《实验经济学》课程教学资源（参考文献）Anomalous Behavior in PublicGoods Experiments.pdf

Anomalous Behavior in Public Goods Experiments: How Much and Why? By THOMAS R. PALFREY AND JEFFREY E. PRISBREY * We report the results of voluntary contributions experiments where subjects are randomly assigned different rates of return from their private consumption. These random assignments are changed round to round, enabling the measurement of individual player contribution rates as a function of that player's investment cost. We directly test these response functions for the presence of warm-glow and/or altruism effects. We find significant evidence for heterogeneous warm-glow effects that are. on average, low in magnitude. We statistically reject the presence of an altruism effect. (JEL C92, C92, H4I) There is a growing body of experimental data from voluntary contribution, public goods environments with a single public good and a single private good. Among tbe many features of tbe data tbat are difficult to explain is tbe apparent frequent use of strictly dominated strategies. Subjects not only give away money wben free-riding is a dominant strategy (R. Mark Isaac et al. [1984, 1994], Isaac and James M. Walker [1988, 1989], and elsewbere), but tbey also often fail to contribute wben it is in their own best interests to do so (Tatsuyoshi Saijo and Hideki Nakamura, 1995). Furtbermore, individual bebaviorover time exbibits erratic patterns, witb many subjects alternating back and fortb between generosity and selfisbness. John O. Ledyard's (1995) excellent survey documents tbese and several otber anomalies. Tbe anomalies might be cause for a serious reexamination of tbe tbeory, as they signal trouble for current economic models of selfish * Palfrey: Division of Humanities and Social Sciences, California Institute of Technology, Pasadena, CA 91125; Prisbrey: Federal Communications Commission, Mass Media Bureau. Policy and Rules Division, 2000 M St.. N.W., Washington, DC 20554, The financial support of the National Science Foundation is gratefully acknowledged. We tbank Roger Gordon, R. Mark Isaac, John Ledyard. Jimmy Walker. Nat Wilcox, and four referees for offering helpful suggestions and comments. The views expressed are those of the authors and do not necessarily reflect the views of the California Institute of Technology or the Federal Communications Commission. bebavior. However, tbe range of environments for which tbese experimental results bave been reported is very narrow, and more importantly tbe designs employed make it difficult, if not impossible, to estimate tbe actual strategies underlying subject behavior. Our design, by changing both tbe information structure and the distribution of preferences, allows the estimation of strategies at botb tbe group and the individual level. As a result, we are able to clearly identify the different sources of some of tbese anomalies. Tbe different environment also provides a chance to see if previous anomalous findings are robust. We employed the following basic design, which is a variation on tbe Voluntary Contributions Mechanism (Isaac et al., 1984). Eacb subject was given an endowment whicb could voluntarily be contributed toward a public good, or kept to be consumed as a private good. Tbe consumption value of the public good depended linearly upon tbe total contributions of tbe group. All the subjects in a group bad the same commonly known, marginal value for tbe public good. But. individual subjects were randomly assigned different marginal values for the private good from a commonly known distribution. In sucb a setup, subjects wbose value for tbe private good is less than their value for tbe public good have a dominant strategy to contribute all of tbeir endowment; subjects wbose value for tbe private good is greater than their value for the public good bave a dominant strategy to keep all of tbeir endowment or to free ride. Subjects repeated tbe game several 829

830 THE AMERICAN ECONOMIC REVIEW DECEMBER 1997 times, eacb time being randomly reassigned a new value for tbe private good. Specifically, our laboratory environment consists of N individuals, eacb endowed with vv, discrete units of a private good. Tbe marginal rate of transformation between the public good and tbe private good is one-for-one, and individual monetary payoff functions are of the form: UiXi, x-,) = VZj Xj + r,(Wi - jc,), where jc, is the individual's contribution. We refer to V as tbe marginal value of tbe public good, and it is tbe same for all individuals. The marginal value of tbe private good is r,. and it is private information. Essentially all of what we think we know about behavior in tbis game is based on experiments in which the marginal valuations of the private good are identical in all periods for all participants in tbe experiments. Witb one exception,' tbe private good valuations exceed the public good valuation, so all subjects bave a dominant strategy to free ride. The central findings from these experiments are summarized below. • Most players in this game violate tbeir one-sbot dominant strategy, witb many contributing upwards of balf tbeir endowment. They do so even wben the marginal valuation of the private good is three or more times that of the public good. • As the marginal valuation of the private good gets closer to the marginal valuation of tbe public good, more violations of tbe dominant strategy are observed. • Subjects can be roughly categorized according to their tendency to violate tbe dominant strategy. • Violations of dominant strategies diminish botb with repetition and witb experience (playing a second sequence of games with a new group). • Violations of dominant strategies to contribute, i.e., wben r, < V, appear to be as prevalent as violations of dominant strategies to free ride (Saijo and Nakamura. 1995). Several possible explanations bave been offered for wby tbere is so much more cooperation than the standard theory predicts. The explanations that bave thus far received the most attention are: ' Saijo and Nakamura (1995). (a) altruistic preferences; (b) warm-glow preferences; (c) repeated game effects, including reputation building; and (d) subject confusion. Tbe first two explanations are similar because they both suggest tbat subjects have a nonmonetary component in tbeir utility function tbat is difficult for tbe experimenter to control, and tbat works in the opposite direction of tbe monetary incentive to free ride. By altruistic preferences we mean that a subject's utility is increasing, not only in bis or her own payoff, but also in tbe total group payoff. Warm-glow preferences mean that the act of contributing, independent of bow much it increases group payoffs, increases a subject's utility by a fixed amount. At first blusb, tbese two effects would appear to be tbe same, but in fact tbey are not. Unlike tbe warm-glow explanation, tbe altruism explanation predicts tbat increases in group size and/or in tbe value of tbe public good should have very large effects on contribution rates. Tbe warm-glow explanation does not depend upon group size or tbe marginal value of the public good. Tbe latter two explanations, (c) and (d). are suggested by tbe tendency for contributions to decline with repetition and with experience. Tbe declines may be consistent with learning or endgame effects. It is possible tbat the typical act of contribution is motivated, perbaps to differing degrees, by eacb of tbese explanations. One purpose of tbese experiments is to accurately measure subject behavior in order to cleanly separate between these explanations and ascertain their relative importance. To do so requires major design innovations relative to tbe standard public goods experiment. In tbe typical past experiments, all subjects witbin a group bad tbe same r,; bere different subjects have different r/s.^ In the past, all subjects ' Thereareafewexceptions, notably Isaac etal, (1985) and Joseph R. Fisher et al. (1995), both of whom consider environments with two incentive types. The latter provides subjects with identical information about other subjects' preferences as in parallel homogeneous preference experiments. The former has several other different features, including nonlinearities, and does not conduct any base-

VOL 87 NO. 5 PALFREY AND PRISBREY: PVBUC GOODS EXPERIMENTS usually had a dominant strategy to free ride, while here the subjects sometimes have a dominant strategy to contribute. In tbe past, subjects repeated tbe decision witb tbe same incentives eacb period; bere tbe subject's incentives cbange eacb period. In earlier experiments, a subject who contributed because of confusion or decision error could not be differentiated from a subject who contributed because of altruism or warm glow. Because r, was always bigger than V. subjects never had an incentive to contribute, and therefore every contribution could be called a decision error. Bebavior motivated by altruism or a warm glow, although potentially observed, could not be separately identified. Furtbermore. it was impossible even to observe noncontribution when r, < V. Tbus there is an inherent limitation in past designs. In our design this problem is eliminated and contribution arising from confusion or decision error can be differentiated from contribution due to nonmonetary components of tbe utility function. Tbus. a key benefit of our design is tbat tbe resulting data allows tbe accurate and unbiased measurement of strategies — measurement tbat controls for tbe possibility of subject error. And, directly from the estimated strategies come estimates of the amount of altruism and warm glow in the individual utility functions. We can also check for tbe robustness of existing results to environments tbat include important features, sucb as diverse preferences and incomplete information, tbat are endemic to natural settings. I. Experimental Design and Procedures There are specific features of our design tbat enable us to address issues that are relevant to understanding other commonly observed patterns of behavior as well. These features are listed below. A sample copy of tbe instructions is in tbe Appendix. 1. Each subject participates in four sequences of ten p>eriods (one decision per period), eacb ten-period sequence with a different group of tbree otber subjects.^ Tbe first two such sequences bave tbe same value of V. The last two sequences also have tbe same value of V. but different from the value in tbe first two sequences. Tbis allows us to identify experience effects. Tbe first sequence witb eacb value of V is coded as inexperienced, and the second sequence as experienced.'' All four sequences occur in a single session tbat lasts approximately 90 minutes. Eacb session includes 16 subjects. 2. In all our environments, subjects receive r,'s tbat are randomly assigned according to a uniform distribution between 1 and 20 in unit increments. We sometimes refer to these as token values. Each time a subject is to make a new decision, he or she is independently and randomly assigned a new r, for that decision. Subjects do not know tbe otber subjects' assignments of r/s, but the distribution is publicly announced at the beginning of tbe experiment. Tbe value of Vis also publicly announced. Therefore, the data contain multiple observations of tbe choice behavior of each individual at different values of r,. and permit tbe estimation of response functions at both tbe individual and aggregate levels. 3. We vary the value of tbe public good. V, between experiments. We have an equal number of observations for each of the four different values of V e {3, 6, 10, 15} (see Table 1). One value. V = 3, bas tbe feature that group efficiency is not maximized when all subjects contribute in every decision period. In that condition, on average. 40 percent of tbe time subjects are assigned a token value tbat is worth more tban four times tbe individual line experiments with homogeneous preferences, Gerald Marwell and Ruth E. Ames (1980) and D. S. Brookshire et al, (1989) have also conducted experiments with heterogeneous preferences, but these are not comparable for other reasons. None of these experiments varied individual incentives across decisions, nor did they provide explicit information about the distribution of incentives in the population. Palfrey and Howard Rosenthal (1991) use an environment similar to the one explored here, but the public good technology is step-level, not linear. ' Fixing the groups for a sequence of ten periods was done lo maintain comparability with past experiments. We also conducted a replication of one of the Isaac et al. (1984) treatments, using our instructions, computer protocol, and subject pool. We obtained results, reported in Palfrey and Prisbrey (1993). that were similar to Isaac et al. (1984). ^ Alternative ways of coding experience produce similar results

832 THE AMERICAN ECONOMIC REVIEW DECEMBER 1997 TABLE 1—SESSION NUMBER AND SEyuENCE NUMBERS FOR EACH OF THE EIGHT TREATMENTS Endowmeot 1 token 9 tokens Session # Sequence #'s Session # Sequence #'s 3 1 1.2 2 1,2 6 3 1,2 4 1.2 V 10 1 3.4 4 3.4 15 3 3.4 2 3.4 Notes: The experiment consisted of four sessions, each with four ten-.peHod sequences. This table indicates session number and sequence numbers for each of the eight treatments. marginal value of the public good. In these cases, contribution reduces group efficiency. 4. We vary the endowment. In one condition, everyone is endowed with one indivisible unit of the private good. In the other condition, everyone is endowed with nine discrete units, and can contribute any number between zero and nine in each period (see Table I). 5. All sessions were conducted at the Caltech Laboratory for Experimental Economics and Political Science, using a collection of computers that are linked together in a network. 6. Each subject was paid cash for each point he or she earned in the session. On average, each individual subject earned approximately $15 in a session. n. Data Analysis We focus mainly on two aspects ofthe data. The first has to do with attempting to identify what we call errors or background noise— behavior that is grossly inconsistent with standard theory. Second, we attempt to measure response functions, the analog to bidding functions in auctions. The response functions address the question: How do contribution decisions depend on the private token values and the public good value, and how do these functions change with our treatment variables, such as experience? We estimate response functions at both the aggregate and individual levels, using probit models. One can interpret our analysis in the context of a random utility model, of the sort found in Daniel McFadden ( 1982), G. S. Maddala (1983), and elsewhere, for the analysis of data with limited dependent variables. For example, in the treatment where subjects have a single indivisible unit of the private good, they face a simple binary decision. We then model the statistical structure by assuming that utility functions have both uncontrolled fixed components (other than the monetary payoff) that we estimate, and an independent Normally distributed random component. Consistent with terminology elsewhere, we call the fixed components the altruism and warm-glow effects, which we differentiate below. The altruism effect measures the additional utihty a subject gains from increasing the monetary payoff to other subjects by one unit (Ledyard, 1995). Formally, an altruist's utility is modeled as a convex combinatioti of the group payoff and his private payoff. The warmglow effect measures the additional utility a subject gains from just the act of contributing a unit of his endowment (James Andreoni, 1988). Altruistic behavior is present in our data if contributions increase with the public good value, other factors held constant. Warm-glow effects are present if contributions increase with an increase in the difference between the public good value and the token value, other factors held constant. Because we separately vary both the token values for individuals and the public good values, we can identify the effects on contribution rates of these two components of the utility function. This is described in detail in Section II, subsection C. A. Some Baselines We first present three different baseline error rates. TTiis gives a rough calibration of a lower hound on the amount of noise in the

VOL 87 NO. 5 PALFREY AND PRISBREY: PUBUC GOODS EXPERIMENTS 833 TABLE 2—THE FREQUENCY OF SPLITTING WHEN THE ENDOWMENT IS NINE AND DIFF > 0. Early Late fnexperienced Experienced 0.36 (182) 0.21 (180) 0.19 (176) 0.07 (170) experiment. By noise, we mean the percent of observed decisions that appear incongruous with nearly any currently accepted theory of rational decision-making. We also compare our baseline with baselines observed elsewhere. Splitting. By splitting, we mean that a subject contributes some fraction of his or her endowment, but not all of it. This is only a possibility in half of our data, the data where subjects have a divisible endowment. Because of the linear structure of the environment, such behavior is not rational even if a subject is altruistic or experiences an additive warm-glow effect. A subject who plays optimally in this environment will always contribute either all or none of his or her endowment, the choice depending on r^ - V.^ Table 2 shows the frequency of splitting in the experiments where subjects could split. One can see two striking features: first, splitting is more prominent among inexperienced suhjects and in the early periods of each tenperiod game; second, splitting almost never occurs when subjects have r, — V < 0. Most splitting can be accounted for by inexperienced subjects who have a dominant strategy to free ride.*" ^' There are possible rationalizations for splitting that we do not consider here. Kay-Yut Chen (1994) constructs a model in which suhjects do not know the payoff they will get from their contribution decisions until they have made their choice. In ihat case, splitting serves a diversification role. It may also be possihle to rationalize splitting if the warm-glow (or altruism) effect is nonlinear in contributions. '' Splitting is heavily concentrated among a few subjects. Only three of the subjects account for 30 percent of all observations of splitting, and six of the subjects account for over half of such observations. At the other end of the scale, nearly 40 percent of the subjects either never split or split only one time (out of 40 chances). These findings contrast somewhat with those of Isaac et al. (1984), who observe splitting in well over half the decisions in their data. Furthermore, in some of their experiments the frequency of splitting does not decline over the course of the ten periods. (See Palfrey and Prisbrey 11993] for details.) Spite. If cooperative behavior (altruism, warm glow, or reputation building) is the main driving force behind the past findings of overcontribution, then we should not observe freeriding from subjects with r, - V < 0. To the extent that violations of dominant strategies to contribute are observed, they might be attributed to effectively random behavior.' This gives us a second kind of baseline, called spite (Saijo and Nakamura, 1995). In our experiments, 4 percent of the decisions violate the dominant strategy to contribute when r^ — V < 0. This number is quite stable across periods and across the experience treatment. Sacrifice. In one treatment, V = 3, the group optimum does not always occur when everyone contributes. In particular, the group payoff is maximized when subjects contribute if and only if r, < 4V = 12. A subject who contributes when r, - 12 < 0 sacrifices more than the entire group benefits. It is hard to imagine any circumstances in which such behavior can be rationalized, except, perhaps, if the warmglow effects from contributing far outweigh private incentives. Surely such behavior cannot be rationalized for altruists, whose utility is a convex combination of group benefits and private benefits. The frequency of this type of contribution also provides, in a slightly different way, a lower bound on the amount of noise. Among inexperienced subjects, sacrifice occurs with the same frequency as spite, but virtually disappears with experience (1 observation out of 129). In summary, the kind of behavior that cannot be explained easily with simple models of warm glow or altruism occurs only rarely in our data, and mostly disappears with experience. ' However, as we show, some of this may be attributable to a negative warm-glow effect in some individuals