For the statistical analysis we use STATA 12. Because experiments often lead to skew distributions (which was also the case hereFootnote 8), we report significance levels from non-parametric Mann-Whitney U tests along with standard independent t tests. To compare proportions across the two treatments, we use a Pearson’s Chi-square test (D’Agostino et al. 1988). All reported p values are two-sided and displayed in italics. In the regressions we let * denote significance at the 10-percent level, ** on the 5-percent level and *** on the 1-percent level. Because we can reject normality, we bootstrap the standard errors for all our regressions (Goncalves and White 2005).
We first look at the overall picture of the data, comparing means and proportions of the threshold with the no threshold treatment. Table 1 illustrates that there are indeed significant differences between both treatments; threshold treatment groups cooperate more, report more effective communication, achieve a higher efficiency, experience fewer tragedies and, hence, earn more money on average than groups in the no threshold treatment. There are no structural differences with respect to the individual variables age and gender, nor to group size.
In Fig. 3, we illustrate the average amount of over- and under-exploitation for both treatments in each period. From this figure, it is obvious that, on average, the threshold treatment implies less over- and under-exploitation in each period compared to the no threshold treatment.
Figure 4 clearly demonstrates the significant difference in average efficiency (see Table 1) between the two treatments; the no threshold treatment is associated with less efficiency compared to the threshold treatment. It is not that surprising to see that efficiency decreases over time for the no threshold treatment. Once there is a depletion case, efficiency drops to zero for that group, bringing down the average efficiency. From Fig. 3 we can also deduce that most inefficiencies in the threshold treatment stem from under-exploitation.
Based on Table 1 and Figs. 3, 4, we cannot reject Hypothesis 1. We find more cases of over-exploitation in the no threshold compared to the threshold treatment. Moreover, the average obtained efficiency in the no threshold treatment is significantly lower.
To test Hypothesis 2, we look into the behavior of cooperative groups. We want to identify groups that were able to reach agreements that were being followed by all group members for the entire experiment. One way of classifying a group as cooperative is to use the average cooperation index (see Sect. 3.2). However, since this variable is self-assessed, one might argue that it is not reliable. Another way of classifying groups is according to the distribution of the earnings, i.e., a Gini coefficient of zero could indicate that the group is a cooperative group because earnings are shared equally. We noticed in the experiment, however, that some groups used a rotating scheme in order to optimize harvest, which implies that one or two subjects in a specific group could earn one resource unit more or less over the entire duration of the experiment, resulting in a slightly higher Gini coefficient (but still lower than 0.01). We use four cooperation categories based on fulfilling only one (either (i) or (ii)), both, or one of the two criteria: (i) groups with a Gini coefficient less than 0.01, (ii) an ‘average cooperation index’ of 5 (maximum possible). The four categories are presented in Table 2.
If we look at Fig. 5, where we illustrate average efficiency over time for cooperative groups (specified for the different cooperation categories) for the two treatments separately, we see that the efficiency of no threshold groups (NT) is now closer to the efficiency obtained by threshold groups (T) (compare Figs. 4, 5).
Table 2 indicates some significant differences though between the threshold and the no threshold treatment; the average efficiency for cooperative groups lies between 0.85 and 0.87 for the threshold treatment and between 0.66 and 0.69 for the no threshold treatment. Mann-Whitney U tests reveal that the differences between the treatments are significant on the 1-percent level regardless of cooperation classification. Depending on classification, there are 14 to 16 cooperative groups in the threshold treatment and 7 to 13 in the no threshold treatment. According to a Pearson’s Chi square test, however, there is no significant difference between the classifications with respect to the number of groups (p value 0.7216).
We reject Hypothesis 2. From Fig. 5, it is clear that cooperative groups do not follow the optimal management strategy (which would correspond to an efficiency of 1). We also note that there is a significant difference between the treatments for cooperative groups.
To summarize, the different treatments produce a significant difference in group behavior (as we predicted in Hypothesis 1). However, the effect is even stronger than predicted (in Hypothesis 2). We explore the experimental results further to gain some insights and understanding about why this could be the case. Table 3 illustrates the results from three linear regressions. We use efficiency as the dependent variable. The first regression is with all groups, the second only with cooperative groups, and the third only with non-cooperative groups (in Table 3 we present the regressions based on cooperation category 1Footnote 9). To capture potential within group correlation, we employ a random effects structure.
The models presented in Table 3 are chosen among several alternative specifications based on their performance with respect to model test (Wald Chi-square) and explanatory power. The alternative specifications show that neither average age in the group, group gender distribution, nor group size can significantly explain the variation of observed efficiencyFootnote 10. The first regression in Table 3 (where these insignificant variables have been excluded from the model) reveals instead that groups playing the threshold treatment, cooperative groups and groups with a higher ‘group knowledge index’ are associated with a higher average efficiency. We can also identify differences in behavior between cooperative and non-cooperative groups. For example, efficiency decreases with the number of periods played for non-cooperative groups but not for cooperative groups. This is not surprising, as we typically find over-exploitation and depletion among non-cooperative groups. The treatment is significant for both groups. According to the theoretical predictions, it should not have any effect for cooperative groups, thus, validating our rejection of Hypothesis 2. The ‘group knowledge index’ also plays a role for cooperative groups but not for non-cooperative groups.
Besides the treatment, whether a group manages to cooperate or not seems to play a crucial role in explaining how the group performs with respect to efficiency. If the group has on average a good knowledge of the resource dynamics also seems to influence achieved efficiency. But what triggers cooperation and what lies behind the knowledge variable?
A linear regression, with the ‘group cooperation index’ as dependent variable shows that groups with effective communication are more likely to cooperate (see Table 4, regression 1). No other variables, including the treatment, can significantly explain how well a group manages to cooperateFootnote 11. Recall that we define effective communication as communication where the group takes advantage of the communication possibility and, moreover, they are able to reach agreementsFootnote 12.
Table 4 (regression 2) reveals that the most influential variable for the ‘group knowledge index’ is the ‘group communication index’. The threshold treatment is, as we know from Table 1, associated with poorer understanding of the resource dynamics, which also becomes evident here (although only at the 10-percent level). How effective the group was at communicating can explain how well they cooperated and how well they understood the resource dynamics, which in turn can explain the variation of efficiency observed. So which groups are more likely to be associated with a higher ‘group communication index’? Table 4 (regression 3) shows that the treatment is the only influential variable. Threshold groups communicated more effectively. It seems that the effectiveness of communication is endogenous to the problem, which in turn suggests that ‘group communication index’ is a “bad” control. To capture the causal effect of communication we, therefore, use a two stage least square (2SLS) regression where we use predicted values from regression 3 in regression 1. Regression 4 in Table 4 presents these results. Effective communication is then associated with a higher level of cooperation. Based on our results we propose the following linkage:
The threat of reaching a critical tipping point triggers more effective communication within the group, which in turn enables not only stronger commitment for cooperation but also knowledge sharing, which can explain why threshold groups managed the resource more efficiently, even when we only consider cooperative groups.