Effects of Risk Framing and Wealth Inequality on Climate Change Mitigation Effort

17October 2016Supplementary material: Avoiding an uncertain catastrophe1

Supplementarymaterial

Effects of risk framing and wealth inequality on climate change mitigation effort

This document contains the following sections:

1. Experiment instructions
2. A more detailed descriptionof the research questions and expectations
3. Results

1. Experiment Instructions

The instructions of treatment T1 are reproduced below in their entirety. Differences in instructions between those of T1 and those of the other treatments are then noted.

T1 (homogeneous endowment, known threshold)

You are about to participate in an experiment on decision-making. If you follow these instructions carefully and make good decisions you can earn a considerable amount of money, which will be paid to you at the end of this experiment in cash.

During the entire experiment, communication of any kind is strictly prohibited. Communication between participants will lead to your exclusion from the experiment and the forfeit of all monetary earnings. Please raise your hand if you have any questions; a member of the research team will come to you and answer your question privately.

There are threeindependent sessions in this experiment, and each session consists of ten rounds (so there will be 30 rounds in total). The three sessions are identical; you are in the same group in each session. At the end of the experiment, one of the three sessions will be chosen at random to be the session that determines your payoff.

In each session, you are a member of a group of six. There are two groups of six in the room. Only the experimenters will know who is in which group. Each member of your group will have an initial endowment of $40.

In each round, each member has to decide how much of his or her endowment to put into a group account: in each period you can put $4, $2, or nothing into the group account. The computer screen will ask you how many dollars you want to put into the group account; each dollar you do not put in the group account stays in your endowment. Any money given to the group account is no longer available to you.

The purpose of the group account is that it decides how likely it is that you and the other five group members can keep the money that remains in your individual endowments. To be precise, if at the end of the ten rounds in the payoff-relevant session, the group account contains $120 or more, each group member definitely can keep what remains in their individual endowments. If the group account contains less than $120, then there is a 50% probability that the money the group members kept for themselves will be lost, in which case each member would leave the experiment with $0, and a corresponding 50% probability of keeping what remained in the individual endowments.

At the end of each round, you will see how much you and the other group members contributed to the group account in that round, and you will see the cumulative contributions to the group account.

At the end of the experiment, the computer will draw random numbers to determine which session is binding, and, if the total cumulative contributions are less than $120, whether you and the members of your group can keep the money in the personal endowments or not.

Control Questions:

Please answer the following questions. Their purpose is to make you familiar with the calculation of cash amounts that result from different decisions on how to allocate your initial endowments.

1. Assume all group members (including you) each put an individual total of $28 over the 10 rounds into the group account.

How much money remains in your individual endowment: ____

What is the probability that the money you kept will be lost: ____

1. Assume all group members (including you) each put an individual total of $12 over the 10 rounds into the group account.

How much money remains in your individual endowment: ____

What is the probability that the money you kept will be lost: ____

1. Assume the other group members (but not you) each put an individual total of $28 over the 10 rounds into the group account, but you put a total of $12 into the group account.

How much money remains in your individual endowment: ____

What is the probability that the money you kept will be lost: ____

1. Assume the other group members (but not you) each put an individual total of $12 over the 10 rounds into the group account, but you put a total of $28 into the group account.

How much money remains in your individual endowment: ____

What is the probability that the money you kept will be lost: ____

If you finish these questions before the others, we advise you to think about additional examples to familiarize yourself further with the decision situation.

T2 (homogeneous endowment, known threshold, variable p)

The instructions of T2 are identical to those of T1 except that the sixth paragraph of T1 is replaced with the following:

The purpose of the group account is that it decides how likely it is that you and the other five group members can keep the money that remains in your individual endowments. To be precise, if at the end of the ten rounds in the payoff-relevant session, the group account contains $120 or more, each group member definitely can keep what remains in their individual endowments. If the group account contains less than $120, then there is a certain probability that the money the group members kept for themselves will be lost, in which case each group member would leave the experiment with $0. This probability depends on the total contribution to the group account; the greater the total contribution the lower is the probability of loss. The probability of loss is computed as follows:

Probability of loss = (120 – Total contribution) / 120

The following table shows the loss probabilities, in percentage terms, for a few total contribution levels:

Total contribution / Probability of loss
$120 and more / 0%
$100 / 17%
$80 / 33%
$60 / 50%
$40 / 67%
$20 / 83%
0 / 100%

For example, if a total of $80 had been contributed to the group account, there would be a 33% probability that the money remaining in the individual endowments would be lost, and a corresponding 67% probability of keeping what remained in the individual endowments. Or if a total of $50 had been contributed to the group account, there would be about a 58% probability that the money remaining in the individual endowments would be lost—that is, (120 – 50) / 120 = 0.583—and a corresponding 42% probability of keeping what remained in the individual endowments.

T3 (homogeneous endowment, unknown threshold)

The instructions of T3 differ from those of T1 in two ways. First, sixth paragraph of T1 is replaced with the following:

The purpose of the group account is that it decides how likely it is that you and the other five group members can keep the money that remains in your individual endowments. To be precise, if at the end of the ten rounds in the payoff-relevant session, the group account contains $X or more, each group member definitely can keep what remains in their individual endowments. If the group account contains less than $X, then there is a 100% probability that the money the group members kept for themselves will be lost, in which case each member would leave the experiment with $0, and a corresponding 0% probability of keeping what remained in the individual endowments. The exact threshold amount $X will be determined randomly at the end of the experiment. It can be any amount between $0 and $120 with each whole dollar amount between $0 and $120 having an equal probability of being selected.

The second difference is in the control questions. For example, the second question of T1 is replaced with:

1. Assume all group members (including you) each put a total of $12 over the 10 rounds into the group account.

How much money remains in your individual endowment: ____

If the threshold amount X is $50, what is the probability that the money you kept will be lost: ____

If the threshold amount X is $100, what is the probability that the money you kept will be lost: ____

T4-T6 (heterogeneous endowment treatments)

The instructions of T4, T5, and T6 differ from those of T1, T2, and T3, respectively, in two ways. First, the fourth and fifth paragraphs of each homogeneous endowment version are replaced with the following two paragraphs:

In each session, you are a member of a group of six. There are two groups of six in the room. Only the experimenters will know who is in which group. Three members of your group will have an initialendowment of $50 each; the other three group members will have an initial endowment of $30 each. You will see your initial endowment on the computer screen at the beginning of the first round.

In each round, each member has to decide how much of his or her endowment to put into a group account: in each round, the members with a $50 endowment can put $5, $3, $2 or nothing into the group account. The members with a $30 endowment can put $3, $2, $1 or nothing into the group account. The computer screen will ask you how many dollars you want to put into the group account; each dollar you do not put in the group account stays in your endowment. Any money given to the group account is no longer available to you.

Second, the control questions of T4-T6 are similar to those of T1-T3 except for differences caused by the differences in endowment. For example the second question of T4 (to be compared with that of T1) is as follows:

1. Assume all group members (including you) each put an individual total of $12 over the 10 rounds into the group account.

How much money remains in your individual endowment if you began with an initial endowment of $50: ____

How much money remains in your individual endowment if you began with an initial endowment of $30: ____

What is the probability that the money you kept will be lost: ____

2.Research questions

Our experimental design crosses two factors, the Endowment that players begin with (either equal or unequal) and the Threat they face (Table 1 of the paper). Threat is a function of the threshold (known or unknown) and the probability of loss if the threshold is not reached (fixed or variable). Treatments T1 and T4 implement a known threshold and fixed loss probability (this threat configuration is called H1, Table 1), treatments T2 and T5 implement a known threshold but a variable loss probability (H2), and treatments T3 and T6 implement an unknown threshold with a fixed loss probability (H3). Treatments T4-T6 are identical to T1-T3, respectively, except for the difference in endowments (Table 1). In treatments T1-T3, each subject begins each round with an endowment of $40. In treatments T4-T6, three “rich” subjects begin each round with endowmentsof $50, and three “poor” subjects receive endowmentsof $30.

We address the following three research questions:

1. What is the effect on success in reaching the “safe” threshold and on group total contributions of continuous change in the chance of a loss versus a discrete change?
2. Does it matter to success and contributions if the uncertainty that subjects face is expressed in terms of loss probability or location of the threshold?
3. What is the effect on success and contributions of income heterogeneity?

3. Results

Basic findings

Success rates

Success rates (with success defined as crossing the “safe threshold” of $120) are listed in Table S1 and indicated in Figure S1. In treatment T1 60% (18 out of 30) of all group opportunities managed to reach the $120 threshold (6, 7 and 5 out of 10 in Rounds 1, 2 and 3, respectively), but in T2 only 25% made it (5, 3 and 1 out of 12 each), and in T3 not a single group made it.In T4 70% (7 of 10 groups in each round) reached the threshold, whereas in T6 not one group made it (Table S2). Groups in T5, however, were much more successful than groups in T6; in T5 the aggregate contributions of 18 groups out of 33 (55%) surpassed the threshold (5, 7 and 6 groups in Rounds 1, 2 and 3, respectively).

In T1 we do not replicate the low success rate found by Milinski et al. (2008) where only one out of ten groups reached the threshold in their treatment with a loss probability of 0.5. The reason for this difference in results between the two treatments is not entirely clear. Barrett (2013) ventures that the main reason for the surprisingly low rate of coordination in Milinski et al.’s study “is almost surely that, by construction, the players were not allowed to communicate” (page 237) and cites Tavoni et al. (2011) as evidence for the positive effect of communication in a similar experiment. However, communication was also not allowed in our experiment and yet we observe clearly stronger coordination and higher contribution levels compared to what Milinski et al. found.

Results of more recent studies also differ from those of Milinski et al. (2008). First,Milinski et al. (2011)implemented a treatment (the “Rich” group without intermediate target, where each subject was given operating funds of 40 and faced a 0.9 probability of losing all remaining funds if the group did not reach the 120 threshold) very similar to the Milinski et al. (2008)treatment with a loss probability of 0.9. Again, communication among subjects was not allowed. The 2011 study found that that all groups reached the 120 threshold, whereas in the 2008 study only 5 of 10 groups did. Second, theBurton-Chellew et al. (2013)“Egalitarian” treatment is quite similar to our T1 treatment, the main difference being that they used a loss probability of 0.7 or 0.8, higher than the 0.5 loss probability in our T1. They did not allow subjects to interact. They found that 7 of their 8 groups reached the 120 threshold, whereas 6 of 10 did in our T1; their groups averaged a total contribution of about 110 and ours reached an average of 113. Thus, our results seem in line with those of other recent studies employing similar treatments.

Contributions

Total contribution levels are listed in Table S2 and shown in Figure S1. Average contributions over all three rounds are $113, $110, and $94 in T1, T2, and T3, respectively. Even the lowest individual group total contribution of all 30 groupsin T3, $64, is much higher than the theoretically predicted contribution of $36. Averaged over the three rounds, total contributions are $116, $116, and $94 in T4, T5, and T6, respectively (Table S2).

A basic difference between H1 and H2 or H3 is evident in Figure S1, regarding the likelihood of reaching the “safe” threshold of $120. In treatment T1, for example, group 1, having reached a total contribution of only $82 in round 1, tried harder in round 2 (reaching $104) and again in round 3 (reaching $118), whereas group 2, having also reached a total contribution of only $82 in round 1, largely abandoned the cause (with total contributions of $72 in round 2 and $36 in round 3). Group 1 in treatment 4 also appears to largely have given up trying to reach the threshold. No such abandonment of the objective of protecting future welfare is evident in the H2 and H3 treatments. While subjects in H1 treatments have a greater incentive to reach the $120 threshold, subjects in H2 and H3 treatments have greater incentive to continue to contribute even if it is likely that the group will not reach the “safe” threshold level.

Also evident in Figure S1 is that, with the exception of the T1 and T4 groups just mentioned, most groups, regardless of treatment, show no consistent trend in contributions across rounds.

A finding worthy of additional discussion is that, of all the treatments, and looking at both success rates and total contribution levels (Tables S1 and S2), results differ most dramatically across rounds for success rate with T2. Fisher’s exact tests for the difference between T1 and T2 indicate no difference in success rate in round 1 (p=0.335) but a difference in rounds 2 and 3 (p=0.046 and p=0.043, respectively). However, the importance of this result is discounted by the fact that T2 total contributions do not differ much across rounds. Examination of Figure S1 shows that several groups in T2 shifted across rounds from barely reaching the $120 threshold in round 1 to just missing it in the subsequent two rounds. For example, in round 2 one group reached a total contribution of $118 and in round 3 one group reached $118 and two groups reached $116. Thus, the notable reduction in success rate across rounds in T2 is more a reflection of the uncertainness of reaching a specific threshold than of the level of effort expended to do so.

Framing

In T2 groups reached the threshold in 9 of 36 opportunities (5, 3 and 1 groups out of 12 in Rounds 1-3, respectively) but in T3 not a single group out of 30 made it (Table S1, FigureS1).And in T5 groups reached the threshold in 18 of 33 opportunities (5, 7 and 6 groups out of 11 in Rounds 1-3, respectively) but in T6 not one of the 30 groups reached 120.

Group average contributions are roughly 20% higher in T2/T5 than in T3/T6 (Table S2, FigureS1).

Statistical tests

Analysis of the first three research questions is performed using data from all six treatments in a single generalized linear mixed model (implemented with the GLIMMIX procedure of SAS) with Threat (three levels), Endowment (two levels), and Round (three levels) as class variables. The model allows comparisons of the different levels of Threat, Endowment, and Round. The Tukey multiple range test is used to adjust for the effect of having performed multiple tests. Two dependent variables are analyzed: success rate is a quantal variable (the group either reached the threshold or not), and total contribution is entered as Gaussian after adjustment with the box-cox transformation (lambda=3) to approximate a normal distribution. A p-value cutoff of 0.05 is used for all tests. The null hypothesis in all tests was of no difference between the two treatments or conditions being compared. Analysis of the fourth research question uses a similar model, with Treatment, Group (rich v. poor) and Round as class variables, and proportion contributed as the dependent variable. For this analysis the box-cox transformation is also used, but with lambda = 1.75.

Statistical test results at the treatment level are summarized in Table S3. Table S5 shows detail that was not fully described in the published paper, dealing with differences between the homogeneous endowment (T1-T3) and heterogeneous endowment (T4-T6) findings for research questions 1 and 2. Results of tests when the endowments are heterogeneous do not entirely match those of the homogeneous endowment treatments, exhibiting somewhat more rejection of the hypotheses.Importantly, success rates and contributions are significantly greater in T1 than in T2 but not significantly greater in T4 than in T5. That is, the results presented in the paper comparing the first two threat configurations (H1 v. H2) are not consistent across endowments: the success rate of T1 exceeds that of T2 (p=0.035) but the success rate of T4 does not exceed that of T5 (p=0.268); and contributions of T1 exceed those of T2 (p=0.019) but contributions of T4 do not exceed those of T5 (p=0.158). This occurs because success rates and contributions in T5 exceed those of T2. Heterogeneity of endowments appears to have enhanced cooperation in the H2 threat configuration. This finding bears future study.