Theories of Commitment, Altruism and Reciprocity: Evidence from Linear Public Goods Games



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Theories of Commitment, Altruism and Reciprocity: Evidence from Linear Public Goods Games

Rachel T.A. Croson

CrosonR@opim.wharton.upenn.edu

April, 1998



Abstract
Theories of commitment, altruism and reciprocity have all been invoked to explain and describe observed behavior in public goods and social dilemma situations. In particular, commitment theories have been used to explain behaviors like water conservation and voting. Theories of altruism are applied in explanation of contributions to charities and intergenerational transfers and bequests. And theories of reciprocity have been invoked to explain gift exchange and labor market decisions. This paper describes a set of experiments which distinguish between these competing theories by testing their comparative statics predictions in a linear public goods setting. Results provide strong support for reciprocity theories over either theories of commitment or of altruism.
Keywords: Reciprocity, Altruism, Experimental economics, Public goods, Charitable contributions
JEL Classification Codes: C9, D64, H41, C72

________________________

*The author thanks Jon Baron, Yan Chan, Robyn Dawes, Jerry Green, Elizabeth Hoffman, Mark Isaac, Eric Maskin, Sara Solnick, Lise Vesterlund, George Wu, participants at the Economic Science Association Fall Meetings as well as seminar participants at the University of Pennsylvania and the University of Iowa for helpful comments. All omissions or mistakes are the responsibility of the author. Funding of experiments from the Economic Science Lab at the University of Arizona is gratefully acknowledged.

1. Introduction

US individuals made over 100 billion dollars of philanthropic contributions in 1995 (Giving USA, 1996). This behavior is inconsistent with traditional utility theory in which individuals care only for their own consumption. A number of alternative theories have been invoked to explain such philanthropic behavior in this and other settings. This paper describes a set of experiments which distinguish between three competing theories: commitment, altruism and reciprocity, by testing their comparative statics predictions in a linear public goods setting.

In commitment theories, individuals choose the actions they would most prefer everyone would choose (Laffont, 1975; Harsanyi, 1980). Thus they choose the action which maximizes their private payoff assuming that everyone else chooses the same action they do. Commitment theories are consistent with observed philanthropic behavior, voluntary cooperation in social dilemmas like water conservation (Laffont, 1975), tax evasion (Baldry, 1987), and voting (Struthers and Young, 1989) as well as voluntary contributions to public goods.

In altruism theories, the consumption of others appears positively as an argument in an individual’s utility function (Becker, 1974; Andreoni, 1989, 1990). Models of altruism are also consistent with observed philanthropic behavior and have been used to explain intergenerational bequests (Becker, 1974), social security and other welfare systems (Coate, 1995), and helping behavior in the workplace (Rotemberg, 1994) as well as voluntary contributions to public goods.

In contrast, Sugden (1984) proposes a theory in which the principle of reciprocity acts as a constraint on traditional individual utility maximization. The principle says (roughly) that an individual may not free, cheap or easy ride when others are contributing. Models of reciprocity are also consistent with observed philanthropic behavior (when others are contributing) and have been used to explain individual behavior in tax evasion (Bordignon, 1993), helping in the workplace (Frey, 1993) and labor markets (Akerlof, 1982, 1984; Fehr and Gachter, forthcoming) as well as voluntary contributions to public goods.

This paper presents four separate experiments designed to distinguish between these theories by comparing their comparative statics predictions. The results of the first experiment (presented in section 4) demonstrate a significant and positive relationship between an individual's own contribution and his beliefs of the contributions of others in his group, consistent with theories of reciprocity and inconsistent with traditional self-interested theories or theories of commitment or altruism. The second and third experiments (presented in section 5) test the robustness of the first experiment by comparing an individual’s own contributions and the actual contributions of others in his group in different settings. Similar results are generated. The final experiment (presented in section 6) further investigates the specific type of reciprocity our subjects demonstrate. We find evidence for middle reciprocity, where players try to match the middle (or average) contribution of the rest of his group, rather than the minimum or maximum.

This paper is organized as follows. Section 2 briefly describes the public goods production function and the voluntary contribution mechanism used in this experiment. Section 3 outlines the three classes of theories and their implications. In section 4 we present the experiment and results designed to distinguish between the competing theories. Section 5 describes two additional experiments designed to test for the robustness of our results. Section 6 describes another experiment which investigates individual behavior in more detail. Finally, section 7 concludes.
2. Pure Public Goods and the Voluntary Contribution Mechanism

Pure public goods are goods that are both nonrival and nonexcludable. The experiments described in this paper use a linear and pure public good to distinguish between our competing hypotheses. The mechanism used to fund the public good is the voluntary contribution mechanism which most closely parallels philanthropic giving or contributing behavior. This mechanism has been examined extensively in previous literature (see Davis and Holt, 1994, chapter 6 and Ledyard, 1995 for complete reviews).



A. The Mechanism

The mechanism is structured as follows. Assume each player i in a group of N identical players has some endowment Ei which can either be contributed to a group account and used to produce units of a public good or can be privately consumed. Call the amount contributed to the group account by i, xi. The individual’s earnings from private consumption is simply the amount consumed (Ei- xi). The individual’s earnings from contributions to the group account is a multiple of the sum of contributions by all participants in the group P(iNxi).

There is a pure public goods problem whenever

This mechanism of contributions to the public good in this game is purely voluntary, similar to the institution of charitable contributions.



B. Related Experiments

Marwell and Ames (1979, 1980, 1981) were the first to test public goods provision behavior in a linear and pure public good using the voluntary contribution mechanism. They find that when subjects play a one-shot, context-free public goods game they contribute around half their endowment to the public good and consume the rest.

Later research suggests that when subjects play a the same public goods game finitely repeated (with a subgame-perfect equilibrium of full free riding), contributions in the first period are similar to those observed in Marwell and Ames, but decrease over time toward the free-riding solution (Davis and Holt, 1994; Ledyard, 1995). Although contributions reach their lowest point in the last period of the game, they do not quite reach the equilibrium outcome of full free riding.

In the first of our experiments, we elicit subjects’ beliefs about the contributions of their group and compare those beliefs with their contributing behavior. Some previous experiments have attempted to investigate the relationship between an individual’s belief and their actions in public goods settings. However, most have deceived subjects about the true contributions of the other players (e.g. Messick et al., 1983; Schroeder et al., 1983; Poppe and Utens, 1986; Fleishman, 1988; Weimann, 1994). There is also a large literature in psychology on belief elicitation and manipulation in prisoners’ dilemma games.

In contrast to most of this previous literature, in the experiment presented in this paper, no deception is used. Instead, players’ beliefs of other players’ behavior are elicited and compared with the players’ own contributions.
3. Three Theories and Hypotheses

In this section we present three types of theories which have been used to explain economic behavior in various settings (including the voluntary provision of public goods) and between which we would like to discriminate; commitment, altruism and reciprocity. In particular, we describe the development of each, point to settings in which it has been used and describe the comparative statics hypotheses which we will test.

In addition to these theories, however, we would like to retain the traditional hypothesis of pure self-interest as a benchmark. This hypothesis posits a utility function in which players are concerned only about their own earnings. In the notation above we have
Ui = (Ei - xi) + Pixi
Whenever
i* = 0, and thus xi*/xj = 0 j≠iN.

When individuals care only about their own payoffs, a pure public goods problem like the one our subjects face generates a unique equilibrium in which all players fully free ride (contribute zero). In this free riding equilibrium, an individual's contribution is independent of what others in the group contribute. Thus our benchmark free riding hypothesis is that (1) subjects will always contribute zero to the public good and (2) (the comparative static prediction) there will be no correlation between what an individual contributes and what others in his group contribute.



A. Commitment Theories

Theories of this kind typically rely on Kantian reasoning on the part of individuals. These theories then go on to generate behavior which involves (1) positive levels of contributions to public goods but also (2) contributions which do not change as the contributions of others changes. Collard (1978, 1983) calls these “Kantian” theories and Sugden (1984) refers to the principle underlying this behavior as the “principle of unconditional commitment.”

Laffont (1975) analyzes the case where individuals believe that others will act as they do, then maximize their utility given that belief. Under these beliefs, he shows that individuals voluntarily contribute nonzero amounts toward public goods and social welfare increases. Similarly, Harsanyi (1980) describes the principle of “rational commitment” in which an individual takes the action “which will maximize social utility if it is followed by everybody in this kind of situation.” (p. 116). For our purposes, this implies that individuals simply contribute the level she would most prefer that every member of the group would contribute (independent of her beliefs). If everyone behaves according to this principle, the argument goes, public goods are funded and social welfare increases.

Commitment theories have been used to describe behavior in water conservation (Laffont, 1975), lack of littering (Laffont, 1975), tax evasion (Baldry, 1987), voting (Struthers and Young, 1989), and other voluntary public goods provision (Bordignon, 1990).

Some evidence for these types of norms has been observed in experimental settings. For example, Baron and Spranca (1997) demonstrate the existence of “protected values.” In their experiments they identified actions (e.g. free riding) which subjects would simply not do, regardless of the (hypothetical) personal gain, or the actions of other subjects. Baldry (1987) and Bosco and Mittone (1997) experimentally examine tax evasion, and report a large role played by moral constraints in individuals’ behavior.

Commitment theories imply that an individual maximizes the utility function


Ui = (Ei - xi) + Pixi

subject to his belief that xi = xj j≠iN

Integrating the constraint into the objective function yields
Ui = (Ei - xi) + PNxi
Whenever
i* > 0, and thus xi*/xj = 0 j≠iN.

So commitment theories have two important implications which we can test in a public goods setting, yielding the commitment hypothesis. First, they predict strictly positive (but constant) levels of contribution. Second, (the comparative static prediction) they predict a zero correlation between one's contributions and the contributions of others. In particular, under commitment theories each individual chooses the level of contributions which they prefer everyone would choose. As the actual contribution level of others changes, one’s own contribution remains stable. Notice, this is the same comparative static prediction as generated by the benchmark theory of self-interest above. Later in our statistical analyses we will look to the absolute level of contributions to distinguish these theories.



B. Altruism Theories

A second set of theories of altruism assume that individuals care directly about the consumption or utility of others. These theories then go on to generate behavior which involves (1) positive levels of contributions to public goods, but also (2) contributions which are negatively related to the contributions of others.

In Becker (1974) for example, an individual’s utility is defined over not only his own consumption, but also the consumption of others (positively in the case of altruism). Collard (1978) distinguishes between this type of altruism, which he calls commodity-related, and altruism in which an individual’s utility is defined over his level of consumption and the utility of others (positively in the case of altruism), which he calls utility-related.

Models of altruism have been influential in explaining economic behavior in many settings, including charitable contributions and volunteer behavior (e.g. Unger, 1991; Smith, Kehoe and Cremer, 1995), social security and other welfare systems (e.g. Coate, 1995), intergenerational bequests and macroeconomic growth (e.g. Rangazas, 1991; Hori, 1992; Chakrabarti, Lord and Rangazas, 1993; Strawcyznski, 1994), fertility (e.g. Becker and Barro, 1988; Tamura, 1994), migration (e.g. Tcha, 1995), safety decisions (Jones-Lee, 1992), rent-seeking (Jones, 1996) and behavior in the workplace (e.g. Rotemberg, 1994). Other studies have examined altruism from an evolutionary perspective, either describing evolutionary reasons for altruistic preferences or determining the evolutionary outcomes of societies with heterogenously altruistic individuals (e.g. Bergstrom and Stark, 1993; Haltiwanger and Waldman, 1993; Samuelson, 1993; Bergstrom, 1995).

However, recently a number of papers have presented theoretical results which challenge theories of altruism (Warr, 1982; Warr, 1983; Roberts 1984; Sugden, 1985; Bergstrom et al., 1986; Andreoni 1988a; Bernheim and Stark, 1988) as well as empirical data inconsistent with these models. For example, models of pure altruism imply full “crowding out” of both voluntary contributions and subsidies (Warr, 1982; Roberts, 1984; Bernheim, 1986; Andreoni, 1988a), although there is little evidence of crowding out empirically (Abrams and Schitz, 1978; 1984; Clotfelter, 1985) or experimentally (Andreoni, 1993). Models of altruism explaining bequests and inter-vivos transfers have similarly found little support in the data (e.g. Cox, 1987; Altonji, Hayashi and Kotlikoff, 1992; Cox and Rank 1992; Hayashi, 1995; Laitner and Juster, 1996; Wilhelm, 1996) as have models for charitable giving (e.g. Khanna, Posnett and Sandler, 1995).

Andreoni (1989, 1990) generalized previous models of altruism to incorporate into an individual’s utility function not only the consumption (or welfare) of others, but also the “warm glow” of giving (a related paper, Abel and Warshawsky, 1988, discusses the “joy of giving” and another, Feldstein, 1975 models a similar process.). Under this model of impure altruism, an individual cares not only about the consumption of others, but also receives some private goods benefit from their gift per se. Andreoni (1990) shows that impure altruism implies only partial crowding out, consistent with the empirical results. Models of impure altruism have been used to explain behavior in the supply of charity services by hospitals (Frank and Salkever, 1991) and contributions to public goods and charities in general (Andreoni, 1989, 1990).

A number of experiments have tested for the existence and malleability of (pure or impure) altruistic preferences. Probably the best-known are experiments in the dictator game (where one individual is given a sum of money to allocate in any way they wish between themselves and another; Camerer and Thaler, 1995 present a review of such experiments). Subjects frequently allocate positive amounts to the other player in the game (Forsythe et al., 1994; Hoffman et al., 1994), and the amounts allocated change with the social distance between the players (Hoffman, McCabe and Smith, 1996), the perception of neediness of the recipient (Eckel and Grossman, 1996b) and other institutional factors. Altruism has also been used to explain experimental behavior in prisoners dilemma games (Andreoni and Miller, 1993; Cooper et al., 1996), public goods games (Palfrey and Rosenthal, 1988; Andreoni, 1995), and bargaining (Forsythe, Kennan and Sopher, 1991).

For purposes of our study, we will test the comparative static predictions of models of pure and impure altruism. Under pure altruism, individuals maximize a utility function which includes both their own private consumption and the consumption generated to the group from the public good as below


Ui = Ui ([{Ei - xi} + Pixi], PNixi)

where Ui1 > 0, Ui11 < 0; Ui2 > 0, Ui22 < 0 (both personal consumption and altruistic consumption are normal goods with decreasing returns)


Whenever
i
* > 0. However, under this assumption xi*/xj < 0 j≠iN. This result is akin to crowding out (see Sugden, 1982, p. 346 for a proof).

Under impure altruism, individuals maximize a utility function which includes the above as well as the amount they contributed to the public good, as below.


Ui = Ui ([{Ei - xi} + Pixi], PNixi, xi)

where Ui1 > 0, Ui11 < 0; Ui2 > 0, Ui22 < 0; Ui3 > 0, Ui33 < 0 (personal consumption, altruistic consumption and warm glow consumption are normal goods with decreasing returns)


Again, whenever
i
* > 0. Also under this assumption, xi*/xj < 0 j≠iN. This result is akin to partial crowding out; an increase in the amount of the public good provided implies a decrease in an individual’s own contribution, although the decrease is smaller than under pure altruism (see Andreoni, 1989, p. 1451 for a proof). Thus our comparative static prediction from both types of theories of altruism (the altruism hypothesis) is that there will be a negative relationship between an individual's own contribution and (his beliefs about) the contributions of others in his group.

C. Reciprocity Theories

A final set of theories of reciprocity assume that individuals reciprocate or match the contributions of others. These theories then go on to generate behavior which involves (1) positive levels of contributions to public goods, but also (2) contributions which are positively related to the contributions of others.

Sugden (1984) describes a model in which individuals profit-maximize subject to an external constraint; the principle of reciprocity. This principle says that an individual must contribute the minimum of (1) the least any other member of his group is contributing and (2) the level of contribution he would most prefer that every member of the group make (the same as the level of contributions he would make under commitment theories). By assuming this principle as a constraint on behavior, Sugden derives the existence of (multiple) equilibria in settings of both identical and nonidentical players.

Reciprocal reasoning has been used to explain empirically observed individual behavior in tax evasion (Bordignon, 1993), gift exchange (Solow, 1994; Kranton, 1996), public goods provision (Hollander, 1990), helping in the workplace (Frey, 1993), joint ventures (Kogut, 1989), and labor markets (Akerlof, 1982, 1984; Fehr and Gachter, forthcoming).

A number of experiments have reported behavior consistent with reciprocity as well. In experimental labor markets, subjects playing the role of firms offer efficiency wages and subjects playing the role of workers respond reciprocally by offering more effort than is individually rational (Fehr, Kirchsteiger and Riedl, 1996; Fehr and Tougareva, 1996; Fehr and Tyran, 1996; Kirchler, Fehr and Evans, 1996; Fehr, Gachter and Kirchsteiger, 1997; Gachter and Falk, 1997; Fehr, Kirchsteiger and Riedl, 1998). A similar result was found in experimental goods markets (Fehr, Kirchsteiger and Riedl, 1993). Reciprocal behavior was also found in experimental bargaining games like the trust game (Berg, Dickhaut and McCabe, 1995; Van Huyck, Battalio and Walters, 1995; Jacobsen and Sadreih, 1996; Abbink, Irlenbusch and Renner, 1997; Guth, Ockenfels and Wendel, 1997; Buchan, Johnson and Croson, 1998) and the common pool resource public goods game (Messick et al., 1983; Schroeder et al., 1983; Poppe and Utens, 1986; Wade-Benzoni, Tenbrunsel and Bazerman, 1996). Other bargaining-type experimental games have also exhibited evidence of reciprocity (Bolton, Brandts and Katok, 1996; Bolton, Brandts and Ockenfels, 1997).

For purposes of our study, we will test the comparative static predictions of models of reciprocity, which predict a significant positive relationship between an individual’s contributions to the public good and those of his group. In our notation, under this theory an individual maximizes his personal utility as below


Ui = (Ei - xi) + Pixi

subject to xi ≥ min (xic, xj jN)

where xic is the optimal level of contribution under commitment theories
Whenever
i* > 0. However, under this assumption in equilibria it can be that xi*/xj > 0 j≠iN. See Result 4 (p. 780) of Sugden (1984) for a proof. This theory is thus consistent with a positive correlation between one's own contribution and the contribution of other members of the group; this prediction will be our reciprocity hypothesis.

It is worth noting that Sugden’s model of reciprocity is a model of simultaneous (not sequential) matching of contributions. Players in this game do not wait to see what others have contributed, and then reciprocate their contributions. Instead, everyone makes contributions at the same time, maximizing their self-interest subject to the principle of reciprocity and given their beliefs of others’ contributions. Thus our test of this theory of reciprocity will (of necessity) be a simultaneous one.



D. Summary

The experiments reported in this paper allow us to discriminate between the comparative statics of three classes of theories of behavior, all of which have been invoked to explain the voluntary provision of public goods. The first class of theories (commitment rules) predicts no correlation between an individual's contribution and the contributions of others, or his beliefs about them (a similar zero correlation is predicted by traditional theories of full free riding). The second class of theories (pure and impure altruism) predicts a negative correlation. Finally the third class of theories (reciprocity) predicts a positive correlation.

It should be noted that all these models are models of one-shot behavior. In experiments, however, subjects seldom play equilibria on their first try. Rather, they adjust their behavior and converge toward equilibria. In order to give these equilibria their best chance, the experimental design involves two 10-fold repetitions of a public goods game (consistent with previous experiments, Davis and Holt, 1994; Ledyard, 1995). Since the equilibria described above are equilibria of the stage game, they are also equilibria of the finitely repeated game (Smith, 1990).

Sections 4, 5 and 6 below present the experiments which distinguish between these different theories.

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