The nature of voluntary public good

Transcription

1 GSIR WORKING PAPERS Economic Analysis & Policy Series EAP09-3 The nature of voluntary public good contributions: When are they a warm glow or a helping hand? Koji Kotani International University of Japan Kent D. Messer University of Delaware and William D. Schulze Cornell University April 2009 Graduate School of International Relations International University of Japan

2 GSIR Working Papers Economic Analysis & Policy Series EAP09-3 The nature of voluntary public good contributions: When are they a warm glow or a helping hand? Koji Kotani Assistant Professor Graduate School of International Relations, International University of Japan Kent D. Messer Assistant Professor of Food and Resource Economics University of Delaware William D. Schulze K. L. Robinson Professor of Agricultural Economics and Public Policy Cornell University Abstract ``Warm glow" has been proposed as an explanation for public good contributions that exceed traditional theoretical predictions, yet little is known about why and when people exhibit warm glow in some voluntary settings. To investigate these issues, this research develops a model for the ``helping hand" hypothesis as an extension of warm glow. The hypothesis asserts that when an external environment faced by the subject seems not to provide a socially optimal level of the public good (non-incentive compatible), the subject, to some degree, gains utility by undertaking socially responsible behavior (offering a helping hand), and thus she over-contributes. Once the mechanism is established to be incentive compatible, the individual no longer offers a helping hand, but instead concentrates on maximizing her personal payoffs as predicted by the Nash equilibrium. Experimental results support the helping hand hypothesis, and show that contributions depend on the efficiency of the mechanism and not whether it is voluntary. We also find that contributions are positively correlated with an induced value of the public good even when free-riding is a dominant strategy in an non-incentive compatible mechanism. This would suggest that people's social preferences depend on an induced value of the public good and possess an efficiency concern. Key Words: public goods, voluntary contributions, experimental economics, warm glow GSIR working papers are preliminary research documents, published by the Graduate School of International Relations. To facilitate prompt distribution, they have not been formally reviewed and edited. They are circulated in order to stimulate discussion and critical comment and may be revised. The views and interpretations expressed in these papers are those of the author(s). It is expected that most working papers will be published in some other form.

3 1 Introduction People have been observed helping each other in situations where no mechanism exists to provide a socially optimal level of a public good, but once such a mechanism is developed, people stop helping each other and focus on their own self-interest. For example, Attanasio and Victor Rios-Rull (2000) note that in some developing countries, if a government does not provide a public insurance system, rural farmers have developed voluntary insurance systems to protect each other. However, after a public insurance system is introduced, the farmers no longer aid each other in this manner. Likewise, direct governmental support of charitable organizations, such as the International Red Cross or the Salvation Army, has been shown to crowd out the amount of voluntary donations from individuals (Le-Grand (2003)). These examples suggest that both motivation and context matter when people make a decision of whether to contribute privately to the provision of a public good. In experimental economics settings, subjects consistently give higher levels of contributions in voluntary public good settings, such as the Voluntary Contributions Mechanism (VCM), than predicted by conventional theory (Davis and Holt (1992) and Ledyard (1995)). That is, the individual does not entirely exhibit selfish behaviors as predicted by the Nash Equilibrium (N.E) in a linear public goods setting, but instead seeks to help the group by over-contributing relative to the private optimum of zero. While a potential explanation for these over-contributions is the private warm glow that people experience from the act of contributing (Andreoni (1989); Andreoni (1990)) 1, 2 no clear consensus exists on the motivation of why and when people over-contribute, especially in the first round of public goods games. In an effort to isolate motivations in such settings, Goeree et al. (2002) conducted a series of single-shot public goods games to measure the relative importance of altruism and 1 This behavior has been referred to by different researchers by different names, such as impure altruism by Palfrey and Prisbrey (1997), other-regarding preferences by Ferraro et al. (2003), and the purchase of moral satisfaction by Kahneman and Knetsch (1992). 2 Some researchers have attributed over-contributions to asymmetric errors when a dominant strategy is the corner solution of free-riding. However, Willinger and Ziegelmeyer (1999) and Keser (1996) show that when a dominant strategy is interior, subjects still over-contribute. 1

4 decision error in voluntary contributions. They conclude that both factors play an important role. This research proceeds in the same spirit as this previous research and seeks to characterize this motivation formally. Of particular interest are when and why people exhibit warm glow or over-contribute. This paper explores these questions by inducing a new voluntary public good mechanism (referred to as the Proportional Contribution Mechanism (PCM)). The PCM can be considered an extension of a matching-grant or a tax-deduction mechanism. The key advantages of the PCM are that (i) it can be modified to be either incentive compatible or not incentive compatible by adjusting one parameter, and (ii) it enables within-subject examination of behavior in single-shot settings. A number of recent studies have developed theoretical frameworks to evaluate the degree to which cooperative behaviors are dependent on motivations and context (see for instance, Charness and Rabin (2002), Brekke et al. (2003), Fehr and Schmidt (1999) and Bolton and Ockenfels (2000), Engelmann and Strobel (2004)). This research adopts a social preference approach as a potential explanation of over-contributions, where people are assumed to be not only self-interested but also concerned with social welfare. By extending these concepts to a voluntary public good setting, we develop the helping hand hypothesis as a potential motivation for over-contributions. Whereas Andreoni (1995) conjectured that warm glow is a feature of non-coercive mechanisms, we hypothesize that contributions are a function of whether the mechanism is incentive compatible. 3 When a person faces an external mechanism that is not incentive compatible and seems unlikely to provide a socially optimal level of the public good, the individual gains some utility by undertaking socially responsible behaviors. Once the mechanism is adjusted to be incentive compatible and thus likely to provide the socially optimal level of the public good, the individual no longer offers a helping hand, but instead concentrates on maximizing her personal payoff so that she follows the N.E. 3 Examples exist where warm glow is not present in coercive mechanism (see for instance, Falkinger et al. (2000) and Messer et al. (2006)). 2

5 The experimental results support the helping hand hypothesis, and that the level of voluntary contributions depends upon the efficiency of the mechanism. Furthermore, we identify that contributions are positively correlated with the induced values of public good. Thus, the level of contributions partly reflects the value of the public good and can be considered partial demand revelation. These results would suggest that people have efficiency concerns when they make voluntary contributions, and once efficiency is achieved, they lose the motivation to help. A series of patterns observed in this experiment are consistent with those in other experimental papers that provide evidence for efficiency concern in people s preferences (See, e.g., Engelmann and Strobel (2004)). 2 Experimental Design and Procedures All experiments were conducted in the Laboratory for Experimental Economics and Decision Research (LEEDR) at Cornell University. The subject pool consisted of ninety undergraduate students recruited from introductory economics and business classes. An experimental session took approximately 45 minutes and each subject earned an average of fifteen US dollars. Subjects were randomly appointed to a computer with privacy shields and assigned to a group of three people. Subjects in the same group were not seated near each other and no communication was allowed between subjects. Subjects received written instructions (Appendix A), and the administrator provided oral instructions and answered any question. All sessions involved the PCM that can be described as follows. w i bg i + 1 N N j=1 π i = g j w i bg i + 1 N G if N j=1 g j G if N j=1 g j > G, where π i is the personal payoff for each subject i, w i is the endowment, g i is the contribution to the public good, b is a proportional contribution parameter, G is the capped return of the public goods, and N is the group size. A key feature of the PCM is that the proportion of 3

6 contribution (referred to as b) can be modified to make the mechanism incentive compatible. When b=1, subjects pay the entire amount of their contribution and the mechanism is the same as a standard VCM. If, instead, b = 0.5, then the subjects have to only pay onehalf of the contribution (similar to a matching-grant or tax deductions). For b 1, the 3 PCM is incentive compatible in groups of three people. The main advantage of the PCM is that subjects willingness to pay (WTP) can be compared in a within-subject single-shot environment in which the mechanism is and is not incentive compatible. Induced values, defined as the maximum payoff each subject can obtain from the public good, are obtained by capping individual payoffs from the public good (see Rondeau et al. (2005)), and we will futher discuss this feature in this section. In these experiments, each subject in a group of three people (N = 3) was endowed with ten experimental dollars (w i = 10). Using these parameters, the individual decision problem is as follows: max π i = g i [0,10] 10 bg i + 1G if G = 3 3 j=1 g j G 10 bg i G otherwise. (1) To understand this choice setting, let us outline several key definitions and important facts of individual contribution problem (1). Definition 2.1 (Induced Value) The induced value of the public good is defined as the maximum payoff each subject can obtain from the public good in a group. The feature originates from the kinked payoff function in the public good at the level of G. In this experiment, the induced values v are equivalent to G /3, which is a Pareto optimal (P.O.) contribution that each subject must give for social or group efficiency. 4

7 Fact 2.1 Pareto optimal allocation is any allocation satisfying G = G if b (0, 1) any allocation satisfying G = 0 if b = 1. Fact 2.2 A N.E. for subject i is any contribution satisfying gi = G G i if b (0, 1/3] gi = 0 if b [1/3, 1], where G i = j i g j. Fact 2.3 (Symmetric N.E.) Under the PCM with N = 3 and w i = If b (0, 1/3), a symmetric N.E. is g i = v = G /3. 2. If b = 1/3, a symmetric N.E. is g i [0, v] = [0, G /3]. 3. If b (1/3, 1], a symmetric N.E. is g i = 0. In fact, strategy g i = 0 is a unique dominant strategy in this case. Fact 2.4 Facts 2.2 and 2.3 yield the following result. incentive compatible if b (0, 1/3] The PCM is. not incentive compatible if b [1/3, 1] In addition, b = 1/3 is the cutoff point that divides the incentive compatibility of the PCM. Hence, at this cutoff, the PCM is not only incentive compatible but also non-incentive compatible. Notice that when b = (0, 1/3], the mechanism is incentive compatible in the sense that subjects are induced to honestly reveal the maximum value of the public good, v. 5

8 To test the helping hand hypothesis, we employ five different values of the proportional contribution parameter b = {0.1, 0.2, 1/3, 0.6, 0.9} for each value of G = {$6, $15, $24}. For b {0.1, 0.2}, then the PCM is incentive compatible so that a symmetric N.E. strategy and a P.O. contribution are to give induced values of v = G /3. If b {0.6, 0.9}, then the PCM is not incentive compatible so that a N.E. strategy is to give nothing, but a P.O. contribution is for each subject to give v = G /3. When b = 1/3, the mechanism is both incentive and non-incentive compatible as noted in Fact 2.4. The choice of these five values of b allows a comparison of how the two incentive (b = {0.1, 0.2}) and the two non-incentive (b {0.6, 0.9}) compatible mechanisms yield different results with one cut-off value of b = 1/3. The experiment procedures are as follows. First, subjects participate in hypothetical practice rounds for up to five minutes. The spreadsheet on each subject s computer screen (equipped with a privacy shield) was programmed with Visual Basic for Applications (VBA) such that each subject could input his own hypothetical contribution and the other two subjects hypothetical contributions for all fifteen treatments. The spreadsheet was programmed so that it generated the payoff consequences in a group after all three contributions were entered. Subjects were also asked to do two primary tasks in the practice: First, try at least the three cases: (i) your contribution is less than others, (ii) the same as others and (iii) more than others. Second, identify the best strategy by imagining how the other two subjects in a group will contribute. The purpose of practice rounds was two-fold: (i) to minimize any confusion and random decision error, and (ii) to give subjects sufficient time to think about each decision. After the practice rounds, subjects participated in rounds that involved monetary payoffs. Each subject submitted one contribution for each value of b = {0.1, 0.2, 1/3, 0.6, 0.9}. This procedure was done for each value of G = {$6, $15, $24}. Therefore, subjects experienced fifteen different contribution situations and determined their contributions without feedback. In other words, each subject did not know his own payoff or the contributions of the other 6

9 subjects in his group until after all fifteen decisions were made. To prevent potential order effects, the order in which the decisions were presented was randomized. As explained to the subjects at the end of the experiment, payoffs were determined by randomly drawing, with replacement, one labeled chip out of five for each of the three cases of G. Each of the five labeled chips represented one of the five possible values of b. 3 The Conceptual Framework of the Helping Hand Hypothesis In this section, we outline the conceptual framework of the helping hand hypothesis. Similar to the approaches by Andreoni and Miller (2002) and Charness and Rabin (2002), we assume that the utility function for subject i is represented as a linear weighting function of her personal payoff and that of others in her group. Assuming a group of three subjects u i (g i ) = π i + λ i π j = w i bg i j i 3 g j + λ i π j (2) j=1 j i where π i = w i bg i j=1 g j represents the personal payoff for subject i = {1, 2, 3} and λ i [0, 1] is a parameter that captures how much individual i cares about the payoffs of others in her group. We employ this separably additive form since a simple weighting function can capture altruistic preferences in the dictator games and many other game-theoretic settings (See, e.g., Andreoni and Miller (2002) and Charness and Rabin (2002)). Additionally, we further assume that each individual may be motivated by some internal motivation called the helping hand. The utility function is given by u i (g i ) = π i + λ i π j + α i f(g i, v) j i = w i bg i g j + λ i π j + α i f(g i, v), j=1 j i (3) 7

10 where α i f(g i, v) is the helping hand term for subject i, and α i R + is a parameter that captures how much subject i is affected by the helping hand motivation. To be consistent with the helping hand hypothesis, we assume that f g (g i, v) > 0, f gg (g i, v) < 0, g i [0, v) and f(v, v) = max g f(g i, v). 4 The helping hand motivation should be interpreted as the strength of feeling of how much individual i wants to give an optimal contribution, irrespective of the payoff consequence. The helping hand can also be considered to be psychological, outcome-insensitive, and related to intrinsic motivation such as morality, while the altruism is outcome-sensitive and directly related to material payoffs including those of others. Therefore, the helping hand motivation is a type of warm glow motivation or impure altruism of the type described by Andreoni, however it extends the concept to characterize the internal motivation for voluntary contribution by relating actual contributions with the induced values of the public good. In the experimental economics literature, warm glow is specified as a linear function of the contribution, g i, i.e., f( ) = cg i where c is some positive parameter to be estimable (See, e.g., Palfrey and Prisbrey (1997) and Goeree et al. (2002)). This specification implies that people obtain more warm glow simply by giving more, whatever external situations are. Thus, it becomes difficult to distinguish such giving from the level of induced values. In contrast, the functional assumptions for the helping hand term capture both the situation where people gain this type of marginal satisfaction and the situation where they do not. The marginal benefit of giving based on the helping hand motivation is diminishing as the voluntary contribution gets closer to induced values of the public good, v, i.e., f gg (g i, v) < 0. 5 Also, the satisfaction from this helping hand motivation is assumed to reach the maximum when each subject contributes the induced values of the public good. 4 We may assume that f g (g i, v) = 0 for g i [v, w i ]. In fact, any assumption that does not affect the result. f(v, v) = max g f(g, v) can be assumed to be consistent with the helping hand hypothesis. 5 This diminishing assumptions in intrinsic motivations are also made in Schulze et al. (2002) and Frey and Oberholzer-Gee (1997). 8

11 The individual problem characterizes the optimum, max g i [0,10] u i (g i ) = π i + λ i π j + α i f(g i, v) = w i bg i G + λ i π j + α i f(g i, v), j i j i subject to G = 3 j=1 g j G, otherwise G = G. Then the first order conditions yield b + 1/3 + 2λ i /3 + α i f g (g i, v) 0. As a benchmark for the prediction, we derive a symmetric N.E. under the assumption that each subject has the belief that the other two subjects in her group behave similarly, i.e., α i = α j, λ i = λ j, i j. This assumption not only simplifies the derivation of the equilibrium but is also based on evidence of experimental research on one-shot social dilemma situations. Dawes et al. (1977) show that in a social dilemma situation, an individual utilizes her own preference as information about what other people will do. They argue: In the end, a subject may have a rational basis for believing that others in a group will do likewise. Whichever the source, the subjects decisions themselves would lead them to believe that others decisions would be like theirs. Elster (1989) supports their findings, and names the process of developing such belief magical thinking. With this assumption, we can derive the unique equilibrium strategy of the individual contribution behavior. Fact 3.1 For b (0, 1/3), λ i [0, 1] and α i R +, the symmetric N.E. is g i = v. Fact 3.2 For b [1/3, 1], the symmetric N.E. strategy for each subject i is as follows. 1. g i = v if λ i > 3b 1 2, 9

12 2. g i is any contribution between 0 and v satisfying α i f g (g i, v) b λ i and equality holds if g i > 0 for λ i [0, 3b 1 2 ) and α i 0, 3. g i = 0 if α i = 0 and λ i 3b 1 2. Recall that α i and λ i are the set of individual specific parameters that characterize voluntary contributions in the optimal strategy. Given the prediction of the symmetric N.E., all the subjects should contribute induced values v when the PCM is incentive compatible. When the PCM is not incentive compatible, then contributions are dependent on parameter values of α i and λ i. The three possible types of individual contribution behaviors are expected. 1. Selfish Type We call subject i selfish type if α i = λ i = 0. Selfish type individuals have the utility of u i = π i, and contribute v for 0 b < 1/3, gi = any value between 0 and v for b = 1/3 (4) 0 for 1/3 < b Pure Altruist We call subject i pure altruist type if α i = 0 and λ i (0, 1]. Pure altruists have the utility of u i = π i + λ i j i π j, and contribute v λ i > 3b 1 gi =, 2 0 otherwise. (5) In addition, we call subject i a perfect altruist if λ i = 1, and note that such individuals contribute g i = v for all the treatments of b = {0.1, 0.2, 1/3, 0.6, 0.9}. 10

13 3. Helping Hand Type We call subject i helping hand type if α i > 0 and λ i 0. Helping hand individuals have the utility of u i = π i + λ i j i π j + α i f(g i, v), and contribute gi = v any value between 0 and v satisfying α i f g (g i, v) b λ i for λ i > 3b 1 2, otherwise. (6) The condition of weak inequality implies that equality holds if gi > 0; otherwise strict inequality holds. This strategy implies that when b = {0.1, 0.2, 1/3}, then the subject contributes gi = v. If b = {0.6, 0.9}, subjects contribute some value between 0 and v, depending on the set of individual specific parameters (α i, λ i ). When b approaches 1, contributions decrease gradually. Finally, the predictions of three types introduced in the above: (i) selfish (ii) pure altruist and (iii) helping hand type, are graphically summarized in figure 1, where the vertical axis is individual contribution, g i, and the horizontal axis is proportional parameter b. Andreoni and Miller (2002) show that in a dictator game, altruistic preferences satisfy the strong axiom of revealed preference, and about 70 percent of subjects altruistic preferences can be represented as a linear weighting utility function of one s own payoff and that of others. They report that one half of the subjects can be classified as the selfish type, that is, u i = π i and about 20 percent are perfect altruists, i.e., u i = π i + π j. Based on their finding, we can conjecture that if people do not hold any helping hand motivation, a majority of subjects behave selfishly so that they follow the strategy of equation (4). On the other hand, perfect altruists should contribute induced values for all the treatments in this experiment. Notice that the introduction of the concept of the helping hand into the altruism framework accounts for the motivation particular to a voluntary contributions game. We claim 11

14 Figure 1: Predictions of three types of individuals that even if most individuals are classified as selfish in the altruism framework, such individuals with the helping hand motive give contributions close to induced values of the public good even when b = 1/3. Alternatively, when b = {0.6, 0.9}, they contribute some intermediate value between 0 and v and gradually decrease their contributions as b is closer to 1. Intuitively, this contribution behavior is possible in the presence of some helping hand motivation, i.e., α i > 0. Recall that the average contribution lies between zero and the P.O. contribution in previous public goods experiments (See, e.g., Davis and Holt (1992) and Ledyard (1995)). 6 Given previous evidence and the data collected from this experiment, the helping hand hypothesis can be translated into a simple regression. That is, we can test if the actual behaviors follow a symmetric N.E. of the helping hand model by running the following regression for each value of v = {$2, $5, $8}. ( g ik = c + β 1 d 1 b 1 ) ( + β 2 d 2 b 1 ) + ɛ ik (7) 3 3 where i = 1,..., 90 denotes the subject index, k = 1,..., 5 denotes the index of exper- 6 In most experiments, a P.O. contribution is in fact to give a whole endowment to a public good. 12

15 iment treatments, b = {0.1, 0.2, 1/3, 0.6, 0.9}, for each induced value of the public good, v = {$2, $5, $8}, ɛ ik represents the disturbances that are peculiar to both individuals and treatments, d 1 is a dummy variable such that d 1 = 1 if b = {0.1, 0.2, 1/3}, otherwise 0, d 2 is a dummy variable such that d 2 = 1 if b = {1/3, 0.6, 0.9}, otherwise 0. Finally, the helping hand hypothesis will be translated into the above regression as follows: Helping Hand Hypothesis 1. ˆβ1 is sufficiently close to zero, neither statistically significant nor economically significant. 7 In other words, economic incentives given by proportional parameter b (0, 1/3] is not an important factor for the contribution decision since the helping hand model simply predicts that subjects contribute induced value v for the public good. The intuition behind this prediction is that internal motivations represented by the helping hand are satiated at the point of g i = v. 2. ˆβ2 is strictly negative, statistically significant and economically significant. In addition, the estimate of ˆβ 2 yields the prediction of over-contributions. In other words, when the PCM is not incentive compatible, subjects will not only be motivated by the helping hand and altruism but will also want to maximize their personal payoffs in contrast to the case of an incentive compatible PCM. Thus, a trade-off exists between selfish motives and both the helping hand motivation and altruism. The helping hand hypothesis asserts that the estimate of ˆβ 2 is negative but statistically significant and that the contributions are some intermediate value between 0 and v. Also, contributions will decrease as b becomes larger. 3. ĉ is statistically significant and close to v. In other words, the estimates of the intercept are equal to the induced values of the public good. 7 We use the term of economic significance as described in McCloskey and Ziliak (1996) and Ziliak and McCloskey (2004). 13

16 Note that ff all of the above three hypotheses are simultaneously satisfied, then the predictions of regression will becomes identical to the one in helping hand type of individuals shown in figure 1. 4 Results and Discussion In this section, we first present the frequency distributions and descriptive statistics of voluntary contributions for each treatment. We then present the regression analysis. Figures 1, 2 and 3 are frequency distributions for each treatment of b = {0.1, 0.2, 1/3, 0.6, 0.9} with v = {$2, $5, $8}, respectively. The shapes of the frequency distributions shift similarly for all the treatments of v = {2, 5, 8} when b changes. When the PCM is incentive compatible for b = {0.1, 0.2, 1/3}, the mode of distribution for each induced value is v. When b = {0.6, 0.9} and the PCM is not incentive compatible, the frequency distributions exhibit diminishing frequency over higher contributions. Note that a number of subjects responded as if they were perfect altruists by contributing v even when b = {0.6, 0.9} for all induced values. On average, 10 percent of the individuals contribute the induced value, even though the dominant strategy is to give nothing for selfish behavior in this case. These proportions approximate those found in related research. For example, 20 percent of individuals were classified as perfect altruists in a dictator game (Andreoni and Miller (2002)). This evidence is consistent with the previous literature in the sense that some small portion of individuals is highly altruistic so that they give induced values even when the mechanism is not incentive compatible. A majority of individuals follow the pattern of contribution behaviors underlying the frequency distribution and contribute induced values of v or close to v when b = {0.1, 0.2, 1/3}. Yet when b = {0.6, 0.9}, most subjects reduce contributions, and the degree of reduction varied across individuals: A large portion of individuals contribute between 0 and v, while the remainders become free-riders. Intuitively, such results correspond with the helping hand 14

17 hypotheses. The potential cost of contributions strongly impacts a subjects contribution behavior when the mechanism is not incentive compatible. When the mechanism is incentive compatible, the cost does not have the same degree of impact. Table 1 shows the mean and median of contributions for each treatment. This result can be understood better by combining the results from the frequency distributions. The modes of the frequency distributions for b = {0.1, 0.2, 1/3} correspond to v, and at the same time, the medians shown in table 1 are identical to these modes except the case of b = 1/3 and v = $8. This again confirms that many individuals give the induced values when the mechanism is incentive compatible. Alternatively, when the PCM is not incentive compatible of b = {0.6, 0.9}, the mean and median are between zero and v. This result is consistent with typical VCM experiments in that the average contributions are between zero and an efficient contribution. However, the new feature of this result is that when the cost of voluntary contribution is systematically increased from b = 1/3 to b = 0.9, contributions inversely react as the mean and median decrease. Although the PCM with b = 1/3 can also be viewed as non-incentive compatible, many individuals give contributions close to v. When b = {0.6, 0.9}, contributions lies between 0 and v and gradually decrease. Figure 5 shows how the change in induced values of the public good, v = {$2, $5, $8}, affects the mean and median of contributions for each proportional parameter b. The induced value of the public good is the horizontal axis, while the mean and median contributions are plotted in the vertical axis. The five lines each represent the mean/medians of contributions for the treatment of b = {0.1, 0.2, 1/3, 0.6, 0.9}, respectively. An additional 45 degree line, when contributions equal v, is also drawn to show the degree of demand revelation by comparing the five lines with that 45 degree line. First note that the median and the mean contributions are positively related to induced values. In particular, under the non-incentive compatible PCM, contributions remain positively related with induced values of the public good, despite the N.E. of selfish individuals of giving nothing. This corroborates the finding by Rondeau et al. (2005) that voluntary 15

18 contributions have a positive relationship with induced values even when the mechanism is not incentive compatible. Second note that the mean and median of contributions more closely approximate the 45 degree line of induced values as proportional parameter b gets smaller. When the PCM is incentive compatible of b = {0.1, 0.2}, they are very close or identical to the 45 degree line. This implies that the PCM is indeed demand revealing when the cost of voluntary contribution gets sufficiently small. However, when the PCM is not incentive compatible of b = {0.6, 0.9}, then the slope of the lines gets flatter. Given the aforementioned statistical results, we run a quantile regression of equation (7) for each value of v and test if the estimates of parameters conform to the helping hypothesis. The quantile regression technique proposed by Koenker and Bassett, Jr. (1978) is applied since this technique is a robust and more efficient than the least squares (LS) approach where the error term may not be normally distributed and varies systematically with independent variables. In our case, the frequency distributions show that as the independent variable, b, systematically changes the shape of the distribution in the dependent (response) variable of contributions g i, and thus the assumption of normality is violated. Therefore, the LS approach may not be appropriate. However, for the purpose of the comparison, the LS estimates are also presented. The quantile regressions estimate one parameter vector for each quantile under weaker assumptions of the error term than those of the LS approach. The requirement is that Quant θ (ɛ θi b) = 0 for θ [0, 1], and no other distributional assumptions are made. The quantile regression can be applied by pooling the panel data naively and the estimator is still consistent (Lipsitz et al. (1997) and Jung (1996)). The standard errors of parameters of interest are derived by non-parametric bootstrap methods (See Buchinsky (1998)). In addition, several quantile regressions for θ = {0.3, 0.4, 0.5, 0.6, 0.7, 0.8} could be run to clarify the heterogeneity of contribution behaviors. Alternatively, the random effects model is 16

19 employed for the LS approach. 8 The quantile regressions above the median (θ = {0.8, 0.7, 0.6, 0.5}) show that the helping hand hypothesis seems to hold. The estimates of the intercept are sufficiently close to the induced values of v, while ˆβ 1 is not statistically significant at the 0.05 level or economically insignificant so that ˆβ 1 0 for all the quantile regressions above the median of θ = {0.8, 0.7, 0.6, 0.5} (See Table 2). 9 In contrast, ˆβ2 is statistically significant for all the levels of the quantile regressions, and the estimates show that contributions decrease as b gets bigger. These results imply that when the PCM is incentive compatible, most subjects do not change their contribution behavior and instead follow a symmetric N.E strategy. When the PCM is not incentive compatible, subjects gradually reduce their contributions as b gets close to 1. Note that the LS estimates are not similar to the quantile regressions above the median (See Table 2). The apparent cause for this discrepancy are the outliers observed in the experiments and that the distributions of contributions are not symmetric such as a normal distribution. Therefore it may be concluded that the quantile regressions better capture the distribution of contribution behaviors. Figures 6 shows the prediction of each regression presented in Table 2. These figures again confirm that quantile regressions above the medians are generally consistent with the helping hand hypothesis of figure 1. What can we learn from the regression and statistical results? First, contributing induced 8 The Wu-Hausman test was conducted. The result was in favor of the random effects model against the fixed effects model. 9 In the case where b = 1/3, v = 8 and θ = 0.5 the estimate of the intercept is 6, and ˆβ 1 is and statistically significant (See Table 2). This exception to the broad trend is due to the fact that the number of subjects who contributed more than induced values did not reach the median for lack of several subjects, though many subjects still contribute close to v. This result may be paralleled with that in Saijo and Nakamura (1995). They also considered the incentive compatible voluntary contribution mechanism, however a dominant strategy is full contribution out of endowment. They found that many subjects did not make full contribution as theory predicts and concluded that the observed behaviors may be motivated by spiteful motive to increase the ranking of ultimate payoffs among subjects in a group rather than maximizing his/her own payoff. In turn, our results in frequency distributions show that as induced values, v, increases from $2 to $8 in the incentive-compatible PCM especially with b = 1/3, the number of subjects who contributed induced values gradually decreases. Thus, we conjecture that when the required contribution for group efficiency is close to a whole endowment even under the efficient mechanism, a different kind of motives such as spitefulness may emerge. This would also be an interesting topic to be addressed in the future. 17

20 values of the public good is pervasive in an incentive compatible PCM, while high heterogeneity of contributions is observed in a non-incentive compatible PCM as shown in quantile regressions and frequency distributions. On the whole, contributions are decreasing in b, and seem to indicate that the helping hand motivation plays a role. Second, the induced values of the public good may be a key determinant to characterize over-contributions observed in this experiment. Economic theory predicts that a zero contribution is a unique dominant strategy for b = {0.6, 0.9}. However the frequency distributions are clearly different across v = {2, 5, 8} for the same value of b = {0.6, 0.9}, and also high induced values positively impact over-contributions. Thus, we further conjecture that the helping hand term may have the property of being at least weakly increasing in v, i.e., f v (g i, v) 0. 5 Conclusion This paper examined the nature of voluntary public good contributions in single-shot settings. The conceptual framework and model of the helping hand motivation were formulated, and a new voluntary public goods mechanism, referred to as the Proportional Contribution Mechanism (PCM) was described. Experimental results suggest that people follow both helping hand and selfish motives. Furthermore, the nature of over-contributions or warm glow is dependent not on whether a public good mechanism is voluntary, but upon the efficiency of the voluntary mechanism. When the mechanism is incentive compatible, subject report (warm-glow free) values for public goods via voluntary contributions, while when the PCM is not incentive compatible contributions are decreasing as b increases, but are positively correlated with induced values. Thus, these over-contributions, in part, reflect the value for the public good and can be considered partial demand revelation. These trends observed in the experimental results are novel and can only be explained by the presence of helping hand type motivations and suggests the pepole s social preferences somehow depend on an induced value of the public good and poseess an efficiency concern. 18

21 At the individual level, it must be noted that data and regression analyses remain incomplete when the PCM is not incentive compatible. Consistent with previous VCM research, the quantile regressions reveal a variety of individual contribution behaviors. A significant portion of subjects follow the helping hand prediction, another group contributes at levels equivalent to their induced values, and a small fraction of subjects continuously free-ride. However, we did not estimate a set of individual specific parameters because of the small degrees of freedom. Identifying these types of cooperative behaviors may require a new experimental design and remains a question to be addressed in the future. 19

22 Table 1: Summary of Contributions ($) for each treatment v = $2 (G = $6) b = 0.1 b = 0.2 b = 1/3 b = 0.6 b = 0.9 Mean Median N.E [2.00,0.00] v = $5 (G = $15) b = 0.1 b = 0.2 b = 1/3 b = 0.6 b = 0.9 Mean Median N.E [5.00,0.00] v = $8 (G = $24) b = 0.1 b = 0.2 b = 1/3 b = 0.6 b = 0.9 Mean Median N.E [8.00,0.00]

23 Table 2: Estimates of Regressions for Different Induced Values Q 30 Q 40 Q 50 Q 60 Q 70 Q 80 LS v = $2 Constant 1.00* 1.75* 2.00* 2.00* 2.00* 2.00* 1.57* e e β * e e e e e β * -3.09* -3.53* -1.76* -1.76* * v = $5 Constant 3.50* 4.00* 5.00* 5.00* 5.00* 5.00* 4.00* e β * -4.29* -2.39e e e e β * -5.74* -7.06* -6.09* -5.29* -3.53* -4.32* v = $8 Constant 4.00* 5.00* 6.00* 7.50* 8.00* 8.00* 5.53* β * * -8.57* e e * β * -7.08* -8.82* -9.70* -8.82* -5.29* -5.85* Notes: N = 450 for each induced value. significance below <0.05. Additional regression statistics are available from the authors upon request. 21

24 Figure 2: Histogram of v = $2 for b = {0.1, 0.2, 1/3, 0.6, 0.9} 22

25 Figure 3: Histogram of v = $5 for b = {0.1, 0.2, 1/3, 0.6, 0.9} 23

26 Figure 4: Histogram of v = $8 for b = {0.1, 0.2, 1/3, 0.6, 0.9} 24

27 Figure 5: Mean, Median and Induced Value for each treatment of b = {0.1, 0.2, 1/3, 0.6, 0.9} 25

28 Figure 6: Prediction of Quantile Regressions for v = {$2, $5, $8} 26

29 Appendix A In this section, a part of experiment instructions is presented. A complete set of all experimental instructions is available upon request from the corresponding author. Introduction Experiment Instructions Welcome to an experiment in the economics of decision-making. In the course of the experiment, you will have opportunities to earn money. Any money earned during this experiment is yours to keep. It is therefore important that you read these instructions carefully. Please do not communicate with other participants during the experiment. In today s experiment, you are part of a group which consists of three people. Members of this group are assigned randomly and will be announced to you, but no communication is allowed during the experiment. To begin with, you and everyone else will be given $10. You are free to spend this money in any way that you wish. Once you have read and understood these instructions, you will be asked to submit a bid to a group investment fund (group fund) out of the $10. Any money NOT contributed to the group fund is put into a private account and is yours to keep. Your earnings will be the amount of money in your private account plus your payoff from a group fund. Private account Any money NOT contributed to the group fund is put into your private account. Suppose you decided your bid to the group fund. The amount in your private account is then calculated as $10 (b Your bid to a group fund), where b is drawn from {0.1, 0.2, 0.333, 0.6, 0.9}. Here, b specifies the proportion of your bid you have to pay to the group fund. If b = 0.333, you have to pay 33.3% of your bid to the group fund, and the amount of money in your private account is yours to keep. For example, suppose that b = and you decided to bid $6.20 to a group fund, then your private account would be $7.93 (= $10 (0.333 $6.20)). Here are other four examples: Ex-1 Suppose that b = 0.1 and you decided to bid $3 to a group fund. Then your private account would be $9.7 (= $10 (0.1 $3)). Ex-2 Suppose that b = 0.2 and you decided to bid $4 to a group fund. Then your private account would be $9.2 (= $10 (0.2 $4)). 27

30 Ex-3 Suppose that b = 0.6 and you decided to bid $10 to a group fund. Then your private account would be $4 (= $10 (0.6 $10)). Ex-4 Suppose that b = 0.9 and you decided to bid $5 to a group fund. Then your private account would be $5.5 (= $10 (0.9 $5)). Group investment fund The money you bid to the group investment fund will be added to the bids from the other two members in your group. The sum of all of the three bids is called the group investment fund (group fund). The group fund can purchase shares at a price of $1.00 each. The fund can purchase a maximum of 15 shares. Hence 15 shares will be purchased if the sum of bids made to the group investment fund by members of your group equals or exceeds $15. If the sum of all bids made by members of your group is below $15, all the money received by the group fund will be used to purchase shares. Each member of your group will receive a personal payoff for each share purchased by the group fund. In this experiment, the personal payoff is $1/3 ($ ) per share and is the same for each member of your group. In other words, the sum of all bids made by members of your group is divided by the number of members of the group. Your earning from the group fund depends on the sum of bids to the group fund. There are three possible outcomes: 1st OUTCOME: The sum of bids to the group fund is LESS THAN $15. In this case, all of the group fund will go toward the purchase of shares. Everyone in your group will receive the personal payoff from the group fund. Your payoff will be equal to the number of shares purchased by the fund multiplied by $1/3 (personal payoff per share). For example, if the sum of the bids is $8.44, the group fund will purchase 8.44 shares and your payoff from the group fund is $2.81: 8.44 $1/3 = $8.44/3 $ nd OUTCOME: The sum of bids to the group fund is EXACTLY $15. If the sum of bids equals $15, the group fund will purchase all 15 shares. In this case, you will receive your highest possible personal payoff from the investment. The other two members of your group will also receive the highest possible personal payoff from the investment. That is, the payoff is $5.00: 15 $1/3 = $15/3 = $ rd OUTCOME: The sum of bids to the group fund is GREATER THAN $15. Even though the sum of bids exceeds $15, the group fund will purchase only 15 shares. In this case, you and the other two members still receive the highest possible personal payoff from the group fund, that is, $5.00 (15 $1/3). However, note that no matter how much money is invested in the group fund, no more than 15 shares can be purchased. For example, 28

31 suppose the group fund is $ In this case, only 15 shares will be purchased and the rest of money, $9.84 (= $24.84 $15.00), will disappear and will NOT increase your payoff. Your earnings Your earnings are the amount of money in your private account plus payoff from a group fund. This is calculated as: Some Examples ($10 b Bid into group fund) + (Payoff from group fund) (Ex.1) Suppose that b = 0.1 and you decide to bid $3.00 to the group fund. Consequently your private account is $9.70 (= $ $3.00). Also suppose that the total bids of the other two members to the group fund are $5.40. So, the sum of bids to the group fund is $8.40 (=$3.00+$5.40). In this case, your earnings are $12.5: where ($ $3.00) + ($1/3 8.40) = $12.5, The amount of money in your private account is $9.70 (= $ $3.00), The payoff from a group fund is $2.80. (= $1/3 8.40). (Ex.2) Suppose that b = 0.2 and you decide to bid $7.00 to the group fund. Consequently your private account is $8.60 (= $ $7.00). Also suppose that the total bids of the other two members to the group fund are $9.00. So, the sum of bids to the group fund is $16.00 (=$7.00+$9.00). In this case, your earnings are $13.60: where ($ $7.00) + ($1/3 15) = $13.60, The amount of money in your private account is $8.60 (= $ $7.00), The payoff from a group fund is $1/3 15 = $5.00. Here note that since the total bids to a group fund, $16.00, are more than $15, the payoff from a group fund is still $1/3 15 = $5.00 and the rest of money $1.00 (= $16.00 $15) will disappear and will NOT increase your payoff. (Ex.3) Suppose that b = and you decide to bid $4.50 to the group fund. Consequently your private account is $8.50 (= $ $4.50). Also suppose that the total bids of the other two members to the group fund are $4.40. So, the sum of bids to the group fund is $8.90 (=$4.50+$4.40). In this case, your earnings are $11.46: where ($ $4.50) + ($1/3 8.90) = $11.47, 29

32 The amount of money in your private account is $8.50 (= $ $4.50), The payoff from a group fund is $2.97 (= $1/3 8.90). (Ex.4) Suppose that b = 0.6 and you decide to bid $6.40 to the group fund. Consequently your private account is $6.16 (= $ $6.40). Also suppose that the total bids from the other two members to the group fund are $8.60. So, the sum of bids to the group fund is $15.00 (= $ $8.60). Then your earnings are $11.16: where ($ $6.40) + ($1/3 15) = $11.16, The amount of money in your private account is $6.16 (= $ $6.40), The payoff from a group fund is $5.00 (= $1/3 15). (Ex.5) Suppose that b = 0.9 and you decide to bid $5.00 to the group fund. Consequently your private account is $5.50 (= $ $5.00). Also suppose that the total bids of the other two members to the group fund are $ So, the sum of bids to a group fund is $19.00 (=$5.00+$14.00). Then your earnings are $10.50: where Procedures ($ $5.00) + ($1/3 15) = $10.50, The amount of money in your private account is $5.50 (= $ $5.00), The payoff from a group fund is $1/3 15 = $5.00. Here note that since the total bids to a group fund, $19.00, are more than $15, the payoff from a group fund is still $1/3 15 = $5.00 and the rest of money $4.00 (= $19.00 $15) will disappear and will NOT increase your payoff. First, the members of your group will be announced to you and you will be asked to determine one bid for each value of proportion b = {0.1, 0.2, 0.333, 0.6, 0.9}. In other words, you will need to submit five bids in total, depending on the proportion b = {0.1, 0.2, 0.333, 0.6, 0.9}. After the announcement of your group members, you will do the following steps: Step-1 Input your bid for each value of proportion b = {0.1, 0.2, 0.333, 0.6, 0.9} in the spreadsheet. (Note you need to submit five separate bids.) Hit Enter and click the button submit on the screen for each bid you submit. Step-2 After all of the bids in your group are submitted, a value of proportion b = {0.1, 0.2, 0.333, 0.6, 0.9} will be randomly chosen by picking one chip out of a bag in which there are five chips, each representing one of the five possible values for proportion b = {0.1, 0.2, 0.333, 0.6, 0.9}. 30

33 Step-3 Do NOT click any update button at this point! At the end of the experiment, the administrator will give you the permission and then click update only in the same column of the selected value of proportion b in the Step-2. Accordingly, the computer automatically generates your payoff on the screen. Again, note that all of your payoffs will be calculated at the end of the experiment. Your payoff in each part depends on the random draw, your bid and your group members bids. The summation of your payoffs obtained from each part is your total payoff in this experiment. Thus, do think carefully how you will bid each time since every bid you made will significantly impact your total payoff. Your total earnings are the experimental earnings, and one experimental dollar is US dollars. Thus, each $1 you earned in this experiment is worth about US $ In other words, 4.5 (=1/ =4.5) experimental dollars is worth US $1 so that the exchange rate is 4.5 : 1. It is very important that you clearly understand these instructions. Please raise your hand if you have any questions. Please do not talk with other participants in the experiment. References Andreoni, J. (1989). Giving with impure altruism: Applications to charity and Ricardian equivlaence. Journal of political economy, 97(6): Andreoni, J. (1990). Impure altruism and donations to public goods: A theory of warm-glow giving. Economic journal, 100: Andreoni, J. (1995). Cooperation in public-goods experiments: Kindness or confusion? American economic review, 85: Andreoni, J. and Miller, J. (2002). Giving according to GARP: An experimental test of the consistency of preferences for altruism. Econometrica, 70(2): Attanasio, O. and Victor Rios-Rull, J. (2000). Consumption smoothing in island economies: Can public insurance reduce welfare? European economic review, 44: Bolton, G. E. and Ockenfels, A. (2000). ERC: A theory of equity, reciprocity and competition. American economic review, 90(1): Brekke, K. A., Kverndokk, S., and Nyborg, K. (2003). An economic model of moral motivation. Journal of public economics, 87: Buchinsky, M. (1998). Recent advances in quantile regression models: A practical guideline for empirical research. Journal of Human Resources, 33(1): Charness, G. and Rabin, M. (2002). Understanding social preferences with simple tests. Quarterly journal of economics, 117: