Investing in Institutions for Cooperation

Transcription

1 Investing in Institutions for Cooperation Alexander Smith Xi Wen September 18, 2014 Abstract We present a public good game experiment on making the tradeoff between investing in contribution productivity and contributing to provision. Subjects collectively decide (by voting) how much to invest in augmenting the technology for producing the public good. They then make individual voluntary contributions to provision, as in conventional public good games. Relative to the social optimum, the subjects do well with investment; the primary source of loss is their contribution behavior. As far as the tradeoff between investment and contributions, absolute contribution amounts are not significantly related to investment, suggesting that following high investment, the incentive effect of having an efficient production technology is offset by the budget effect of having less money available to contribute. JEL Classifications: C71; C91; C92; H41 Keywords: Public good games; Endogenous institutions; Production technology; Contribution productivity We thank conference participants from the 2013 North American ESAs in Santa Cruz, the 2014 International ESAs in Honolulu and the 2014 North American ESAs in Fort Lauderdale. We thank seminar participants from Worcester Polytechnic Institute (WPI), the College of the Holy Cross, the University of Massachusetts at Lowell and Temple University. Financial support from Worcester Polytechnic Institute (WPI) is gratefully acknowledged. Corresponding Author; Department of Social Science and Policy Studies (SSPS), Worcester Polytechnic Institute (WPI), 100 Institute Road, Worcester, MA, USA, 01609; Phone: ; Fax: ; adksmith@wpi.edu. Department of Social Science and Policy Studies (SSPS), Worcester Polytechnic Institute (WPI), 100 Institute Road, Worcester, MA, USA, 01609; xwen@wpi.edu. 1

2 1 Introduction Some public goods are provided jointly by institutions and individuals. Institutions provide the technologies for producing the public goods using voluntary contributions from individuals. With national defense, for example, the military is an institution that requires the contributions of individuals who join the armed forces in order to produce the public good. With the environment, organizations like the Environmental Protection Agency (EPA) sponsor and conduct research, and participate in policy development. But this only creates the technology necessary for having a good environment. For good environmental quality, households need to make responsible decisions, informed by current knowledge and policies, about things like waste management and energy usage. In this paper, we examine how people make the tradeoff between investing in the productivity of institutions that produce public goods (the efficiency of technologies for producing public goods) and contributing to provision. 1 Subjects receive endowments of money and vote within their groups over the common amount of money that each subject in the group will invest in the productivity of contributions, mimicking voting over tax policies in real economies. Next, subjects make voluntary contributions to the provision of the public good, as in conventional public good games (Marwell and Ames, 1979; Isaac, Walker and Thomas, 1984). Since investment in productivity has diminishing returns, the game has an interior social optimum in which subjects invest a specific proportion of their endowments in productivity and then contribute the rest of their money to provision. We find that subjects do well with choosing investment levels, but not as well with contributions. Investment starts out above the optimum, but approaches the optimum with repetition, in spite of the comparatively small payoff benefits associated with making better investment decisions. The primary source of loss for subjects (relative to the social optimum) is their contribution behavior. As in conventional public good games (see Ledyard (1995) 1 Our view that institutions for producing public goods are essentially production technologies parallels Jean Tirole s (1988) theory of the firm as a production technology. 2

3 and Chaudhuri (2011)), subjects contribute significantly more than the Nash prediction of nothing, but fall well short of the social optimum. As far as the tradeoff between investment and contributions, there is no significant evidence that absolute contribution amounts vary as a function of investment. Since subjects in groups that make large investments have less money left to contribute in the contribution stage, this suggests that the incentive effect of having high contribution productivity is roughly offset by the budget effect of having less money left to contribute. Consistent with this interpretation, regressions of contribution percentages, which implicitly control for the budget effect by normalizing contribution amounts according to the amount of money subjects have in the contribution stage, indicate that there is indeed a significant incentive effect, with subjects contributing larger proportions of their remaining money after investing large amounts. Our evidence on the incentive effect matches Isaac and Walker s (1988) finding that contributions are increasing in the marginal per capita returns (MPCRs) of public goods. Our decision environment is different from theirs though, because our subjects choose contribution productivity. The reason that it is important to study public good provision in an environment in which contribution productivity is chosen endogenously by subjects rather than given exogenously by the experimenter is that in real economies, even though in the present day, the level of technology for producing many public goods is naturally occurring and requires no further investment, in the past, some combination of time, effort and money was expended to develop the current technology. With lighthouses, for example, over hundreds of years, people determined the best building architectures, light sources and optical means for focusing the light. Today, the more relevant investment decision seems to be how much to invest in electronic (GPS) navigation systems as traditional lighthouse technology becomes obsolete. However, the example illustrates the fact that in real economies, the technology for producing public goods is not exogenous. It either has to be developed or was developed in the past. Previous papers on endogenous institutions in public good games focus mainly on the 3

4 endogenous determination and subsequent effects of punishment mechanisms (Gurerk, Irlenbusch and Rockenbach, 2006; Tyran and Feld, 2006; Ertan, Page and Putterman, 2009; Kosfeld, Okada and Riedl, 2009; Sutter, Haigner and Kocher, 2010; Putterman, Tyran and Kamei, 2011; Markussen, Putterman and Tyran, 2014). Our paper contributes to this literature more broadly by instead examining the endogenous determination of contribution productivity. On the topic of the endogenous determination of the benefits of cooperation, Dal Bo, Foster and Putterman (2010) have subjects vote over implementing a policy that changes the payoffs in a prisoner s dilemma game in a manner that promotes cooperation. An important difference between Dal Bo, Foster and Putterman s (2010) paper and ours is that we have subjects make the investment and contribution decisions many times, allowing us to use fixed effects estimation to control for individual-specific unobservable characteristics that potentially cause both investment and contribution behavior. Since Dal Bo, Foster and Putterman (2010) have subjects make the policy decision only once, they need additional design elements (random implementation of the preferred policy) to control for the endogenous selection of subjects to their policy (decision) environments. Other papers (Sutter, Haigner and Kocher, 2010; Markussen, Putterman and Tyran, 2014) use supplementary treatments to address the endogeneity. Norton and Isaac (2010) also study the endogenous determination of the benefits of cooperation. They examine a team production environment in which each group has a manager who chooses contribution productivity. The other subjects then make voluntary contributions to provision. The experiment is like ours in that subjects determine contribution productivity, but different because contribution productivity is not chosen by the contributing subjects. Finally, in Isaac and Norton (2013), subjects vote over taxes that serve as preliminary contributions to the public good, which can later be supplemented by voluntary contributions. There is thus an endogenous institutional choice, but no opportunity to augment the production technology. Our paper contributes to the previous literature in three main ways. To begin, to our 4

5 knowledge, we are the first to have contributing subjects choose contribution productivity. By having them incur a cost for augmenting the production technology, we learn about how people make the tradeoff between having more efficient technologies for producing public goods and having more money left to contribute to provision. Second, we make a methodological contribution by showing that in a repeated game environment, fixed effects estimation can be used to control for individual-specific unobservables that potentially underlie both institutional choice and cooperative behavior. On this issue, in contrast to Dal Bo, Foster and Putterman (2010), we find that in our continuous action space, repeated game, the endogenous institutional choice has small effects on the estimated relationship between institutional choice and subsequent cooperative behavior. Finally, we learn that subjects collectively do a good job of choosing the level of institutional development/contribution productivity. The primary source of loss relative to the social optimum is contribution behavior, which provides support for continued efforts to understand free riding behavior and how it can be prevented. 2 The Experiment Subjects were randomly and anonymously assigned to groups of four that were fixed for ten rounds of decision-making. At the beginning of each round, each subject received an endowment of 10 lab dollars (LD; later converted to USD at a rate of 1 LD = 0.1 USD). Each round consisted of two stages: the investment stage and the contribution stage. Investment: In the investment stage, subjects voted over how many LD each subject in the group would invest in the productivity of contributions to the public good (each subject invested the same amount). Specifically, each subject submitted a number between 0 and 10 (inclusive; up to one digit after the decimal point was allowed). The investment level was the median of the four votes (mean of the two middle votes). Each subject then had the investment level deducted from her endowment of 10 LD and contribution productivity was determined according to the productivity rule: 5

6 M = 0.1 I (1) where I is investment and M represents productivity because M stands for multiplier (the amount by which the sum of contributions was multiplied to determine each subject s share of the group account). The productivity rule is illustrated in Figure 1. If there is no investment, there is no productivity (I = 0 M = 0). With full investment (I = 10), productivity is high (M = 1), but subjects have no money left to contribute to provision. The returns to investment are diminishing (M II < 0). Figure 1: M as a Function of Investment Contributions: Following the vote over the investment level, subjects were informed of their group s M, and then they proceeded to the contribution stage, which was for the most part the same as in conventional public good games. Subjects chose how much of their money to contribute to the group account and how much to keep for themselves. However, instead of having their full endowments of 10 LD, subjects had a budget of 10 I LD. Also, the productivity of contributions was the M that was endogenously chosen in the investment stage. As such, the payoffs were: 4 π s = 10 I c s + M(I) c t (2) t=1 where c s is the contribution of subject s, whose four group members are indexed by t. Payoffs are equal to the endowments of 10 LD, less the investment level (I) and voluntary contribution (c s ), plus M (which is a function of the investment level) times the sum of contributions. At the end of each round, subjects were told the sum of contributions to their group account and their payoffs in the round. The next round then began with another vote over the investment level. At the end of the ten rounds, each subject s ten payoffs were converted to USD and added to a $5 show-up fee to determine her final earnings. 6

7 Payoff Functions: Under different assumptions about the percentage of money with which subjects begin the contribution stage that they contribute to the public good, payoffs can be plotted as a function of investment (see Figure 2). For example, assuming that subjects contribute 100% of the money with which they begin the contribution stage (c = 100%), payoffs are given by the blue (top) line. If subjects invest nothing, productivity is zero, and contributing everything gives them payoffs of zero. On the other hand, if they invest everything, productivity is maximized, but they have nothing left to contribute. Payoffs are once again zero. By investing 3.33 LD, and then contributing everything that they have left in the contribution stage, payoffs are maximized at LD for each subject. This is similar to the maximum attainable payoffs of 16 in conventional public good games when groups of four subjects are endowed with 10 each and the MPCR is 0.4, a common parameterization in the literature (see Ledyard (1995)). The green (bottom) line is payoffs under the assumption that the contribution percentage is zero. In this case, it is best to invest nothing because investment in productivity is wasted. It is expenditure that does not provide any benefits or returns. The red (middle) line is an intermediate case in which the contribution percentage is 50%. With an investment of 2.5 LD, payoffs are maximized at LD, demonstrating that the optimal investment level is positively related to the contribution rate. Figure 2: Payoffs as a Function of Investment 2.1 Nash Equilibrium and Social Optimum Nash Equilibrium: Under the traditional assumption of individual wealth maximization, the subgame perfect Nash equilibrium can be determined by backward induction. In the contribution stage of the final round, everyone free rides and contributes nothing. Anticipating this, there should be no investment in the final round. In light of this outcome in the final round, the same behavior occurs in the second to last round, and every round prior to that, up to and including the first round. Thus, the subgame perfect Nash equilibrium is for every 7

8 round to have: 1. A set of votes (v 1, v 2, v 3, v 4 ) such that v 1 = v 2 = v 3 = 0 v 4, and 2. Contributions c 1 = c 2 = c 3 = c 4 = 0. The votes achieve an investment level of I = 0, and since there are no contributions, the payoffs are 10 LD (subjects simply keep their endowments). Social Optimum: In contrast to the subgame perfect Nash equilibrium, as suggested by Figure 2, the social optimum is for every round to have: 1. A set of votes v 1 v 2 v 3 v 4 such that (v 2+v 3 ) 2 = 10 3, and 2. Contributions c 1 = c 2 = c 3 = c 4 = The votes result in an investment level of I = 3.33, and when subjects subsequently contribute everything that they have left (6.67 LD each), the payoffs are LD. 2.2 Hypotheses An important difference between the investment and contribution stages is the potential to free ride. In the investment stage, free riding is impossible because everyone invests the same amount. In the contribution stage, free riding is always an option, as in conventional public good games (Marwell and Ames, 1979; Isaac, Walker and Thomas, 1984). This insight underlies both of our hypotheses. Hypothesis 1: Subjects do well with investment. We expect that the lack of a free riding opportunity in the investment stage will help subjects do well with investment. Specifically, we expect that they will choose investment levels close to the social optimum and that investment decisions will not be the primary source of loss relative to the social optimum. Furthermore, we anticipate that investment 8

9 decisions will improve with repetition of the game. In particular, we think that investment levels will approach the optimal amounts (which depend on contribution behavior). Hypothesis 2: Significant free riding in the contribution stage. In light of the vast previous public good game literature documenting free riding behavior (see Ledyard (1995) for a comprehensive survey and Chaudhuri (2011) for a survey of post-ledyard (1995) research), we expect significant free riding in the contribution stage. We anticipate that this will be the primary source of loss relative to the social optimum. Consistent with the previous literature, we expect that free riding will increase with repetition of the game, but that contributions will remain significantly above zero (on average). The anticipated trend in contributions implies a divergence of contributions from the social optimum. 3 Results The experiment was programmed and conducted with the experiment software z-tree (Fischbacher, 2007). A total of 88 subjects participated (11 sessions of eight subjects each). The data set thus consists of observations from 22 independent groups. There are 880 individual votes and contributions, and 220 investment levels (determined at the group-level). The experiment lasted 45 minutes and average total earnings were $ Understanding the Trends The trends of average votes and investment are very similar. Favoring brevity, we focus on the trend of average investment, since it is investment that determines payoffs (through its effect on M). However, a figure comparing the trends of average votes and investment is provided in the Appendix. Figure 3 plots average investment by round. It was 4.45 LD in round 1, but fell to 3.45 LD in round 10, creating a path consistent with Hypothesis 1. The investment levels imply 9

10 Ms in the range of , which are high compared to most MPCRs in the literature (Ledyard, 1995), indicating that when subjects choose the productivity of contributions, they tend toward high productivity, even when it is costly to do so. 2 Figure 3: Average Investment by Round Figure 4 shows average contributions by round. They started at 2.91 LD in round 1, declining to 2.64 LD by round 10. Contributions are above the Nash prediction of zero, but also far short of the socially optimal 100%, consistent with Hypothesis 2. Finally, Figure 5 illustrates average contribution percentages by round, where contribution percentage is the percentage of money with which a subject began the contribution stage that she contributed to the group account (contribution% = contribution ). The average contribution percentage 10 I begins at 0.53 and falls to Figures 4 and 5: Average Contributions by Round and Average Contribution Percentages by Round The optimal level of investment is 3.33 LD only if the subsequent contribution percentage is 1; it is lower for lower contribution percentages. In light of this, Figure 6 plots average optimal or ideal investment by round, where ideal investment is calculated at the grouplevel, based on each group s average contribution percentage in the round. Average ideal investment started at 2.54 and declined to Since both investment and ideal investment declined, an important question is how the difference between them changed over time. Figure 7 shows the trend of the average difference between investment and ideal investment, which started at 1.92 and fell to The difference is diminishing, indicating that investment was approaching the optimal amounts, as suggested by Hypothesis 1. Figures 6 and 7: Average Ideal Investment by Round and Average Difference between Investment and Ideal Investment (by Round) 2 A figure plotting average M by round is also shown in the Appendix. 10

11 It is not clear that any of the trends are convergent, and so instead of estimating convergence equations, as in Noussair, Plott and Reizman (1995) and Eckel and Grossman (2005), we simply plot linear time trends. We make no claims about what might happen beyond the range of our data (beyond round 10), but assert that the linear trends do a good job of capturing what happens between rounds 1 and 10. The regressions underlying the linear trends are reported in Table 1. Investment is a group-level variable. For contributions and contribution percentages, we use group-level averages in each round as the units of observation. Ideal investment (investment ) and the difference between ideal investment and investment are calculated at the group-level. OLS results are reported, but random and fixed effects specifications give identical results, all of which are consistent with the intuition provided by the figures. Table 1: Regressions on a Linear Time Trend Changes in Average Payoffs: Using the linear trend predicted values of investment and average contribution percentages in rounds 1 and 10, we can calculate how the changes in each variable affected average payoffs. A summary of such calculations is given in Table 1. Predicted investment is 4.57 LD in round 1 and the predicted contribution percentage is 0.59, giving a payoff of LD. In round 10, predicted investment, contribution percentage and payoff are 3.57 LD, 0.45 and LD. The payoff gain associated with investment decreasing from 4.57 LD to 3.57 LD is completely offset (and then some) by the contribution percentage decreasing from 0.59 to At both investment levels, the payoff benefit of full contributions is large. In fact, at an investment level of 3.57 LD, with full contributions, the payoff is LD, which is almost equal to the social optimum of LD. The bottom two rows are based on the optimal investment levels for contribution percentages of 0.59 and Even at these low investment levels, full contributions give large gains in payoffs. The findings thus support Hypotheses 1 and 2. In particular, the primary source of loss is contribution behavior and not the investment decisions. Subjects do well with investment in 11

12 spite of the low payoff benefits associated with making better investment choices. 3 Table 2: Payoffs as a Function of Investment and Contribution Percentage - Linear Trend Predicted Values 3.2 Regression Analysis Our regression analysis focuses on identifying the determinants of investment and on characterizing the relationship between investment and contribution behavior. Since subjects in the same groups always had the same investment levels (because investment was determined at the group-level), most of the variation in our data that is relevant for our analysis occurs between groups, rather than among subjects within the same groups. For this reason, we conduct the analysis at the group-level, focusing our attention on investment (a grouplevel variable), average contributions (calculated at the group-level) and average contribution percentages (also at the group-level). Investment: We begin by regressing the investment levels chosen by each group in each round on a measure of average contributions in the previous round and the round (see Table 3). For the measure of average contributions, we must choose between average absolute contributions and average percentage contributions since the two variables are highly correlated (Pearson and Spearman s ρ = 0.79, p < 0.01). Since the latter variable provides slightly more explanatory power than the former (as indicated by R 2 s), we include only the latter in the model. Table 3: Regressions of Investment, Average Contributions, and Average Contribution Percentages 3 A table parallel to Table 2, but using the actual values of investment and contribution percentages (instead of the predicted values) is shown in the Appendix. The numbers are slightly different, but the qualitative story is exactly the same. We favor using the linear trend predicted values because the linear trend smoothes out the statistical variation that occurred from round to round. The Appendix also has a figure showing average payoffs by round. 12

13 In model (1)(a random effects specification), unit increases in average percentage contributions in the previous round are associated with LD increases in investment, indicating that lower average percentage contributions in one round are associated with lower investment levels in the next round. The effect seems very large in magnitude, but it is important to remember that the potential range in percentage contributions is only from 0 to 1, and for the most part, the averages varied from 0.4 to 0.6. Nothing close to a unit increase ever occurred. The effect of repetition is that investment decreased by an average of LDs in each round. 4 Model (2) is the parallel fixed effects specification. 5 In this model, group-level fixed effects control for group-specific characteristics that might affect both investment and contribution behavior, preventing any time invariant omitted variables (such as a high predisposition for being cooperative) from biasing the estimates. The effects of the regressors are estimated using the within group variation that occurs over time. However, the results are very similar. In particular, the effect of average percentage contributions in the previous round is smaller, but the difference is less than half a standard error. 6 Average Contributions: The remaining regressions provide evidence on the relationship between investment and contribution behavior. 7 In theory, investment could promote higher or lower contributions. After investing large amounts, subjects have a higher incentive to contribute because contribution productivity is higher (the incentive effect ). However, subjects also have less money available (the budget effect ). Our regressions aim to determine whether one effect dominates the other. In model (3), we regress the average contribution of each group in each round on in- 4 Regressions using the method of Arellano and Bond (Arellano and Bond, 1991; not shown, but available upon request) indicate that investment does not have a significant autoregressive component (the first lag of investment is not significant). 5 We favor random and fixed effects specifications over tobit because they are more conservative in terms of the significance of the regressors. 6 Since M is a monotonic transformation of investment, regressions of M provide the same insight as the regressions of investment. 7 Here again, the results are the same if we use M instead of investment. We favor using investment because the subjects voted over investment specifically, which in turn determined M. 13

14 vestment and the round. 8 The effect of investment is not significant, suggesting that to the extent that there are significant incentive and budget effects, they approximately offset each other. Model (4) is the corresponding fixed effects model, which uses group-level fixed effects to control for time invariant unobservables, and estimates the effects of the regressors using within group variation. The results are very similar to model (3). A potential concern with models (3) and (4) is that the level of investment (a regressor) determines the range of potential values for average contributions (the dependent variable), potentially introducing correlation between one of the regressors (investment) and each regression s error term. Such endogeneity would bias estimates of causal effects. However, in practice, few subjects exhausted their budgets (it happened 109 out of a possible 880 times ( = 12.4%)), and in both regressions, the correlation between investment and the error term is small and insignificant (model (3): Pearson s ρ = 0.02, p = 0.82; Spearman s ρ = 0.08, p = 0.26; model (4): Pearson s ρ = 0.02, p = 0.78; Spearman s ρ = 0.08, p = 0.24). Also, the aim of the regressions is estimating the partial correlation between investment and average contributions, not identifying the underlying causal model. Even so, in model (5), we estimate the effect of investment using instrumental variables (IV). Specifically, we use lagged investment as an instrument for investment (for a full explanation of using lagged variables as instruments for endogenous regressors, please consult Smith (2013)). The results are very similar. Specifically, investment once again does not have a significant effect, providing further support for the conclusion that the incentive and budget effects of investment roughly offset each other. Average Contribution Percentages: Since calculating contribution percentages normalizes the data by dividing contributions by the amounts of money with which subjects began the contribution stage, the regressions of average contribution percentages implicitly control for the budget effect. These regressions identify the incentive effect of investment (having 8 Arellano and Bond (1991) estimates do not provide significant evidence that average contributions are autoregressive. The same is true for average contribution percentages. 14

15 higher contribution productivity). In model (6), LD increases in investment are associated with unit increases in average contribution percentages, a finding consistent with Isaac and Walker s (1988) result that subjects contribute more when the MPCR from the public good is higher. However, our decision environment is different from theirs because in our experiment, subjects choose contribution productivity. Model (7) is the fixed effects version of model (6). Model (7) controls for time invariant omitted variables potentially correlated with investment and contributions, but the results are very similar to those from model (6). Interpreted in conjunction with the results from models (3) - (5), models (6) and (7) indicate that investing large amounts and having higher contribution productivity creates a significant incentive effect that promotes contributions. However, absolute contributions are not significantly related to investment because the incentive effect of investment is offset by a budget effect that is approximately equal in magnitude and opposite in direction. 4 Conclusion We present a public good game experiment on making the tradeoff between investing in contribution productivity and contributing to provision. In spite of doing well with investment, subjects do poorly with maximizing their payoffs in the contribution stage, making their contribution behavior the primary source of loss relative to the social optimum. Regarding the tradeoff between investment and contributions, contribution percentages are increasing in investment, indicating that there is a significant incentive effect of contribution productivity. Absolute contributions, on the other hand, are invariant to investment, suggesting that the incentive effect of investment is offset by a budget effect similar in magnitude. We conjecture that subjects do well with investment because all group members invest the same amount, making it impossible to free ride in the investment stage. In the contribution stage, free riding is common, as in conventional public good games. The finding that subjects 15

16 do well with investment suggests that with equal political power and a median voter rule, people on average make good decisions about investing in institutions. This should strengthen our confidence in people s collective abilities to choose appropriate levels of institutional development and the size of government. The finding that the primary source of loss is contribution behavior supports continued research efforts to understand how people make contribution decisions. Finally, our experiment provides a basic methodology for examining future research topics ranging from how income inequality affects demand for contribution productivity to how communication helps coordinate the tradeoff between investment and contributions. A question that remains unanswered by this study though is why subjects continued to invest significant amounts even when their payoffs on average ended up only marginally higher than their initial endowments. A potential explanation is that they were consistently optimistic about the contributions of others. Optimism in repeated public good games is well-documented (Fischbacher and Gaechter, 2010; Gaechter and Renner, 2010; Smith, 2013), but its role in this novel decision environment still merits further investigation. 16

17 References Arellano, C. and S. Bond (1991). Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations. Review of Economic Studies, 58(2), Chaudhuri, A. (2011). Sustaining Cooperation in Laboratory Public Goods Experiments: A Selective Survey of the Literature. Experimental Economics, 14(1), Dal Bo, P., A. Foster and L. Putterman (2010). Institutions and Behavior: Experimental Evidence on the Effects of Democracy. American Economic Review, 100(5), Eckel, C. and P. Grossman (2005). Managing Diversity by Creating Team Identity. Journal of Economic Behavior and Organization, 58(3), Ertan, A., T. Page and L. Putterman (2009). Who to Punish? Individual Decisions and Majority Rule in Mitigating the Free Rider Problem. European Economic Review, 53(5), Fischbacher, U. (2007). z-tree: Zurich Toolbox for Ready-made Economic Experiments. Experimental Economics, 10(2), Fischbacher, U. and S. Gaechter (2010). Social Preferences, Beliefs, and the Dynamics of Free Riding in Public Goods Experiments. American Economic Review, 100(1), Gaechter, S. and E. Renner (2010). The Effects of (Incentivized) Belief Elicitation in Public Goods Experiments. Experimental Economics, 13(3), Gurerk, O., B. Irlenbusch and B. Rockenbach (2006). The Competitive Advantage of Sanctioning Institutions. Science, 312(5770), Isaac, R. and D. Norton (2013). Endogenous Institutions and the Possibility of Reverse Crowding Out. Public Choice, 156(1-2), Isaac, R. and J. Walker (1988). Group Size Effects in Public Goods Provision: The Voluntary Contributions Mechanism. Quarterly Journal of Economics, 101(1), Isaac, R., J. Walker and S. Thomas (1984). Divergent Evidence on Free Riding: An Experimental Examination of Possible Explanations. Public Choice, 43(2),

18 Kosfeld, M., A. Okada and A. Riedl (2009). Institution Formation in Public Goods Games. American Economic Review, 99(4), Ledyard, J. (1995). Public Goods: A Survey of Experimental Research. In John H. Kagel and Al E. Roth Handbook of Experimental Economics. Princeton University Press, Princeton, NJ. Markussen, T., L. Putterman and J.-R. Tyran (2014). Self-Organization for Collective Action: An Experimental Study of Voting on Formal, Informal and No Sanction Regimes. Review of Economic Studies, 81(1), Marwell, G. and R. Ames (1979). Experiments on the Provision of Public Goods 1: Resources, Interest, Group Size, and the Free-Rider Problem. American Journal of Sociology, 84(6), Norton, D. and R. Isaac (2010). Endogenous Production Technology in a Public Goods Enterprise. In R. Mark Isaac and Douglas A. Norton Research in Experimental Economics Volume 13: Charity with Choice. Emerald, Boston, MA. Noussair, C., C. Plott and R. Riezman (1995). An Experimental Investigation of the Patterns of International Trade. American Economic Review, 85(3), Putterman, L., J.-R. Tyran and K. Kamei (2011). Public Goods and Voting on Formal Sanction Schemes. Journal of Public Economics, 95(9-10), Smith, A. (2013). Estimating the Causal Effect of Beliefs on Contributions in Repeated Public Good Games. Experimental Economics, 16(3), Sutter, M., S. Haigner and M. Kocher (2010). Choosing the Carrot or the Stick? Endogenous Institutional Choice in Social Dilemma Situations. Review of Economic Studies, 77(4), Tirole, J. (1988). The Theory of Industrial Organization. MIT Press, Cambridge, MA. Tyran, J.-R. and L. Feld (2006). Achieving Compliance when Legal Sanctions are Non- Deterrent. Scandinavian Journal of Economics, 108(1),

19 Table 1: Regressions on a Linear Time Trend (1) (2) (3) (4) (5) dependent variable: investment ave contribution ave contribution% investment investment investment round *** (0.030) constant 4.680*** (0.184) ** (0.025) 3.235*** (0.141) *** (0.004) 0.607*** (0.024) *** (0.016) 2.755*** (0.076) * (0.027) 1.925*** (0.169) method OLS OLS OLS OLS OLS groups rounds n R Notes: Robust standard errors are reported in parentheses. ***: p <.01; **: p <.05; *: p <.1 19

20 Table 2: Payoffs as Function of Investment and Contribution Percentage - Linear Trend Predicted Values contribution% investment round 1 = 0.59 round 10 = 0.45 optimal = 1.00 round 1 = round 10 = optimal = optimal59 = optimal45 =

21 Table 3: Regressions of Investment, Average Contributions, and Average Contribution Percentages (1) (2) (3) (4) (5) (6) (7) dependent variable: investment investment ave cont ave cont ave cont ave cont% ave cont% ave cont% *** (0.519) 1.908*** (0.536) investment (0.099) round ** (0.042) constant 3.462*** (0.467) ** (0.042) 3.573*** (0.422) *** (0.026) 3.969*** (0.505) (0.100) ** (0.026) 3.980*** (0.416) (0.139) *** (0.030) 3.837*** (0.668) 0.053*** (0.013) *** (0.004) 0.361*** (0.066) 0.051*** (0.013) *** (0.004) 0.367*** (0.056) method RE FE RE FE IV-2SLS RE FE groups rounds n R Notes: Robust standard errors are reported in parentheses. ***: p <.01; **: p <.05; *: p <.1 21

22 Figure 1: M as a Function of Investment Figure 1: M as a Function of Investment M Investment 22

23 Figure 2: Payoffs as a Function of Investment Figure 2: Payoffs as a Function of Investment Payoff Payoffs(c=100%) Payoffs(c=50%) Payoffs(c=0%) Investment 23

24 Figure 3: Average Investment by Round Figure 3: Average Investment by Round 5 4 Investment 3 2 Actual Linear Trend Round 24

25 Figure 4: Average Contributions by Round Figure 4: Average Contributions by Round 4 3 Contributions 2 1 Actual Linear Trend Round 25

26 Figure 5: Average Contribution Percentages by Round Figure 5: Average Contribution Percentages by Round Contribution% Actual Linear Trend Round 26

27 Figure 6: Average Ideal Investment by Round Figure 6: Average Ideal Investment by Round 3 Ideal Investment 2 1 Actual Linear Trend Round 27

28 Figure 7: Average Difference between Investment and Ideal Investment (by Round) Figure 7: Average Difference between Investment and Ideal Investment (by Round) 2 Invesmtent - Ideal Investment Actual Linear Trend Round 28

29 Appendix Table 4: Payoffs as Function of Investment and Contribution Percentage - Actual Values contribution% investment round 1 = 0.53 round 10 = 0.43 optimal = 1.00 round 1 = round 10 = optimal = optimal53 = optimal43 =

30 Figure 8: Average Votes and Investment by Round Figure 8: Average Votes and Investment by Round 5 4 Votes / Investment 3 2 Votes Investment Round Average votes and investment start out very close to one another, but move apart over time. The mean and median votes are initially very similar. With repetition of the game, the median vote (which determines investment) starts falling below the mean as the distribution of votes develops some skewness. 30

31 Figure 9: Average M by Round Figure 9: Average M by Round M Round 31

32 Figure 10: Average Payoffs by Round Figure 10: Average Payoffs by Round Average Payoffs Round 32

33 Instructions This is an experiment in decision-making. Decisions result in monetary payoffs to be paid in cash at the end of the experiment. Payments are considered compensation for the time and effort put into making decisions. The experiment lasts a total of about 45 minutes. Please refrain from speaking with others during the experiment. If you have any questions, raise your hand and an experimenter will assist you. You will be randomly assigned to a group of 4 people. Since the assignment occurs over the computer network, you will not know which other people in the room have been assigned to the same group as you. The experiment consists of 10 rounds of decision-making. Each round has 2 stages: the investment stage and the contribution stage. I will start by explaining the contribution stage and then come back to the investment stage in a few minutes. The contribution stage proceeds as follows: 1. Each person begins the contribution stage with a certain amount of money (denoted in lab dollars; LD). The exact amount will be explained in a few minutes. 2. Each person must decide how much of his/her money to contribute to the group account. Contributions may include up to 2 digits after the decimal point. Any amounts not contributed to the group account are simply kept by the person. 3. The contributions of your 4 group members will be added up and each person will receive M times the sum of the 4 contributions. Therefore, the payoffs of each person in each round will be: amount kept + M * (sum of contributions). So let s say that each person begins the stage with 8 LD, each person keeps 4 LD and contributes 4 LD, and M is 0.5. Each person s payoff will be: ( ) = 12 LD. 4. M is a number between 0 and 1, so for each LD that you contribute to the group account, you personally will get less than 1 LD back. However, each other person in 33

34 your group will also receive M LD as a result of your contribution. Similarly, you will benefit from the contributions that your group members make. This is the incentive to make contributions. The contribution stage occurs after the investment stage. The purpose of the investment stage is to determine the value of M in the contribution stage. The investment stage proceeds as follows: 1. Each person receives 10 LD. 2. Each person votes on how many LD each person in his/her group will invest in M. Each person in your group will invest the same amount. M is determined according to the following equation: M = 0.1 investment where investment is the amount invested by each person. So if the investment amount is 2.5 LD, M will be = 0.25 = 0.5. If the investment amount is 4.9 LD, M will be = 0.49 = 0.7. Two special cases are that investment = 0 M = 0 and investment = 10 M = Here s how the voting works: Each person enters an investment amount between 0 LD and 10 LD (inclusive; up to 1 digit after the decimal point is allowed). The highest and lowest votes are dropped and the investment amount is the average of the 2 middle votes. Thus, if the votes are 1, 2, 3 and 4, the investment amount will be 2.5 LD. If the votes are 0, 4, 4 and 7, the investment amount will be 4 LD. 4. The investment amount is subtracted from each person s 10 LD, and he/she begins the contribution stage with the amount that remains. If the investment amount is 3 LD, each person will begin the contribution stage with 7 LD. If the investment amount is 10 LD, each person will have 0 LD left, and will have no money left to contribute in the contribution stage. Each of the 10 rounds follows exactly the same process. The groups of 4 are fixed for the whole sequence of 10 rounds. At the end of the 10 rounds, payoffs from the 10 rounds will 34

35 be added up and converted to real money at a rate of 1 LD = 0.1 USD. This amount will be added to a $5 show-up fee to determine your final earnings. You will be asked some demographic questions and also to provide some contact information. Payments will be made in a private manner. Let me briefly summarize the experiment in the order that each stage will occur: 1. You will be randomly and anonymously assigned to a group of 4 over the computer network. 2. You will complete 10 rounds of decision-making in these groups. 3. You start each round with 10 LD. 4. In the investment stage, you vote over how much each member of your group will invest in M. 5. Your group s investment in M determines M in the contribution stage. 6. You begin the contribution stage with 10 LD less the investment level that your group chose. 7. You decide how much to contribute to the group account. 8. The sum of your group members contributions to the group account are multiplied by M and added to any money that you kept to determine your payoff in the round. 9. After the 10 rounds, payoffs are added up and converted to real money. Are there any questions? 35