Experimental evidence shows that utility models incorporating other-regarding preferences often explain choice data better than the classical economic model with selfish actors. Consequently, numerous social preference models have been proposed and many such model have received great attention in the literature. (For example, according to our most recent search of Google Scholar on November 21, 2012, Fehr and Schmidt’s [3
] inequality aversion model is cited 5299 times, approaching the 7454 citations of Adam Smith’s “The Theory of Moral Sentiments”). It is also acknowledged that there is heterogeneity in preferences, i.e
., some actors are selfish, whereas some actors have other-regarding preferences to varying degrees (e.g., [3
]). This heterogeneity is often invoked as an important factor to explain why, under some experimental conditions, results seem to converge to the classical economic model’s predictions, while under other conditions, results deviate significantly from the classical model.
Introducing other-regarding preferences in micro-economic models and acknowledging heterogeneity in preferences, however, creates the need to also model actors’ beliefs about others’ preferences. In many cases (without dominant equilibria), predictions of micro-economic models depend strongly on actors’ beliefs about others’ behavior. Beliefs about others’ behavior, in turn, depend on actors’ beliefs about others’ preferences. Thus, modeling actors’ own preferences is necessary but not sufficient to obtain behavioral predictions. In addition to actors’ own preferences, actors’ beliefs about others’ preferences should also be dealt with. Otherwise, empirical tests of utility models are incomplete because the observed behavior could be the result of not only own preferences, but also beliefs about others’ preferences. In the behavioral economics literature uncertainty about others’ utilities, thus beliefs about others’ preferences are typically dealt with via the application of the Bayesian-Nash equilibrium [5
] with “rational beliefs” (e.g., [3
]). Beliefs are assumed to be independent of own preferences, and actors are assumed to know the actual distribution of preferences in the “population”. While making sense theoretically, this concept may not be empirically solid. Social psychology studies often demonstrate clear biases in expectations, as summarized by the “false” consensus hypothesis [6
], the triangle hypothesis [7
], or the Cone model of Iedema [1
] indicating that actors’ own social preferences and expectations about others’ social preferences may not be independent. See also [8
] for a critic of Bayesian-Nash equilibrium within the experimental economics context. We investigate actors’ beliefs about others’ preferences empirically. Particularly, we focus on the relationship between own preferences and beliefs about others’ preferences.
There is a rich literature on belief formation and learning (recent examples include [10
]) which are not among the topics of the current paper. Comparable existing studies on beliefs in the micro-economics literature focus mainly on the relationship between the actor’s behavior
and the actor’s beliefs about others’ behavior
]), or between the actor’s preferences
and the actor’s beliefs about others’ behavior
]). In our view, a micro theory, such as a social utility model, should be the theoretical basis of the analysis of both the actor’s own behavior and the actor’s beliefs about others’ behavior. If we are to explain actors’ own behavior with a utility model, we should also explain actors’ beliefs with the same utility model. Thus, the distinctive feature of our study is that we explicitly analyze the relationship between actors’ own preferences
and their beliefs about others’ preferences
, nested in the same utility model. We estimate two other-regarding preference parameters for a variant of the Charness and Rabin [18
], an extension of Fehr and Schmidt [3
] utility specification, using choice data in binary Dictator Games. Simultaneously, we estimate the moments of the distribution of actors’ beliefs about others’ other-regarding preferences, conditional on own other-regarding preferences, with incentivized belief elicitation. To be clear, analyzing the relationship between preferences and beliefs about others’ preferences, we deviate from rational beliefs –yet rational beliefs remain a special case of our model where the aforementioned relationship is absent–. However, we do assume that people’s preferences are described by the utility model we use, and
people think that other people’s preferences are given by the same utility model.
Because the main focus of this study is on the relationship between beliefs and preferences, we restrict our attention to a single utility model, namely a variant of Charness and Rabin [18
], which is an extension of the inequality aversion model of Fehr and Schmidt [3
]. Although we provide an assessment of empirical fit of the model, the primary aim of this paper is not
testing the utility model used in this paper or finding the utility model that best explains our data. This has been done extensively in the literature. We are aware of other relevant social motives and other successful models of other-regarding preferences (e.g., [19
]). Yet, because the model of Charness and Rabin [18
], and of Fehr and Schmidt [3
] which is contained in Charness and Rabin are among the most cited and applied social utility models, describing the relationship between actors’ own motives and beliefs within this framework is useful. In addition, in our study, we use data on simple Dictator Games. In such games, preferences given by the model used here are in line with other potentially relevant types of motives, e.g., maximin preferences and inequality aversion. Finally, variants of other-regarding preferences given by Charness and Rabin [18
] are a common theme in other disciplines such as social psychology (e.g., [23
]), and rational choice sociology (e.g., [24
]). Thus, our results would be relevant for a variety of disciplines. In addition, the simple shape of the function we use yields substantial convenience in statistical analyses.
An important contribution of this paper, however, is it’s statistical methodology. We use a hierarchical Bayesian method to estimate the other-regarding preferences and the moments of the distribution of actors’ beliefs about others’ other-regarding preferences. Hierarchical Bayesian methods have some practical advantages over their hierarchical frequentist counterparts [26
]. First and foremost, incorporating strong numerical estimation procedures, Bayesian methods are very flexible. They could be relatively easily applied to many complex statistical models. Relying on the maximum likelihood approach, however, frequentist methods are limited in this sense. For example, the simultaneous analysis of own other-regarding preferences and beliefs that we perform in this paper is nearly impossible within the frequentist framework. In addition, the Bayesian approach provides a strong and flexible tool to assess model fit via posterior predictive sampling [27
], which we exploit in the current paper. Assessing model fit for relatively complex models as ours within the frequentist framework is, again, very difficult. In addition to those practical advantages of Bayesian methods, given that one uses fairly uninformative priors the results of the Bayesian methods converge to “would be" Maximum Likelihood estimates [26
]. In other words, (some of) the Bayesian results obtained using uninformative priors may be interpreted as frequentist estimates. Our statistical analysis is implemented in OpenBugs [29
]. We provide the estimation routine as a supplementary file so that other scholars could replicate, modify, and apply the routine.
The main results of the hierarchical Bayesian analysis are the following:
Result 1: There is a strong increasing monotonic relationship between own other-regarding preferences and beliefs about average other-regarding preferences.
Result 2: There is a U-shaped association between own other-regarding preferences and beliefs about the variance in others’ other-regarding preferences for one of the two parameters in the utility model, namely α. For the other β parameter, the same relationship is insignificant.
Result 3: The utility model that we use and the model for beliefs that we develop below explain the choices and beliefs of subjects in binary Dictator Games adequately.
We want to elaborate on how this current paper improves on a previous study of the authors [2
]. In the current paper we use a richer dataset, combining data from two experiments. Thus statistical power is improved. Second, [2
] employs a different
other-regarding preference model, namely the social orientation model, a model predominantly used in social psychological literature. In the social orientation model in [2
], actors are interested in absolute inequality as they are assumed to not differentiate between advantageous and disadvantageous forms of inequality. Despite using a different utility model in this paper, we still find some support for the cone effect. This further reinforces the existence of the cone pattern, at least for some type of other-regarding preferences. Thirdly, and most importantly, [2
] uses a two step estimation method that predicts individual social preference parameters in the first step, and in the second step uses these individual estimates to model beliefs. As we acknowledge in [2
], this two step estimation procedure is flawed as in the second step it does not take into account measurement error in the first step. In this paper, the Bayesian estimation routine solves this problem as simultaneous estimation of preferences and beliefs becomes possible.
The organization of the paper is as follows. After describing the experimental procedure, we describe the model for other-regarding preferences and beliefs in detail. We then move on to the details of the hierarchical Bayesian analysis where we briefly compare the Bayesian method with a frequentist alternative. A final discussion of the main results concludes the paper.
5. Discussion and Conclusions
In this study, we investigate the relationship between an actor’s beliefs about others’ other-regarding preferences and her own other-regarding preferences using a hierarchical Bayesian method. We estimated the other-regarding preferences parameters, α and β, of actors using choice data from binary Dictator Games. Simultaneously, we estimated the distribution of actors’ beliefs about others’ α and β, conditional on own α and β, with incentivized belief elicitation. We demonstrated some advantages of the Bayesian method over its hierarchical frequentist counterparts including its flexibility in dealing with relatively complex models with many free parameters, as well as the possibility of a sound assessment of model fit even for complex models using posterior predictive sampling.
Besides describing the benefits of the hierarchical Bayesian method, the paper presents interesting results. We found that there is a positive monotonic relationship between own other-regarding preferences and the belief about average
other-regarding preferences. This is not an unprecedented finding (e.g., [8
]), although our study is perhaps novel in demonstrating this relationship in light of a specific preference model. What is probably more novel is that we also found a strong U-shaped association between own other-regarding preferences and variance
in beliefs about others’ other-regarding preferences for the α
parameter. This result can also be interpreted in the following way. Selfish actors, i.e.
, those with approximately zero α
, also expect most others to be selfish as well. Thus, these selfish actors fit the classical economic model in terms of both their preferences and their beliefs. As α
deviate from selfishness, however, actors expect more variation in the population while still expecting others to be similar to themselves on average. The association between preferences and variance in beliefs for the β
parameter however is insignificant. Another finding to be noted is that variance in beliefs is in general much higher for the α
parameter than for the β
Why beliefs vary with own type and mechanisms yielding the particular relationships between own motives and beliefs that we describe in this paper is an open question. This question is tackled mainly within social psychology. We hope that our study will bring the social psychological literature on the relationship between types and beliefs about others’ types to the attention of experimental economists. The positive relationship between own preferences and beliefs about preferences in the population is in line with what social psychologists call the “false" consensus effect [6
The consensus effect literature typically does not investigate variance
in beliefs (or uncertainty) about others’ preferences. Consequently, our result on the relationship between own other-regarding preferences and expected variance of others’ preferences is as novel in the social psychological literature as it is for economics. The triangle hypothesis [7
], structured assumed similarity bias [47
], and the cone model [1
] are three hypotheses proposed in the social psychological literature each of which indirectly proposes a certain relationship between own preferences and expected variance in others’ preferences. We refer to [2
] for a detailed description of those hypotheses. Among those three hypotheses, our results support partially the cone model. The cone effect, as discussed by [1
] is caused by several factors. We apply those factors to the context of this paper. First, in line with the consensus effect all types –actors with certain values of
– expect their own type to be more common in the population. Secondly, in addition to their own types, all types expects selfishness to be another common type in the population, because selfishness is a common stereotype about others. These two effects overlap when the expectations of selfish people are considered. As a result, expected variance is smaller for selfish people. We should note, however, that the cone effect is observed for the α
parameter. For the β
parameter variance in beliefs is stable, that is, it does not depend on own β
. Without further research, we can only speculate why the cone pattern emerges for the α
parameter but not for the β
parameter. As the social psychological literature shows, biases in beliefs such as the cone or the consensus effects are stronger for situations where information is scarce and uncertainty is high [6
]. Our findings show that uncertainty about others’ preferences is much higher for the α
parameter than that for the β
parameter as the variance in beliefs is smaller for β
than for α
. In line with this, also the relationship between own other-regarding preferences and the belief about average
other-regarding preferences is much stronger for α
than for β
. Thus, probably the cone and the consensus effects are stronger for the α
parameter because subjects are more uncertain about others’ α
than others’ β
Irrespective of the exact causal mechanisms, these clear associations between own other-regarding preferences and beliefs about others’ other-regarding preferences that we document in this paper call for more elaborate and accurate application of other-regarding utility models. In the experimental economics literature, beliefs are typically assumed to be rational. That is, actors are assumed to know the actual distribution of preferences, and this distribution is independent of own preferences. We showed that these assumptions are problematic. If one disregards egocentric biases in beliefs by assuming rational expectations, one may obtain misleading results, such as incorrect predictions or inflated/incorrect estimates of social motives. Without modeling beliefs, modeling social preferences is not enough to derive accurate behavioral predictions for many interaction situations. We also hope that our findings on the distribution of own other-regarding preferences, beliefs about others’ other-regarding preferences, and the relationship between the two will provide an empirical basis for future theoretical work that may incorporate these biases in beliefs into more complex game-theoretic models.
Before closing, we want to address some methodological caveats. As we explicitly discuss in the methods section, in our experimental design subjects decide in multiple binary Dictator Games. Additionally, a subject is paired with multiple other subjects as a recipient. We pay for all decisions, dictator and recipient. We analyze data assuming that subjects treat each Dictator Game as a one-shot game, rather than all games as one big game. This is a potentially problematic assumption. We believe that this feature of our design corresponds to a more general and important methodological issue in the literature. To estimate other-regarding preference parameters with good statistical precision, one needs several conditionally independent observations from each subject and a relatively large subject pool. Similarly, constraining subjects to play in a single decision role, e.g., the dictator or the recipient role reduces the sample size substantially. Paying for all decisions has the potential drawback that a subject may not treat a particular game independent from other games, e.g., maximize utility over all sets of games. It is possible to devise statistical models to analyze choices taking potential dependence between games. Yet, we think it is unlikely that subjects are maximizing utility over all games. Thus, even one could adapt the statistical model to include potential dependences between a subjects’ choices over several games, such a model would be implausible, at least for most subjects. An alternative payment protocol, paying for a randomly selected game instead of all games may solve this potential dependence problem. In simple single person setups, paying for all or paying for a randomly selected game does not seem to matter [48
]. However, paying for a randomly selected game has its own problems in situations that involve more than 1-person, such as Dictator Game. For example, [48
] shows that introducing a random payment scheme may reduce the influence of game outcomes on choice by introducing potential path-dependent utility. Thus, it is not clear if random payment protocol solves the problem at all. We think that this is an important methodological issue and leave the discussion to future research that will systematically compare the repercussions of using alternative designs and payment methods.