Understanding the nature of cooperation variability

Journal of Public Economics 120 (2014) 134–143

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Understanding the nature of cooperation variability Toke R. Fosgaard a, Lars Gårn Hansen a,⁎, Erik Wengström b,c a b c

University of Copenhagen, Department of Food and Resource Economics, Rolighedsvej 25, 1958 Frederiksberg C, Denmark University of Copenhagen, Department of Economics, Øster Fairmagsgade 5, 1353 København K, Denmark Lund University, Department of Economics, Box 7082, S-220 07 Lund, Sweden

a r t i c l e

i n f o

Article history: Received 13 September 2013 Received in revised form 11 July 2014 Accepted 15 September 2014 Available online 22 September 2014 JEL classification: D03 D64 H41 C72 C93

a b s t r a c t Our paper investigates framing effects in a large-scale public good experiment. We measure indicators of explanations previously proposed in the literature, which when combined with the large sample, enable us to estimate a structural model of framing effects. The model captures potential causal effects and the heterogeneity of cooperation behavior. We find that framing only has a small effect on the average level of cooperation but a substantial effect on behavioral heterogeneity explained almost exclusively by a corresponding change in the heterogeneity of beliefs about other subjects' behavior. The impact of changes in preferences and game form misperception is on the other hand negligible. © 2014 Elsevier B.V. All rights reserved.

Keywords: Framing Public goods Internet experiment Simulation Heterogeneous sample

1. Introduction Cooperation between people is not only decisive for human welfare, but also a malleable endeavor where the reasons for success or failure can be elusive. We know that people's behavior responds to economically irrelevant changes in the description of the decision situation (see for instance: Andreoni, 1995a; Sonnemans et al., 1998; Park, 2000; Cubitt et al., 2011a, 2011b; Dufwenberg et al., 2011; Fosgaard et al., 2011; Ellingsen et al., 2012; Cappelen et al., 2013), but it is less clear what mechanisms drive the situational variability of cooperation. Some studies have investigated to what extent cooperation preferences are context dependent (Brewer and Kramer, 1986; McCusker and Carnevale, 1995; Weber et al., 2004; Goerg and Walkowitz, 2010; Iturbe-Ormaetxe et al., 2011) while other studies focus on how context influences beliefs about others' cooperation behavior (Sonnemans et al., 1998; Dufwenberg et al., 2011; Ellingsen et al., 2012). Finally, yet another set of studies have explored context-specific misperceptions of the incentive structure (Ferraro and Vossler, 2010; Fosgaard et al., 2011). However, one limitation of the previous studies is that they typically study one determinant at a time.

⁎ Corresponding author.

http://dx.doi.org/10.1016/j.jpubeco.2014.09.004 0047-2727/© 2014 Elsevier B.V. All rights reserved.

Our goal is to evaluate the relative importance of all of the determinants previously documented as being important, within the same study to determine their relative importance. We do this by conducting a largescale experiment which measures cooperation in public good games in two distinct, but economically equivalent, contexts: framing the cooperation decision as taking from a public good vs. giving to a public good (Andreoni, 1995a). We measure the level of cooperation along with the main determinants: preferences, beliefs, and misperception of game incentives. This makes it possible for us to identify and estimate a structural model that decomposes the framing effect into parts which are explained by framing induced changes in each of these determinants and a residual unexplained effect. We find that changes in beliefs about others' behavior are a major determinant of framing effects on cooperation. In comparison, changes in cooperation preferences and misperceptions- though present - have negligible effects. We also identify a sizable framing effect that is not transmitted through any of these mechanisms. Another finding of our study is that the relatively small framing effect on mean contributions masks substantial shifts in the underlying distribution. This has not been reported previously in the literature, presumably because of limited sample sizes. More specifically, framing has a significant effect on the heterogeneity of cooperation levels and we find that essentially all of this effect can be explained by increased heterogeneity in beliefs.

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These results contribute to our understanding of cooperation variability specifically but may also have implications for related basic issues in economics. One such issue is whether human preferences are robust to contextual changes (Camerer and Thaler, 1995; Levitt and List, 2007), while another is the importance of changes in beliefs about other people's behavior (Nyarko and Schotter, 2002; Battigalli and Dufwenberg, 2009; Fischbacher and Gächter, 2010). Finally, our findings may be relevant for the discussion on the relationship between limited cognition and behavior (Köszegi and Rabin, 2008a, 2008b; Bernheim and Rangel, 2009; Chou et al., 2009; Cason and Plott, forthcoming). The connection between these basic issues and cooperation has been a lively research topic during recent decades. The remainder of this paper is organized as follows. The next section introduces our conceptual model and Section 3 outlines our experimental design. In Section 4 the experimental results are reported and Section 5 presents our model estimations and how we disentangle the choice determinants. The decomposition of the determinants is presented in Section 6 while Section 7 concludes the paper with a discussion of our findings. 2. Our conceptual model The conceptual model that we use to guide our study is illustrated in Fig. 1. Its core is suggested by Fischbacher and Gächter (2010). We extend their model to accommodate misperception and framing. When cooperating about the production of a public good, Fischbacher and Gächter argue that subjects formulate a contribution strategy based on their conditional cooperation preferences. The contribution strategy states the subjects' preferred contribution conditional on different levels of contributions made by other subjects.1 Subjects then determine their actual contribution to the production of a public good by combining their contribution strategy with their belief about other subjects' contributions. We extend this core model because a number of studies have found that many subjects misperceive the incentives to contribute to the production of a public good (Andreoni, 1995b; Houser and Kurzban, 2002) and in our own recent study (Fosgaard et al., 2011) we show that framing can substantially affect the level of this misperception. Our conceptual model allows for five main paths through which framing can affect contributions. The paths are directly related to the types of framing effects that have been suggested in the prior experimental literature: a) Framing effects through beliefs: Sonnemans et al. (1998), Dufwenberg et al. (2011) and Ellingsen et al. (2012) have suggested that framing effects on people's beliefs are an important mechanism behind framing effects on contribution behavior. In our model, framing can affect beliefs directly (arrow 1 in Fig. 1). b) Framing effects through cooperation preferences: This effect reflects a shift in the subjects' underlying preferences for cooperation caused by the change in framing. The effect is captured by arrow 4 in Fig. 1. The existence of such an effect is supported by McCusker and Carnevale (1995) and Iturbe-Ormaetxe et al. (2011) who argue that subjects have reference dependent utility and are loss averse, and that framing affects the reference point. Another piece of support is Van Dijk and Wilke (2000) who suggest that subjects' ‘focus’ on personal and group outcomes may shift. For our purpose, we argue that if subjects have reference dependent or ‘focus’ dependent utility functions (e.g. exhibit loss aversion) and these are affected by framing, we should find a significant effect from framing on contribution strategies when controlling for changes in misperception. c) Framing effects through misperception: Ferraro and Vossler (2010) and our own previous contribution (Fosgaard et al., 2011) suggest 1 The strategy indicates the subject's preferred contribution if others on average contribute nothing, if they contribute 1 dollar, etc.

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that it is meaningful to distinguish between subjects' underlying cooperation preferences and subjects' misperception of the incentives of the game (e.g. the extent to which subjects correctly understand which contribution strategy maximizes their own vs. group income). Ferraro and Vossler manipulate whether contributions are labeled donations or investments, and find that this affects the degree to which their subjects contribute to a public good played with computers (a proxy for confused contributions). In Fosgaard et al. (2011), we find that give/take framing has important effects on subjects' perception of the game and that this explains most of what looks like framing effects on the underlying contribution preferences.2 Arrow 3 in Fig. 1 captures the framing effect on contributions that comes from such misperception driven differences in cooperation strategies. We also allow misperception to influence contributions via beliefs (arrow 2). d) Unexplained framing effects: Finally, we allow for framing effects which work through other mechanisms than those proposed above (arrow 5). Introducing this unexplained effect allows us to evaluate how much of the systematic variation that framing induces is explained by the explicitly modeled mechanisms and helps avoid evaluation bias. From the outset, we have designed our experiment to identify the central mechanisms suggested in the literature. Therefore, the concrete components of any unexplained effect are unknown to us and can only be subject to speculation. In conclusion, the model presented in Fig. 1 incorporates elements which are in the literature suggested as core mechanisms through which framing affects contributions. As such, the model does not add any new elements, but rather it attempts to structure the existing elements and their interactions. One thing that the model does illustrate is the danger of investigating framing effects with an incomplete model. If omitted explanatory variables are not controlled for in the analysis, an estimated framing effect may become biased, because it may pick up effects which work through the omitted variables. Note also that the model only captures different mechanisms that can transmit a change in framing into a change in contributions. We do not try to explain subjects' baseline cooperation levels, only how these may change because of changes in framing. The idea of our experiment (we report the Experimental design in the following section) is to generate sound indicators for the key variables in Fig. 1, for a large subject pool that we randomly allocate to two different frames of the public good game. With this data, we then estimate the causal effects (the arrows) indicated in Fig. 1, including the supplementary unexplained framing effect which captures framing effects tedhat are not explained by our conceptual model. The effects of misperception on contribution strategies found in our experiment (the part of arrow 3 between ‘frame’ and ‘contribution strategy’) have been reported in our prior paper Fosgaard et al. (2011). In the present paper we extend this by also modeling the affect this has on subjects' contributions (the rest of arrow 3) and (for the first time) report results from this experiment on framing effects through preferences (arrow 4) and beliefs (arrows 1 and 2). Then we incorporate all these results into a comprehensive model allowing us to estimate the relative importance of the different determinants of framing effects on contributions. 3. Experimental design 3.1. General outline of the experiment We conducted an artefactual field experiment over the Internet in the summer of 2008.3 Naturally, running the experiment over the Internet 2 This result is consistent with Cason and Plott (forthcoming) who show that misperceptions of the incentives of the game can cause framing effects in preference elicitation tasks. 3 See http://www.econ.ku.dk/cee/iLEE/iLEE_home.htm for a detailed description of the experiment platform. The platform has been used for numerous studies on different topics; see, e.g. Thöni et al. (2012).

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1. Belief

2. Frame

Mispercepon

Contribuon

3.

4.

5.

Cooperon preferences

Contribuon strategy

Unexplained effect

Fig. 1. Framing and causal effects in our conceptual model.

not only has several advantages but also implies a loss of control compared to standard lab procedures. However, we find qualitatively similar framing effects in a study conducted with students in the lab at the University of Copenhagen which indicates that the mode of implementation does probably not have a severe impact on our findings (see Section 6 of the Supplementary information for more details). The main benefit of using the Internet for our experiment is that we can reach a large and heterogeneous subject pool. Initially, the Danish National Bureau of Statistics (Statistics Denmark) randomly selected 18,027 individuals between 18 and 80 years old residing in Denmark. An invitation to participate in the experiment was sent to each selected potential subject via ordinary mail.4 In the invitation letter, subjects were given the Internet address of the experiment and a personal login code. The experiment was open for one week, and during this week, subjects could log in and out as they wished. After the experiment closed, subjects could log in again to receive feedback on the experimental results and type in their bank account number after which their earnings during the experiment were transferred to the account. After logging onto the webpage with their personal log-in code, subjects were randomly allocated to either the ‘give to the Public Good frame’ or the ‘take from the Public Good frame’ (Andreoni, 1995a; Cubitt et al., 2011a, 2011b; Dufwenberg et al., 2011; Park, 2000). Subjects first played a standard one shot public good (PG) game, a belief elicitation, and a ‘strategy version’ of the public good game (see descriptions below). Subjects were then asked incentivized questions testing their misperception of the game's incentives. Finally, they were asked to complete a series of cognitive ability and personality trait tests and background questions. Only the PG games and the game perception questions were framed. The remaining tests were completely identical for all subjects. A total of 2042 subjects completed the experiment, with 1366 subjects in the give treatment and 676 in the take treatment.5 On average subjects earned 300 Danish kroner (DKK), approximately $60, during the course of the entire experiment (including the payments from a risk elicitation task that we do not use). Subjects spent on average 50 min completing the experiment.

4 See the Supplementary information for a translation of the invitation letter and to find a link to screenshots from the experiment. 5 Two thirds of the participating subjects were allocated to the give treatment and the remaining one third were allocated to the take treatment. The reason for the uneven (but still random) allocation of subjects between the treatments is that the data from the give treatment have also been used for other papers, and hence these data received a higher priority.

3.2. Details Initially, subjects played a standard PG game, in which subjects were randomly divided into groups of four. Each subject was given control of 50 DKK (≈$10) and was allowed to allocate this sum freely between a contribution to a common pool (i.e. the public good) or private income reserved for oneself. In the give frame, subjects were initially given the 50 DKK as a private endowment, and were then asked what part of this endowment they wanted to contribute to a common pool. In the take frame, the 50 DKK was initially allocated to the common pool and subjects were then asked how much they wanted to withdraw from the common pool and instead reserve for themselves as private income. Under both frames, the money allocated to the common pool was doubled and shared equally among all group members. Hence, subjects' earned the amount they reserved as private income plus a quarter of the final value of the contributions to the common pool. If subjects only care about personal income, we expect everyone to contribute 0, since the marginal private return of contributing 1 DKK to the common pool is only 1/2 DKK. After the standard PG game, subjects were asked to state their beliefs about the average contribution of the other three group members. Subjects were rewarded for belief accuracy using the quadratic scoring rule.6 After completing the standard PG game, each subject played the strategy version of the PG game (strategy game) with the same framing. We applied the game developed by Fischbacher et al. (2001) for eliciting subjects' contribution strategies. Initially, subjects were divided into new groups of 4 and informed of this. Each subject was asked to make both an unconditional contribution and a profile of allocations to the PG conditional on different levels of contributions from other group members. First, the unconditional contribution was elicited in exactly the same way as in the previous standard PG. Subjects were then asked to indicate their contribution conditional on values of the three other group members' average contributions which varied from 0 to 50 DKK in steps of 5 DKK. When calculating payoffs, we used the elicited unconditional contributions for three randomly selected group members while the contribution of the fourth subject was based on the elicited conditional contribution profile using the average of the unconditional contributions from the other three group members. Since contribution strategies are conditional on other group members' contributions, these should not be affected by beliefs about the

6 Subjects received an additional payment in DKK of 10 − 0.004 d2 ≥ 0, where d is the difference between the belief and the true value.

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other group members' contributions. As shown by Fischbacher et al. (2001) and Fischbacher et al. (2012), the strategy method gives incentives to disclose precisely the conditional contribution profile, which underlies the unconditional contribution elicited in the standard PG game.7 Right after the strategy game, subjects were asked six incentivized control questions to test for misperception. We used the conditional setup introduced in the strategy game. The first three questions asked subjects what public good contribution they should make if they wanted to maximize their own income, when the others, on average, contributed 0 DKK (question 1), 25 DKK (question 2) and 50 DKK (question 3). In the last three questions, subjects were asked what contribution they should make if they wanted to maximize the income of the group, when the others, on average, contributed 0 DKK (question 4), 25 DKK (question 5) and 50 DKK (question 6). It was emphasized that each question only had one correct answer and that subjects earned 5 DKK for each correct answer. We interpret incorrect answers to these questions as misperceptions about how to implement the specified goals in the public good game. 4. Results Fig. 2 presents the distributions of contributions for subjects exposed to the give and the take frames. Using the Kolmogorov–Smirnov test, we conclude that the distributions are clearly different (p = 0.000) and that the give distribution of contributions exhibits substantially less variance than the take distribution (tested with Levene's robust test statistic for the equality of variances, p = 0.000). There is also a slightly higher mean contribution in the take treatment (35.51) compared to the give frame (34.75). Despite being small, the difference is significant (p = 0.0163, two-tailed Mann–Whitney test). Some prior studies find a framing effect in the same direction as we do (e.g. McCusker and Carnevale, 1995), some find no significant framing effects (e.g. Cubitt et al., 2011a) but most prior studies report a framing effect on mean contributions in the opposite direction.8 Fig. 2 also illustrates that the main difference between frames are found in the tails of the distribution where subjects choose to contribute nothing or everything. Subjects in the take frame more often choose these extreme values than subjects in the give frame do.9 The subjects' distributions of beliefs about what other group members on average contribute are presented in Fig. 3. These distributions also differ significantly between frames (p = 0.000, the Kolmogorov– Smirnov test), with the give distribution again exhibiting substantially less variance than the take distribution (tested with Levene's robust test statistic for the equality of variances, p = 0.000). The average belief about what others contribute is slightly lower in the take treatment (29.79), compared to the give frame (31.81) with the difference being clearly significant (p = 0.0009, two tailed Mann–Whitney test). This direction of the framing effect on mean beliefs is also found by, e.g. Dufwenberg et al. (2011). In our experiment, the framing effects on mean beliefs and mean contributions go in opposite directions; 7 This assumes that the subjects assign non-degenerate probabilities to each of the given average contributions of the others. In case this is not true and the subjects assign a zero probability to one of the proposed contribution levels, the subject is indifferent with regard to the amount to state. In principle it could also be that contribution preferences do not depend on the average contributions, but rather on the distribution of contributions in the group or the strategy profiles of the others. 8 In a lab study implemented using a standard z-tree computer interface and a sample of Danish first year university students, we observe the same direction of the framing effect as in our Internet sample. Moreover, when we restrict attention to those participants in our Internet sample who reported that they were students, we also find the same direction of the framing effect. Taken together, the direction of the framing effect that we observe does not appear to be driven by the fact that our experiment was conducted with a nonstandard subject pool over the Internet. See more information about this comparison in Section 6 of the Supplementary information. 9 In the give frame 4.6% and 37.0% of the subjects contribute nothing and everything respectively, while this is the case for 8.7% and 51.0% of the subjects in the take frame.

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going from give to take increases contributions but leads to lower beliefs. In contrast, the direction of the framing effect on the variance is the same for contributions and beliefs, with the take treatment generating a higher variance. As for contributions, the use of extreme values of stated beliefs is substantially greater in the take frame compared to the give frame.10 To summarize how framing affects contribution strategies we categorize all subjects as one of three types (in the spirit of Fischbacher et al., 2001): Conditional cooperators: subjects whose contribution strategies indicate a positive correlation between their own contribution and that of other subjects.11 Free riders: subjects whose contribution strategies indicate a zero contribution irrespective of what others contribute, and others: subjects who do not fall into any of the two categories above. The effect of framing on the proportions of subjects with these types of contribution strategies is presented in Table 1. There is a substantial framing effect with less conditional cooperators and more free riders and others in the take than in the give frame. The difference in distributions between frames is highly significant using the Pearson's chi square test (p = 0.000). Table 2 presents the proportion of subjects who have misperceptions about how to implement the two goals (maximizing own and group income) we ask about. It is clear that a large proportion of subjects have such misperceptions and that there is substantially more misperception in the give frame than in the take frame (p = 0.000, Pearson's chi square test). This discrepancy between frames is driven by a higher fraction of subjects failing to understand what contribution maximizes own income in the give frame, whereas the ability to understand what behavior maximizes the group's income is generally easier and not different across framing (see Section 1 of the Supplementary information for a more detailed description). To summarize: framing has a highly significant effect on contributions and on our indicators of all three underlying causes or mechanisms through which this framing effect may work (beliefs, preferences, and misperceptions). Thus, off hand, it seems as if all three possible mechanisms for transmitting the framing effect to contributions may be important. To disentangle these and evaluate their relative importance, we estimate and simulate our developed model.

5. Estimating a model for decomposing framing effects In this section, we specify and estimate the structural model of framing, developed in Section 2, using our experimental data. In Section 6, we then use this model to decompose the total framing effect on contributions measured in our experiment into parts working through beliefs, preferences, and misperceptions. This allows us to quantify the relative importance of the possible mechanisms through which framing could work and to quantify the importance of any remaining unexplained framing effect on contributions. In the experiment, we measure the exogenous framing variable as well as 4 out of the 5 endogenous variables (misperception, contribution strategies, beliefs and contributions) introduced in the conceptual model (see Fig. 1). Although we do not observe cooperation preferences directly, we can nevertheless estimate the framing effect which works through them (arrow 4 in Fig. 1) since our conceptual model implies that any framing effect on contribution strategies, which does not go via misperception (which we observe), must go through cooperation preferences. By including a direct framing effect on contribution strategies in our estimations, we can therefore (under the assumptions of our conceptual 10 In the give frame 0.81% believed that the average contribution from other group members was nothing, whereas 18.3% believed everything was contributed. In the take frame however, these numbers were 4.3% for no contributions and 26.5% for everything being contributed. 11 More precisely, our definition is that the contributions are monotonically increasing and the relation between the contribution of the average of other group members' contributions has a positive and significant (at 10% level) Spearman rank.

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Fig. 2. Distribution of contributions for each frame.

model) interpret this as the effect of framing which works through cooperation preferences. Finally, we do not measure an indicator of unexplained framing effects directly. However, the direct causal links between framing and contributions provide us with a test of our conceptual model. If we do find a significant direct effect of framing on contributions (arrow 5 in Fig. 1) it will indicate that the conceptual model is incomplete and that there are important unexplained mechanisms which transmit the effect of framing into contributions. We therefore include this direct effect in the empirical model. Formally, the empirical specification of our model is the following recursive system: MisperceptionðmpÞ :

  mp ¼ g mp f r; x; emp

Contribution strategyðcsÞ : Belief ðblÞ :

cs ¼ g cs ðmp; f r; x; ecs Þ

bl ¼ g bl ðmp; f r; x; ebl Þ

Contribution ðcnÞ :

cn ¼ g cn ðpc; bl; f r; x; ecn Þ where pc ¼ f ðbl; csÞ

where fr is a frame dummy, x is a vector of exogenous control variables and emp, …, ecn are the stochastic variables which capture the effects of unobserved exogenous variables. We use an extensive battery of control variables including measures of cognitive ability, big five personality traits, gender, and age. 12 As the control variables include potentially important causes of correlation between equations (e.g. personality trait and cognitive ability) we assume that the stochastic variables (emp, ecs, ebl and ecn) are independent when estimating the equation system. In the estimations, misperception (gmp) is modeled as a binary probit. Beliefs (gbl) are modeled as a multinominal probit.13 Contribution

strategies (gcs) are modeled as a two-step process where a subject's strategy type follows a multinominal probit and the specific profile is selected randomly among the set of observed profiles for subjects of this strategy type, and with the same degree of misperception and under the same frame.14 Finally, contributions (gcn) are modeled as a multinominal probit15 where we followed Fischbacher and Gächter (2010) and first combined belief (bl) and contribution strategy (cs) to generate the subjects' preferred contribution (pc), and then used both preferred contribution and beliefs as explanatory variables in the estimation of the actual contributions. That is, by including both preferred contributions (which depend on beliefs) and beliefs in the final estimation, we allow beliefs to affect contributions beyond their role in generating the preferred contribution. Fischbacher and Gächter (2010) find clear evidence for this, and we want our empirical model to nest theirs. The preferred contribution, pc = f(bl, cs), is found as the contribution indicated in the subject's contribution strategy that corresponds to his stated belief about the average contributions of others. We include first-order effects of controls and both first and secondorder effects of endogenous explanatory variables (i.e. we include squared endogenous variables as regressors in all probit models). These specifications are quite flexible and imply that we impose less restrictive functional relationships on the key endogenous variables than other studies have done. For example, in addition to the linear functional form assumed by Fischbacher and Gächter (2010) for the contribution equation, a large class of other functional forms is accommodated. Table 3 gives an overview of the estimation results by presenting Wald tests of significance of each variable in each equation. Consistent with the experimental results the Wald tests indicate that the estimated models for all four equations are highly significant and that all the key variables (fr, mp, bl, and pc) are highly significant in all the equations where they enter as explanatory variables. Some control variables are significant in most equations, while others are only significant in one equation. The patterns we find seem reasonable. Cognitive ability, for instance, is not significant for the equations that determine

12

See the Supplementary information for a full description of the exogenous variables. The belief variable is in practice categorical since almost all subjects report beliefs that are divisible by 5. The few observations that were not a multiple of 5 (around 2% of the observations) were rounded to the nearest 5 kroner. 13

14 The last step is not carried out for perfect conditional cooperator and free rider types, since their profiles are given per definition. 15 Like beliefs, contributions were in practice rounded to the nearest multiple of 5.

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Fig. 3. Distribution of beliefs for each frame.

contribution, belief, and preference, but is significant for the misperception equation. This seems plausible since misperception concerns the ability to understand the game for which cognitive skills are a key resource whereas the other equations are more related to the subjects' behavioral attitude for which cognitive skills are not necessarily an important explanation. As indicated in Table 3, the Supplementary information presents the complete set of estimation results for each equation (these are very spacious because we run several estimations and because three of them are multinominal probit models). Inspection of these reveals that the patterns of estimated parameters seem consistent with the patterns of experimental results reported above. 6. Disentangling framing effects The estimated model reflects the underlying structure illustrated in Fig. 1. We can therefore use it to evaluate the relative importance of preferences, beliefs, and misperception for transmitting the framing effect on contributions and to evaluate the proportion of the total framing effect that is not transmitted through these mechanisms. For any given subject we can calculate the estimated model's prediction of her contribution (cn) in the take frame by inserting the subject's characteristics (x, emp, ecs, ebl, ecn) and fr = take into the four estimated model equations and solving them recursively. First we draw emp, …, ecn from the assumed distributions. Then, we insert (fr, x, emp) into gmp(.) to find mp and then in the same way we insert (mp, fr, x, ebl) into gbl(.) to find bl. By inserting (mp, fr, x, ecs) into gcs(.) we find the subject's contribution type. We then randomly allocate a specific contribution strategy (cs) from the set of strategies reported by subjects with the subject's contribution type and values of mp and fr. Thus the allocated contribution

strategies reflect the variation and likelihood of the strategies we have observed in our experiment for this type of subjects. Finally inserting (cs, bl) into f(.) we find pc and inserting (pc, bl, fr, x, ecn) into gcn(.) we find the models prediction of the subject's contribution (cn). By repeating this procedure after setting fr = give in all equations (but leaving the subject's characteristics (x, emp, ecs, ebl, ecn) unchanged) we can calculate the same subject's predicted contribution in the give frame. The difference between the predictions under the two frames gives us the predicted effect from changing the frame from take to give for a given subject characterized by (x, emp, ecs, ebl, ecn). We can then calculate the part of the total framing effect working through beliefs by repeating this calculation while only changing the value of the framing variable in the belief equation (i.e. leaving fr = take in the other equations). This procedure neutralizes the parts of the framing effect going through other determinants so that the calculated contribution change only reflects the part of the total framing effect that is transmitted through a framing induced change in beliefs. Thus, by only changing the framing variable for one determinant at a time we can identify the part of the total framing effect that is transmitted through each determinant as well as the remaining framing effect that is not transmitted through any of the modeled determinants. For this to be a meaningful decomposition of the total framing effect our model must be a good representation of the behavior of our subjects. We therefore initially check how well the model predicts our subjects' actual behavior in the experiment in a number of ways. First, we test if our model can predict our subjects' actual behavior (within sample). We compare the distributions of misperception, beliefs, contribution strategy types and contributions found in the experiment, with the corresponding distributions simulated by our model and find no significant

Table 1 Distribution of contribution strategies for each treatment.

Conditional cooperators Free riders Others ∑ Pearson's Chi2 (2)

Give (n = 1366)

Take (n = 676)

68% 15% 17% 100% p = 0.000

56% 21% 23% 100%

Table 2 Level of misperception for each treatment.

Misperception Correct perception Pearson's Chi2 (1)

Give (n = 1366)

Take (n = 676)

51% 49% p = 0.000

41% 59%

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differences between simulated and actual distributions. We then check if our model can predict out of sample behavior. We compare the distribution of contributions of subjects originally placed in the take (give) frame simulated for the give (take) frame with the distribution of actual contributions in the give (take) frame. Again, we do not find any significant differences between the distributions. We conclude that our model captures the systematic variation in our data well (a comprehensive description of the tests and results can be found in Section 5 of the Supplementary information). Initially, we simulate the total framing effect on contributions for our entire sample following the procedure above. We simulate the contributions for all subjects in the give frame (i.e. all frame variables set to give and all endogenous variables which enter equations are those simulated for the give frame). We then simulate the corresponding distribution of contributions when all subjects are ‘placed’ in the take frame (i.e. all frame variables set to take and all endogenous variables which enter equations are simulated for the take frame). In the following, we focus on how moving from the take to the give frame affects the mean and the standard deviation of the distribution of contributions.16 The simulated framing effect on the mean of contributions is the difference between the means of the simulated distributions for the two frames. Corresponding to this, the simulated framing effect on the standard deviation of contributions is the difference between the standard deviation of the simulated distributions for the two frames. The simulated total framing effect on the mean of contributions is shown in Fig. 4 (right bar), while the simulated total framing effect on the standard deviation of contributions is shown in Fig. 5 (right bar). The simulated effects correspond almost exactly to the observed framing effects in the experimental data. The indicated 5% confidence intervals around the simulated effects are found by bootstrapping (see, e.g. Efron and Tibshirani, 1993 or Varian, 2005).17 The bootstrapped confidence intervals are conditional on the functional form of the estimated model correctly reflecting the actual data generating process. However, given the models ability to reproduce our subjects' actual contributions this seems a reasonable assumption. Note also that the bootstrap confidence intervals for simulated framing effects on contributions take into account the added uncertainty of applying endogenous variables (mp, bl, cs) calculated from estimated equations rather than observed values. This is why the simulated net effect on mean contributions is insignificant while the framing effect on observed contributions reported in Section 4 is significant. Applying the same procedure, we then use the simulation model to decompose the total framing effect into the five paths depicted in Fig. 1. Starting with all subjects in the take frame, we only let the framing change affect one of the underlying mechanisms at a time. The five paths by which the original framing effect can be transmitted to contributions are: Framing via beliefs (arrow 1 in Fig. 1) Framing via misperception and beliefs (arrow 2 in Fig. 1) Framing via misperception and contribution strategies (arrow 3 in Fig. 1) Framing via preferences (arrow 4 in Fig. 1) Unexplained framing effect (arrow 5 in Fig. 1). In Fig. 4, we show the simulated partial framing effects on mean distributions and in Fig. 5 the corresponding partial effects on the contribution distributions standard deviation. See the Section 4 of the Supplementary information for more details on the simulation procedure. 16 Framing also significantly effects higher order distribution moments but the quantitatively most important effects are on the first two distribution moments. 17 We randomly draw subjects from the original subject pool with replacement and reestimate and re-simulate 250 times. We calculate differences in means and standard deviations of the resulting distributions each time. The presented effects in Figs. 4 and 5 are the means in the two distributions of calculated differences while the confidence interval is the 2.5 to 97.5 percentile span in the two distributions. See the Supplementary information for details.

Looking at Fig. 4, we see that though the net framing effect is small, there is a substantial framing effect through beliefs, which drives mean contributions up and a substantial unexplained framing effect, which drives mean contributions down. Thus, the increase in mean beliefs that we see as we move to the give frame has the expected effect of increasing contributions. However, a slightly stronger unexplained framing effect counteracts this and ends up causing a (small) net reduction in mean contributions. There is also a significant, but in comparison small, increase in mean contributions working through misperception. Interestingly the relatively small total framing effect on mean contributions (Fig. 4) masks a relatively large framing effect on the standard deviation of the distributions (Fig. 5). Thus, even though mean contributions do not change much; the subjects' contribution behavior is in fact affected substantially by framing. From Fig. 5 it is clear that the framing effects on beliefs can explain most of the total framing effect on the standard deviation of the contribution distribution. All the other effects, including the unexplained effect, are small and insignificant (though the confidence interval around the unexplained effect is relatively large). Thus, the substantial reduction in belief variance in our data, can explain most of the reduction in contribution variance. From the decomposed effects in Figs. 4 and 5, it is clear that compared to beliefs, the framing effects working through misperception and preferences are small. The estimated effects for both mean and standard deviation are close to zero and standard errors are quite tight around this. Even though misperception has a significant and important effect on contribution strategies the effect this has on the distribution of contributions, while still statistically significant on mean contributions, is small compared to the effect of the framing induced change in beliefs. The effect on the distribution of contributions that we identify as going through a change in preferences is not significant. Although the confidence intervals around the preference effects are larger than around the misperception effects it seems safe to conclude that if there is an effect over preferences it is small compared to that of beliefs. In addition to the importance of effects going through beliefs we also identify an unexplained framing effect on mean contributions of the same magnitude but the opposite direction. One possible reason for the unexplained effect could be that subjects are more uncertain about what others will do in the take frame than in the give frame. This is compatible with the greater heterogeneity of beliefs in the take frame. If subjects feel worse about giving too little than about giving too much compared to others, the greater uncertainty could then explain the substantial unexplained negative effect on mean contributions in Fig. 4. Subjects that are uncertain about their beliefs in the take frame may insure against the risk of giving less than others by contribution over their point beliefs. As subjects become more certain of beliefs in the give frame, they are less prone to insure themselves by contributing over their point beliefs. Taken together, moving to the give frame increases mean beliefs and reduces subjects' uncertainty (which could be why belief heterogeneity decreases). The effect of this would be a reduction in the heterogeneity of contributions (which we observe), an increase in mean contributions because of the increase in mean beliefs (as identified by our simulation) and at the same time reduced insurance contributions because of less uncertainty about beliefs (causing the negative unexplained effect).18 However, this is just a speculation. The unexplained framing effect could also be caused by mechanisms outside our model. At any rate, the fact that we find two 18 One way to view this is that, in the give treatment, there is less uncertainty regarding the social norms governing the choice situation. This is consistent with people spending more effort on understanding the game in the take frame which was argued in Fosgaard et al. (2011). Regarding the effects of norm uncertainty and framing, Dreber et al. (2013) argue that higher norm uncertainty in the generalized ultimatum game (in which the responder can only reduce the proposer's payoff by a small fraction) compared to the dictator game (in which the responder cannot affect the proposer's payoff at all) may explain why framing matters in the former game but not in the latter. Their reasoning is that framing is less influential in situations with a clearly established norm such as in the dictator game.

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Table 3 Wald tests of explanatory variables.

Frame (fr) Misperception (mp) Belief (bl) Belief2 Preferred contribution (pc) Preferred contribution2 Agreeableness Conscientiousness Extroversion Neuroticism Openness Cognitive ability Age Gender (1: female, 0: male)

Equation 1

Equation 2

Equation 3

Equation 4

Misperception (mp)

Contribution strategy (cs)

Belief (bl)

Contribution (cn)

20.4⁎⁎⁎

35.5⁎⁎⁎ 215.0⁎⁎⁎

116.2⁎⁎⁎ 24.2⁎⁎⁎

102.8⁎⁎⁎

12.7⁎⁎ 3.6 10.3⁎⁎ 7.4 6.5 7.7 24.6⁎⁎⁎ 10.2⁎⁎

29.2⁎⁎⁎ 10.9 9.9 11.4 9.2 9.5 51.3⁎⁎⁎ 30.5⁎⁎⁎

0.7 3.7⁎ 7.2⁎⁎⁎ 3.4⁎ 1.8 79.6⁎⁎⁎ 0.1 0.17

More information: Section in Supplementary information presenting the full estimation result: Type of model estimated Overall model significance (Wald test score and p value in brackets)

Section 3.1 Probit 129.7 (0.000)

Section 3.2 Multinominal probit 346.4 (0.000)

Section 3.3 Multinominal probit 297.1 (0.000)

207.2⁎⁎⁎ 213.0⁎⁎⁎ 37.2⁎⁎⁎ 37.4⁎⁎⁎ 21.1⁎⁎ 11.2 15.3 15.8 17.1⁎ 10.8 19.8⁎⁎ 10.76

Section 3.4 Multinominal probit 1072.4 (0.000)

The shown numbers are the Wald Chi-square test statistics for setting all coefficients of the indicated variable to zero in the indicated multinomial equation.⁎⁎⁎ p b 0.01. ⁎⁎ p b 0.05. ⁎ p b 0.1.

find a small and insignificant effect of framing effects working through preference changes. 7. Conclusions We investigate framing effects in a game of public good production. We measure indicators of beliefs, misperceptions and preferences which are the three main explanations proposed in the literature and use a substantially larger subject pool than prior studies. This enables us to estimate a structural model which captures all three causal effects and the behavioral heterogeneity of our subject pool while controlling for unexplained effects. The structural model allows us to decompose the total framing effect into parts working through each of these causal mechanisms. We find that framing has only a small effect on the average level of cooperation, but that this masks a substantial framing effect working via beliefs which is neutralized by an equally sized unexplained framing effect working in the opposite direction. Perhaps more important, we find a substantial framing effect on behavioral heterogeneity across our subjects. Cooperative behavior is

5%

+

+

+

=

- 5%

0

+

- 10% - 15 %

Change in mean contribution

10%

strong underlying framing effects with opposite signs fits well with the mixed results on the direction of the net framing effect on mean contributions in the literature. When a relatively small net effect is caused by two large opposite underlying effects of the same magnitude, small changes in setting, subject pool, etc. can cause the sign of the net effect to change. Our results are in line with recent studies that find important framing effects which work through beliefs (Dufwenberg et al., 2011; Ellingsen et al., 2012; Sonnemans et al., 1998). We add to this in several ways. First, our results show that framing which works through beliefs has an important effect on the variance of the contribution distribution in addition to the effect on mean contributions (which has been the sole focus of earlier investigations). We also provide sound evidence indicating that in comparison the two other proposed explanations (framing induced changes in preferences and misperception) have a negligible effect on the distribution of contributions. Our study incorporates the significant effect of misperceptions on contribution strategies shown on the same data set by Fosgaard et al. (2011). However, the effect that this change in contribution strategies has on subjects' actual contributions is small compared to the effect of changing beliefs. Finally, we

1. Belief

2. Misperception 3. Misperception via preference via belief

4. Preferences

5. Unexplained

Total

Fig. 4. Simulated effects (and 95% confidence intervals) on mean contribution when moving all subjects from the take frame to the give frame.

T.R. Fosgaard et al. / Journal of Public Economics 120 (2014) 134–143

+

+

=

+

-10%

0

+

-20% -30%

Change in standard deviation

10%

142

1. Belief

2. Misperception 3. Misperception via belief via preference

4. Preferences

5. Unexplained

Total

Fig. 5. Simulated effects (and 95% confidence intervals) on the standard deviation of contributions when moving all subjects from the take frame to the give frame.

much more heterogeneous in some settings than in others and we show that this can be explained almost exclusively by a corresponding change in the heterogeneity of beliefs about other subjects' cooperative behavior. In contrast, we find that the impact of framing on both the mean and variance of cooperation transmitted through changes in preferences and game form misperception is small in comparison. The finding of preference stability across frames corroborates a stream of recent studies from different contexts such as social dilemmas (e.g. Ellingsen et al., 2012), dictator games (Dreber et al., 2013) and preference elicitation (Cason and Plott, forthcoming). An important implication of our results is the observation that even when changes of setting for a cooperative venture have little effect on the mean level of cooperation, there can be substantial changes in the heterogeneity of cooperation driven by changes in the heterogeneity of beliefs. Cooperation is often repetitive in nature so that beliefs are quickly aligned once cooperation gets under way, however, the initial heterogeneity in beliefs and cooperation can be critical for the likelihood of a cooperative venture being undertaken in the first place. Our result suggests that subtle and economically irrelevant changes in setting can have substantial effects on initial belief and cooperation heterogeneity and through this has potentially important effects on the likelihood of cooperation ventures being initiated. Investigating the effects and causes of belief heterogeneity would seem a promising avenue of investigation. The sizeable unexplained framing effect on mean contributions also warrants further investigation. We conjecture that the unexplained effect is linked to belief uncertainty and hence related to the differences in belief heterogeneity between frames that we observe. Finally, we hope that we have demonstrated the usefulness of combining experimental investigations and structural modeling to disentangle potential explanations and that this approach may prove useful for other researchers.

Acknowledgments We gratefully acknowledge the generous funding provided by the Carlsberg Foundation. Wengström is grateful for the financial support from the Wallander-Hedelius Foundation. We are deeply thankful to Jean-Robert Tyran for initiating and administrating the large-scale experiment upon which this paper is built. We thank Steffen Andersen, Giovanna Devetag, Tore Ellingsen, Peter Martinsson, Marco Piovesan and conference participants at the 6th and 7th Nordic Conferences on

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