Investing in Institutions for Cooperation

Investing in Institutions for Cooperation Alexander Smith Xi Wen March 20, 2015 Abstract We present a voluntary contribution mechanism public good game experiment on 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 and subsequently make individual voluntary contributions to provision, as in conventional public good games. Investment increases the incentive to contribute by raising the return on contributions to the public good ( the incentive effect ), but also leaves subjects with less money from which to make their contributions ( the budget effect ), making the relationship between investment and contributions an empirical question. Compared to the game s social optimum, the subjects do well with investment; the primary source of loss is their contribution behavior. Regarding the relationship between investment and contributions, absolute contribution amounts are not significantly related to investment, suggesting that the incentive and budget effects approximately offset each other. Keywords: Public good games; Endogenous institutions; Production technology; Contribution productivity JEL Classification: C71; C91; C92; H41 Corresponding Author; Department of Social Science and Policy Studies (SSPS), Worcester Polytechnic Institute (WPI), 100 Institute Road, Worcester, MA, USA, 01609; Phone: + 1 508 831 6543; Fax: + 1 508 831 5896; Email: adksmith@wpi.edu. Department of Social Science and Policy Studies (SSPS), Worcester Polytechnic Institute (WPI), 100 Institute Road, Worcester, MA, USA, 01609; Email: xwen@wpi.edu. 1

1 Introduction Some public goods are provided jointly by institutions and individuals: institutions provide the technology for producing the public good 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 provide the public good. With the environment, organizations like the Environmental Protection Agency (EPA) sponsor and conduct research, and participate in policy development, creating the technologies necessary for having a good environment. But households need to make responsible decisions about things like waste management and energy usage in order for us to achieve high environmental quality. In this paper, we study (1) investment in the productivity of an institution that produces a public good, and (2) subsequent voluntary contributions to the provision of the public good. 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 augmenting the technology for producing the public good. Next, they make individual voluntary contributions to the provision of the public good, as in conventional public good games (Marwell and Ames 1979; Isaac et al. 1984). The game has an interior social optimum in which subjects invest a specific proportion of their endowments in productivity and contribute the rest of their money to provision. Our intention is capturing the key features of the real world process of determining the size of public institutions through the political (voting) process and then subsequently supporting those institutions by making individual voluntary contributions to the provision of the public goods that the institutions provide. Examples of such public goods include national defense, environmental quality, and to a lesser extent, healthcare and education, which are not public 1 We capture the productivity of the institution by the efficiency of the technology for producing the public good. 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

goods in the strict sense, but do have significant positive externalities. 2 In healthcare and education, the institutions are often funded by government (through the tax system), but provision depends critically on the people who work as nurses and teachers, partly as a way of making contributions to society, and members of the community who volunteer their time at local hospitals and schools, and sometimes donate money. Subjects have a single, fixed endowment in each period of the game from which to make their investments in productivity and contributions to provision. The game thus captures differences between the USA and Europe, for example, where people typically vote to have income taxed at a higher rate, have better funded (and in many ways more productive) public institutions, but then, as a result of the higher taxes, have fewer private resources remaining from which to make individual voluntary contributions. The experiment design allows us to study, at the individual level, how people substitute between investing in productivity and contributing to provision. Our aim is not to capture the provision of public goods by charities that have their organizational structures determined by a board of directors and donors who are typically different people. We want to focus on situations in which the investors are also the contributors. Norton and Isaac (2010) examine what happens when some subjects choose the contribution productivity faced by others. In our experiment, subjects do well with choosing investment, and we hypothesized, for a variety of reasons, that this would help them overcome the free riding that is pervasive in the voluntary provision of public goods (Ledyard 1995; Chaudhuri 2011). The first reason is that voting for a high investment level sends a signal of a willingness and potential intention to cooperate that could serve as a coordination mechanism for subjects. Second, even though the money spent on investment is sunk once the subjects begin the contribution stage, it is well documented that people allow sunk costs to affect their decision-making, exhibiting a preference for continuing an endeavor once an investment of money, time, or effort has been made (Arkes and Blumer 1985). Finally, Dal Bo et al. (2010) report that the effect of a 2 Healthcare is more applicable in countries with universal healthcare than in countries without it. 3

policy on cooperation is greater when subjects choose the policy themselves that when it is imposed exogenously. In our environment, this suggests that subjects should be more willing to cooperate after they choose the productivity of contributions. Our two-step public good provision procedure does not overcome the canonical free riding problem. Subjects initially choose investment levels above the social optimum, but investment approaches the optimum with repetition of the game, in spite of the comparatively small payoff benefits associated with making better investment decisions. Subjects primary source of loss (relative to the social optimum) is their contribution behavior. As in conventional public good games, they contribute significantly more than the Nash prediction of nothing, but fall well short of the social optimum. Regarding the relationship, or substitution between, investment and contributions, investment has two main implications for contributions. First, investment increases the incentive to contribute by raising the return on contributions to the public good ( the incentive effect ). Second, it leaves the subjects with less money from which to make their contributions ( the budget effect ), making the relationship between investment and contributions a question of whether the incentive or budget effect dominates. We fail to find significant evidence that absolute contribution amounts vary as a function of investment, suggesting that to extent that there are significant incentive and budget effects, they approximately offset each other. A potential explanation for this is that after investing a lot, subjects want to contribute more, but cannot because of their budget constraints. However, very few subjects ever exhaust their budgets. Contribution percentages, in contrast to absolute contributions, account for the budget effect by normalizing contribution amounts according to the amount of money that subjects have in the contribution stage. Contribution percentages are increasing in investment, indicating that there is indeed a significant incentive effect, a result matching Isaac and Walker s (1988) finding that contribution percentages are increasing in the marginal per capita return (MPCR) of public goods. Our decision environment is markedly different from theirs though, 4

because in our experiment, contribution productivity is endogenously determined by subjects during the investment stage of the game. Previous papers on endogenous institutions in public good games focus mainly on the implementation and subsequent effects of punishment mechanisms (Gurerk et al. 2006; Tyran and Feld 2006; Ertan et al. 2009; Kosfeld et al. 2009; Sutter et al. 2010; Putterman et al. 2011; Markussen et al. 2014). Our paper contributes to this literature more broadly by instead examining the endogenous determination of contribution productivity. On the topic of determining the benefits of cooperation, Dal Bo et al. (2010) have subjects vote on a policy that changes the payoffs in a prisoner s dilemma game in a manner that promotes cooperation. An important difference between Dal Bo et al. s (2010) paper and ours however 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 et al. (2010) have subjects make the policy decision only once, they require 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 et al. 2010; Markussen et al. 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. Their experiment is like ours in that subjects determine contribution productivity, but it is 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. 5

Our paper contributes to the previous literature in three main ways. First, to the best of our knowledge, we are the first to have contributing subjects in a public good game choose contribution productivity. By having subjects incur a cost for augmenting the production technology, we create a mechanism that allows us to learn about how people make the tradeoff between having more efficient technologies for producing public goods and having more money to contribute to provision. Our decision environment therefore allows us to provide new evidence on how choosing institutional environments affects subsequent cooperative behavior, which complements the prisoner s dilemma game findings of Dal Bo et al. (2010). Specifically, we find that choosing contribution productivity does not help to overcome the free riding that is typical in voluntary contribution mechanism (VCM) public good games. 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 unobservable characteristics that potentially underlie both institutional choice and behavior. This is different from the typical debate about whether random and fixed effects models give different results when analyzing panel data. We are to our knowledge the first in the experimental economics literature on endogenous institutional choice to demonstrate that fixed effect estimation can successfully be used to control for the endogenous selection of subjects to their decision-making environments. Third, our results provide new evidence on the nature of free riding in the provision of public goods. In our environment in which subjects invest in contribution productivity and subsequently contribute to provision, subjects collectively do a good job of choosing levels of institutional development/contribution productivity. Their primary source of loss relative to the social optimum is their contribution behavior, highlighting the importance of understanding the reasons for which people free ride on the voluntary contributions of others. 6

2 The Experiment Subjects are randomly and anonymously assigned to groups of four that are fixed for ten rounds of decision-making. At the beginning of each round, each subject receives an endowment of 10 lab dollars (LD; later converted to USD at a rate of 1 LD = 0.1 USD). Each round consists of two stages: the investment stage and the contribution stage. In the investment stage, subjects vote over how many LD each subject in the group will invest in the productivity of contributions to the public good (each subject invests the same amount). Specifically, each subject submits a number between 0 and 10 (inclusive; up to one digit after the decimal point is allowed). The investment level is the median of the four votes (mean of the two middle votes). 3 Each subject has the investment level deducted from her endowment of 10 LD and contribution productivity is determined according to the productivity rule: M = 0.1 I (1) where I is investment and M represents productivity because it stands for multiplier (the amount by which the sum of contributions is multiplied to determine each subject s return from the public good). 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 positive (M I > 0), but diminishing (M II < 0). The diminishing returns to investment incorporate empirical realism, and move the social optimum of the game away from the center of the action space, where it would be located if the relationship 3 With four person groups, there is not a unique vote that is the median vote. However, four person groups are the most common in the literature (Ledyard 1995; Chaudhuri 2011), and we want for our main departure from the previous literature to be the addition of the investment stage, and not changes in group size, changes to the conduct of the contribution stage, etc... 7

between I and M was linear. 45 Figure 1: M as a Function of Investment Following the vote over the investment level, subjects are informed of their group s M, and they proceed to the contribution stage, which is for the most part the same as in conventional public good games (Marwell and Ames 1979; Isaac et al. 1984). Subjects choose how much of their money to contribute to the public good and how much to keep for themselves. However, instead of having their full endowments of 10 LD, subjects have a budget of 10 I LD. Also, the productivity of contributions is the M that is endogenously chosen in the investment stage. As such, the payoffs are: 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 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. Having subjects complete the contribution stage with a budget of 10 I LD allows us to later analyze how they make unconstrained allocations between investing, contributing, and keeping money for themselves. An alternative design would give subjects separate budgets for investing and contributing, but this would restrict the potential to substitute between investment and contributions. We opt to not constrain decisions in this manner. Specifying payoffs as linear in contribution is consistent with the bulk of the previous literature on VCM public good games (Ledyard 1995; Chaudhuri 2011). Again, we want for our primary 4 The endogenous determination of M introduces the possibility that M could be less than 0.25, making the contribution stage of the game no longer a social dilemma. However, the concavity of M means that a very low investment level is required for this to happen. The lowest investment level that occurred was I = 0.75 and this resulted in an M of M = 0.27. 5 The investment stage adds a level of complexity to the conventional public good game. To prevent confusion, the instructions (see Appendix) include multiple examples of determining M from different sets of votes. We are probably also helped by the fact that we are an engineering school, with students who are generally very comfortable with equations. They all do a year of calculus as freshman in order to fulfill general degree requirements. 8

departure from the previous literature to be the addition of the investment stage, and not changes to the VCM. At the end of each round, subjects are told the sum of contributions to their group account and their payoffs in the round. The next round begins with another vote over the investment level. At the end of the ten rounds, each subject s ten payoffs are converted to USD and added to a $5 show-up fee to determine her final earnings. 2.1 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 payoffs of zero. On the other hand, if subjects invest everything, productivity is maximized, but there is nothing left to contribute. Payoffs are once again zero. By investing 3.33 LD, and then contributing everything remaining in the contribution stage, payoffs are maximized at 15.40 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 11.25 LD, demonstrating that the optimal investment level is positively related to the subsequent contribution percentage. Figure 2: Payoffs as a Function of Investment 9

2.2 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 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 = 20 3. 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), their payoffs are 15.40 LD. 2.3 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 10

good games (Marwell and Ames 1979; Isaac et al. 1984). This insight underlies our first two 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 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 2a: Incomplete cooperation in the contribution stage. In light of the vast previous public good game literature documenting free riding behavior (Ledyard 1995; Chaudhuri 2011), we expect less than complete cooperation 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 cooperation will decrease with repetition of the game, but that contributions will remain significantly above zero (on average). The trend that we anticipate implies a divergence of contributions from the social optimum. In spite of the large amount of previous evidence that supports Hypothesis 2a, there are reasons to believe that cooperation in the contribution stage could be better than what is typically observed (Ledyard 1995; Chaudhuri 2011). As such, we propose an alternative hypothesis: Hypothesis 2b: High cooperation in the contribution stage. The first reason to believe that cooperation might be higher than usual is that the addition of the investment stage to the standard, linear, VCM public good game gives subjects a chance to signal any intentions that they might have to cooperate. The investment stage 11

could thus potentially help coordinate activity in the contribution stage, and this could promote contributions. Second, it has previously been demonstrated that people allow sunk costs to affect their decision-making (Arkes and Blumer 1985), so even though the investment is sunk, the fact that subjects incurred a cost to invest might make them more inclined to contribute. Third, Dal Bo et al. (2010) report that subjects are more cooperative when they choose the parameters of their decision environments than when the payoff structure is exogenously imposed upon them, suggesting that we should see elevated contributions in our game. The psychological arguments of course neglect the economic incentives that tie contributions to investment, which are the basis for our final two hypotheses. Hypothesis 3a: Contributions are positively related to investment. After investing a large amount, subjects have a more productive technology for producing the public good, which provides a stronger incentive for them to contribute ( the incentive effect ). However, they also have less money remaining from which to make contributions ( the budget effect ). If the incentive effect dominates the budget effect, contributions will be positively related to investment. Alternatively: Hypothesis 3b: Contributions are negatively related to investment. If the budget effect dominates the incentive effect, contributions will be negatively related to investment. There is no ex ante reason to favor either Hypothesis 3a or 3b. 3 Results The experiment was programmed and conducted with the experiment software z-tree (Fischbacher 2007) using students recruited from introductory micro- and macroeconomics courses at our school. All students at our school are required to complete two social science courses, 12

and about half do so by enrolling in at least one introductory economics course, reducing the extent to which the subjects are an unrepresentative sample of the student population. The sessions occurred between September of 2013 and February of 2014, typically during the first few weeks of the term, before the students had had significant exposure the college level economics. A total of 88 subjects participated in the experiment (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 $15.31 (including the $5 show-up fee). 3.1 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 the trends of many of the key variables. Average investment was 4.45 LD in round 1 and fell to 3.45 LD in round 10, creating a path consistent with Hypothesis 1 that subjects do well with investment. The investment levels imply Ms in the range of 0.6 0.7, which are high compared to most MPCRs in the literature (Ledyard 1995), indicating that when subjects choose contribution productivity, they tend toward high productivity, even when it is costly to do so. 6 Figure 3: Trends of Key Variables Average contributions started at 2.91 LD and declined to 2.64 LD. The average amount of money remaining at the end of the contribution stage is also plotted; it began at 2.64 LD and 6 A figure plotting average M by round is also shown in the Appendix. 13

increased to 3.91 LD. Since the absolute contribution amounts do not account for the fact that different subjects began the contribution stage with different amounts of money (after having chosen different investment levels), Figure 4 plots 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 public good (contribution% = contribution). The average contribution percentage begins at 0.53 and falls to 0.43. In general, 10 I contributions are above the Nash prediction of zero, but far short of the socially optimal 100%, providing support for Hypothesis 2a (incomplete cooperation) in favor of Hypothesis 2b (high cooperation). Figure 4: 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, we also plot average optimal or ideal investment by round (see Figure 3), where ideal investment is calculated at the group level in each round, based on each group s average contribution percentage in the round. Average ideal investment started at 2.54 LD and declined to 2.03 LD. Since both investment and ideal investment declined, an important question is how the difference between them changed over time. The average difference started at 1.92 LD and fell to 1.41 LD. It is diminishing, indicating that investment was getting closer to the optimal amounts, as suggested by Hypothesis 1 that subjects do well with investment. It is not clear that any of the trends are convergent, and so instead of estimating convergence equations, as in Noussair et al. (1995) and Eckel and Grossman (2005), we simply estimate linear 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 are reported in Table 1. Investment is a group level variable. For contributions, remainders, 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 also calculated at the group 14

level. OLS results are reported, but random and fixed effects specifications give very similar results, all of which are consistent with the intuition provided by the figures. Table 1: Regressions on a Linear Time Trend 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 2. Predicted investment is 4.57 LD in round 1 and the predicted contribution percentage is 0.59, giving a payoff of 10.89 LD. In round 10, predicted investment, contribution percentage, and payoff are 3.57 LD, 0.45, and 10.45 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 0.45. 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 15.37 LD, which is almost equal to the social optimum of 15.40 LD. The bottom two rows are based on the ideal investment levels for contribution percentages of 0.59 and 0.45. Even at these low investment levels, full contributions give large gains in payoffs. The findings thus support Hypotheses 1 and 2a. In particular, the primary source of loss is contribution behavior and not the investment decisions. Subjects do well with investment in spite of the low payoff benefits associated with making better investment choices. 7 Table 2: Payoffs as a Function of Investment and Contribution Percentage - Linear Trend Predicted Values 7 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 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. 15

3.2 Regressions Our regression analysis focuses on individual behavior by identifying the correlates of votes, and on characterizing the relationship between investment and contributions. We begin by regressing the votes of each subject in each round on investment in the previous round, the subject s contribution in the previous round, and the round (see Table 3). In model (1)(random effects specification), unit increases in investment and contributions in the previous round are associated with 0.178 and 0.161 LD increases in votes, indicating that lower investment and contributions in one round are associated with lower votes in the next round. The effect of repetition is that votes decreased by an average of 0.060 LDs per round. 8 Table 3: Regressions of Votes, Contributions, and Contribution Percentages Model (2) is the parallel fixed effects specification. 9 In this model, subject level fixed effects control for individual-specific characteristics that might affect both votes 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 subject variation that occurs over time. The results are somewhat different. The effect of investment in the previous round is smaller and the effect of contributions in the previous round is now only weakly significant. The effect of the time trend, in contrast, is now significant at a conventional level (5%). We favor the results of the fixed effects specification because it controls for the endogenous selection of subjects to their decision-making environments. 10 8 Regressions using the method of Arellano and Bond (Arellano and Bond 1991; not shown, but available upon request) indicate that votes do not have a significant autoregressive component (the first lag of votes is not significant). Also, there is no significant tendency for subjects to adjust their votes in response to how their votes compared to those of their other group members in the previous round. 9 We favor random and fixed effects specifications over tobit because they are more conservative in terms of the significance of the regressors. 10 Group level regressions of investment and M provide similar insight regarding behavior. 16

The remaining regressions provide evidence on the relationship between investment and contributions. 11 In theory, investment could promote higher or lower contributions. As suggested by the development of Hypotheses 3a and 3b, it all depends on whether the incentive or budget effect of investment dominates in the determination of contributions. Our regressions aim to answer this question. In model (3), we regress contributions on investment and the round. 12 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 subject level fixed effects to control for time invariant unobservables, and estimates the effects of the regressors using within subject variation. The results are very similar to model (3), and fail to provide significant evidence for either of Hypotheses 3a or 3b that contributions are increasing or decreasing in investment. A potential concern with models (3) and (4) is that the level of investment (a regressor) determines the range of potential values for contributions (the dependent variable), 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 ( 109 880 = 12.4%)), and in both regressions, the correlation between investment and the error term is small and insignificant (model (3): Pearson s ρ = 0.01, p = 0.79; model (4): Pearson s ρ = 0.01, p = 0.73). Also, the aim of the regressions is estimating the partial correlation between investment and contributions, and not identifying the underlying causal model; we are simply interested in determining if contributions are increasing or decreasing in investment when controlling for the time trend. Even so, for exploratory purposes, we estimate the effect of investment using instrumental variables (IV) estimation in model (5). Specifically, we use lagged investment as an instrument for investment (for a full explanation of using lagged variables as instruments 11 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. 12 Arellano and Bond (1991) estimates do not provide significant evidence that contributions are autoregressive. The same is true for contribution percentages. 17

for endogenous regressors in the analysis of experimental data, please consult Smith (2013)). The results are very similar. Investment once again does not have a significant effect, providing further support for the conclusion that the incentive and budget effects that investment has on contributions approximately offset each other. Since calculating contribution percentages normalizes the data by dividing contributions by the amounts of money that subjects have in the contribution stage, the regressions of contribution percentages implicitly account for the budget effect. These regressions identify the incentive effect of investment (having higher contribution productivity). In model (6), LD increases in investment are associated with 0.053 unit increases in 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. 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, but opposite in direction. We as a result fail to find significant support for either of Hypotheses 3a or 3b that contributions are increasing or decreasing in investment. 4 Conclusion We present a public good game experiment on 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 relationship between 18

investment and contributions, absolute contribution amounts are not significantly related to investment, suggesting that the incentive and budget effects of investment approximately offset each other. Contribution percentages, in contrast, are positively related to investment, indicating that there is a significant incentive effect of contribution productivity. 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, we had a variety of reasons for suspecting that subjects might be able to overcome the free riding typical of VCM public good games, but incomplete cooperation was pervasive. The finding that subjects 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/or the size of government. Our finding that the primary source of loss is contribution behavior, on the other hand, supports continued research efforts to understand how people make decisions about voluntary contributions. Our experiment provides a methodology for examining future research questions related to how people substitute between investing in the efficiency of technologies for producing public goods and contributing to provision. We imagine that this tradeoff could be affected by a variety of factors that are beyond the scope of this study, such as income inequality, group identity, communication, etc... One seemingly important question that remains unanswered by this study is why subjects continue to invest significant amounts even when their payoffs on average end up only marginally higher than their initial endowments. A possible explanation is that they are consistently optimistic about the contributions of others. Optimism in repeated public good games is well-documented (Gaechter and Renner 2010; Smith 2013), but its role in this decision environment perhaps merits further investigation. 19

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Kosfeld, M., Okada, A., & Riedl, A. (2009). Institution formation in public goods games. American Economic Review, 99 (4), 1335-1355. Ledyard, J. (1995). Public goods: A survey of experimental research. In J. Kagel and A. Roth (Ed.), Handbook of Experimental Economics. Princeton: Princeton University Press. Markussen, T., Putterman, L., & Tyran, J.-R. (2014). Self-organization for collective action: An experimental study of voting on formal, informal and no sanction regimes. Review of Economic Studies, 81 (1), 301-324. Marwell, G., & Ames, R. (1979). Experiments on the provision of public goods 1: Resources, interest, group size, and the free-rider problem. American Journal of Sociology, 84 (6), 1335-1360. Norton, D., & Isaac, R. M. (2010). Endogenous production technology in a public goods enterprise. In R. M. Isaac and D. Norton (Ed.), Research in Experimental Economics Volume 13: Charity with Choice. Boston: Emerald. Noussair, C., Plott, C., & Riezman, R. (1995). An experimental investigation of the patterns of international trade. American Economic Review, 85 (3), 462-491. Putterman, L., Tyran, J.-R., & Kamei, K. (2011). Public goods and voting on formal sanction schemes. Journal of Public Economics, 95 (9-10), 1213-1222. Smith, A. (2013). Estimating the causal effect of beliefs on contributions in repeated public good games. Experimental Economics, 16 (3), 414-425. Sutter, M., Haigner, S., & Kocher, M. (2010). Choosing the carrot or the stick? Endogenous institutional choice in social dilemma situations. Review of Economic Studies, 77 (4), 1540-1566. Tirole, J. (1988). The Theory of Industrial Organization. MIT Press, Cambridge, MA. Tyran, J.-R., & Feld, L. (2006). Achieving compliance when legal sanctions are non-deterrent. Scandinavian Journal of Economics, 108 (1), 135-156. 21

Table 1: Regressions on a Linear Time Trend (1) (2) (3) (4) (5) (6) dependent variable: investment ave contribution ave remainder ave contribution% investment investment investment round -0.111*** (0.030) constant 4.680*** (0.184) -0.054** (0.025) 3.235*** (0.141) 0.165*** (0.038) 2.085*** (0.197) -0.016*** (0.004) 0.607*** (0.024) -0.067*** (0.016) 2.755*** (0.076) -0.045* (0.027) 1.925*** (0.169) method OLS OLS OLS OLS OLS OLS groups 22 22 22 22 22 22 rounds 1-10 1-10 1-10 1-10 1-10 1-10 n 220 220 220 220 220 220 R 2 0.051 0.018 0.079 0.057 0.081 0.011 Notes: Robust standard errors are reported in parentheses. ***: p <.01; **: p <.05; *: p <.1 22

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 = 4.57 10.89 9.59 14.68 round 10 = 3.57 11.70 10.45 15.37 optimal = 3.33 11.81 10.60 15.40 optimal59 = 2.73 11.95 10.84 15.19 optimal45 = 2.35 11.89 10.88 14.83 23

Table 3: Regressions of Votes, Contributions, and Contribution Percentages (1) (2) (3) (4) (5) (6) (7) dependent variable: vote vote contribution contribution contribution contribution% contribution% investment 1 0.178*** (0.049) contribution 1 0.161** (0.064) 0.075 (0.054) 0.125* (0.064) investment - - -0.156 (0.099) round -0.060* (0.033) constant 3.354*** (0.500) -0.072** (0.034) 3.960*** (0.456) - - - - - - - - - - -0.071*** (0.026) 3.965*** (0.503) -0.159 (0.100) -0.072** (0.026) 3.980*** (0.414) -0.092 (0.222) -0.088** (0.0308) 3.837*** (1.105) 0.053*** (0.013) -0.010*** (0.004) 0.359*** (0.066) 0.051*** (0.013) -0.011*** (0.004) 0.367*** (0.056) method RE FE RE FE IV-2SLS RE FE subjects 88 88 88 88 88 88 88 rounds 2-10 2-10 1-10 1-10 2-10 1-10 1-10 n 792 792 880 880 792 880 880 R 2 0.070 0.050 0.018 0.018 0.018 0.091 0.091 Notes: Standard errors adjusted for clustering at the group level are reported in parentheses. ***: p <.01; **: p <.05; *: p <.1 24

Figure 1: M as a Function of Investment Figure 1: M as a Function of Investment 1 0.8 M 0.6 0.4 0.2 0 0 1 2 3 4 5 6 7 8 9 10 Investment 25

Figure 2: Payoffs as a Function of Investment Figure 2: Payoffs as a Function of Investment 16 14 12 10 Payoff 8 6 4 2 Payoffs(c=100%) Payoffs(c=50%) Payoffs(c=0%) 0 0 1 2 3 4 5 6 7 8 9 10 Investment 26

Figure 3: Trends of Key Variables Figure 3: Trends of Key Variables 5 4 Lab Dollars (LD) 3 2 1 0 1 2 3 4 5 6 7 8 9 10 Round Investment Remainders Contributions Ideal Investment Investment - Ideal Investment 27

Figure 4: Average Contribution Percentages by Round Figure 4: Average Contribution Percentages by Round 0.6 0.5 Contribution% 0.4 0.3 0.2 0.1 0 1 2 3 4 5 6 7 8 9 10 Round 28

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 = 4.45 10.46 9.53 14.81 round 10 = 3.45 11.23 10.35 15.39 optimal = 3.33 11.29 10.42 15.40 optimal53 = 2.57 11.48 10.71 15.07 optimal43 = 2.28 11.44 10.74 14.75 29

Figure 5: Average Votes and Investment by Round Figure 5: Average Votes and Investment by Round 5 4 Votes / Investment 3 2 Votes Investment 1 0 1 2 3 4 5 6 7 8 9 10 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

Figure 6: Average M by Round Figure 6: Average M by Round 0.8 0.6 M 0.4 0.2 0 1 2 3 4 5 6 7 8 9 10 Round 31

Figure 7: Average Payoffs by Round Figure 7: Average Payoffs by Round 12 10 Average Payoffs 8 6 4 2 0 1 2 3 4 5 6 7 8 9 10 Round 32

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: 4 + 0.5 (4 + 4 + 4 + 4) = 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

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 0.1 2.5 = 0.25 = 0.5. If the investment amount is 4.9 LD, M will be 0.1 4.9 = 0.49 = 0.7. Two special cases are that investment = 0 M = 0 and investment = 10 M = 1. 3. 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