How to introduce subsidies on contributions to public goods:
Gradually versus quickly?
Ruby Braak* July 2017
Supervisor: Dr. A. Van der Veen Second reader: Prof. Dr. J.H. Sonnemans
Abstract
Governments need to operate effective given their tight budgets. This study examines whether policy makers could increase the effectiveness of subsidies on contributions to public goods when considering the way of the subsidy implementation and the framing of the subsidy announcements and tests whether the effectiveness relates to the population-size. These questions are addressed within a twenty-days during experiment with online surveys in which subjects participated in a public good game (PGG). The findings show a larger, though insignificant, increase in the contributions after a quickly versus gradually introduced subsidy. Moreover, the level of contributions increases in the gradual treatment when the PGG is framed such that associations to norms for cooperation are given. Nonetheless, this effect is insignificant over all treatments. Furthermore, the framing does not seem to influence the effectiveness of the subsidy. The effect of the population-size on the effectiveness cannot be ruled out.
JEL Classifications: C12, C99, D03, H41
*Student MSc Economics, Track Behavioral Economics and Game Theory, Faculty Economics and Business, University of Amsterdam, Amsterdam, The Netherlands, Student number: 10610324, Number of ECTS: 15.
2 Statement of Originality
I, Ruby Braak, take full responsibility for the contents of this document and declare that the text and the work presented in this document is 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.
3 Contents
1. Introduction ... 4
2. Literature review ... 6
2.1 Public good and subsidy ... 6
2.2 Public good game ... 7
2.2.1 Empirical findings ... 8
2.3 Influences on human behavior ... 9
2.3.1 Change blindness ... 9
2.3.2 Social norms ... 10
3. Hypotheses ... 10
4. Experimental design ... 12
4.1 Setup experiment ... 12
4.2 Public good game ... 15
4.3 Treatments ... 16
4.3.1 Subsidy introduction: gradually versus quickly ... 16
4.3.2 Group-size: six versus three ... 18
4.3.2 Associations to norms for cooperation: framed versus non-framed ... 19
5. Results ... 20
5.1 Characteristics participants ... 20
5.2 Graphical representation ... 21
5.3 Non-parametric tests ... 23
5.3.1 Hypothesis 1 and Hypothesis 2 ... 23
5.3.2 Hypothesis 3 ... 26 5.4 Regression analysis ... 28 5.4.1 Change in contributions ... 28 5.4.2 Level of contributions ... 30 6. Discussion ... 32 7. Conclusion ... 34 8. Appendix ... 36 Appendix A ... 36 Appendix B ... 36 Appendix C ... 38 Appendix D ... 39 9. References ... 42
4 1. Introduction
Governments all over the world seem to introduce subsidies on contributions to public goods. The way of implementing these subsidies varies. One way is to introduce the subsidy in one step, instantaneously; another way is to introduce the subsidy in small steps, gradually. Mostly, subsidy changes occur in small steps (Kickert & Van der Meer, 2011). Governments get even tighter budgets. Therefore, it is relevant to identify the way of introducing a subsidy to public goods that results in the lowest cost for governments and thus is the most effective.
Offerman and Van der Veen (2015) examine this in a laboratory experiment. The authors wonder whether the positive effect of subsidies on contributions to public goods is partly lost when introduced slowly over time. Their interest is based on the boiling frog story: if a frog is put into a pot with boiling water it jumps out immediately, while if the frog is put into a pot of water that is slowly heated it does not move (Cattani et al. 2006). Similarly, humans are expected to be less responsive to small compared to large changes. Offerman and Van der Veen confirm this expectation. They show that a subsidy introduction of 75% is more effective when implemented quickly compared to gradually. These findings suggest that the way of introducing a subsidy on contributions to public goods is a determinant of the effectiveness of the subsidy and should therefore be considered by policy makers. However, there might be problems with the external validity of their results. The purpose of our paper is to replicate, in a different setting, and extend the study of Offerman and Van der Veen (2015) with the aim to recommend governments with respect to their subsidy policies.
Offerman and Van der Veen set up a lab experiment of 28 minutes consisting of a dual task, an individual and a group task, in which participants could earn money. 1 The group task is modeled as a public good game (PGG) in which groups of six subjects participate. During the game a subsidy of 75% is introduced either gradually or quickly. The instructions of the experiment are defined similarly for all participants. Compared to their experiment our experiment differs in three ways:
i. Conduct online surveys for 20 days instead of a lab experiment of 28 minutes ii. Form groups in the PGG with either three or six individuals instead of only groups
with six individuals
iii. Describe instructions in two ways instead of in one way
1 Participants earn money with the individual task for every second they keep a randomly moving red dot inside a box. Subjects are able to move this box upwards, downwards and to the left or the right by pressing different buttons. This task is meant to mimic the fact that in real life people have to make decisions continuously.
5 These experimental differences also allow testing the robustness of the findings of Offerman and Van der Veen (2015).
In our study, we examine the effects of a gradual and quick subsidy introduction on the effectiveness of subsidies within an experiment with online surveys over a period of 20 days, while Offerman and Van der Veen address the effects within a laboratory experiment of 28 minutes. The extension of the time frame of the experiments could alter the results, since the question what way of subsidy implementation is most effective is related to time.2 Besides, the switch from a laboratory experiment to an experiment with online surveys could also change the results. Although, both experimental methods can have issues with external validity, changing the set up of the experiment allows testing for the robustness of the findings of Offerman and Van der Veen (2015) and for some of the potential problems with external validity. Additionally, the results of the studies can be compared based upon a difference in the design of the PGG. Offerman and Van der Veen form groups in the PPG consisting of six individuals and find significantly different effects of a subsidy introduction on contributions when implemented quickly compared to gradually. Though, the authors do not test whether the group-size in the PGG influences these effects. Previous studies indicate that group-size affects the level of contributions (Hamburger et al., 1975; Isaac& Walker, 1988). The group-size might also affect the change in contributions, the difference in contributions before and after a subsidy introduction. It is relevant to test for this potential effect in the context of this study, since governments implement public subsidies to diminish costs for population groups that are larger than groups that are likely to be formed within controlled experiments. This implicates that the external validity of the results is reduced if the group-size in the PGG significantly alters the results. Therefore, we form groups of either six or three individuals in our experiment in order to test for this possibility. Furthermore, we extend the study of Offerman and Van der Veen (2015. Offerman and Van der Veen focus solely on determining the most effective way of implementing a subsidy, while we consider also another factor that might be relevant in effectively introducing subsidies. This aspect is related to announcements of subsidy introductions by governments. Humans are sensitive for the formulation of these announcements. Phrased differently, framing influences human behavior (Tversky & Kahneman, 1985). Therefore, it might be interesting to determine the effect of subsidies on behavior when alternating the framing of the implementation announcements. According to Rege and Telle (2004) contributions to a public good increase
6 if situations are framed such that individuals are given associations to norms for cooperation. These findings suggest that policy makers could influence the effectiveness of subsidies dependent on the framing of the announcements of subsidy introductions. In our study, we examine both the relation between subsidy implementation and time and the framing of the announcements as determinants of the effectiveness of subsidies. This allows examining the importance of determining the most effective way of implementing a subsidy.3 Overall, the aim of this paper is to answer the following research question: What is the most effective way of introducing a subsidy on contributions to public goods, gradually versus quickly, controlling for population-size and associative norms for cooperation?
Our results show that the change in contributions, which approximates the effect of the subsidy introduction, is larger when the subsidy is introduced quickly compared to gradually.4 However, this finding is insignificant. The effect of the group-size on the change in contributions is ambiguous. The framing of the instructions of the PGG does affect the level of contributions in the gradual treatment, though the effect is insignificant over all treatments, while the framing does not affect the change in contributions. These results are discussed and outlined in this paper. The remainder of the paper is organized as follows. Section 2 contains related literature and Section 3 outlines the hypotheses. Section 4 describes the experimental design. Subsequently, Section 5 gives an overview of the empirical results. Section 6 includes the discussion and Section 7 concludes the paper. In this last section an answer to the research question is formulated.
2. Literature review
This section outlines relevant theoretical and empirical work. First, the concepts public good and subsidy are described. Subsequently, empirical results related to public good games of previous studies are discussed. Finally, two types of influences on human behavior within the context of this study are outlined.
2.1 Public good and subsidy
Governments implement subsidies with the aim to increase contributions to public goods. However, what is meant with the concepts public good and subsidy?
3 Thus, the relevance of determining if either a gradual or quick introduction of a subsidy is most effective. Offerman and Van der Veen (2015) focus on these different types of implementation. However, given associations to norms for cooperation might be even more relevant in determining the effectiveness of subsidies.
4 The change in contributions equals the average contribution after the subsidy implementation minus the average contribution before the subsidy implementation.
7 Public goods are described as goods being non-rival and nonexclusive. The property of a good being non-rival implicates that the availability of that good is not reduced if someone consumes it. The feature of a good being non-exclusive means that one person or a group cannot exclude others from the consumption of that good. Public goods are acknowledged for having benefits that cannot be easily restricted to a single person or group of individuals (Stiglitz, 1999).5 The definition formulated by Stiglitz is used in this paper. Governments may provide subsidies to public goods. De Moor and Calamai (1997) define subsidies as follows:
“ Subsidies comprise all measures that keep prices for consumers below the market level or keep prices for producers above market level or that reduces costs for consumers and producers by giving direct or indirect support”.
In the context of our study, the government implements subsidies in order to reduce the costs of private contributions to public goods. These contributions are required for the provision of public goods. The subsidy is denoted in terms of percentages. The higher the percentage, the lower the actual cost of contribution for individuals.6
2.2 Public good game
In existing literature, the public good game is extensively used in experiments to examine contribution levels and cooperation (for example: Offerman et al., 1996; Fehr & Gächter, 2002; Fischbacher & Gächter, 2010). In public good games participants are assigned to groups.7 Each subject receives an endowment of points or money and divides this endowment between a private and public account. The points or money that is attributed to the public account is multiplied by a pre-specified factor and subsequently divided among the individuals in the group, irrespective of the contributions of the members. The main findings with respect to contributions in public good games in the context of our study are outlined in the paragraph below.
5 For instance, street lights.
6 The cost of contributing one unit to the public good equals one unit if the subsidy equals 0%, while the cost of contributing one unit to the public good equals zero units if the subsidy equals 100%. 7 Subjects may or may not know with whom they form a group in the PGG.
8 2.2.1 Empirical findings
Our paper examines three aspects of subsidy introductions on contributions to public goods: the implementation, the population-size and the formulation of the announcements.
Offerman and Van der Veen (2015) focus their study on determining the most effective way of implementing a subsidy on contributions to public goods. As mentioned, the authors investigate the responses of individuals to a slow versus a quick increase of the introduced subsidy in a series of laboratory experiments. Individuals participate in a linear public good game in which selfish participants have a dominant strategy to contribute zero, irrespectively of the subsidy rate. During the public good game, participants do not receive feedback about the contributions of the other subjects. Therefore, the game is in essence a one-shot game. The authors mention that empirical findings related to public good games indicate that individuals seem to react to the productiveness of a contribution to a public good. Therefore, they expect to find positive contributions if subsidies are introduced. Offerman and Van der Veen increase the subsidy rate from 0 % to 45%, either gradually or quickly. They find no significant differences between the treatments with respect to the effect of the subsidy on the contribution levels of the participants. However, if the subsidy rate increases from 0% to 75%, contributions increase substantially when subsidy is introduced quickly, while contributions increase at most modestly when subsidy is introduced gradually. In our study, we examine whether these results related to a subsidy introduction of 75% replicate within a non-laboratory setting.
Literature related to the effect of the group-size in public good games on contributions approximate the population-size effect. Empirical studies focus on examining the effect of the group-size within a PGG accompanied with the effect of the marginal per capita return (MPCR). The MPCR equals the return in units that an individual receives when contributing one unit to the public good. Isaac et al. (1984) started examining the effect of the group-size and the MPCR. Isaac and Walker (1988) extent this research and determine the effects of altering these two parameters, both together and independently. The authors find no evidence for the idea that purely increasing the number of individuals per group decreases the contribution levels. However, contributions are lower in larger groups if the increase in group-size is accompanied with a decline in the marginal return of the public good. Thus, if increasing the group-size reduces the MPCR, the effect of the MPCR on the level of contributions is dominant. Offerman and Van der Veen (2015) state that increasing the subsidy level on contributions to public goods corresponds to increasing the MPCR. However, there exists no literature that distinguishes between the effects of the group-size, the
9 MPCR and the subsidy level within a PGG. In our study, we define the term Net Cost of Contribution to test for the simultaneous effects of the group-size, MPRC and subsidy level within a PGG.
Rege and Telle (2004) argue that economic studies have shown that social norms could augment cooperative behavior within public good settings. In their study, the authors examine whether the use of specific language could suggest such norms and therefore enhance cooperation. Rege and Telle organized lab experiment in which strangers participated in a PGG in either the associative or non-associative-treatment. In the associative treatment, the participants were allocated to groups and were referred to as a “community”. During the game, participants had to make decisions about contributions to a public good. These contributions were collected in a box with the name “community box”. In the non-associative treatment, the instructions of the PGG did not include the word community and the matched participants were referred to as “participants in the experiment”. The name of the box in which the contributions of the participants were collected was called “box”. The authors expected that the contributions in the associative-treatments would exceed the contributions in the non-associative-treatment. The experimental results show that the mean of the contributions increased from 34.4% to 55.1% after including these associative words in the instructions of the experiment.8 In this paper, we test whether giving individuals these associations results in similar increases in contributions within an experimental setting in which a subsidy is introduced.
2.3 Influences on human behavior
The aim of our study is to determine the effect of subsidy policies on human behavior. This section discusses the phenomenon change blindness and social norms as this could explain the responses of individuals with respect to subsidy introductions.
2.3.1 Change blindness
In this study, the conjecture that humans tend to ignore small environmental changes is examined within a PGG with a varying subsidy rate. Various studies within other fields using different experiments confirm this conjecture. Within psychology, this phenomenon is referred to as change blindness, “ the inability to detect changes to an object or scene” (Simons and Levin, 1997). Observers believe in their ability to directly detect sufficiently large changes (Levin et al. 2000). However, empirical results indicate that under various
10 conditions individuals fail to observe a change even though the change is large or repeatedly conducted (Simons and Levin, 1997). Rensink (2002) outlines various types of changes that result individuals to be subject to change blindness. One of which is a gradual change, a transition from one to another view occurring slowly over time. People tend to have difficulties with observing such alterations (Simons et al., 2000).
2.3.2 Social norms
Social norms are imposed rules by communities, with the feature that the members of a community share these rules (Elster, 2000). These norms are related to the feeling of moral obligation, which may result in altruistic behavior (Schwartz, 1977). In other words, social norms can be specified as an impulse for desirable behavior within a community with sanction rules (Kandori, 1992). Moreover, several studies have shown that social norms enhance cooperative behavior within public good contexts (North, 1981; Andreoni, 1990; Holländer, 1990).
3. Hypotheses
This section outlines three hypotheses. These hypotheses are formulated according to the relevant literature.
The first hypothesis is related to the way of the subsidy implementation. Contributions are expected to increase more after an introduction of a subsidy when this subsidy is quickly introduced compared to when this subsidy is gradually introduced. This expectation is line with the experimental findings of Offerman and Van der Veen (2015).
Hypothesis 1. The effect of a subsidy introduction on contributions to public goods is stronger for a quickly introduced compared to a gradually introduced subsidy
The second hypothesis is focused on the potential effect of the population-size. However, literature does not indicate what effect to expect when varying this size. Previous studies show that contributions tend to increase with an increasing MPCR. Offerman and Van der Veen (2015) state that subsidy introductions could be interpreted as an increase in the MPCR. However, there are no experimental studies that combine a changing MPCR with an implementation of a subsidy. In this study, we define the Net Cost of Contribution (NCC) in order to combine the effects of a change in the MPCR and an implementation of a subsidy.
11 The NCC represents the net cost of contributing one unit to a public good and is calculated as follows:
𝑁𝑒𝑡 𝐶𝑜𝑠𝑡 𝑜𝑓 𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 = 1 − 𝑀𝑃𝐶𝑅 − 𝑆𝑢𝑏𝑠𝑖𝑑𝑦
The expectation is that the lower the NCC the higher the contributions, since contributions increase with an increasing MPCR and subsidies could be interpreted as an increase in the MPCR.9 In our experiment, we compare the effect of a subsidy introduction for groups with two different group-sizes in order to test whether this effect is influenced by the population-size. At the start of our experiment, the NCC is lower for the smaller groups. However, the NCC is equal for the groups of both group-sizes at the end of the experiment. Therefore, we expect that the level of contributions is higher for the smaller groups at the beginning of the experiment and that the level of contributions is equal for all groups at the end of the experiment. This implicates that we expect that the effect of the subsidy is smaller in the smaller groups compared to the effect of the subsidy in the larger groups in our experiment. This expectation suggests that an increase in the population-size does not decrease the effect of a subsidy.
Hypothesis 2. The effect of subsidy on contributions to public goods does not decrease when the population-size increases
The third hypothesis is related to associations given to individuals. Contributions are expected to be higher when associations to norms for cooperation are given to individuals. This expectation is in line with the experimental results of Rege and Telle (2004).
Hypothesis 3. Contributions to public goods are higher when giving individuals associations to norms for cooperation
However, our interest in this study is to determine whether the effectiveness of subsidies is stronger influenced due to the effect of giving individuals associations to norms for cooperation than due to the effect of the way of introducing the subsidy. Therefore, we
9 Notice that the MPCR and subsidy are formulated in terms of benefits and the NCC is formulated in terms of costs. Thus, the NCC is the inverse of the sum of the MPRC and the subsidy rate.
12 compare these two effects. In the next sections, we discuss the experimental design and subsequently give the results of the hypotheses tests.
4. Experimental design
The experimental design is discussed in this paragraph. The experiment consisted of online surveys and ended with a general questionnaire.
4.1 Setup experiment
Every subject received, before the start of the experiment, a personal participant number, which remained the same during the experiment. The experiment started with instructions (see Appendix A). Each participant received an email with a link to the instructions, which were also attached as PDF-file. This allowed the subjects to read the instructions again during the experiment. After reading the instructions, the subjects had to correctly answer six control questions (see Appendix B). These questions were asked in order to ascertain that the subjects understood the instructions. Every participant received the same control questions in the same order. This ascertained that all subjects were influenced by the control questions similarly. Subjects had to answer four additional control questions if two or more of their answers to the first six control questions were incorrect.10
The experiment consisted of online surveys designed within the software program Qualtrics.11 The experiment started the 22th of May 2017. Participants received an email with a link to a survey every Monday till Friday, with exception of the 25th and 26th of May and the 5th of June, which are public holidays in the Netherlands. Subjects did not receive links to surveys in the weekends and on these specified days. Additionally, the text in the emails the subjects received differed per day. These methodological choices are made in order to enhance the chance the participants filled out the questionnaire. The participants earned points based on their decisions in the experiment. For three out of the seventy-two participants, which are randomly selected, the earned points are exchanged for money at the end of the experiment at a rate of 1 euro for 40 points. Participants are randomly assigned to only one of the six treatments in the experiment, which indicates the between-subjects design. The details of the treatments are summarized in Table 1.
10 Four out of the seventy-two subjects had to answer the additional control questions.
11 This program allows designing online-surveys and pre-programming the time of sending the surveys and reminders.
13 Table 1 Main features treatments
Treatment Max subsidy Increase subsidy Group-size N
Gradual - 6 0.75 Gradual 6 14 Quick - 6 0.75 Quick 6 14 Gradual – 6F 0.75 Gradual 6 14 Quick – 6F 0.75 Quick 6 14 Gradual - 3 0.55 Gradual 3 8 Quick - 3 0.55 Quick 3 Total 8 72
Notes: 6 indicates a group of six in the PGG; 3 indicates a group of three in the PGG; F indicates framed instructions of the PGG.
The experiment consisted of two parts. In Part 1, the subjects received online surveys consisting of five questions each. The first four questions were the same for all participants, irrespectively of the treatment. The order of the first four questions differed each day, but was similar for all participants. This setup avoids that the attention of participants is diminished during the experiment. Without randomization in the order of the questions, the subjects would know which question to be the next and therefore are likely to not even read the questions. The order of the questions is kept similar for all participants to ensure that the participants are affected by the order of questions similarly. Three of these four questions were statements on which subjects had to respond based on a Likert-type scale (Matell and Jacoby, 1971). 12 The statements were:
I. Today I feel fit and I have a lot of energy to do things II. Today I feel stressed due to work and/or work pressure III. Today I expect that I have to or will spend a lot of money
For the other question the participants had to complete the following sentence given seven multiple-choice options based on the Likert scale: “Today I would describe my mood as …”.13 These first four questions are related to the activities and feelings of the participant on a
12 The subjects had to select one of the following seven options of the Likert-type scale: strongly agree, agree, slightly agree, neither agree nor disagree, slightly disagree, disagree or strongly disagree 13 The subjects had to select one of the following seven options: extremely good, moderately good, slightly good, neither good nor bad, slightly bad, moderately bad or extremely bad.
14 particular day. These questions were asked for two reasons. Firstly, the questions may distract people from the fifth question in which the subjects participate in a public good game (PGG) with a changing subsidy rate, which will be explained below. The participants are triggered to consciously think about other activities and decisions that day. This set up resembles real life situations in which a subsidy change is one of the many things changing during a day and therefore is not always notified. Therefore, alternating the order of questions, which is done in many studies, would be no improvement of the experiment. Moreover, subjects in all treatments are distracted from the question related to the public good game in a similar way. Offerman and Van der Veen (2015) included an individual task in their experiment to distract people and mimic the fact that in real life people are confronted with decisions continuously. Secondly, including these questions allowed generating control variables for the estimation of the value of the contributions in the PGG.
The fifth question of every survey was related to a PGG. The subjects participated in a PGG, which was modeled in different ways. This is discussed in the next section. The subjects were informed they would receive surveys of Part 1 consisting of five questions for in between 18 and 25 working days. The exact number of days is not given in order to prevent an artificial endgame effect (Keser and Van Winden, 2000). In total, the participants received these surveys on 20 days. The setup of the surveys is included in Appendix C. Thereafter, Part 2 started, which consisted of one questionnaire (see Appendix C). In this questionnaire, subjects’ value orientations are elicited in order to obtain a measure of their social preferences. Subjects received an amount, which was by 50% chance determined by their own choice and by 50% chance determined by a choice of another participant in the experiment. The participants had to choose a division of points between their selves and one randomly chosen other participant subject to the constraint of (Self)2 + (Other)2 = (400)2.14 The subjects were given sixteen options. These options and the corresponding measures of the social preferences of the subjects are included in Appendix D (see Figures 6 and 7 and Table 9). Offerman and Van der Veen (2015) retrieved this measure by asking a similar question.15 The
14 The subjects chose a division by selecting one of the sixteen points illustrated on a circle (see Figure 7, Appendix D). The horizontal axis referred to points given to one self and the vertical axis referred to points given to the other. The participants were notified that the participant that would be affected by their decision was not the same participant as the participant that determined the division that would affect their amount of points.
15 The subjects in the experiment of Offerman and Van der Veen (2015) were able to select any point on the circle. Thus, the participants were not restricted to sixteen options. Therefore, the value orientation test in this paper is less precise compared to the one conduced by Offerman and Van der Veen.
15 experiment ends after Part 2. The subjects received an email to inform them about the end of the experiment and thank them for their participation. Furthermore, the subjects could indicate whether they would like to receive a summary of the experimental results. The three participants that were randomly selected for payment received an additional email with a confirmation and calculation of their earnings. The earnings in euros equaled 15.89, 16.49 and 15.26. Thus, the total payment was 47.65 euro.
4.2 Public good game
All subjects participated in a PGG. The game was modeled differently, depending on the treatment. The main features of the game are outlined in this paragraph.
Each subject was randomly matched with either two or five other participants, resulting in groups of three or six individuals. The matches remained the same during the experiment. On every survey-day, a day on which surveys of Part 1 were send, subjects received an endowment of 10 points and determined how many points of this endowment to contribute to the public good. Each point contributed to the public good is multiplied by the factor 1.2 for all groups and subsequently equally divided between either the 3 or 6 group-members. This implicates that each group-member received 0.4 or 0.2 from each point contributed to the public good for groups of three and six members, respectively. This specification is replicated from the study of Offerman and Van der Veen (2015). However, they considered groups of six members only. The consideration of groups with different group-sizes resulted in a different MPCR for the groups.16 Subjects can change their contribution every survey-day. Corrections for missing values are conducted by filling out the latest contribution level submitted by the participant. However, data of subjects is eliminated in case of five or more missing values.
The contributions of the participants are subsidized at a varying rate. If the subsidy equaled st on day t, subject i actually paid a cost of (1 − st) ci,t for a contribution of ci,t (0≤ ci,t ≤10). Thus, on day t subject i earned (in points)
𝜋!,!(𝑐!,!) = 10 − 1 − 𝑠! 𝑐!,! + 0.4 ! 𝑐!,!
!!! If assigned to a group of 3 members 𝜋!,!(𝑐!,!) = 10 − 1 − 𝑠! 𝑐!,! + 0.2 ! 𝑐!,!
!!! If assigned to a group of 6 members Subjects were informed that the subsidy might change during the experiment and would never exceed 0.80 (or 80%). The subsidy rate was given above the fifth question, which asked for
16 the contribution level of the subjects. The subsidy was underlined in case of a change with respect to the previous survey-day.17 This way, subjects noted the change even when they were distracted due to the first four questions of the survey. The subjects were informed that all individuals assigned to the same group would face the same subsidy rate and that the change of the subsidy was outside of their control. Subjects were not informed about the contributions made by their group-members and their earnings during the experiment.18 These experimental details have two analytical advantages. Firstly, the decisions of the participants are affected similarly, since the specification of anonymous group members and no feedback about the earnings during the experiment is similar for all subjects. This feature allows for a direct comparison between the decisions of the subjects within the same treatment. The decisions of the participants would have been influenced differently if group-members were not anonymous. Secondly, contribution decisions are independent across participants, since subjects are not informed about the contributions of the other group-members while participating in the PGG. Hence, decisions could be interpreted as independent individual decisions. Notice that in most cases in the real world individuals receive also little or no information about other individuals’ contributions.
4.3 Treatments
The main features of the six treatments are summarized in Table 1 above. The three properties based on which the treatments differ are discussed in this section.
4.3.1 Subsidy introduction: gradually versus quickly
The first difference between the treatments is the way of introducing the subsidy. Each treatment is either indicated as Gradual or Quick. The first hypothesis, whether contributions are higher with a quickly versus gradually introduced subsidy, is tested based on this difference in the specification of the treatments. Thus, comparing the gradual and quick treatments allows determining which way of increasing the subsidy rate is most effective.
In all treatments, the subsidy remained 0 for the first three survey-days. In the treatments with groups consisting of six participants, Gradual – 6, Quick – 6, Gradual – 6F and Quick – 6F, the subsidy was increased until it reached the maximum subsidy of 0.75. In the treatments with groups consisting of three participants, Gradual – 3 and Quick – 3, the
17 In the experiment conducted by Offerman and Van der Veen (2015) the subsidy rate turned red for a second in case of a subsidy change in order to make sure that the participants noticed the change, even though they were focused on the individual task.
17 subsidy was increased until it reached the maximum subsidy of 0.55. In the gradual treatments, the subsidy raised with an average of 0.05 (0.037) per survey-day for the treatments with groups consisting of six (three) participants until the subsidy reached its maximum at the 18th survey-day. A clear pattern in the magnitude of the subsidy changes is avoided to minimize potential boredom of the subjects due to the predictability of the subsidy. In the quick treatments, the subsidy was instantaneously raised from 0 to the maximum subsidy on the 18th survey-day. In all treatments, the subsidy remained at the maximum, either 0.75 or 0.55, for the last three survey-days. The development of the subsidy differs from its development in the study of Offerman and Van der Veen (2015) in which the subsidy is abruptly introduced at the beginning of the PGG for the Quick treatments.19 The chosen pattern in this paper ensures that the maximum subsidy is reached at the same day for all treatments, which increases the validity of the comparisons between the treatments. Figure 1 and Figure 2 display the development of the subsidy for the gradual and quick treatments with group-size six and three, respectively.
Figure 1. Development of the subsidy over time
Note: Treatments Gradual-6, Gradual-6F, Quick-6, and Quick-6F
19 Offerman and Van der Veen (2015) increased the subsidy of the Quick treatments after 4 minute from 0% to 75%. 0 10 20 30 40 50 60 70 80 1 3 5 10 15 18 20 S u b si d y i n % Day Gradual Quick
18 Figure 2. Development of the subsidy over time
Note: Treatments Gradual-3 and Quick-3
4.3.2 Group-size: six versus three
The second difference between the treatments is the group-size in the PGG. In each treatment, the groups in the PGG consisted of either six or three participants, as mentioned earlier. The second hypothesis, whether the effect of subsidy on contributions to public goods does not decrease when the population-size increases, is tested based on this difference in the specification of the treatments.
The maximum subsidy in the PGG differed for the treatments with groups consisting of six and three participants, which was 0.75 and 0.55, respectively. This design ascertains that the Net Cost of Contribution (NCC) is equal for all treatments when subsidy reached its maximum. Remember, the NCC is formulated as the cost of contributing one point to the public good corrected for the MPCR and the subsidy rate.
𝑁𝑒𝑡 𝐶𝑜𝑠𝑡 𝑜𝑓 𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 = 1 − 𝑀𝑃𝐶𝑅 − 𝑆𝑢𝑏𝑠𝑖𝑑𝑦
The treatments with groups in the PGG consisting of six participants are Gradual – 6, Quick – 6, Gradual – 6F and Quick – 6F. The NCC in these treatments equaled 0.05 when subsidy reached its maximum, since the MPCR equaled 0.2 and the maximum subsidy 0.75. This specification is replicated on basis of Offerman and Van der Veen (2015). Therefore, comparisons between the experimental results are allowed. In our study, the NCC is equal for all treatments if the maximum subsidy is reached. Thus, the NCC also equaled 0.05 for the
0 10 20 30 40 50 60 70 80 1 3 5 10 15 18 20 S u b si d y i n % Day Gradual Quick
19 treatments with groups in the PGG consisting of three participants, which are Gradual – 3 and Quick – 3, when subsidy reached its maximum. For these treatments, the MPCR equaled 0.4 and the maximum subsidy 0.55. Table 10 presents the subsidy rates and NCC for all treatments on the twenty survey-days (see Table 10, Appendix D).
The experimental design allows comparing the contributions of participants of the different treatments based on the NCC. However, the direct comparisons between contributions of the treatments are limited to the last three survey days.20 This seemed the best-suited solution for making a comparison possible between the contributions of the participants assigned to groups of six and participants assigned to groups of three subjects. Two other specifications were considered. The first other potential not-choosen specification was setting the maximum subsidy at 0.75 for all treatments. However, this would result in a negative cost of contribution for participants assigned to groups of three subjects, which means that contributing is a dominant strategy for these individuals.21 The treatments are not comparable if in some of the treatments contributing is a dominant strategy. Therefore, this option was not chosen. The second other potential not-choosen specification was altering the maximum subsidy such that this subsidy rate would be equal for all treatments while contributing would not become a dominant strategy.22 However, the maximum subsidy for the treatments with group-size six in the PGG should be 0.75 in order to replicate Offerman and Van der Veen (2015). The comparison between the experimental results of the two studies is one of the main purposes of this paper. Therefore, this second option was not adapted.
4.3.2 Associations to norms for cooperation: framed versus non-framed
The third difference between the treatments is the formulation of the instructions. The third hypothesis, whether contributions increase when giving individuals associations to norms for cooperation, is tested based on this difference in the specification of the treatments.
In the instructions of the framed treatments, which are Gradual – 6F and Quick – 6F, the word “community” is included to give associations to norms for cooperating. This method is, as mentioned earlier, based on the article of Rege and Telle (2004). In our experiment, both the instructions and the surveys designed for the participants in these framed treatments include the word “community”. Moreover, the word “group” is avoided in the instructions for
20 Remember, in all treatments the maximum subsidy is reached at the 18th survey-day.
21 For groups of three participants, contributing is a dominant strategy when subsidy exceeds 0.60, since the MPCR equals 0.40.
22 Thus, the subsidy should not exceed 0.60. In fact, the subsidy should also not equal 0.60 in order to keep the NCC positive in both treatments.
20 the other treatments, since this word might also give associations to norms for cooperation. There are no framed treatments with groups of three in the PGG, since there is no literature suggesting that the effect of the framing might differ between groups with a different size.
5. Results
This section outlines the results. The characteristics of the participants are displayed and the test statistics related to the hypotheses are discussed. Subsequently, the contributions within the PGG are graphically illustrated and the regression analysis is outlined.
5.1 Characteristics participants
In total, 72 subjects were selected for participating in the experiment. However, 10 of the 72 dropped out due to more than 5 missing filled-out surveys or incorrect answers to the control and additional control questions.23 Thus, 62 subjects participated in the experiment, which were allocated over the six treatments. Table 2 summarizes the characteristics of the subjects per treatment.
Table 2 Characteristics of the participants
Treatment N Males Economics Game Theory Cooperator Noticed Yes Gradual - 6 13 3 (23.1%) 8 (61.5%) 6 (46.2%) 11 (84.6%) 11 (84.6%) Quick - 6 12 6 (50.0%) 6 (50.0%) 5 (41.7%) 12 (100%) 12 (100%) Gradual – 6F 12 6 (50.0%) 6 (50.0%) 7 (58.3%) 11 (91.7%) 6 (50.0%) Quick – 6F 12 6 (50.0%) 8 (66.7%) 5 (41.7%) 8 (66.7%) 8 (66.7%) Gradual - 3 7 1 (14.3%) 2 (28.6%) 3 (42.9%) 5 (71.4%) 3 (42.9%) Quick – 3 Total 6 62 3 (50.0%) 26 1 (16.7%) 31 0 (0%) 26 4 (66.7%) 51 3 (50.0%) 43
Notes: Economics refers to the number of participants that are studying or have studied Economics; Game Theory refers to the number of participants that have followed a course related to Game Theory; Cooperator refers to the number of participants that selected option B, C or D in the Value Orientation Test (see Table 9 Appendix D); Noticed Yes refers to the participants that responded with (strongly) agree to the statement: “During the experiment, I have noticed all subsidy changes”; Percentages between the brackets.
23 9 participants were dropped based on more than 5 missing filled-out surveys and 1 participant was dropped based on incorrectly answering the control and additional control questions.
21 The treatments Gradual – 3 and Gradual – 6 consist of the most female participants. Quick – 6F contains the most subjects that are studying or have studied Economics, while the most subjects who followed a course related to Game Theory are represented in the Gradual – 6F treatment. The treatment Quick – 6 consists of the most participants defined as cooperators. In the treatments Gradual – 3 and Quick – 3 relatively the least participants noticed the changes of the subsidy during the experiment.
5.2 Graphical representation
In this section, the average contributions over time are shown in graphs and the patterns are discussed. The aim of this section is to give some preliminary conclusions.
Figure 3 illustrates the average contributions over time for the treatments Gradual – 6, Quick – 6, Gradual – 3, and Quick – 3.
Figure 3 Average contributions over time
Note: Treatments Gradual-6, Quick-6, Gradual-3, and Quick-3
At first glance, the effect of the subsidy implementation seems to be somewhat larger in the quick treatments compared to the gradual treatments. The figure shows that the average contribution in the Quick – 6 treatment increases substantially on the 18th day, the day on which the subsidy is implemented in one step, while the average contribution increases by degrees in the Gradual – 6 treatment. The average contribution on the last three days of the
0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 C on tr ib u ti on Day
22
experiment is almost identical for these treatments. The average contribution on last three days is substantial higher in the quick treatment compared to the gradual treatment when comparing the Quick – 3 and Gradual – 3. However, the average contributions in the Quick – 3 treatment do not follow the expected pattern of constant average contributions until the 17th survey day and an instantaneously jump in the average contributions on the 18th survey-day. The patterns in the figure indicate that the first hypothesis, which states that the effect of a subsidy on contributions to public goods is stronger for a quickly introduced compared to a gradually introduced subsidy, might hold. Furthermore, the graph of the average contributions over time does not directly suggest that the second hypothesis holds. According to this hypothesis, the average contributions should be higher in treatments with groups consisting of three participants at the start of the experiment, which is the case. However, the average contributions are not equal at the end of the experiment, as was expected. The average contributions are higher at the last three survey-days for the groups with the size of three participants in the quick treatments, while the average contributions on these days are higher for the groups with the size of six participants in the gradual treatments.
Figure 4 shows the average contributions over time for the treatments Gradual – 6, Gradual – 6F, Quick – 6, and Quick – 6F.
Figure 4 Average contributions over time
Note: Treatments Gradual-6, Gradual-6F, Quick-6, and Quick-6F
0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 C on tr ib u ti on Day
23
The graph shows similar trends for Gradual – 6 and Gradual – 6F and for Quick – 6, and Quick – 6F. The average contributions in the Gradual – 6F exceed the average contributions in the Gradual – 6 on all twenty survey-days. However, the average contributions are similar over time for the Quick – 6, and Quick – 6F. These patterns suggest that the third hypothesis, which states that contributions are higher when giving individuals associations to norms for cooperation, is confirmed for the gradual treatment, but does not hold in the quick treatments.
However, our interest is to determine whether the effect of a subsidy on contributions is stronger influenced due to giving individuals associations to norms for cooperation than due to the way the subsidy is introduced. The patterns seem to indicate that this is not the case. 5.3 Non-parametric tests
In this section, the results of non-parametric tests are discussed. These results give an idea about the validity of the specified hypotheses in our paper.
5.3.1 Hypothesis 1 and Hypothesis 2
The first two hypotheses are related to the effect of the implementation of the subsidy, or stated differently, the difference between the contributions before and after the subsidy introduction. For each participant, we calculated the average contribution on the first three survey-days, which are the days before the start of the rise of the subsidy, and the average contribution on the last three survey-days, which are the days after the subsidy reached its maximal level in every treatment. Figure 5 displays the mean of the average contributions of the participants per treatment before and after the implementation of the subsidy.
Figure 5 Mean contributions before and after the subsidy introduction
Notes: Pre refers to the average contribution before the subsidy introduction; Post refers to the average contributions after the subsidy introduction.
0 1 2 3 4 5 6 7 8 9
Gradual -6 Quick - 6 Gradual - 6F Quick - 6F Gradual - 3 Quick - 3
Mean c on tribution Pre Post
24 The figure shows that the average contributions increase after the subsidy introduction in all treatments, which is in line with the expectations. The average contributions before and after the subsidy implementation are compared per treatment with the non-parametric Wilcoxon-Signed- Rank-Sum test. For this test, it is not needed to assume that the difference between the averages is normally distributed.24 The results are summarized in Table 3. The increase in the average contribution after the subsidy implementation is significant in the treatments with groups in the PGG consisting of six individuals.25 However, this increase is not significant in the treatments with groups consisting of three individuals.26
Table 3 Responses to the subsidy introduction
Treatment Max subsidy N Pre (SD) Post (SD) WMP (p-value) Gradual - 6 0.75 13 3.49 (3.33) 6.56 (1.80) 0.0020 Quick – 6 0.75 12 3.33 (1.90) 6.53 (2.85) 0.0205 Gradual – 6F 0.75 12 4.39 (3.10) 7.92 (1.91) 0.0185 Quick – 6F 0.75 12 3.53 (1.96) 6.64 (1.64) 0.0025 Gradual - 3 0.55 7 3.71 (3.08) 5.14 (3.79) 0.3508 Quick - 3 0.55 6 4.11 (3.44) 7.22 (2.03) 0.1159
Notes: Pre refers to the mean of the average contribution before the subsidy introduction; Post refers to the mean of the average contributions after the subsidy introduction; WMP refers to the Wilcoxon Matched-Pairs Signed-Ranks test; Standard deviations between the brackets.
Subsequently, we calculated the difference between the average contribution before and after the subsidy introduction for each participant. This difference approximates the effect of the subsidy implementation on the contributions of individuals to public goods. The differences are compared between the treatments with the non-parametric Wilcoxon-Mann-Whitney test. For this test, it is not needed to assume that the dependent variable is normally distributed.27
Table 4 summarizes the test statistics.
24 The Wilcoxon signed rank sum test is the non-parametric version of a paired samples t-test 25 The p-values 0.0020, 0.0205, 0.0185 and 0.0025 are less than the critical value 0.05. 26 The p-values 0.3508 and 0.1159 exceed the critical value 0.05.
25
The first hypothesis is related to the difference in the effect of the subsidy between the gradual and quick treatments. Therefore, the following treatments are compared: Gradual – 6 versus Quick – 6, Gradual – 6F versus Quick – 6F, and Gradual – 3 versus Quick – 3. The increase in the average contribution after the subsidy implementation is larger in the quick treatments compared to the gradual treatments in the two of these three comparisons.28 However, neither of these differences is significant. Therefore, there is no evidence for the validity of Hypothesis 1, which states that the effect of a subsidy on contributions to public goods is stronger for a quickly introduced compared to a gradually introduced subsidy, according to these test statistics.
Table 4 Comparisons of the effects of the subsidy introduction
Treatment Max subsidy N Difference (SD) WMW (p-value)
Gradual – 6 0.75 13 3.08 (1.97) 0.9565 Quick – 6 0.75 12 3.19 (3.75) Gradual – 6F 0.75 12 3.53 (3.77) 0.5247 Quick – 6F 0.75 12 3.11 (2.43) Gradual – 3 0.55 7 1.43 (3.53) 0.3901 Quick – 3 0.55 6 3.11 (4.24) Gradual – 6 0.75 13 3.08 (1.97) 0.1214 Gradual – 3 0.55 7 1.43 (3.53) Quick – 6 0.75 12 3.19 (3.75) 0.9626 Quick – 3 0.55 6 3.11 (4.24)
Notes: Difference represents the mean of the difference between the average contribution on the last three survey-days minus the average contribution on the first three survey-days; WMW refers to the Wilcoxon-Mann-Whitney test; Standard deviations between the brackets.
The second hypothesis is related to difference in the effect of the subsidy between the treatments with group-size six and group-size three in the PGG. Therefore, the following
28 The Difference is larger in the quick treatment compared to the gradual treatment in the first and third comparison, since 3.19 exceeds 3.08 and 3.11 exceeds 1.43, respectively.
26
treatments are compared: Gradual – 6 versus Gradual – 3, and Quick – 6 versus Quick – 3. According to this hypothesis, the effect of the subsidy introduction should be larger in the treatments with group-size six compared to in the treatments with group-size three. As mentioned, this effect is significant in the treatments with group consisting of six participants, while it is not significant in the treatments with groups consisting of three individuals. The difference in the effect is nearly weakly significant for the comparison between the gradual treatments.29 However, this difference is not significant for the comparison between the quick treatments.30 Moreover, the second hypothesis is based upon the expected differences in the average contributions before and after the subsidy introduction for the treatments with group-size six and three in the PGG. However, these values are not significantly different. The results are summarized in Table 11 in Appendix D. Hypothesis 2 cannot be confirmed based on these test statistics.
The experimental results show no significant evidence supporting the hypotheses. However, the directions of estimated effects correspond with the expectations according to the hypotheses.
5.3.2 Hypothesis 3
The third hypothesis is related to the level of contributions. For each participant, we calculated the average contribution in the experiment. The average contributions are compared between different treatments with the non-parametric Wilcoxon-Mann-Whitney test. Table 5 displays the mean of the average contributions of the participants of four treatments and the corresponding test statistics. Hypothesis 3 states that contributions are higher when giving individuals associations to norms for cooperation. Therefore, we compare the difference in the mean of contributions of the framed and non-framed treatments: Gradual – 6 versus Gradual – 6F and Quick – 6 versus Quick – 6F. The results show that the average contributions are significantly higher in the framed treatment given that subsidy is introduced gradually. However, this is not the case if the subsidy is quickly implemented. These test statistics do not clearly indicate whether Hypothesis 3 holds.
29 The p-value of the WMW test between the effects of the subsidy in the Gradual – 6 and Gradual – 3 treatments equals 0.1214. Results are weakly significant if the p-value is less than 0.10.
30 The p-value of the WMW test between the effects of the subsidy in the Quick – 6 and Quick – 3 treatments equals 0.9626.
27 Table 5 Mean contributions in the treatments
Treatment Max subsidy N Mean (SD) WMW (p-value)
Gradual - 6 0.75 13 5.34 (0.17) 0.0001
Gradual – 6F 0.75 12 6.37 (0.19)
Quick – 6 0.75 12 3.88 (0.17) 0.7959
Quick – 6F 0.75 12 3.84 (0.16)
Notes: WMW: Wilcoxon-Mann-Whitney test; standard deviations between the brackets.
However, we are mainly interested in the effect of the framing in comparison with the effect of the way of the subsidy introduction on the effectiveness of a subsidy implementation. Therefore, we compare the difference between the average contributions before and after the subsidy introduction for the framed versus non-framed treatments and the gradual versus quick treatments. Table 6 indicates that the effect of the framing is not significant in both the gradual and quick treatments, neither is the effect of the way of the subsidy introduction. The sizes of the effects are addressed in the next section with the regression analyses.
Table 6 Comparisons of the effects of the subsidy introduction
Treatment Max subsidy N Difference (SD) WMW (p-value)
Gradual – 6 0.75 13 3.08 (1.97) 0.9565 Quick – 6 0.75 12 3.19 (3.75) Gradual - 6 0.75 13 3.08 (1.97) 0.4454 Gradual – 6F 0.75 12 3.53 (3.77) Quick – 6 0.75 12 3.19 (3.75) 1.0000 Quick – 6F 0.75 12 3.11 (2.43)
Notes: Difference represents the mean of the difference between the average contribution on the last three survey-days minus the average contribution on the first three survey-days; WMW: Wilcoxon-Mann-Whitney test; standard deviations between the brackets.
28 5.4 Regression analysis
In this last section, the results of the regression analysis are discussed. This analysis is needed to make the first impressions based on the graphical illustrations and the non-parametric tests statistically precise and to control for background variables of participants.
5.4.1 Change in contributions
The first two models estimate the effect of the subsidy introduction, which is defined as the change in the average contributions before and after the subsidy implementation. For each participant, we calculated the change in contribution, which is the average contribution on the last three survey-days minus the average contribution on the first three survey-days. This way the contributions are normalized since the contributions are corrected for differences in the initial contributions between participants. Table 7 displays the estimated regressions with the change in contribution as dependent variable.
The first hypothesis states that the effect of a subsidy on contributions to public goods is stronger for a quickly introduced compared to a gradually introduced subsidy. The regression coefficients in Regression 1 and Regression 2 of the explanatory variable Gradual are negative, - 0.415 and - 0.957, respectively. This indicates that the participants in the quick treatments reacted stronger to the subsidy introduction compared to the participants in the gradual treatments, which is in line with the expectation. However, the coefficients are not significantly different from zero.31 Therefore, the first hypothesis cannot be confirmed based on the estimated regressions. The second hypothesis states that the effect of a subsidy on contributions to public goods does not decrease when the population-size increases. In our experiment, this hypothesis implicates that the effect of subsidy introduction is expected to be stronger for groups consisting of six individuals compared to for groups consisting of three individuals. Though, the regression coefficient of the explanatory variable Groups of three is not significant in both estimations.32 Thus, Hypothesis 2 cannot be confirmed based on the estimation results. The third hypothesis is related to the framing of subsidy announcements and the level of contributions. However, our main interest is the comparison between the effect of the framing of the announcements of subsidy introductions and the effect of the way of implementing a subsidy on the effectiveness of a subsidy. Therefore, the coefficients of Gradual and Framing in Regression 1 and Regression 2 are relevant. The absolute value of the
31 The p-value of the coefficient Gradual equals 0.575 and 0.229 in Regression 1 and Regression 2, respectively.
32 The p-value of the coefficient Group of three equals 0.969 and 0.750 in Regression 1 and Regression 2, respectively.
29
coefficient of Gradual exceeds the absolute value of the coefficient of Framing in both regressions. This suggests that the way of implementing a subsidy, either gradually or quickly, has more impact on the effectiveness of the subsidy than the framing of the subsidy announcements. However, the coefficients of Gradual and Framing are not significant in both regressions. Thus, both the framing of the announcements and the way of the subsidy implementation have no significant effect on the change in contributions, which approximates the effect of the subsidy introduction in our experiment.
Table 7 OLS Regression: Change in contribution
Y = Change in Contribution Regression 1 Y Regression 2 Y
X Marginal effect (SE) p-value Marginal effect (SE) p-value
Gradual -0.415 (0.736) 0.575 -0.957 (0.787) 0.229
Group of three -0.040 (1.015) 0.969 0.356 (1.111) 0.750
Framed 0.398 (0.828) 0.633 0.702 (0.861) 0.419
Male -1.172 (0.874) 0.186
Economics study -0.570 (0.988) 0.566
Game Theory course 1.321 (0.958) 0.174
Cooperator 1.059 (1.058) 0.322 Related 0.080 (0.268) 0.765 Noticed 0.494 (0.130) 0.000 0.537 (0.135) 0.000 Constant 0.227 (1.054) 0.831 -0.779 (1.673) 0.643 N 62 62 R2 0.219 0.284
Notes: Dependent variable is the change in contributions; Gradual =1 if subject is assigned to gradual treatment, Gradual =0 otherwise; Group of three =1 if subject is assigned to treatment with group-size three in the PGG, Group of three =0 otherwise; Framed =1 if subject is assigned to framed treatment, Framed =0 otherwise; Male =1 if subject is male, Male =0 otherwise; Economics study =1 if subject studies or has studied Economics, Economics study =0 otherwise; Game Theory =1 if subject has followed a course related to Game Theory, Game Theory =0 otherwise; Cooperator =1 if subject select B, C or D in the value orientation test of Part 2, Cooperator =0 otherwise; Related and Noticed report the chosen value of the Likert scale (see Table 12, Appendix D); Robust standard errors are presented in the parentheses.
The estimation results control for background effects. Males change their contributions on average less compared to females, though the effect is insignificant. Participants who are studying or have studied Economics tend to increase their contributions less compared to the
30
other participants. However, this difference is also insignificant. Furthermore, the change in contributions is not significantly affected when subjects followed a course related to Game Theory. Subjects defined as cooperators within the experiment do not alter their contributions significantly different compared to non-cooperators. Moreover, the increase in contributions after the subsidy implementation is not affected by how related the subjects felt with their matched participants. 33 However, the estimated coefficients of Noticed indicate that the change in contributions is significantly positively affected if participants notice the changes in the subsidy.34
5.4.2 Level of contributions
The dependent variable in the third and fourth estimated regression shown in Table 8 is the level of contributions. These regressions are based upon panel data, twenty observations per participant. Thus, the number of observations equals 1240. Hypothesis 3 is related to the level of contributions and states that contributions are higher in the framed versus non-framed situations. The estimated regressions indicate that the framing of situations increases the level of contributions of individuals on average. However, the coefficients are not significantly different from zero. 35 Thus, the third hypothesis cannot be confirmed based on the estimated models.
Furthermore, we controlled for the potential effects of background variables on the level of contributions to public goods. In Regression 3, the background variables Male, Economic Study and Game Theory course are excluded, since these variables have no significant effect on the experimental results. Furthermore, the level of contributions is not significantly affected if individuals feel fit, are stressed or expect to spend a lot of money. The level of contributions is neither affected based on whether felt related to their matched participants. However, subjects’ mood is estimated to have a significant effect on the level of contribution. On average, the better a subject’s self-observed mood, the higher the contributions. Furthermore, the estimated coefficients of Noticed indicate that the level of contributions is significantly positively affected if participants notice the changes in the
33 Remember, the dependent variable is normalized. The background variables potentially influence the level on contributions. Therefore, the variables might have no significant effect in the estimated regressions in Table 7 since we corrected for the initial contribution levels of the participants.
34 The p-value of the coefficient Noticed equals 0.000 in Regression 1 and Regression 2.
35 The p-value of the coefficient Framing equals 0.258 and 0.249 in Regression 1 and Regression 2, respectively.
31
subsidy. The estimated regressions indicate that cooperators tend to contribute more compared to non-cooperators. Though, the result is only weakly significant in Regression 3.36 Table 8 OLS Regression: Level of contributions
Y = Level of Contribution Regression 3 Y Regression 4 Y
X Marginal effect (SE) p-value Marginal effect (SE) p-value
Gradual 1.350 (0.542) 0.013 1.403 (0.586) 0.017
Groups of three 1.083 (0.753) 0.150 1.051 (0.812) 0.196
Framed 0.694 (0.613) 0.258 0.735 (0.638) 0.249
Male -0.244 (0.648) 0.706
Economics study 0.444 (0.737) 0.547
Game Theory course -0.666 (0.716) 0.352
Cooperator 1.229 (0.729) 0.092 1.144 (0.785) 0.145 Mood 0.402 (0.059) 0.000 0.324 (0.079) 0.000 Fit 0.073 (0.062) 0.240 Stress -0.025 (0.048) 0.601 Spend 0.041 (0.044) 0.344 Related -0.032 (0.198) 0.872 Noticed 0.231 (0.068) 0.001 0.240 (0.067) 0.000 Constant -0.743 (0.983) 0.450 -0.523 (1.231) 0.671 N 1240 1240 R2 (between) 0.099 0.106
Notes: Dependent variable is the level of contributions; Gradual =1 if subject is assigned to gradual treatment, Gradual =0 otherwise; Group of three =1 if subject is assigned to treatment with group-size three in the PGG, Group of three =0 otherwise; Framed =1 if subject is assigned to framed treatment, Framed =0 otherwise; Male =1 if subject is male, Male =0 otherwise; Economics study =1 if subject studies or has studied Economics, Economics study =0 otherwise; Game Theory =1 if subject has followed a course related to Game Theory, Game Theory =0 otherwise; Cooperator =1 if subject select B, C or D in the value orientation test of Part 2, Cooperator =0 otherwise; Mood, Fit, Stress, Spend, Related and Noticed report the chosen value of the Likert scale (see Table 12, Appendix D); Robust standard errors adjusted for 62 clusters are presented in the parentheses.
36 The p-value of the coefficient Framing equals 0.092 and 0.145 in Regression 3 and Regression 4, respectively. Results are weakly significant if the p-value is less than 0.10.
