PROMOTING ENVIRONMENTAL COOPERATIVE BEHAVIOUR: ANALYSING PROVISION POINT MECHANISMS, INTER-GROUP
COMPARISONS AND TIME PREFERENCES
by
Sil Boedi Scholte (11265302)*
Thesis (15 ECTS) submitted in partial fulfilment of the requirements for the Master of Science
degree in Economics: Behavioural Economics and Game Theory in the Graduate Faculty of Economics & Business of
The University of Amsterdam
December 2018
Thesis supervisors: prof. dr. Arthur Schram dr. Joël van der Weele
* Email: silboedi@gmail.com
Statement of Originality
This document is written by Student Sil Boedi Scholte who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
ABSTRACT
How can environmental cooperation best be promoted in order to increase contributions to real-world public goods? This thesis studies how environmental cooperative behaviour is affected by a provision point mechanism, by intra-group -and inter-group comparison, and by time preferences. A laboratory experiment was conducted that applied a provision point mechanism in a repeated public goods game and varied the information feedback per group (intra-group comparison only vs. additional inter-group comparison). In addition, participants made financial and environmental choices in a CTB-survey in order to investigate differences in discounting between these two domains and to determine correlations with cooperative behaviour. Results suggest that the provision point mechanism strongly promoted public good contributions, as thresholds were reached with great accuracy by all groups. Second, participants were not significantly influenced by receiving additional inter-group comparison. Data does confirm a net-effect in the direction of conditional cooperation and the presence of inequity aversion. Lastly, no difference was found between financial and environmental time preferences and no correlation was found with cooperation. This thesis concludes with critical remarks on the use of inter-group comparison with regards to mechanism design and discusses temporal discounting in different domains.
TABLE OF CONTENTS
ABSTRACT ... 4
I. INTRODUCTION ... 7
I. MOTIVATION ... 7
II. RESEARCH QUESTION AND CONTRIBUTION ... 9
III. SUMMARISED FINDINGS ... 9
IV. THESIS STRUCTURE ... 10
II. LITERATURE REVIEW ... 11
I. BEHAVIOUR IN PUBLIC GOODS GAMES WITH PROVISION POINT MECHANISMS ... 11
II. THE INFLUENCE OF CONFLICT AND COMPARISON ON COOPERATION WITHIN AND BETWEEN GROUPS ... 13
III. TIME PREFERENCES IN FINANCIAL AND ENVIRONMENTAL DOMAINS ... 16
III. METHODOLOGY ... 20
I. EXPERIMENTAL DESIGNS,PROCEDURES AND PAYOFF FUNCTION ... 20
A. Designs ... 20
B. Procedures ... 22
C. Payoff Function ... 23
II. HYPOTHESES ... 23
III. DATA ANALYSIS... 25
A. Estimation of Aggregate Time Preferences ... 25
B. Analysing Cooperative Behaviour ... 27
IV. RESULTS ... 28
I. SUMMARY STATISTICS ... 28
II. PUBLIC GOOD CONTRIBUTIONS ... 28
A. Aggregate Analysis ... 28
B. Estimating Effects to Intra- and Inter-Group Comparison... 30
III. TIME PREFERENCES ... 33
A. Aggregate Analysis ... 33
B. Estimating Aggregate Preferences ... 36
IV. RELATIONSHIP BETWEEN TIME PREFERENCES AND COOPERATIVE BEHAVIOUR ... 38
V. POSSIBLE LIMITATIONS ... 38
V. DISCUSSION AND CONCLUSION ... 41
I. INTERPRETATION OF FINDINGS ... 41
A. Public Good Contributions ... 41
B. Time Preferences ... 43
C. Time Preferences and Cooperative Behaviour ... 44
II. MAIN CONCLUSIONS ... 45
III. SUGGESTIONS FOR FUTURE RESEARCH ... 46
APPENDICES ... 47
APPENDIX 1:INSTRUCTIONS ... 47
A. Instructions Part 1: All participants ... 47
B. Instructions Part 2: All participants ... 48
C. Instructions Part 3: Red & Blue Groups ... 50
D. Instructions Part 3: Green Group ... 51
A. Part I – Air Quality Discounting Survey ... 52
B. Part II - Financial Discounting Survey ... 56
APPENDIX 3:CHOICE SETS PART 1 ... 60
APPENDIX 4:EXPERIMENTAL SETTING ... 61
APPENDIX 5:CORRELATION BETWEEN TEMPORAL DISCOUNTING AND COOPERATION ... 62
I. INTRODUCTION i. Motivation
This thesis aims to better understand the fascinating and complex determinants of human cooperation. The issue of cooperation is to design environments and mechanisms such that they encourage individuals to help others even though there is a risk that this reduces their relative earnings. How can we improve cooperation among people to increase contributions to real-world public goods? How can we best conserve energy together? What are the best ways to decrease the usage of cars and aeroplanes? More specifically, this thesis studies how cooperative behaviour is affected by a provision point mechanism, by intra-group -and inter-group comparison and by temporal discounting; all of which are trivial factors that influence environmental behaviour specifically. Better understanding in what way these elements affect cooperative behaviour can be of great benefit to enhance both environmental intra-group cooperation and collective efficiency in the real world. Proper insights of this type of cooperative behaviour could help to shape more effective policies with regards to urgent sustainability issues (e.g. global warming and CO2 emissions) and environmental goals, such as made in the Paris Agreements of 2015.
Three features are relevant for this research and have been of academic interest in the past: provision point mechanisms, the influence of inter-group comparison on intra-group behaviour, and temporal discounting (i.e. time preferences). Firstly, as environmental issues appear to be distant and intangible despite their urgency, the use of thresholds or intermediate goals could be useful in promoting cooperative behaviour and collective efficiency. For example, all EU-countries have agreed to emit 20% less greenhouse gasses in 2020 than in 1990. A provision point mechanism (or assurance contract) binds group members to their pledge of contributing to an action or public good by specifying a total contribution threshold to be met. It can be used in collective decision-making problems, such as that of the free rider. Some studies have included incentives such as thresholds that participants have to reach in every round of a repeated public goods game, but only a few incorporated a provision point that is applicable over the course of an entire game. There is a lack of evidence, but some data suggest that increases
in any type of threshold increases contributions but at the same time decreases the probability of the targets being reached (Ledyard, 1997). Studying a variety of provision point mechanisms in experiments could enable a better depiction of environmental decision-making dilemmas, representing global environmental goals and thus elicit more relevant data (Bougherara et al., 2011).
Secondly, it is relevant for environmental issues to study what elements can enhance contribution when separate groups exist without any actual competition and/or conflict involved. An appropriate experimental depiction of an actual environmental setting would be to assume heterogeneity of participants and to analyse the development of strategies through repeated interactions, such as adjusting your household’s energy consumption when receiving information of your neighbours’ consumption in real life. Nevertheless, research conducted on the influence of behaviour exposure in the environmental context is lacking. Most research that focuses on elements that enhance cooperation in abstract public goods has assumed homogeneity of social preferences and mainly focused on monetary punishments, non-monetary mechanisms (e.g. expressions of disapproval), advice giving and assortative matching (Chaudhuri, 2011). Previous research has also focused on direct reciprocity of cooperation from person to person and the contagion of cooperation from person to person to person within networks (Fowler & Christakis, 2010). Finally, even the interactions between groups has been studied, as conflict and competition greatly influence cooperative behaviour and collective efficiency in, for example, public goods games. However, as mentioned before, it remains rather unclear whether the mere exposure of defective/cooperative behaviour is contagious when different groups can solely observe each other. Testing this within the environmental realm might indicate important clues about cooperation exposure in steering future environmental behaviour between neighbourhoods, cities and even countries.
Thirdly, temporal discounting, which is the process of determining the present value of an outcome that is to be received in the future, is relevant for many types of decision making as people are constantly challenged with choices in which they either take gains/losses now or in the future. For example, discounting can decrease the subjective value of an outcome as the delay to its receipt increases (Green et al., 1996). More specifically, an example of discounting in environmental decision making could be that the value of a CO2 emission-free planet is very much decreased due to the enormous
delay of its realisation (for most people even beyond their lifetime). Much research has been conducted to understand if temporal discounting functions are exponential or (quasi-) hyperbolic over time and if there exists a difference between various domains, such as between monetary and personal health realms. More and more research has also focused on studying discounting functions in the environmental domain, but results are inconsistent. Environmental decision making specifically seems to be challenged by multiple dimensions besides temporal discounting, such as uncertainty, spatial and social issues, which complicates this research topic (Gattig & Hendrickx, 2007). Thus, it is necessary to further study how environmental discounting functions and, specifically, to investigate what its relationship is with cooperative behaviour.
In summary, in order to make a relevant contribution to the current academic literature and our understanding of environmental cooperative behaviour, this thesis will combine an analysis on the influences of a provision point mechanism, intra-group -and inter-group comparison and temporal discounting.
ii. Research Question and Contribution
The following research question will be addressed in this thesis:
How is cooperative behaviour influenced by intra –and inter-group comparison when a provision point mechanism is present and what type of time preferences best describe this decision-making?
More specifically, this thesis aims to contribute to our understanding of the influence of provision point mechanisms, of behaviour exposure between groups, and of environmental discounting within a public goods game setting.
iii. Summarised Findings
The data collected suggest that provision point mechanism as issued in this experiment strongly promoted public good contributions, as thresholds were reached by all groups.
Second, participants were not significantly influenced by the treatment of additional inter-group comparison besides intra-group cooperation. Data does confirm inequity aversion (with a stronger distaste for disadvantageous inequality than for advantageous ones) and a net-effect in the direction of conditional cooperation rather than social comparison. Lastly, no difference was found between financial and environmental preferences and, therefore, no difference in correlation with cooperative decision-making. In addition, temporal discounting did not significantly correlate with cooperative behaviour. Thus, this thesis provides no evidence of a role for inter-group comparison in promoting cooperative behaviour when using this type of provision point mechanism and of distinct correlations with this behaviour for different time preferences.
iv. Thesis Structure
The structure of this thesis follows its actual research process in which, firstly, the academic context is provided to define the scope and relevance of the research topic, and, secondly, the experiment is introduced and its findings are reported and interpreted. Thus, after this Introduction, Chapter II presents a literature review that outlines the theoretical foundations and points to gaps in the existing academic knowledge with regards to provision point mechanisms in public goods games, the inter-group comparison – intra-group cooperation effect and environmental discounting. This chapter will not only serve as a framework for understanding the scope of the current study, but also illustrates the need for further research on the topic of cooperation between groups and the intuition for having certain hypotheses. Chapter III outlines the methodology used in conducting this research and justifies the experimental design, procedures and tools for data analysis. Chapter IV presents the results based on the laboratory experiment and provides statistical data detailing significant insights that will help in answering the research questions with regards to cooperative behaviour in and between groups. Subsequently, chapter V interprets these results by combining existing knowledge and theories with the data collected in the experiment. It aims to reflect on the hypotheses that were formulated as mentioned above. A conclusion and suggestions for further results are also provided. Finally, experimental documents and other files of interest are provided in the Appendices and all references used are listed in References.
II. LITERATURE REVIEW
i. Behaviour in Public Goods Games with Provision Point Mechanisms
The provision of public goods in many organisations and societies depends on the voluntary contributions that people provide. Unfortunately, not only do standard theoretical economic models predict that behaviour within voluntary contribution mechanisms will be inefficient, also much academic research provides this evidence based on conducted experiments (Isaac & Walker, 1988; Davis & Holt, 1993). From this it is known that, for example in repeated, linear public goods games without communication, contributions tend to start at around 40–50% and decrease to 10–20% after ten rounds (Fischbacher & Gächter, 2010; Ledyard, 1997). The type of behaviour observed is labelled as conditional cooperation, a phenomenon in which players approximately match the previous contribution of their groupmates (Fischbacher et al., 2001). In addition, Offerman et al. (1996) provide insights on decision making with regards to voluntary contributions in public goods using individuals’ value orientations and their expectations of others. They stress that the different beliefs that people have towards one another play a vital role in determining the behaviour in these settings and offer a method to obtain an independent measure of these beliefs. Through their method they found that those participants labelled as individualistic significantly contribute less in a public goods game than those labelled as cooperative.
The environment, representing one of the largest and most complicated public goods due to its dependency on global contributions and its large time scale, also falls prey to inefficient behaviour. Rondeau et al. (1999) accurately conclude the following:
“Relying on funding mechanisms that inaccurately reflect contributors’ preferences suggests that socially desirable public goods are produced at sub- optimal levels and underscores the need for a contribution mechanism capable of revealing the demand for public goods in natural conditions” (p. 456).
In aiming to steer participants in providing more optimally, a provision point mechanism can be introduced, which is an instrument that installs a contribution threshold that participants are required to meet – either in a certain round or by the end of the game –
in order to accomplish an achievement (e.g. providing a public good or receiving an individual payoff). It is often used as a tool to increase public good contributions by having participants pledge their individual contribution and only requiring them to make the actual contributions once a certain threshold is reached by the group. So, it lowers the risk of everyone’s investment and therefore increases contributions. Isaac et al. (1989) were one of the first to test the effects of including a provision point mechanism and indeed found that this instrument, in combination with a money-back guarantee (i.e. a feature assuring that contributions are returned if the provision point is not met), did improve public good contributions. In addition, they still found “cheap riding” for low and medium provision point levels (p.234). Similarly, a meta-analysis of multiple experiments using a simple provision point mechanism shows that the higher the threshold, the more public contributions are made (Croson & Marks, 2000). Cadsby & Maynes (1999) provide experimental evidence and found that the money-back guarantee especially promoted public goods provision when the provision point was high, while its absence actually discourages public provision when the point is high. In addition, in aiming to make the provision point mechanism more realistic, they show that the option of having continuous contributions instead of binary ones significantly enhance public goods provision. In expanding on the money-guarantee rule, Zubrickas (2014) added a bonus to the refund when the provision point was not reached and showed that public provision is even further improved. Furthermore, Bose & Rabotyagov (2018) propose a more radical improvement of the provision point mechanism by adding the element of a lottery. A lottery prize of 15 experimental tokens was included, where the chances of winning were proportional to the participant’s public contribution. They found that a lottery combined with a provision point significantly increases the level and frequency of public good contributions compared to only using a provision point mechanism.
Clearly, various types of provision point mechanisms are effective in promoting public goods provision. Some studies have already used these instruments to study environmental decision making specifically and found that, for example in Rose et al. (2002), it increased public goods contributions. Nevertheless, money-back guarantees were installed in this study as well, which inaccurately depicts the decision-making mechanism that is in place for real-life environmental choices. Thus, in order to properly study environmental behaviour, it is necessary to design a suitable public goods game
that not only considers that actions can not be withdrawn but also that public contributions are only profitable if done collectively. This thesis’ experiment does include both of these elements in its provision point mechanism, further explained in Chapter III.
ii. The Influence of Conflict and Comparison on Cooperation within and between Groups
Much research has been done to investigate the elements that influence and foster cooperative behaviour between individuals and within groups. As such, many studies have investigated the phenomenon of conditional cooperation, in which people’s willingness to contribute depends on other people’s contribution (Fishbacher et al. 2001). Conditional cooperation results in heterogeneous contributions that decline over time due to the slight bias of selfishness but are much higher than predicted by standard economic theory. Beyond this basic premise, other researchers have applied various setups in public goods games to study their effects on cooperation. Examples include arbitrary labels of recognition (Nowak, 2006), (altruistic) punishment (Fehr & Gächter, 2002), feedback and supervision (Nikiforakis, 2010), and silent identification (Bohnet & Frey, 1999). Due to the different dynamics and results, it is important to differentiate between studies that have focused on networks, in which some individuals interact more often than others, and those that focused on spatial structures, where interaction is designed so that it is equal for all participants. For example, Jordan et al. (2013) argued that many interactions outside of the laboratory and in the real world are dynamic, meaning people can regulate themselves with whom they interact. Therefore, they conducted a social dilemma experiment and found that while selfish behaviour was contagious in more dynamic networks, cooperative behaviour was not. On the other hand, in relatively fixed networks, both cooperative and selfish behaviours were contagious. In addition, Fowler & Christakis (2010) showed that in both public goods games with and without punishment participants were influenced by fellow group participants’ contributions in their future interactions even though these were with others that had not been part of the initial interaction. This so-called cascade of cooperative behaviour lasted for various rounds and had a reach of up to three degrees of separation. Evidently, cooperative behaviour has a long-lasting effect, but does it also transcend groups/networks and function in between them?
Recently, researchers have focused more and more on identifying circumstances that foster cooperative behaviour beyond (in)direct interactions between individuals and dynamics within groups and networks. For example, evidence suggests that, when a group is in a structural conflict with another group, cooperation within the group not only increases (Benard & Doan, 2011; Bornstein, 2003), but norm enforcement also rises, such as altruistic punishment (Benard, 2012; Sääksvuori et al., 2011). This phenomenon is called the inter-group conflict – intra-group cooperation/cohesion effect. However, though inter-group competition might enhance intra-group cooperation, it has also been shown that outcomes are collectively inefficient due to the generated costs of conflict (Dawes, 1980; Gould, 1999). Studying cooperation enhancement in more detail within a setting of inter-group interaction (i.e. not conflict per se) and focusing on results both within the group and as groups collectively, could be beneficial in understanding the arrangement of public goods in real life.
Interestingly, the hypothesis that inter-group comparison (i.e. without any presence of actual conflict or competition) would increase intra-group cooperation and collective efficiency directly contradicts the traditional economics perspective which would state that the exposure of another group’s behaviour (without a direct effect on one’s own payoffs) should not have any effect on an individual’s utility-maximisation rationality, nor on a player’s rational cooperation; that is, another group would not change a player’s beliefs about fellow group members’ altruism and would not alter a tit-for-tat strategy (Kreps et al., 1982). Nevertheless, one could also argue that through Bayesian updating of beliefs someone could re-establish what he/she thinks is normal or fair to provide in the public account based on another group’s behaviour.
Evidence from behavioural economics and social psychology provide insights of actual behaviour. For example, it is known that players are likely to adjust own contributions according to peer group members’ contributions due to inequity aversion (Bolton & Ockenfels, 2000). In addition, ample research from the field of social psychology not only indicates that comparison happens between individuals and within groups, but even that inter-group comparison is at the core of social identity theory (Tajfel & Turner, 1986). This theory states that group members are inclined to positively diverge from other groups by enlarging relative distinctions between their members of their own and other group(s). This means that, even without conflict between groups over tangible assets, groups
would be likely to initiate and/or partake in an effort by increasing intra-group cooperation in order to enhance their social identity. In the context of public goods games with inter-group comparison this would translate into higher public goods provision. More specifically, Böhm & Rockenbach (2013) stress two contradicting forces: conditional cooperation on the one hand would lead to a public goods contribution reduction of a player over time, while, on the other hand, a relatively high provision level for the own group would require him/her to increase this contribution. They conducted a laboratory experiment in which participants played a repeated public goods game. They used a 2x2 between-subjects design in which they not only varied the information participants would get but also the provision environment. So, after each round, subjects received either only information on the intra-group average contribution or information on both the intra-group and the inter-group average contributions, depending on their randomly assigned treatment group. Secondly, depending on the treatment, subjects were either in a group of three with an individual 0.7 return on cooperation or in a group of 4 with a return of 0.4. For every token invested in the private account, the player would receive €0.025 and for every token invested in the public account, every group member received either €0.0175 or €0.01, depending on the treatment in place. In conclusion, they state that “social inter-group interactions by means of mere inter-group comparisons are a powerful method to increase efficiency in human cooperation” (Böhm & Rockenbach, 2013; p. 2). Also, Tan & Bolle (2007) conducted research on the effects of inter-group comparison on intra-group cooperation by experimentally comparing public goods games without comparison, with comparison and with comparison and additional incentives to win. They also find that inter-group comparison without using additional incentives has an effect on participants’ behaviour: contributions decrease in response to having contributed relatively more than the other group in a round, while they increase when they contributed relatively less. Finally, Cardenas & Mantilla (2015) conducted an experiment in which participants would be informed about both their relative individual and group performance after each round in a repeated public goods game in which one treatment only included inter-group comparison and the other included incentivised inter-group competition. They also found that, with mere inter-group comparison, groups with relative lower public contributions in one round tend to increase their contributions in the next, while the opposite is true for relative performances with individuals. In addition, when competition is incentivised, and participants’ payoff also depends on the relative group
performance, this effect is stronger and individuals contribute significantly more to the group.
However, other researchers, like Jordan et al. (2017), find that when comparing thresholds and inter-group comparison, thresholds are most decisive in determining the increase in cooperation whereas comparison does not do so independently. In addition, it has also been found that information about the behaviour of other individuals and other groups actually reduces intra-group cooperation (Burton-Chellew et al., 2013). Burton-Chellew et al. (2013) stress that their data indicates that individuals mainly aim egocentrically to improve their personal position instead of that of the group, which leads to less cooperation in the end.
Evidently, intra-group comparison influences behaviour. But it is yet to be determined when and how inter-group comparison changes behaviour. This thesis aims to build further upon the current understanding of influencing intra-group cooperation through not only using a provision point mechanism but also by allowing for inter-group comparison within a laboratory experiment as explained in the next chapter.
iii. Time Preferences in Financial and Environmental Domains
Having established the need for a better understanding of the influences of provision point mechanisms and inter-group comparisons on cooperative behaviour, this section focusses on grasping what the relationship is between time preferences and cooperative behaviour. More specifically, a better understanding of how temporal discounting influences environmental decision making in a group setting can generate new insights relevant for real life matters.
Time preferences are a fundamental determinant of decision-making, as people are continuously challenged with choices in which they have to decide to take gains (or losses) now or in the future. For example, smoking a cigarette now generates immediate payoff to some people but has negative consequences for one’s health in the future. Temporal discounting is the process that guides this form of decision making, which, for example, indicates the decrease of subjective value of an outcome as the delay to its
receipt increases (Green et al. 1996). Traditional economic models assume that the discounting function is exponential in time; this means that, as time delay increases, preferences decrease monotonically and remain consistent. However, experimental evidence is mixed: some recent research in behavioural economics and neuroeconomics suggests that discounting functions are actually hyperbolic or, more specifically, quasi-hyperbolic and provide supporting evidence for the existence of time inconsistency and preference reversal (Camerer et al., 2005; Laibson, 1997; Phelps & Pollak, 1968; Tian et al., 2016; Vuchinich & Simpson, 1998). Several studies argue that exponential discounting becomes a more realistic function as more and more factors are properly accounted for, such as applying variations in sooner times, later times, slopes of budgets and relative risks within models of discounted expected utility (Andreoni & Sprenger, 2012; Richards & Green, 2015).
In order to better understand discounting and come to a more widely supported discount function, more and more research has diversified in not only studying monetary rewards but also other gains (and losses) such as in personal health (Kang & Ikeda, 2014; 2016), body image, dating partners, cigarettes and medical treatment (Weatherly et al., 2010). Nevertheless, research that has focused on discounting environmental goods remains uncommon. This is problematic as environmental issues are more urgent and global than ever before and policies could benefit from a proper understanding of environmental decision-making. Only few studies have focused on discounting environmental goods: Richards & Green (2015), for example, compared subjects’ rate of intertemporal time preference for both financial and environmental goods using multiple price-lists (MPL) and matrix multiple price lists (MMPL). MPL experiments are a common instrument to distinguish between time preference and risk aversion. Subjects are presented a series of binary choices that differ only in price (future reward for example), such as in Harrison et al. (2002) and Andersen et al. (2008). MMPL instruments were used to overcome the simplicity of MPL experiments by varying more than one attribute (e.g. costs, delay, green space improvement) row-by-row and column-by-column. Using both instrument approaches, Richards & Green (2015) find that discount functions for environmental goods are hyperbolic, but those for financial goods are not; this latter result is different than what has been found in previous research (Loewenstein & Prelec, 1992). Their data also show that discount rates for environmental goods are 50% lower than for financial goods. In addition, some research has been done on discounting
the perceived risk of environmental commodities. For example, expanding on the fact that discounting processes appear to be similar across different outcome dimensions (outcomes that are uncertain, temporally delayed, spatially distant and/or socially distant), Gattig & Hendrickx (2007) investigated whether discounting mechanisms are also similar across various domains, namely risk in financial choice, personal health issues and environmental decisions. They conclude that, compared to other domains, temporal discounting is significantly less prominent in environmental risks. Also, Viscusi et al. (2008) focused on discounting environmental goods; they estimate discount rates for environmental quality based on a survey with environmental policy choices filled out by over 2,000 respondents. Here, the environmental good in the choice context is water quality, of which they vary its improvements costs and the time when the improvements will occur. Their results indicate that time preferences were more consistent with a hyperbolic than with an exponential function, estimating the hyperbolic discounting parameter 𝛽 to lie in the range from 0.48 to 0.61 (where the difference between 1 and 𝛽 indicates how much the function breaks from the exponential discounting model). They also found that those who are more connected to the good at stake (in this case regular visitors to water bodies) have low discount rates, whereas those who do not visit consistently have high discount rates.
Moreover, in an effort to directly compare discounting in different domains, Hardisty & Weber (2009) conduct three studies in which subjects made choices between financial, environmental, and health gains and losses that took effect either now, with a delay of 1 or of 10 years. They found that choices in all domains showed hyperbolic discounting patterns and that, as expected, losses were discounted less than gains in all domains. In addition, although discounting of financial and environmental payoffs did not differ significantly, health gains and losses showed a more extreme discount function compared to the other two domains. As indicated by the researchers, one of the shortcomings of this study is that it fully relies on self-reported responses to hypothetical scenarios. Although no differences have been found by studies that have compared temporal discounting for real and hypothetical financial outcomes (Johnson & Bickel, 2002; Kirby, 1997), hypothetical environmental outcomes come with a difficulty: it remains a challenge to properly construct environmental scenarios that realistically
match financial and health situations (which are much more tangible for most people). Environmental decision-making in the real world differs in many ways, which could affect self-reported time preferences in simplified choices. Therefore, Hardisty & Weber (2009) strongly recommend that future research requires ingenuity in order to properly verify the limits and assumption of economic models with real-world phenomena.
Taking this into account and having a similar approach to this thesis, Jacquet et al. (2013) studied the effect of both intra- and intergenerational discounting on cooperative behaviour with a collective-risk group experiment. They conclude that, as the present generation will mainly bear the costs of environmental cooperative behaviour whereas future generations will mostly benefit, intergenerational discounting leads to a significantly lower level of cooperation than intragenerational discounting does. Results from Curry et al. (2008), Harris & Madden (2002) and Milinski et al. (2008) support the view that “discounting correlates with cooperation such that individuals who highly devalue future rewards cooperate less frequently” (Stevens & Hauser, 2004, p. 63).
Nevertheless, other research indicates there is no significant role for time preferences in determining cooperation levels (Kim, 2016). For example, as opposed to temporal discounting, Wu et al. (2017) find that other factors such as reputation and trust in others do explain cooperative behaviour. In addition, theoretical proof indicates that a variation on an iterated Prisoner’s Dilemma still allows cooperation to overcome strong discounting (Stephens, 2000).
Evidently, research on discounting in different domains remains inconclusive. More insights on the relation of different time preferences and cooperation would enable a better understanding of the motives for different behaviours connected to those distinct domains, and vice versa. Therefore, this thesis will combine a study of two forms of temporal discounting together with an experiment on cooperation.
The following chapter elaborates on the experimental design and procedures used for the experiment of the current study, not only aiming to investigate the effects of a provision point mechanism and inter-group comparison on intra-group cooperative behaviour, but also to see what type of time preference most correlates with the cooperative behaviour as elicited through the public goods game. In addition, it provides hypotheses on the expected results.
III. METHODOLOGY
i. Experimental Designs, Procedures and Payoff Function
In order to address the research question as stated in the introductory chapter, a laboratory experiment was conducted in a lecture hall at the Roeterseiland campus of the University of Amsterdam (UvA), following the ethical guidelines and procedures of the Graduate Faculty of Economics & Business. All participants gave informed consent to participate voluntarily, after guaranteeing anonymity throughout the entirety of the experiment and in the analyses of the data. The experiment existed of three parts, which will be explained by design, procedure and payoff. In total, two sessions of the full experiment were run, lasting between 60 and 75 minutes each.
A. Designs
Part 1 exists of a survey in which all participants (24 people) are asked 45 Convex Time Budget (CTB) questions in order to determine their time preferences (both discounting and curvature), as in Andreoni & Sprenger (2012a and 2012b). A (3 × 3) design is implemented with three earlier payment dates, t = (0, 7, 35) days from the experiment date, crossed with three delay lengths, k = (35, 70, 98) days. Tokens allocated to earlier payments have a value of at while tokens allocated to later payments have a value of at+k.
In all cases, at+k is €0.20 per token and at varies from €0.20 to €0.14 per token. Thus, there
are nine (t, k) cells and within each cell are five CTB questions with varying values for earlier payments (at), making a total of 45 questions. One example question looks like:
“Allocate 100 tokens: … tokens at €0.18 in 7 days, and … tokens at €0.2 in 35 days” (see Appendix 2A).
In addition to financial discounting, this experiment not only aims to test if environmental discounting develops in a similar manner, but also how it correlates with the actual behaviour in Parts 2 and 3. Therefore a second, similar survey is filled out by all participants, using air improvement as an indicator for environmental preferences. Again, a (3 × 3) design is implemented with three earlier air improvement days, t = (0, 7, 35) days from the experiment date, crossed with three delay lengths, k = (35, 70, 98) days.
Tokens allocated to earlier air improvement have a value of at while tokens allocated to
later payments have a value of at+k. In all cases, at+k is 20% air improvement per token
and at varies from 14% to 20% per token. Thus, there are nine (t, k) cells and within each
cell are five CTB questions with varying earlier improvements, making a total of 45 questions. One example question looks like: “Allocate 100 tokens: … tokens at 17% air improvement in 35 days, and … tokens at 20% air improvement in 98 days” (see Appendix 2B).
All in all, the number of observations was 24x45=1080 financial CTB questions and 24x45=1080 environmental ones, totalling at 2160 observations. The choice sets are displayed in the table in Appendix 3. This table includes the gross interest rate (at+k/at =
1+r) and the daily rate in percentages ((1 + 𝑟)&/(), which are all variables that were not presented to the participants.
Parts 2 and 3 of the experiments use a 2 (level of comparison: INTRA vs. INTER) x 1 (level of provision point) between-subjects design. The repeated public goods game consists of 5 rounds in both Part 2 and Part 3 and all players receive an endowment of 10 experimental monetary units (EMUs) per round. No money-back guarantee is installed. In both Parts 2 and 3 the provision points are set at 70 EMUs to be reached in 5 rounds. The number of 5 rounds is established because of practical reasons and time limitations. The provision points levels are set at 70, making it undividable by 4 in order to avoid a focal point of equal contributions. Decisions are incentivised, as every player has a chance of winning his/her own respective number of contributed EMUs of one round in Euros. All participants are randomly and anonymously assigned to a group, labelled by blue, red or green, in which they remain throughout the entire experiment. Members in the green group only receive information about their own group’s contribution after every round in both Parts 2 and 3. Members in the red and blue groups would also only receive information on their own group’s contribution after every round in Part 2 but would receive additional information on the contributions of the respective other group after every round in Part 3 (see Appendix 1 for the participants’ instructions). The experiment involves no deception of participants and there are no additional ethical concerns. All in all, there were 120 observations in both Part 2 and Part 3. Or, to clarify, 80 observations
of the green group (the INTRA/INTRA treatment) and 160 of the red and blue groups (the INTRA/INTER treatment).
B. Procedures
All participants were recruited to take part in an experiment on decision-making for data collection of a MSc thesis within a Master’s programme in Economics at the UvA. On arrival, all participants drew a numbered card to determine their table number, which unknowingly also assigned them to a specific treatment group. Printed instructions and both CTB-surveys were already placed on the tables when participants entered the laboratory site. All instructions, also of Parts 2 and 3, were read aloud by the experimenter. After all rounds in Parts 2 and 3, investment sheets were picked up, data was aggregated, and feedback was included on the new investment sheets that were handed out before the start of the consecutive round.
At the beginning of each round of Parts 2 and 3, participants received an endowment of 10 EMUs and were given the choice to either invest in Account A (the private account) or Account B (the public account). While every EMU invested in Account A could give that specific player €1, every EMU invested in Account B represented 1 EMU invested for the entire group. In this experiment, the provision point mechanism meant that the assigned level of contributions had to be invested in Account B in order for any player in the group to receive any payoff according to his/her respective contributions made in Account A of a random round. Any EMU in excess of Account B with regards to the threshold would not be refunded to players. A provision point mechanism of 70 EMUs was in place, meaning that a minimum group total of 70 EMUs needed to be invested in account B in order for any player within that group to be able to receive an actual payoff. At the end of the experiment, one random player and one random round was chosen in both Part 2 and 3 in order to determine who will receive what payoff, based on his/her investment in account A in that specific round. This payoff would only be paid out if the provision point was reached after a maximum of 5 rounds in that Part of the experiment. This is explained in more detail in the next section. Earnings were paid out anonymously and in cash, as envelopes were distributed at the end of the experiment containing the participants’ earnings.
C. Payoff Function
Part 1 did not have any payoffs or incentives, as it was too ambiguous to adopt a financial payoff that a participant would receive based on his/her data in the environmental CTB survey. Therefore, both surveys were filled out according to participants stated preferences and without the inclusion of any payoffs.
Incentives were included for the experiment in Parts 2 and 3. Let n be the number of players in the group, where each player i is endowed with e = 10 EMU’s. Next, we denote the action set of a player i by 𝐴* = {0, 1, … , 𝑒}, i.e. a player decides how many EMU’s, 𝑐* ∈ 𝑒*, he/she will contribute to Account B (the public account) and with that how many he/she will invest in Account A (the private account), which has a per token payoff equal to 1 Euro. The number of rounds per Part is indicated by 𝑡 = {1, 2, … , 5}. Thus, Player i’s payoff in tokens is determined as follows:
∏ (𝑐* &, 𝑐:, … , 𝑐;) = 𝑒*<− 𝑐*<, 𝑖𝑓 ∑< 𝑐*
<A& + ∑<<A&𝑐B ≥ 70 (1) That is, a randomly chosen individual only receives his/her payoff based on the number of tokens invested in Account A of a randomly chosen round if the total group amount invested in Account B is equal to or exceeds 70 EMU’s after at least 5 rounds. Again, only one randomly chosen participant in Part 2 and one in Part 3 is chosen to receive actual payoff according to the above-mentioned function.
ii. Hypotheses
Based on the previously cited literature, this thesis provides three hypotheses of expected outcomes. Firstly, research has indicated that cooperative behaviour within public goods games is responsive to the use of provision point mechanisms, both within an environmental paradigm and beyond. The current experiment applies an innovative provision point mechanism that reflects an environmental decision-making setting (as there is no money-back guarantee, there are only pay-offs when the threshold is reached and there are no refunds of excess investments in the public account with regards to the threshold), which is expected to strongly promote cooperative behaviour due to the
limited means to obtain payoffs. In addition, it is hypothesised that the inter-group comparison will promote intra-group cooperation and overall efficiency. Besides previously conducted research with regards to the effect of comparison between groups in public goods games, indications from both inequity aversion and social identity theory strongly suggest that cooperation is promoted most when both feedback on the own and the other group is provided. Therefore, including inter-group comparison in the experiment could improve cooperation resulting in reaching the provision point more often and/or accelerating the process towards it. Thus, the hypotheses look like this:
Hypothesis 1
H0: Inter-group comparison does not promote intra-group cooperation nor overall efficiency significantly in repeated public goods games with a provision point mechanism.
H1: Inter-group comparison does promote intra-group cooperation and/or overall efficiency significantly in repeated public goods games with a provision point mechanism.
Secondly, based on previously performed research by Viscusi et al. (2008) it is expected that both environmental and financial discount rates as measured in Part 1 of this thesis will be (quasi-)hyperbolic functions. In addition, it is expected that environmental discounting rates are significantly higher than financial discounting rates. Although Hardisty & Weber (2009) find data suggesting no difference, their method of using descriptive scenario’s is debatable (as is indicated by themselves as well). Perhaps, by using a more appropriate set of choices, it becomes evident that environmental decisions are discounted heavier due to its intangibility relative to financial choices. Therefore, by using identical binary choice-dilemma’s for both environmental and financial decision-making tasks, the hypothesis states:
Hypothesis 2
H0: Environmental and financial choice sets are discounted similarly.
H1: Environmental choice sets are discounted more and have a larger present bias compared to financial choices.
Finally, using the data collected on the CTB surveys, it is predicted that there exists a negative correlation between discount rates and cooperative behaviour. As stated in Stevens & Hauser (2004), for example, expected prospective payoffs have to be discounted appropriately for cooperation to work, as reciprocal altruism requires suffering instant costs for prospective payoffs (p. 63). Although this line of reasoning would also create the expectation that cooperation is significantly less at the beginning at the game compared to the end, the limited number of rounds is very likely to dampen this trend and, thus, is expected to be unobservable. In addition, building forth on the expected outcome of hypothesis 2, it expected that environmental time preferences have a stronger negative correlation with cooperative behaviour than financial ones. Thus, the last hypothesis states:
Hypothesis 3
H0: Cooperative behaviour in a repeated public goods game does not correlate with either financial or environmental time preferences.
H1: Cooperative behaviour in a repeated public goods game has a stronger negative correlation with environmental time preferences than with financial ones.
iii. Data Analysis
All data were analysed within Excel and the statistical STATA environment (Stata/SE 15.1 for Mac (64-bit Intel)).
A. Estimation of Aggregate Time Preferences
In order to properly estimate time preferences of participants, data from the CTB-surveys has been used to estimate temporal discount rates. Similar to Andreoni & Sprenger (2012a), an econometric approach for estimating the quasi-hyperbolic discounting model is proposed and applied to the choice data from the CTB-surveys. This thesis aimed to use the quasi-hyperbolic 𝛽 − 𝛿 model (Laibson, 1997; Phelps & Pollak, 1968), in which the standard exponential (compound) discounting equation is taken as a basis with discount factor 𝛿. In addition, 𝛽 represents a supplementary discount factor for all future time moments. The 𝛽 − 𝛿 model is often used to display present-biased preferences and
assumes a quasi-hyperbolic discounting model with a constant relative risk aversion (CRRA) utility function. In Andreoni & Sprenger (2012a) a consumption of 𝑐<+ 𝑐<F( is evaluated at time 0 as:
𝑈(𝑐<, 𝑐<F() = H&(𝑐<+ 𝑤&)H+ 𝛽𝛿( &
H(𝑐<F( + 𝑤:)H (2) , with 𝛽, 𝛿 ∈ [0, 1], where 𝛿 is the standard discount factor per period, 𝛽 is the present bias, 𝛼 is the curvature parameter and 𝑤& and 𝑤: are background consumption parameters1. However, this model did not converge due to the high number of parameters to be estimated and the invariability of the data collected. Therefore, a simpler 𝛽 − 𝛿 model was used, such as can be found in Lührmann et al. (2013):
𝑈(𝑐<, 𝑐<F() = 𝑐<H + 𝛽<K𝛿(𝑐
<F(H (3)
where 𝑡L is a time indicator that remains 1 whenever time 𝑡 represents the present. 𝑐< and 𝑐<F( denote the payment values, while 𝛼 signifies the curvature of the utility function. For simplicity’s sake, background consumption is fixed at zero. In addition, participants are asked to optimise their payoffs subject to the budget received in the experiment, for which the constraint is:
𝑃𝑐<+ 𝑐<F( = 𝑌 (4)
Here, P represents the gross interest rate and Y is the endowment (i.e. 10 EMUs in this experiment). Thus, optimising (3) subject to (4) results in the next condition:
𝑥< = 𝑌(𝑃𝛽𝑡0𝛿𝑘) 1 𝛼−1 1+𝑃(𝑃𝛽𝑡0𝛿𝑘) 1 𝛼−1 (5)
1 As defined in Andersen (2008), background consumption is the optimised real-life
consumption estimated on current wealth and income, before permitting any influence of money as presented in the experiment.
From this simple condition, it is possible to pinpoint participants’ present bias, 𝛽, through variations in the earlier date for receiving EMUs, 𝑡L. In addition, by changing the values of the delay length, 𝑘, we can identify the discount rates, 𝛿. While 𝛽 = 1 implies standard, time-consistent (exponential) preferences, 𝛽 < 1 implies time-inconsistent, present-biased preferences. In other words: 𝛽 discounts all future intervals consistently, while 𝛿 does so exponentially. The condition as defined in (5) is used to investigate how well this model converges to the data that was collected in Part 1 of this thesis’ experiment.
B. Analysing Cooperative Behaviour
Non-parametric tests are used to analyse results of Parts 2 and 3 and, in order to compare the differences between the independent groups, one –and two-tailed p-values of Mann-Whitney U tests are reported as the dependent parameter is not-normally distributed. Also, R-values are specified to estimate the effect sizes.
IV. RESULTS
This chapter presents the results of the data collected and upholds the following structure: first, the data is summarised and standard statistics are provided; second, discount rates are calculated for both financial and environmental decision and more sophisticated regression models are used to investigate the influence of the treatments on public good contributions; finally, the relationship between the discount rates and public goods contribution is explored.
i. Summary Statistics
The data presented in this chapter are obtained from a double-session experiment ran at the University of Amsterdam. In total, 24 participants participated in the experiment, 12 in each session. The average age of the participants was 31.8 years, 41.7% was female and 58.3% male. Of all participants, exactly 2/3 was a student (of which 8 participants from the field of Economics) and 1/3 was none-student. Each participant made 10 decisions in the public goods game, totalling to 240 observations in total, of which 120 observations had the INTRA-treatment in the first 5 rounds, 80 had the INTER-treatment in the second 5 rounds and 40 remained in the INTRA-treatment as a control group. In addition, the same 24 participants also filled out 45 CTB-questions on financial choices and another 45 CTB-questions on environmental choices. This totals 1080 data points for both surveys.
In order to maintain a similar order as in Chapters II and III, first the experiments’ results of Parts 2 and 3 will be presented and only after those of Part 1.
ii. Public Good Contributions
A. Aggregate Analysis
All decisions on the allocation of experimental EMUs for the repeated publics goods game have been collected in Parts 2 and 3 of the experiment. The summary statistics of these parts are presented in Table I below. First, a Shapiro-Wilk test was conducted to establish whether the data follows a normal distribution. Based on the Shapiro-Wilk test, we can reject that the public good contributions are normally distributed (p < 0.05). Given these results, non-parametric tests were preferred in further analyses.
Second, it is observed that the minima and maxima were almost always to be found at the extremes of 0 and 10. Although these could technically be considered as outliers, they are more likely to represent tactical choices of public goods contributions due to the strategic nature of the experiment. Insufficient data could also cause this non-normal distribution, which is further described in the limitations section.
Table I: Summary Statistics of Parts 2 & 3
Obs. Mean St. dev. Min. Max. Avg. total
Mean Public Good Contribution Overall 240 3.68 2.06 0 10 73.58 Overall Rounds 1-5 120 3.64 1.99 0 10 72.83 INTRA (G) 40 3.68 1.64 0 9 73.5 INTRA (B+R) 80 3.63 2.16 0 10 72.5 Overall Rounds 6-10 120 3.72 2.13 0 10 74.33 INTRA Control (G) 40 3.5 1.54 1 8 70 INTER (B+R) 80 3.83 2.38 0 10 76.5
The average public good contribution across all participants, regardless of treatment, was 3.68 EMU’s per round, with a standard deviation of 2.06 and ranging from 0 to 10 (see Table I). Overall allocations in Rounds 6-10, regardless of treatment, was on average 0.08 EMU’s higher than in Rounds 5-10. More specifically, the Blue and Red Groups who received the INTER-treatment in Rounds 6-10 contributed 0.20 more on average in those second five rounds compared to the first five. In contrast, the Green group that controls for possible learning by receiving the INTRA-treatment over the course of 10 rounds decreased their public good contribution with 0.18 in the second half. Notably, there exists an upward trend in public goods contributions and the standard deviation for those changing from the INTRA- to the INTER-treatment, while both contributions and standard deviations tend to decrease for those remaining in the INTRA-treatment over the course of all 10 rounds. Figures 1 & 2 below provide a better visualisation on the development of public good contributions throughout the 10 rounds, in which the different groups have been clustered according to their assigned (non-)treatment.
B. Estimating Effects to Intra- and Inter-Group Comparison
This section further investigates whether the trends observable in the data are significant. First, in order to study the effects of receiving additional inter-group comparison besides only first receiving intra-group comparison on public good contributions (i.e. within-subject changes for those in the Blue and Red treatment groups), a two-sample Wilcoxon
rank-sum (Mann-Whitney) test was applied. This test shows that contributions for the INTER-treatment (3.83) are not significantly higher compared to the contributions the same group made when they received the INTRA-treatment (3.63) (z-value = -0.370, p = 0.7116). Secondly, another Wilcoxon rank-sum test investigated whether contributions changed significantly over time due to learning optimal strategies, which is applicable to those in the Green treatment group. For example, over the course of ten rounds they might discover how to optimally contribute as little as possible to the public good and as much as possible to the private account per round, while still achieving the group’s provision threshold. However, results of this test also show that public good contributions in the INTRA-treatment group (3.5) is not significantly lower than before, when receiving the same INTRA-treatment (3.68) (z-value = 0.669, p = 0.504). Finally, in order to see whether the INTER-treatment (3.83) elicits significantly higher public good contributions than the INTRA-treatment (3.5), a one-tailed Mann-Whitney U test was used as a comparison is made between subjects (i.e. between-subject differences for Green treatment group vs. Blue & Red treatment groups). This test reveals that, although there is a positive trend, inter-group and intra-group comparison combined does not lead to higher public good contribution when compared to solely intra-group comparison (p = 0.46). Therefore, H0 of Hypothesis 1 as formulated in section III.ii cannot be rejected: inter-group comparison does not (positively) affect public good contributions with this provision point mechanism in place. Nevertheless, given the limited size of samples for this experiment (N=24), outcomes of statistical test should be interpreted with caution due to its low power.
More specifically, it is investigated if participants cooperate conditionally and how participants’ contributions change depending on their previous behaviour in relation to the group’s behaviour. Similar to Böhm & Rockenbach (2013), mixed-effects models were used due to the nature of repeated measures in this experiment. In order to control for interdependencies between error terms, participants and intra-groups were treated as random effects in the INTRA-treatment, while matched groups were additionally kept as a random effect in studying the INTER-treatment. This test allows us to see how much variance there is at each level as it permits intercepts to vary while keeping slopes fixed. In predicting the contribution change (the difference between one’s current contribution compared to one’s previous round contribution), the intra-contribution deviation (the
difference between one’s previous contribution and the group’s average previous contribution) is used as a predictor for the INTRA-treatment and, additionally, the inter-contribution deviation (the difference between the one’s group’s average previous contribution and the other group’s average previous contributions) is used for investigating the INTER-treatment. Notably, using the data retrieved from the Green treatment groups in the INTRA-treatment, the intra-contribution deviation significantly affected the contribution change in the public good with b = -0.81, SE = 0.13 and p = 0.000. However, based on the data collected from the Blue and Red treatment groups in the INTER-treatment, only the intra-group deviation had a significant negative effect with b = -0.70, SE = 0.10 and p = 0.000. The inter-group deviation provided a slight, but insignificant, positive coefficient which is estimated at b = 0.27, SE = 0.31 and p = 0.39.
Besides testing for effects of intra- and inter-group comparison on cooperation separately, the collected data has also been analysed on conflicting incentives in order to study how participants behave when intra-group conditional cooperation and inter-group comparisons are contradictive. That is, how would one change his/her public good contribution when intra-group comparison is advantageous/disadvantageous while inter-group comparison is disadvantageous/advantageous? Both the individual deviation from the intra-group’s average public good contribution was calculated for each round, as well as the relative inter-group differences for the treatment groups. This way the mean contribution change of (dis)advantageous intra- and inter-group comparison could be computed, of which the results are summarised in Table II on the next page. It becomes evident that a disadvantageous intra-group deviation leads to a larger decrease compared to the decrease as a reaction on an advantageous intra-group comparison, with b = -0.97, SE = 0.21 and p = 0.000 and b = -1.18, SE = 0.23 and p = 0.000, respectively (similar to Böhm & Rockenbach, 2013). For the Blue and Red Groups who not only received intra-group but also inter-group information in Part 3 due to their treatment, the rise in public good contribution is significantly larger when one’s group is relatively cooperating less well than when one’s group is ahead of the others: respectively b = -0.83, SE = 0.18, p = 0.000 and b = -0.59, SE = 0.179, p = 0.001.
More specifically, Table II presents more details of the changes in the average public good contribution when diving deeper into the variety of advantageous and disadvantageous combinations in intra- and inter-group comparison. All mean
contribution changes for intra-group advantageous evaluations are clearly positive, with intra-group comparison, additional advantageous inter-group comparison and additional disadvantageous inter-group comparison at increases of 0.60, 1.17 and 0.70 EMUs, respectively. On the other hand, all mean contribution changes for disadvantageous intra-group evaluations are evidently negative with intra-group comparison, additional advantageous inter-group comparison and additional disadvantageous inter-group comparison at decreases of -0.92, -0.81 and -1.11 EMUs, respectively. The implications of these insights are discussed in detail in the next chapter.
iii. Time Preferences
A. Aggregate Analysis
All experimental allocations from the CTB data that have been collected in Part 1 of the experiment are identified as decisions of standard intertemporal optimisation dilemmas. The aggregate analysis of these results is displayed in Table III and Figures 3 & 4 below. Here, the mean number of tokens chosen earlier is plotted against the gross interest rate. Separate graphs are used for the different values of k (k = 35, 70, 98 days) and separate points are plotted for the various value of t (t = 0, 7, 35 days) in order to demonstrate the relationship for discount rates as clearly as possible. Similar to the results found in Andreoni & Sprenger (2012a), for each delay length, k, the mean number of tokens related
Table II: Mean Contribution Change by Advantageous and Disadvantageous Intra- and Inter-group Comparison of Parts 2 & 3
Advantageous
(own contribution less than other group members)
Disadvantageous
(own contribution more than other group members)
INTRA * INTER + ** INTER - *** INTRA * INTER + ** INTER - ***
Mean Change Public Good Contribution
0.60 1.17 0.70 -0.92 -0.81 -1.11
Notes. * Intra-group comparison only
** Advantageous inter-group comparison (own group contributed more than other groups) *** Disadvantageous inter-group comparison (own group contributed less than other groups)
to earlier payments falls monotonically with the gross interest rate. In addition, it is also evident that for both financial and environmental experimental responses, the
Table III: Summary Statistics of Part I
Obs. Mean St. dev. Min. Max.
Financial: Mean Tokens Earlier Overall 1080 55.01 24.93 2.5 95.58 k = 35 360 45.33 31.88 2.5 95.58 t = 0 120 57.57 20.94 35.38 87.29 t = 7 120 60.19 27.45 32.5 95.58 t = 35 120 18.2 31.76 2.5 75 k = 70 360 58.65 22.56 17.29 93.13 t = 0 120 65.36 18.17 45 91.54 t = 7 120 58.15 25.01 31.38 93.13 t = 35 120 50.62 26.25 17.29 87.5 k = 98 360 61.66 20.77 30.63 93.46 t = 0 120 68.64 17.05 47.13 93.46 t = 7 120 61.34 22.09 35.71 92.79 t = 35 120 54.98 24.78 30.63 91.17 Obs. Mean St. dev. Min. Max.
Environmental: Mean Tokens Earlier Overall 1080 52.40 24.07 5.21 91.13 k = 35 360 41.44 27.59 5.21 91.13 t = 0 120 55.59 22.56 33.17 91.13 t = 7 120 49.03 24.63 26.96 91.04 t = 35 120 19.70 25.19 5.21 64.58 k = 70 360 56.11 21.01 30.54 93.79 t = 0 120 58.82 23.05 34.08 93.79 t = 7 120 58.43 20.88 38.46 91.33 t = 35 120 51.07 23.03 30.54 88.42 k = 98 360 59.64 20.47 30.25 94.25 t = 0 120 63.84 20.78 43.46 94.25 t = 7 120 59.01 23.47 33.75 93.04 t = 35 120 56.08 21.10 30.25 85.50
apportioned tokens to earlier payoffs rises with an increase in k. In addition, the mean number of allocated earlier tokens for k = 35 is significantly smaller when t = 35 relative to t being 0 or 7. However, for k = 70 and 98, the mean number of earlier tokens allocated is nearly identical for all values of t, especially for the experimental responses of the environmental CTB-questions. In addition, as indicated by the level of the standard de-
Figure 3: Mean Experimental Responses over Time: Financial CTB-survey
