Motives for giving: a reanalysis of two classic public goods experiments.

• Author: Ashley, Richard

1. Introduction

   One of the primary social problems studied by economists is how to fund the provision of public goods. What makes the public goods problem so interesting is the tension between the theoretical equilibrium prediction that the level of voluntary contributions should be zero and the common result in the lab and in the field that public goods are nevertheless produced. The theorists' response has been to develop and calibrate new theoretical models that are consistent with observed behavior across a variety of games including the public goods game (for example, Andreoni 1989, 1990; Fehr and Schmidt 1999; Bolton and Ockenfels 2000).

   Experiments have been used to investigate the factors affecting levels of public good provision and to examine alternative theories of giving. For the most part, experimental research has focused on the Voluntary Contribution Mechanism (VCM), where the quantity of the public good is a linear function of contributions, as a vehicle for examining the public goods problem (see Ledyard 1995 for a survey). Experimental results typically show contributions that are substantially above what theorists expect, but that nevertheless fall below socially optimal levels. Much has been discovered about average behavior in many variations of this game, and regularities in behavior from VCM experiments and other types of games have provided fodder for the development of new theories.

   In this article we mine the archive of data from two classic studies in search of evidence to support or refute theories about the motives for individual behavior. These two studies were originally designed with specific research goals in mind and focused on the response of aggregate giving to differences in the experimental parameters. The focus of the field is now reoriented toward the study of individual-level behavioral motivations. Our work highlights the extent of subjects' response to information about the behavior of other group members and the implications of the resulting dynamic patterns in the data for proposed theories. As with many studies using field data, we examine new theories using data sets collected for a different purpose. An obvious advantage to this approach is that new analysis of old data also provides a low-cost alternative to new experiments for distinguishing among theories.

   The nature of subjects' responses to others' decisions can help distinguish alternative motives for giving. Pure altruism implies that, because subjects care only about the total amount of the public good produced, they will decrease their contributions in response to an increase in giving by others (Andreoni 1990). Pure warm glow predicts that a subject will be unresponsive to the donations of others, because they care only about their own contribution to the public good. Reciprocity (Gintis 2000, ch. 11; Dufwenberg and Kirchsteiger 2004) suggests that subjects may try to coordinate on a level of giving; that is, as Kurzban et al. note, "players are generally willing to contribute to the public good only if others are doing so at similar levels" (2001, p. 1665). Inequality aversion (Fehr and Schmidt 1999; Bolton and Ockenfels 2000) also implies that, with common endowments, subjects will seem to coordinate on a common level of giving.

   The difference between the implications of the latter two has to do with the asymmetry of response. Theories of reciprocity predict only

   that agents will try to do what other members of their group do. In contrast, the Fehr and Schmidt theory of inequality aversion can be distinguished from general reciprocity in that it allows for the possibility that agents will respond differently when their contributions are above rather than below average. To preview, our results from analysis of the dynamics in the data support reciprocity in the form of inequality aversion as a motive for giving but little for reciprocity in the form of matching of others' contributions, less for warm glow, and least for pure altruism.

   Experimental studies are often designed in order to distinguish between alternative theories. This type of experiment is designed so that different motivations produce different decisions. An excellent example of such a study is Engelmann and Strobel (2004), where subjects make choices among several possible allocations for themselves and two other persons. The allocations are designed specifically to parse motives for giving. Our research approach is different and has more in common with studies using observational data. We examine these theories using data sets collected for a different purpose. The data sets we choose for this project are from well-cited works examining aspects of public goods giving, enhancing the value of revisiting and reanalyzing their results in light of theoretical and econometric advances in the field. An obvious advantage to this approach is that new analysis of old data also provides a low-cost alternative to new experiments for distinguishing among theories.

   Of course, we are not the first to study individual effects or dynamics in VCM data. (1) Solow and Kirkwood (2002) look for relationships between gender, group identity, and contributions; they account for censoring but not dynamics. Other studies have shown that manipulating information can significantly affect the level and dynamic pattern of contributions. Selective announcement of information about others' contributions (as in Harbaugh 1998; Kurzban et al. 2001; Houser and Kurzban 2005), use of "robot" or predetermined decisions to vary the feedback subjects receive (for example, Ferraro and Vossler 2010) or the announcement of an initial large contribution (Vesterlund 2003; Andreoni 2006) can substantially affect subjects' actions. Gunnthorsdottir, Houser, and McCabe (2007) consider dynamics and censoring but adopt a limited specification of individual effects. Croson, Fatas, and Neugebauer (2005) compare giving in VCM and weakest link mechanism games, and they find strong evidence that subjects attempt to match others' contributions. Chaudhuri, Graziano, and Maitra (2006) study the effect of intergenerational advice in a linear VCM. Bardsley and Moffatt (2007) use data from a unique variation on the VCM to estimate a mixture model to distinguish altruists from reciprocators.

   The analysis in the articles by Chaudhuri, Graziano, and Maitra (2006), Croson, Fatas, and Neugebauer (2005), Ferraro and Vossler (2010), and Houser and Kurzban (2005) is most similar to our own, and the paper by Bardsley and Moffatt (2007) has a related structure. These authors econometrically model subjects' reciprocity, that is, their response to information about previous period outcomes. All find that giving is positively related to the giving of others for at least a fraction of subjects. Importantly, however, none of these studies allow for asymmetric response by subjects to situations where they are above or below average giving. Allowing for asymmetric response is necessary to permit testing of the full range of theories we examine. (2)

   A secondary contribution of our approach is that it allows us to test for differences in dynamics induced by the common practice of randomly rematching subjects. (3) This methodology was developed in order to induce strategic independence of decisions from period to period. We find strong dependence between rounds for the randomly rematched sample, suggesting that this technique fails at its intended purpose.

2. Motives for Giving

   The Voluntary Contribution Game is structured as follows. Subjects typically are divided into groups of 2 to 10 persons. Each subject is given an endowment that must be allocated between a private account and a group account. The private account provides a fixed return per unit to the individual. Contributions to the group account pay to each member of the group the marginal per capita return (MPCR) times the total of the group's contributions. For example, for each dollar invested, the private account might return $1, while the group account returns $0.50 to each member of the group. The game is repeated for a number of rounds.

   Experimental research on public goods has focused largely on the VCM (see Ledyard 1995). Subjects are divided into groups and given an endowment to allocate between a private and a group account. The private account provides a fixed return; contributions to the group account pay to each member MPCR times the total of the group's contributions, with MPCR > 1/n, where n is the number of subjects. This creates a tension between socially optimal and payoff-maximizing strategies.

   For a purely self-interested player, the dominant strategy in the VCM is to contribute zero. Because most subjects make positive contributions, it is clear that they analyze the game differently or have different motives. We focus on four such motives--altruism, warm glow, and two types of reciprocal...