Abstract
This paper explores how threshold uncertainty affects cooperative behaviors in the provision of public goods and the prevention of public bads. The following facts motivate our study. First, environmental (resource) problems are either framed as public bads prevention or public goods provision. Second, the occurrence of these problems is characterized by thresholds that are interchangeably represented as “nonconvexity,” “bifurcation,” “bi-stability,” or “catastrophes.” Third, the threshold location is mostly unknown. We employ a provision point mechanism with threshold uncertainty and analyze the responses of cooperative behaviors to uncertainty and to the framing for each type of social preferences categorized by a value orientation test. We find that aggregate framing effects are negligible, although the response to the frame is the opposite depending on the type of social preferences. “Cooperative” subjects become more cooperative in negative frames than in positive frames, whereas “individualistic” subjects are less cooperative in negative frames than in positive ones. This finding implies that the insignificance of aggregate framing effects arises from behavioral asymmetry. We also find that the percentage of cooperative choices non-monotonically varies with the degree of threshold uncertainty, irrespective of framing and value orientation. Specifically, the degree of cooperation is highest at intermediate levels of threshold uncertainty and decreases as the uncertainty becomes sufficiently large.
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Notes
There are many other real-world examples, such as the possible disintegration of the Antarctic ice sheet, irreversible global warming and eutrophication for lakes (see, e.g., Ulph and Ulph 1997; Carpenter et al. 1999; Naevdal 2006). A common feature of these environmental and natural resource problems is the existence of the threshold where its location is unknown.
We use the term “uncertainty” to refer to the events with probability distribution, in contrast to “ambiguity,” in which even probability cannot be assigned to each event.
The value orientation test is a simple test developed by Liebrand (1984) to categorize people into several types of social preference.
Suleiman et al. (2001) also manipulated the degree of threshold uncertainty in the continuous contribution settings of PPMs, but they employ two different levels in addition to the case of no uncertainty. Their underlying theories and experimental findings indicate only whether cooperation increases with threshold uncertainty for a given level of threshold means. In contrast, our research uses a wider range of threshold uncertainty with four different levels, holding the value of public goods and threshold means fixed at some level. The degree of cooperation predicted by the Nash equilibrium becomes single-peaked over the domain of threshold uncertainty. This is another unique feature of this study. We will explain that this qualitative prediction can be derived from a situation reflecting realistic contexts of environmental problems and discuss the motivation in relation to economic theory in a later section.
In particular, our experimental results could be considered consistent with the theory in McBride (2006) for an “intermediate” range of threshold uncertainty.
Panel probit models assume that the dependent variable is a cooperative choice made by each subject, and independent variables include rounds and the dummy variable of the last 5 rounds. We also attempted several different specifications of panel probit models. As will be mentioned in the text later, for every specification, \(G3\) is the only treatment that shows a difference in cooperative behaviors over rounds or by the dummy variable. In contrast, Mann–Whitney tests were implemented by simply dividing the sample of observed cooperative behaviors into the two sub-samples of the first five rounds and the latter five rounds. The results show that \(G3\) is again the only treatment that shows statistically significant differences in cooperative behaviors between the first five and the latter five rounds.
Abbreviations
- PPM:
-
Provision point mechanism
- VCM:
-
Voluntary contribution mechanism
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Acknowledgments
We are very grateful to the financial support from the Asahi Glass Foundation, Promotion Mutual Aid Cooperation for Private Schools of Japan, Ministry of Environment, Japan, and Specially Promoted Research from Ministry of Education, Culture, Sports, Science and Technology, Japan (MEXT), and the Grants-in-Aid for Scientific Research C for this research. We also thank anonymous referees, Makoto Kakinaka, Hiroaki Miyamoto and Toshiji Kawagoe for their helpful discussion and comments.
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Appendix
Appendix
This section presents some probit regression results to support that the observed cooperative choices do not change with the first half 5 and the latter 5 rounds or with the 10 rounds. The first regression controls the dummy variable taking 1 when the experimental rounds are between 6 and 10, otherwise 0. This result is shown in Table 13. The second model additionally controls a variable of rounds, \(\{1,2,\ldots ,10\}\). The result is shown in Table 14. Both results illustrate that the only treatment showing some statistical significance is \(G3\) where cooperative choices decay over rounds. Other treatments do not show any significant result.
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Kotani, K., Tanaka, K. & Managi, S. Cooperative choice and its framing effect under threshold uncertainty in a provision point mechanism. Econ Gov 15, 329–353 (2014). https://doi.org/10.1007/s10101-014-0147-4
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DOI: https://doi.org/10.1007/s10101-014-0147-4