? i , = 1, 2, 3, denote the players’ contribution in the Nash equilibrium (NE). Instead of exclusively analyzing group contributions, we also analyze the efficiency of the group contributions. We define efficiency as the relative change of group endowments: P P 2 (α + 2ζ) i s1? (ei − e1i ) ? iP P 1 i −1. = (8) g = 1 e i i i ei

CE

PT

ED

M

In the following, we arrange the initial endowments and, therefore, the corresponding payoffs in increasing order, that is, u1 ≤ u2 ≤ u3 . For three players, the utility function (7) contains four possible cases that correspond to the four treatments of our experiment. First note that the term ‘(a)symmetric’ in this paper refers to the shape of the distribution of endowments in terms of its skewness, which distinguishes our terminology from standard public-good experiments, where it usually refers to (non-)identical endowments. The first case is represented by the control treatment (c) with identical endowments, that is, e11 = e12 = e13 . Here, vi simplifies to vi |c = (1 − 2σ)ui + σuj + σuk , i 6= j 6= k .

(9)

AC

Cases two to four involve non-identical endowments. We consider left-skewed (l) distributions e11 < e12 = e13 , symmetric (s) distributions4 , e11 < e12 < e13 , and rightskewed (r) distributions, e11 = e12 < e13 . The NE for the left-skewed endowment distribution is obtained by maximizing v1 |l = (1 − 2σ)u1 + σu2 + σu3 , v2 |l = (1 − ρl − σ)u2 + ρl u1 + σu3 , v3 |l = (1 − ρl − σ)u3 + ρl u1 + σu3 .

3

(10) (11) (12)

Andreoni and Miller (2002) find it more plausible that ρ ≥ σ, but the reverse could be considered as a social-welfare preference as well. 4 For this distribution to be actually symmetric, we additionally assume that e2 is the mean endowment.

8

ACCEPTED MANUSCRIPT

For the symmetric distribution, players’ maximize v1 |s = (1 − 2σ)u1 + σu2 + σu3 , v2 |s = (1 − σ − ρs )u2 + ρs u1 + σu3 , v3 |s = (1 − 2ρs )u3 + ρs u1 + ρs u3

(13) (14) (15)

and for the right-skewed distribution, they maximize (16) (17) (18)

CR IP T

v1 |r = (1 − 2σ)u1 + σu2 + σu3 , v2 |r = (1 − 2σ)u2 + σu1 + σu3 , v3 |r = (1 − 2ρr )u3 + ρr u1 + ρr u3 .

M

AN US

Plugging values for α, ζ, and the initial endowments into the respective equation vi |z , i = 1, 2, 3, z ∈ {c, l, s, r} gives a unique NE prediction for the individual contri? bution s1? i |z and the resulting efficiency g |z , which only depends on the preference parameters ρ(·) and σ. The actual parametrization of the experiment is displayed in Table 2. We set α = 1.15 and ζ = 0.7. In Table 3 we state the individual and group contribution predictions for the benchmark cases of purely selfish (σ = ρ = 0) and utilitarian (σ = ρ = 1/3) preferences. As can be taken from the table, the optimum number of tokens contributed by a player varies with her own endowment and the shape of the distribution. Individual contributions, group contributions and efficiency are predicted to be higher in groups in which subjects exhibit social preferences in terms of inequality aversion or utilitarian preferences. Hypotheses

AC

CE

PT

ED

Our main hypothesis is that social preferences are a function of the skewness of the endowment distribution. We argue that with an increasing skewness of the income distribution, social distance between the elite and the average citizen becomes larger. Hence, the social weight that the members of the elite assign to the economic wellbeing of those who are worse-off diminishes. As a consequence the elite disregards the positive externality to the average citizen that arises from contributions to the public good. Therefore, the level of contribution chosen by the elite is suboptimal, and the efficiency loss due to low contributions increases with the selfishness of the elite. At the societal level this effect becomes visible both in higher aggregate selfishness and lower societal efficiency. The mechanism can be transformed into formal hypotheses using Table 1. We define φzi as the parameter of individual selfishness. It is equal to the weight that P zis z given to a player’s own induced utility. Aggregate selfishness is given by Φ = i φi . Table 1 gives an overview of the individual and aggregate selfishness parameters ordered by treatment, using equations (9) to (18). The control treatment (identical endowments) and the symmetric treatments (player 2 owns the mean endowment) exhibit a skewness of zero. Hence, if skewness is the main explanatory variable, aggregate selfishness, group contributions, and efficiency should be the same under both treatments (though, of course individual contributions may differ). Our first formal hypothesis therefore is H1 : Φc = Φs , which implies ρs = σ, and g ? |c = g ? |s . Second, we hypothesize H2 : Φr > Φs > Φl , 9

ACCEPTED MANUSCRIPT

Table 1: Individual and Aggregate Selfishness by Treatment

CR IP T

φzi Player Treatment 1 2 3 Φz Control (c) (1 − 2σ) (1 − 2σ) (1 − 2σ) 3 − 6σ Left skewed (l) (1 − 2σ) (1 − σ − ρl ) (1 − σ − ρl ) 3 − 4σ − 2ρl Symmetric (s) (1 − 2σ) (1 − σ − ρs ) (1 − 2ρs ) 3 − 3σ − 3ρs Right skewed (r) (1 − 2σ) (1 − 2σ) (1 − 2ρr ) 3 − 4σ − 2ρr Notes. φzi (Φz ) is the individual average (aggregated) parameter of selfishness, i.e., the weight assigned to one’s own payoff in treatment z according to equations (9)-(18).

M

AN US

which implies ρr < ρs < ρl , and g ? |r < g ? |s < g ? |l . Both hypotheses will be tested using a between-subjects design, where subjects are randomly assigned to one out of the four treatments. The assumption H3 : σ = σz , z ∈ {c, l, s, r}, cannot be directly tested by our experiment, which is designed to investigate the behavior of the elite. However, an indirect test will be performed by checking whether the individual contributions can exactly be predicted by the model (7) if this assumption is imposed. We can not exclude the possibility, however, that alternative models with different σ-values between treatments exist, that are able to do the same.

The Experiment

ED

4

AC

CE

PT

The experiment was conducted in the experimental economics laboratory at the University of Bremen. The experiment was fully computerized using z-tree (Fischbacher, 2007). Subjects, mostly economics students, were recruited using the recruitment system ORSEE (Greiner, 2015). The 144 (89 male, 55 female) subjects were randomly assigned to one out of four treatments. Each treatment involved 2 sessions with 18 subjects each. Subjects received show-up fees of e 5 and could additionally gain up to e 50 depending on their performance in the experiment. 2 subjects per session were selected for payoff by lottery.5 The exchange rate between the experimental currency (tokens) and e was 4:1. Subjects’ average payment was e 9.70. Sessions took about 80 minutes. First, we present and discuss the treatment structure. Then we describe the three steps of our experiment, beginning with the intelligence test, followed by the endowment assignment, and ending with the contribution decision. 5

We used the binary lottery incentive scheme. Assuming that subjects decide in line with expected utility maximization, using such a lottery of paying the corresponding fixed amount should not lead to different behavior. However, Bardsley et al. (2010, p. 265-270) mentioned that this procedure could lead eventually to increased risk-aversion. Therefore, our experimental setting should not lead to ‘artificially high’ contributions.

10

ACCEPTED MANUSCRIPT

4.1

Treatment Structure

CR IP T

In our experiment, we investigate the influence of the shape of the initial endowment distribution on the individual and the aggregate selfishness of the group. Selfishness is measured by the weight that a subject assigns to his or her own utility. The level of selfishness is hypothesized to impact subjects’ contributions and, hence, the efficiency. As noted above, we consider four distributions: the control treatment (c) with identical endowments as well as the left-skewed (l), the symmetric (s), and the right-skewed (r) endowment distributions, see Table 2. Table 2: Overview of Treatments

AN US

Player Treatment 1 2 3 Mean Variance Skewness Gini Control (c) 12 12 12 12 0 0 0 Symmetric (s) 6 12 18 12 36 0 0.22 Left skewed (l) 8 14 14 12 12 -0.71 0.11 Right-skewed (r) 8 8 20 12 48 0.71 0.22 Notes: Rows 2-4: Initial endowments in tokens and mean, variance, skewness and Gini-coefficient of the distribution of endowments.

Intelligence Test

AC

4.2

CE

PT

ED

M

In Table 2 we have listed the treatments and state for each treatment the mean endowment, the variance, the skewness, and the Gini coefficient of the distribution. The mean endowment is identical in all treatments as we do not want to confound our results concerning the role of the shape of the endowment distribution with income effects. As can be taken from the table, inequality in terms of the variance increases from the control treatment to the right-skewed treatment. Inequality also increases in the same ordering if measured by the Gini coefficient, though the symmetric and the right-skewed treatment exhibit the same Gini coefficient. Finally, the left-skewed has the lowest skewness (ν) followed by the symmetric and the control treatment, and these have more skewness than the right-skewed treatment. This also shows the perverse impact of increasing skewness on the Gini coefficient. A strong increase in the variance is compensated by increasing skewness such that the Gini stays constant.

Beside others, Balafoutas et al. (2013) and Cappelen et al. (2013) showed the process of entitlement generation itself to matter for subjects’ redistribution preferences. As the focus of our paper is different, we take the process of entitlement generation as given. Hence, in order to create a perception of feeling entitled, we based the distribution of initial endowments on the performance in an intelligence test. At the beginning of the experiment, subjects received verbal instructions. They were thoroughly informed about the decision task and the payoff mechanism.6 Then, subjects took part in an intelligence test. The test consisted of twelve computer 6

For a transcript of the instructions, see the Appendix. The instructions are not neutrally written. We framed subjects in a way that the experiment is about inequality and growth and

11

ACCEPTED MANUSCRIPT

screens, each involving up to 3 questions. For each screen, there was a time limit of 50 seconds such that the total time for completing the test was 10 minutes. Going back and forth between screens was not possible. The intelligence test covered mathematical, graphical, and linguistic exercises.7

4.3

Assignment of endowments

CR IP T

In the next step, 6 groups of 3 subjects each were formed in each session to generate the distributions listed in Table 2. Our software performed the group-matching according to the following procedure: 1. The 18 subjects of the same session were ranked according to their score in the intelligence test. In order to avoid ties, a random number was drawn from the [0; 1]-interval and added to the score. Subjects were told that, whenever two of them had achieved equal points in the IQ-test, a random draw would secure a unique ranking.

AN US

2. In the control treatment, the subjects ranked 1st, 2nd, and 3rd formed group 1; the subjects ranked 4th, 5th, and 6th formed group 2; and so on; every subject was assigned an initial endowment of 12 tokens.

M

3. In the left-skewed treatment, the subjects ranked 1st, 2nd, and 13th formed group 1; the subjects ranked 3rd, 4th, and 14th formed group 2; and so on; within each group subjects were assigned according to their scores, 14, 14, and 8 tokens, respectively.

ED

4. In the symmetric treatment, the subjects ranked 1st, 7th, and 13th formed group 1; the subjects ranked 2nd, 8th, and 14th formed group 2; and so on; within each group, subjects were assigned according to their scores 18, 12, and 6 tokens, respectively.

CE

PT

5. In the right-skewed treatment, the subjects ranked 1st, 7th, and 8th formed group 1; the subjects ranked 2nd, 9th, and 10th formed group 2; and so on; within each group subjects were assigned according to their scores, 20, 8, and 8 tokens, respectively. These procedure secures comparability between groups within treatments.

AC

that their investment decision has an effect on individual payoffs but also on the growth rate of endowments. Another example of such a ‘macro framing’ used in the instructions of a public good game can be found in e.g. Sadrieh and Verbon (2006). The authors used words like capital, development or investments to frame a standard public good game. We believe that this framing might lead (if at all) to less cooperation in comparison to a standard framing and wording in experiments. We do not see any reason to fear that our framing might have lead to the observed effect of the skewness of the endowment distribution on behavior. We used that framing because this paper is part of a broader project in which we analyze the effect of inequality on aggregated outcomes. 7 The questions were taken from Siewert (2000) which is a standardized IQ-test.

12

ACCEPTED MANUSCRIPT

4.4

Decision Task

Results

ED

5

M

AN US

CR IP T

After the group matching, subjects received detailed information about their actual decision task and the calculation of payoffs using a neutrally designed sample-screen. In particular, we explained the payoff tables, showing the interplay between a player’s own and the other subjects’ contributions in determining his or her own payoff. Subjects had to answer six control questions to ensure that they had understood their tasks and the payoff structure. 95.8% (81.9%) answered at least 4 (5) questions correctly. The correct answers to all control questions were displayed on the next computer screen. At this stage in the experiment, participants were allowed to ask questions regarding the experimental procedure. Afterwards the decision task started with showing subjects their own endowment, e1i , the endowment distribution, and the payoff table. Since players had to consume at least one unit as private consumption, the individualized payoff tables were matrices of the dimension (e1i − 1) × (e1j + e1k − 2).8 Subjects received detailed instructions highlighting the formal relationship between their own and other group members’ contributions and payoffs. Before subjects decided on how much to contribute, they were asked for their expectations concerning the contributions made by the other players. Then subjects could choose their contributions by using a scroll-bar, where subjects were allowed to choose only integer numbers from the closed interval [0; e1i − 1]. For computing the payoff, we used the parametrization α = 1.15 and ζ = 0.7. This parameter combination fulfills the usual restrictions for a public-goods experiment and guarantees even for purely selfish preferences nonnegative predictions for the NE contributions (with one exception, see below).

Predictions

AC

5.1

CE

PT

In this section we present the results of our experiment. The section is subdivided into five subsections. In the next subsection, we present the predicted NE contributions and resulting efficiency for the benchmark cases of purely selfish preferences and utilitarian preferences. Subsection 5.2 presents observed group contributions. Subsection 5.3 explains how we computed the average efficiency. We then test hypotheses H1 and H2 . Subsections 5.4 and 5.5 deal with individual predictions and observations and test H3 .

Table 3 contains the predicted individual and group NE contributions for purely selfish preferences (upper panel) and for utilitarian social preferences (middle panel). The columns on the left-hand side give absolute values in tokens, while the righthand side columns give percentages of the initial endowments. The last column states efficiency in percent. Purely selfish preferences and utilitarian preferences are two ‘natural’ benchmark cases. The first case is the usual game-theoretic prediction, when the individual optimum is totaly exempt from social considerations. Free-riding is the dominating motive, and contributions and efficiency are very low (though not 8

See the Appendix for a sample matrix for players with an endowment of e1i = 12.

13

ACCEPTED MANUSCRIPT

being self-destructive as it could happen with competitive preferences). Note that due to our parametrization of the experiment, we get only one corner-solution for e11 = 6 in the symmetric treatment. Here, relative contributions of the other subjects must be a bit higher, which explains why the group contributions and efficiency deviate slightly from the other treatments. Table 3: Individual and Group Contributions

PT

ED

M

AN US

CR IP T

Tokens Contributed % of Tokens Contributed Player Player Efficiency Treatment 1 2 3 Group 1 2 3 Group Rate (%) Purely Selfish Preferences (σ = ρ = 0) Control (c) 3.73 3.73 3.73 11.19 31.1 31.1 31.1 31.1 -20.7 Left skewed (l) 0.85 5.17 5.17 11.19 10.7 36.9 36.9 31.1 -20.7 Symmetric (s) 0 3.59 7.91 11.50 0 29.9 43.9 31.9 -18.5 Right-skewed (r) 0.85 0.85 9.48 11.19 10.7 10.7 47.4 31.1 -20.7 Utilitarian Preferences (σ = ρ = 1/3) Control (c) 6 6 6 18 50 50 50 50 27.5 Left skewed (l) 4 7 7 18 50 50 50 50 27.5 Symmetric (s) 3 6 9 18 50 50 50 50 27.5 Right-skewed (r) 4 4 10 18 50 50 50 50 27.5 Revealed Preferences Control (c) 4.89 4.89 4.89 14.67 40.8 40.8 40.8 40.8 3.89 Left skewed (l) 3.17 6.25 6.25 15.67 39.6 44.6 44.6 43.5 10.97 Symmetric (s) 2.17 5.25 7.33 14.75 36.2 43.8 40.7 41.0 4.05 Right-skewed (r) 2.92 2.92 8.08 13.92 36.5 36.5 41.0 38.6 -1.42 Notes: Table shows in three separated blocks the individual and aggregated predictions for selfish preferences, utilitarian preferences and observations both in absolute and relative contributions. The last column shows calculated efficiency.

AC

CE

If comparing the control treatment with the treatments with non-identical endowments in terms of the predicted percentaged contributions, we see that subjects with lower endowments are to be expected to contribute less than those with higher endowments not only in absolute terms but also in relative terms. For example, in the right-skewed treatment, players 1 and 2 would be willing to contribute less than 11% of his or her endowment, while players 3 would contribute almost 47%. In the utilitarian-preference case every subject would behave like a neutral social planner. Here, subjects maximize efficiency by contributing half of their endowments.9

5.2

Contributions to the public good

Before we will analyze the effect on efficiency, we present group contributions between treatments.10 Remember that groups were composed by anonymous random 9

Predictions for other specifications of social preferences could easily derived as well by using the appropriate ρ and σ specification. 10 We used homogeneity χ2 -tests to check whether socio-demographics (gender, field of study, age, semester) differ between treatments. We did not find any significant differences. Differences

14

ACCEPTED MANUSCRIPT

AN US

CR IP T

matching, that is, subjects knew their own endowment and the distribution of endowments but they did not know with whom they were matched or their rank in the IQ-test. We utilize this fact to generate a large number of independent group observations by permuting group members with identical endowment values (see Davis and Holt, 1993).11 Note that the individual decisions of all subjects with the same endowment from a single treatment were defined as a subset. For example, in the symmetric treatment, we defined 3 subsets, one for each endowment value, with 12 entries each (36 subjects per treatment). Now, we took all feasible compositions of decisions (drawing with replacement) from these 3 subsets by considering the constraint that only 1 entry from each subset can be matched. This yielded 123 = 1728 permutations for the symmetric treatment. Hence, we had to pay only 36 instead of 576 subjects for a given group-N . In the control treatment, 36 subjects were endowed with 12 tokens each. Hence, there are 36!/(3! × 33!) = 7140 possible matchings for 3-player groups. The symmetric treatment involved three distinct ranks with 12 subjects each, yielding 123 = 1728 permutations. For the right-skewed and left-skewed treatments, we analogously obtain 12!/(2! × 10!) × 12 = 3312 group permutations. In the following, we therefore compute standard errors and test statistics based on these large numbers of group permutations. Table 4: Comparison of Group Contributions Among Treatments

PT

ED

M

Contributions Std. Treatmenta Treatment (mean) Error c l s r Control (c) 14.67 0.044 — < 0.01 0.35 < 0.01 Left skewed (l) 15.67 0.066 < 0.01 — < 0.01 < 0.01 Symmetric (s) 14.75 0.077 0.35 < 0.01 — < 0.01 Right-skewed (r) 13.92 0.053 < 0.01 < 0.01 < 0.01 — a Notes. Significance level (p) of a two-sided t-test on equality of the respective group contributions.

AC

CE

Table 4 presents the mean of group contributions between treatments. Group contributions are highest in the treatment with a left skewed distribution with a mean of 15.67. In the control treatment, group contributions are on average 14.67 and are almost equal to the mean in the symmetric treatment (14.75). Lowest group contributions are observed in the treatment with a right skewed distribution with a mean of 13.92. Group contributions are significantly different between treatments except for the symmetric and the control treatment.12 Figure 1 additionally provides a graphical display of cumulative frequencies of group contributions both for real groups (sub-figure a) and permuted groups (sub-figure b). Except for a small between treatments cannot be traced back to differences of participants between treatments. 11 The technique of using group permutations is also used in other public good games, e.g. Hauser et al. (2014), Rondeau et al. (2005) and Brandts and Schram (2001). 12 We also used non-parametric Mann-Whitney-U-Tests which yields the same results. Moreover, regressions with group contributions as the dependent variable and treatment-dummies (symmetric, left-skewed and right skewed) as independent variables show that symmetric is not significant whereby right skewed is negative and significant and left skewed is positive and significant.

15

ACCEPTED MANUSCRIPT

5.3

Efficiency

ED

M

AN US

CR IP T

interval, contributions in groups treated with a right-skewed endowment distribution dominate left-skewed.13 In the Appendix, we additionally present the analysis of individual contributions. Table 10 (in the Appendix) states the mean observed absolute and relative individual contributions by treatment and endowment (the same numbers as in Table 3) and the respective standard errors. As can be taken from the table, subjects on average contributed about 40% of their endowments, which is in line with the public-goods literature (Ledyard, 1995; Chaudhuri, 2011). Though the group analysis led to clear-cut results concerning treatment effects, the between-treatment variation of individual relative contributions seems to be rather low (and standard errors relatively high). Note, however, that the scope of ‘sensible’ individual contributions is narrow by experimental design due to the fact that we induced interior socially optimal and Nash equilibrium solutions. Table 11 (also in the Appendix) reports the results of regressing the log of endowment on the log of individual contributions, that is, the estimated coefficient gives the elasticity of contributions with respect to endowment. The null hypothesis of proportionality (i.e. the elasticity is equal to one) cannot be rejected (Regression 1).14 When controlling for treatment effects in Regression 2 by interacting log endowment with treatment dummies, the interactions exhibit the right signs (right/left skewed endowments lead to a lower/higher elasticity than symmetric endowments) as suggested by the group analysis. However, as indicated by the numbers stated in Table 11, the interactions turn out to be insignificant. This apparent discrepancy between individual and group level is due to the fact that groups are heterogenous (right skewed groups involve two poor and one elite subject, while left skewed groups involve only one poor and two elite subjects), which reinforces the individual treatment effect at the group level.15

13

CE

PT

The lower panel of Table 3 contains the individual and group contributions as well as the efficiency rates obtained from our experiment. A first inspection of numbers shows that the results are almost perfectly in line with the experimental publicgoods literature (Ledyard, 1995). Average contributions fall short of the utilitarianpreference NE prediction (the social optimum in a public-goods game) but excel the purely-selfish-preference NE prediction (the individual optimum in a public-goods game). The exceptions to this rule and the treatment-specific patterns of individual

AC

Note that the results stay qualitatively similar if ‘real’ (i.e. payoff relevant) instead of permuted groups are considered. Comparing the distributions of group contributions between right-skewed and left-skewed endowment distributions by means of a χ2 test, gives χ2 = 2.667 (p = 0.102) though there are only 12 ‘real’ observations per treatment. 14 Similar regressions as in Table 11 for absolute contributions clearly support a positive relationship between endowments and contributions. Additional regressions show that the expectation about other‘s contributions has a positive effect on own contributions which is a standard result in public good games (Ledyard, 1995; Chaudhuri, 2011). However, the expectation of how group members will contribute does not depend on the own rank in the society. 15 Of course, one could enforce significance at the individual level, too, simply by hiring sufficiently many subjects until standard errors get small enough. However, since the focus of the present paper is on the group level, where treatment effects turned out to be significant, we decided in favor of resource efficiency.

16

0

5

10

AN US

0

.2

CR IP T

Cumulative Frequencies .4 .6 .8

1

ACCEPTED MANUSCRIPT

15 20 Group Contributions

right skewed

25

30

25

30

left skewed

AC

CE

0

.2

PT

ED

Cumulative Frequencies .4 .6 .8

M

1

(a) Real Groups

0

5

10

15 20 Group Contributions

right skewed

left skewed

(b) Permutated Groups

Figure 1: Cumulative Frequencies of Group Contributions

17

ACCEPTED MANUSCRIPT

contributions will be commented in the next subsection. Here, we focus at the group level. Table 5: Actual versus Predicted Benchmark Efficiency

CR IP T

Efficiency Std. Significance Levela Treatment (%) Error Selfish Utilitarian Control (c) 3.89 0.313 < 0.01 < 0.01 Left skewed (l) 10.97 0.468 < 0.01 < 0.01 Symmetric (s) 4.05 0.545 < 0.01 < 0.01 Right-skewed (r) -1.42 0.375 < 0.01 < 0.01 a Notes. Significance level (p) of a two-sided t-test on equality of the respective efficiency.

AN US

Table 6: Comparison of Efficiency Among Treatments

ED

M

Efficiency Std. Treatmenta Treatment (%) Error c l s r Control (c) 3.89 0.313 — < 0.01 0.35 < 0.01 Left skewed (l) 10.97 0.468 < 0.01 — < 0.01 < 0.01 Symmetric (s) 4.05 0.545 0.35 < 0.01 — < 0.01 Right-skewed (r) -1.42 0.375 < 0.01 < 0.01 < 0.01 — a Notes. Significance level (p) of a two-sided t-test on equality of the respective efficiency.

AC

CE

PT

Table 5 and 6 state the mean efficiency and their standard errors by treatment. Table 5 compares observed efficiency with benchmark efficiencies. The last twocolumns report significance levels of t-tests on the equality of the respective efficiencies between observations per treatment and both benchmarks. The table clearly confirms the picture conveyed by Table 3 that the actual efficiencies lie in between the selfish and the utilitarian predictions. Hence, we can conclude, not unexpectedly, that our subjects behaved neither purely selfish nor as neutral welfare maximizers. We are much more interested, however, in the ranking of the actual group outcomes among treatments. This piece of information is provided by Table 6. As can be taken from the table, all rates of efficiency differ significantly, except for the control treatment and the symmetric treatment. The rank ordering of the treatments in terms of efficiencies is therefore given by g ? |r < g ? |c = g ? |s < g ? |l . This pattern of efficiencies confirms the second part of hypotheses H1 and H2 , respectively. The analysis of aggregated contributions (Table 4) and efficiencies (Tables 5 and 6) are perfectly in line. This has to be the case because the higher the contribution the higher is the efficiency if contributions lie in between both benchmark cases. It remains to be shown, however, that this pattern of efficiency is consistent with the representation of skewness-adjusted social preferences (7). 18

ACCEPTED MANUSCRIPT

5.4

Identifying σ and ρ.

g ? |c =

CR IP T

Remember the general definition of the NE efficiency (8). For each treatment z ∈ {c, l, s, r}, we know the interest rate α = 1.15, the positive externality parameter ζ = 0.7, the individual and group endowments (see Table 2), and actual efficiency gˆ? |z as well as its standard error (see Table 5). The individual contributions s1? i that enters equation (8) is itself a function of these known values, and the unknown parameters σ and ρz . In order to identify σ ˆ and ρˆz we use the fact that the control treatment endows every subject with the same token amount. Hence, there is no elite, and the ρ-parameter drops out of the efficiency equation for the distribution with identical endowments,16 which is given by 1 α2 (1 − 2σ) + 2αζ(1 − σ) + 4ζ 2 σ · −1. 2 α(1 − 2σ) + ζ(1 − σ)

Plugging all known values into (19) gives

18 · σ − 23 −1, 60 · σ − 37

AN US

gˆ? |c = 0.0389 = 1.275 ·

(19)

(20)

ED

M

which can easily be solved for σ. Now, we have to account for the fact, that gˆ? is a random variable with mean 3.89% and standard error 0.313%. Hence, our estimate for σ ˆ is a random variable itself. In order to obtain a confidence interval for σ ˆ , we therefore run the following Monte Carlo simulation: We pick 1,000 draws from a normally distributed random variable with mean 0.0389 and standard deviation 0.00313, and plug them into (20). The 51st and 950th largest σ ˆ s are the lower and upper bound of an 90% confidence interval for the mean of σ ˆ . The result of this procedure is given in the second column of Table 7.

PT

Table 7: Estimates for σ ˆ and ρˆ by treatment

AC

CE

Control (c) Left Skewed (l) Symmetric (s) Right Skewed (r) σ ˆ ρˆ ρˆ ρˆ mean 0.2313 0.3388 0.2334 -0.0220 std. dev. 0.0018 0.0062 0.0078 0.0492 90% [0.2283; [0.3285; [0.2199; [-0.1113; CI 0.2344] 0.3489] 0.2460] 0.0509] Notes. σ ˆ is the weight assigned to subjects who are at least on a par with oneself. ρˆ is the weight assigned to subjects who are worse-off. Estimates are based on 1000 random draws (Monte Carlo simulation). CI=confidence interval.

Our estimate for σ ˆ is 0.2313, lies, of course, between the utilitarian preference (σ = 1/3) and the purely selfish preference (σ = 0), and exhibits a relatively small variance. In the next step, we can plug our estimate for σ ˆ into the NE efficiency 16

This shows that we cannot directly test H3 .

19

ACCEPTED MANUSCRIPT

CR IP T

equations for the other treatments. Again, we account for the fact that σ ˆ and gˆ? |z , z ∈ {l, s, r}, are random variables by running 1000 Monte Carlo trials. The resulting estimates for ρˆz are given in columns 3 to 5 of Table 7. It struck right away that we get a different estimate for each treatment. A glance at Table 2 and the ρˆz -estimates in Table 7 shows that the better-off weight indeed decreases in the skewness of the endowment distribution, that is, ρˆr < ρˆs < ρˆl . This confirms the first part of Hypothesis H2 . Furthermore ρˆs does not significantly differ from σ ˆ, confirming the first part of Hypothesis H1 . Note that the variance of the distribution cannot explain this preference pattern because control treatment and symmetric treatment exhibit equal rates of efficiency (and their skewness is ν = 0) but their variances differ (0 versus 36). Likewise, the Gini coefficient is bigger for the symmetric treatment (0.22) than for the control treatment (0). Table 8: Observed Selfishness by Treatment

ED

M

AN US

φzi Player Treatment 1 2 3 Φz Control (c) 0.5374 0.5374 0.5374 1.5936 Left skewed (l) 0.5374 0.4299 0.4299 1.3972 Symmetric (s) 0.5374 0.5353 0.5332 1.6059 Right skewed (r) 0.5374 0.5374 1.0440 2.1188 z z Notes. φi (Φ ) is the individual (aggregate) parameter of selfishness, i.e., the weight assigned to one’s own payoff in treatment z.

AC

CE

PT

Table 8 gives the individual and aggregate parameters of selfishness under the proviso that (7) is the right model. Individual selfishness is defined as the weight assigned to one‘s own payoff, which differs between players and treatments (see equations 9-18). Therefore selfishness is a function of the parameters ρ and σ. It nicely shows that selfishness is almost equal in the control and the symmetric treatments both at the individual and the aggregate level. Selfishness of the better-off subjects is highest in the right skewed treatment; here better-off subjects exhibit purely self-interested preferences. In contrast to this, the left skewed treatment induces the (two) better-off subject to become more caring with respect to the worse-off subjects. None of the standard specifications of social preferences with constant better-off weight ρ can explain this pattern.

5.5

Individual contributions

Finally, we have to show that σ ˆz = σ ˆ , z ∈ {c, l, s, r}, cannot be rejected. As noted above, since the estimate of σ ˆ in the control treatment was used to derive the ρˆz s under this auxiliary assumption, we cannot directly test H3 . However, if we are able to show that the model (7) correctly predicts the individual contributions of 20

ACCEPTED MANUSCRIPT

CR IP T

each player and in each treatment, one cannot deny that the skewness-adjusted CR model (7) is a sensible description of our subjects’ behavior. Note that there might be alternative models with treatments-specific σ-parameters that fit the data as well; these models, however, would be less parsimonious. Let s¯1? ˆ1? i |z denote the observed mean of player-type i’s contribution and s i |z the ˜3 : corresponding contribution predicted by the model. The auxiliary hypothesis H 1? 1? ˆ and ρˆz estimates s¯i |z = sˆi |z , i = 1, 2, 3, z ∈ {c, l, s, r} is tested by plugging the σ into the individual NE contributions equations and comparing them with the actually ˜ 3 cannot be rejected. Again, we observed data. If they do not differ significantly, H care for the randomness of the observed and predicted individual contributions as well as the preference parameters by running 1000 Monte Carlo trials in order to compute sˆ1? i |z and its variance. Table 9: Predicted versus Observed Individual Contributions

Player 1 Player 2 Player 3 1? 1? 1? 1? 1? s¯1? s ˆ Test s ¯ s ˆ Test s ¯ s ˆ Test 1 z 1 z 2 z 2 z 3 z 3 z 4.89 4.89 0.00 (see Player 1) (see Player 1) (2.25) (0.01) 0.00 12 1000 1.00 Left skewed (l) 3.17 1.50 1.67 6.25 7.08 -0.83 (see Player 2) (1.70) (0.06) 1.26 (2.54) (0.07) -0.51 12 1000 0.23 24 1000 0.61 Symmetric (s) 2.17 0.95 1.22 5.25 4.89 0.36 7.33 8.84 -1.51 (1.53) (0.07) 0.96 (2.22) (0.03) 0.24 (1.97) (0.13) -1.04 12 1000 0.35 12 1000 0.81 12 1000 0.32 Right-skewed (r) 2.92 2.86 0.06 8.08 8.20 -0.12 (see Player 1) (1.25) (0.06) 0.05 (2.64) (0.19) -0.07 24 1000 0.96 12 1000 0.94 Notes. First row: means and differences, second row: standard errors and t-value of a Welch test, third row: number of observations and p-value of a two-tailed Welch test.

PT

ED

M

AN US

Treatment Control (c)

AC

CE

˜ 3 . The two-tailed Welch tests cannot reject Table 9 shows the results of testing H the null hypothesis of equality between the experimentally observed and the predicted contributions. This result applies to all treatments and all players.17 Therefore, we can conclude that the skewness-adjusted three-person model (7) is able to correctly describe and predict the behavior of subjects in our experiment. In the left-skewed and the symmetric treatments we see, however, a slight tendency of the model to underestimate the true contributions of worse-off players and to overestimate the contributions of better-off players. If actual case numbers in the experiment were larger,18 we would less likely still be able to reject the null hypothesis. 17

The result for the control treatment is trivial, because here ρˆ does not enter the NE contribution equation of player 1. 18 Unfortunately, we cannot inflate the number of individual observations by permutation as in the investigation of group contributions. This makes the application of the Welch test a bit problematic, which actually requires at least 30 observations on each random variable.

21

ACCEPTED MANUSCRIPT

6

Summary and Conclusion

AC

CE

PT

ED

M

AN US

CR IP T

Recent papers in psychology have shown that, in some situations, members of the higher social class behave less ethically than lower-class individuals (e.g. Piff et al., 2012). The basic idea of our model is that people who are better-off – the members of the elite – become more selfish when the skewness of the endowment distribution increases, because the social distance between the “elite” and the rest of society becomes larger. We report the results of a laboratory experiment that was designed to test the hypothesis that skewness-adjusted social preferences (based on social preferences `a la Charness and Rabin, 2002) are able to describe how social preferences of the betteroff subjects are affected by the shape of the endowment distribution. The statistical analysis unequivocally confirms that the model is able to correctly describe and predict the observed behavior of subjects. In those treatments where inequality in terms of skewness of the distribution of initial endowments is largest, the selfishness of the best-off subjects is most pronounced and, consequently, aggregate contributions to the public good are smallest. In addition to previous findings in Cote et al. (2015) and Heap et al. (2016), we show that inequality in terms of the skewness of the endowment distribution has a significant effect on selfishness of the better-off subjects. Moreover, we can draw the conclusion that efficiency is lowest if the endowment distribution is right-skewed. The observation that group contributions in our experiment lies somewhere between the purely-selfish Nash equilibrium and the social optimum belongs to the ‘exhibits’ of experimental economics (Bardsley et al. 2010) and makes us confident that our findings are not an artefact of our specific framing, parametrization, payoff scheme or non-linearity of the game. How significant is the observed negative impact of inequality on aggregated payoff in economic terms? The welfare effect of skewness can easily be assessed by means of the relative payoff differential between the left- and the right-skewed treatments. Remember that payoffs were computed as one fourth of the product of private consumption and the returns from the public good. When moving from the left-skewed to the right-skewed distribution, the observed selfishness of the society increased by not less than 52%. Consequently, contributions decreased by about 12%. As compared to the social optimum, in which every utilitarian subject contributes exactly one half of her initial endowment, an average right-skewed group therefore lost e 3.59 or 5.0% of the maximum payoff of e 71.55 while an average left-skewed group lost only e 1.16 or 1.7% of e 69.53.19 At first sight the skewness-effect seems to be relatively small, yet it might cause significant welfare effect. Of course, one has to be very cautious with trying to carry over laboratory results to the world outside the lab. Nevertheless, we argue that our experimental findings can be transferred into the ‘real world’ and are likely to be even stronger there: Our sample – students – was relatively homogeneous and the induced inequality among them was relatively ‘weak’. Outside the lab, inequality has many more and ‘stronger’ facets like income, wealth, status symbols, housing, and health. A by-product of our experimental analysis is that we are able to show that neither 19

The difference of maximum payoffs is due to the nonlinearity of the payoff function which ‘punishes’ the more equal left-skewed distribution.

22

ACCEPTED MANUSCRIPT

AC

CE

PT

ED

M

AN US

CR IP T

the variance nor the Gini coefficient (which relies heavily on the variance-related principle of transfers) are able to produce such a pattern of behavior. This result also sheds light on the inadequateness of using the Gini coefficient in empirical studies on inequality and aggregated outcomes like growth.

23

ACCEPTED MANUSCRIPT

References [1] Acemoglu, Daron & Johnson, Simon & Robinson, James (2005): Institutions as a Fundamental Cause of Long-Run Growth, in: P. Aghion und S. Durlauf [Eds.]: Handbook of Economic Growth, 385-472, North-Holland.

CR IP T

[2] Anderson, Lisa R. & Jennifer M. Mellor & Jeffrey Milyo (2008): Inequality and public good provision: An experimental analysis, The Journal of Socio-Economics 37, (3), 1010-1028. [3] Andreoni, James & Miller, John (2002): Giving according to GARP: An Experimental Test of the Consistency of Preferences for Altruism, Econometrica 70, (2), 737-753.

AN US

[4] Balafoutas, Loukas & Kocher, Martin G. & Putterman, Louis & Sutter, Matthias (2013): Equality, equity, and incentives: An experiment, European Economic Review 60, 32-51. [5] Bardsley, Nicholas/Cubitt, Robin/Loomes, Graham/Moffatt, Peter/Starmer, Chris/Sugden, Robert (2010): Experimental Economics: Rethinking the Rules, Princeton University Press, Princeton und Oxford. [6] Bergstrom, Theodore & Blume, Lawrence & Varian, Hal (1986): On the Private Provision of Public Goods, Journal of Public Economics 29, 25-49.

M

[7] Bolton, Gary E. & Ockenfels, Axel (2000): ERC: A Theory of Equity, Reciprocity, and Competition, American Economic Review 90, (1), 166-193.

ED

[8] Brandts, Jordi & Arthur Schram (2001): Cooperation and noise in public goods experiments: applying the contribution function approach, Journal of Public Economics 79, (2), 399-427.

PT

[9] Buckley, Edward & Croson, Rachel (2006): Income and wealth heterogeneity in the voluntary provision of linear public goods, Journal of Public Economics 90, (4-5), 935-955.

AC

CE

[10] Cappelen, Alexander W. & Konow, James & Srensen, Erik . & Tungodden, Bertil (2013): Just Luck: An Experimental Study of Risk Taking and Fairness, American Economic Review 103, (4), 1398-1413. [11] Chan, Kenneth & Mestelman, Stuart & Moir, Rob & Mller, Andrew (1996): The Voluntary Provision of Public Goods under Varying Income Distributions, Canadian Journal of Economics 29, (1), 54-69. [12] Chan, Kenneth & Mestelman, Stuart & Moir, Robert & Muller, Andrew (1999): Heterogeneity and the voluntary provision of public goods, Experimental Economics, 2, (1), 5-30. [13] Charness, Gary & Rabin, Matthew (2002): Understanding Social Preferences With Simple Tests, Quarterly Journal of Economics 117, (3), 817-869.

24

ACCEPTED MANUSCRIPT

[14] Chaudhuri, Ananish (2011): Sustaining cooperation in laboratory public goods experiments: a selective survey of the literature, Experimental Economics 14, 4783. [15] Cherry, Todd & Kroll, Stephan & Shogren, Jason (2005): The impact of endowment heterogeneity and origin on public good contributions: evidence from the lab, Journal of Economic Behavior and Organization 57, 357-365.

CR IP T

[16] Cote, Stephane & Julian House & Robb Willer (2015): High economic inequality leads higher-income individuals to be less generous, Proceedings of the National Academy of Sciences, 112, (52), 15838-15843. [17] Davis, Douglas & Holt, Charles (1993): Experimental Economics, Princeton University Press, Princeton. [18] Erlei, Matthias (2008): Heterogeneous social preferences, Journal of Economic Behavior and Organization 65, 436-457.

AN US

[19] Fehr, Ernst & Schmidt, Klaus M. (1999): A Theory Of Fairness, Competition, And Cooperation, Quarterly Journal of Economics 114, (3), 817-868.

M

[20] Fehr, Ernst & Schmidt, Klaus M. (2006): The economics of fairness, reciprocity and altruism- experimental evidence and new theories, in: S. Kolm und J. Ythier [Eds.]: Handbook of the Economics of Giving, Altruism and Reciprocity, 1, Elsevier. [21] Fischbacher, Urs (2007): z-tree: Zurich toolbox for ready-made economic experiments, Experimental Economics 10, 171-178.

ED

[22] Glaeser, Edward & Scheinkman, Jose & Shleifer, Andrei (2003): The injustice of inequality, Journal of Monetary Economics 50, 199-222.

PT

[23] Greiner, Ben (2015): Subject pool recruitment procedures: organizing experiments with ORSEE, Journal of the Economic Science Association, 1, (1), 114-125.

CE

[24] Grossmann, Igor & Varnum, Michael (2011): Social Class, Culture, and Cognition, Social Psychological and Personality Science 2, (1), 81-89.

AC

[25] Hauser, Oliver P & Rand, David G & Peysakhovich, Alexander & Nowak, Martin A (2014): Cooperating with the future, Nature 511, (7508), 220–223. [26] Heap, Shaun P. Hargreaves & Abhijit Ramalingam & Brock V. Stoddard (2016): Endowment inequality in public goods games: A re-examination, Economics Letters 146, 4-7.

[27] Isaac, R. Mark & James M. Walker (1988): Group size effects in public goods provision: The voluntary contributions mechanism, The Quarterly Journal of Economics, 103, (1), 179-199. [28] Isaac, R. Mark & Walker, James M (1998): Nash as an organizing principle in the voluntary provision of public goods, Experimental Economics 1, (3), 191-206. 25

ACCEPTED MANUSCRIPT

[29] Laury, Susan K. & Holt, Charles A. (2008): Voluntary provision of public goods: experimental results with interior Nash equilibria, in: C. R. Plott and V. L. Smith [Eds.]: Handbook of experimental economics results, Vol. 1 Elsevier, 792-801. [30] Ledyard, John O. (1995): Public goods: a survey of experimental research, in: J. H. Kagel und A. E. Roth [Eds.]: Handbook of Experimental Economics, Princeton University Press, 111-194.

CR IP T

[31] Keser, Claudia, Markstdter, Andreas & Schmidt, Martin, Schnitzler, Cornelius (2014): Social Costs of Inequality - Heterogeneous Endowments in Public-Good Experiments, cege Discussion Paper, 217, University of Gttingen. [32] Kraus, Michael & Pfiff, Paul & Keltner, Dacher (2011): Social Class as Culture: The Convergence of Resources and Rank in the Social Realm, Current Directions in Psychological Science 20, (4), 246-250.

AN US

[33] Kraus, Michael & Keltner, Dacher (2009): Signs of Socioeconomic Status: A Thin-Slicing Approach, Psychological Science 20, (1), 99-106. [34] Lammers, Joris & Galinsky, Adam & Gordijn, Ernestine & Otten, Sabine (2012): Power Increases Social Distance, Social Psychological and Personality Science 3, (3), 282-290.

M

[35] Organisation for Economic Co-operation and Development (2015): In It Together: Why Less Inequality Benefits All. OECD Publishing.

ED

[36] Piketty, Thomas (2015): Putting Distribution Back at the Center of Economics: Reflections on Capital in the Twenty-First Century, Journal of Economic Perspectives 29, (1), 67-88.

PT

[37] Piff, Paul & Stancato, Daniel & Cte, Stphane & Mendoza-Denton, Rodolfo & Keltner, Dacher (2012): Higher social class predicts increased unethical behavior, PNAS 109, (11), 4086-4091

CE

[38] Reuben, Ernesto & Arno Riedl (2013): Enforcement of contribution norms in public good games with heterogeneous populations, Games and Economic Behavior 77, (1), 122-137.

AC

[39] Rondeau, Daniel & Gregory L. Poe & William D. Schulze (2005): VCM or PPM? A comparison of the performance of two voluntary public goods mechanisms, Journal of public economics 89, (8), 1581-1592. [40] Sadrieh, Abdolkarim & Verbon, Harrie (2006): Inequality, cooperation, and growth: An experimental study, European Economic Review 50, 1197-1222. [41] Siewert, Horst H. (2000): sellschaft, Hamburg.

Intelligenztest, 3. Edition, Moderne Verlagsge-

[42] Sokoloff, Kenneth & Engerman, Stanley (2000): History Lessons: Institutions, Factors Endowments, and Paths of Development in the New World, Journal of Economic Perspectives 14, (3), 217-232. 26

ACCEPTED MANUSCRIPT

[43] Sutter, Matthias & Weck-Hannemann, Hannelore (2003): On the effects of asymmetric and endogenous taxation in experimental public goods games, Economics Letters 79, (1), 59-67. [44] Trautmann, Stefan & van de Kuilen, Gijs & Zeckhauser, Richard (2013): Social Class and (Un)Ethical Behavior: A Framework, With Evidence From a Large Population Sample, Perspectives on Psychological Science 8, (5), 487-497.

CR IP T

[45] Vesterlund, Lise (2012): Voluntary giving to public goods: moving beyond the linear VCM, Handbook of experimental economics 2.

AC

CE

PT

ED

M

AN US

[46] Zelmer, Jennifer (2003): Linear Public Goods Experiments: A Meta-Analysis, Experimental Economics 6, 299-310.

27