C. Monica Capra, Tomomi Tanaka, Colin Camerer, Lauren Munyan,
Veronica Sovero, Lisa Wang, and Charles Noussair 1
Abstract:
The existence of multiple equilibria is one explanation for why some countries are rich while others are poor. This explanation also allows the possibility that changes in political and economic institutions might help poor countries "jump" from a bad economic equilibrium into a better one, permanently increasing their output and income. Experiments can be used to study complex processes like the effect of institutions on economic growth. The control that experiments afford allows structural parameters to be changed, policies to be added and subtracted, and economic outcomes to be precisely measured. In this paper, we study a simple experimental economy in which agents produce output in each period, and can allocate the output between consumption and investment (the experiment builds on the design of Lei and Noussair, 2002, 2003). Capital productivity is higher if total investment is above a threshold. Because of the threshold externality, there are two equilibria—a suboptimal “poverty trap” and an optimal “rich country” equilibrium—which differ by a factor of approximately three in the agent income they create. In baseline sessions, in which agents make independent decisions in a decentralized economy, the economies typically sink into the poverty trap and the optimal equilibrium is never reached. However, the ability to communicate before investing, or to vote on binding “industrial policy” proposals, improves average earnings. Combining both of these simple institutions enables all of the economies to escape the poverty trap. This experimental environment constitutes a platform onto which many more complex features can be added.
Why are some countries rich while others are poor? There are many possible explanations, including differences in resources or geography (Sachs and Warner, 1995), economic and political systems (e.g., Baumol, 1986; Barro and Sala-i-Martin, 1995; Barro, 1997), openness to international trade, country-specific cultural (Knack and Keefer, 1999) and historical factors (Acemoglu et al,
2001), and a multiplicity of equilibria (Rosenstein-Rodan, 1943; Murphy, Shleifer and Vishny, 1989).
1 Capra and Noussair: Department of Economics. Emory University, 1602 Fishburne Dr, Atlanta, GA 30322-
2240, USA. Camerer, Munyan, Sovero, Tanaka, and Wang: Department of Economics, Division of the
Humanities and Social Sciences, Baxter Hall 228-77, California Institute of Technology, Pasadena, CA 91125,
USA. We gratefully acknowledge financial support from Emory University and the California Institute of
Technology. We would like to thank audiences at George Mason and McGill Universities, as well as at the
Economic Science Association Regional Meetings in Tucson, Arizona, USA in October 2004 and at the
International Meeting on Experimental and Behavioral Economics in Cordoba, Spain, in December 2004, for useful comments. We thank Vivian Lei and Kenneth Matheny for numerous insights about how growth models can be made operational in the laboratory.
1

Indeed, the problem is not a lack of answers for why there is cross-country wealth disparity; the problem is that there are too many plausible answers, which are hard to clearly separate with available data.
This paper illustrates how simple experimental political economies can be used to study the influences on economic growth. The focus in this study is on institutional features of the economies.
We construct experimental macroeconomies with multiple Pareto-ranked equilibria in which simple and highly stylized versions of basic institutional structures are applied. We then compare their performance in terms of equilibrium selection, output, welfare, and consumption with each other and with theoretical benchmarks. The environment we consider in this particular study is one in which suboptimal economic growth may occur because of the existence of multiple equilibria.
Experiments like these are clearly highly simplified compared to the economies we hope to understand. Despite their simplicity, experiments have some scientific advantages over the study of field data for some specific types of research questions, such as the role of particular institutions in promoting economic growth. In naturally occurring economies, institutions and institutional changes typically arise endogenously, rather than randomly, so that there is an inherent sample bias when attempting to attribute economic performance to institutional differences.
2 Different institutions also tend to co-occur in clusters (for example, democratic voting and freedom of the press), rendering it difficult to isolate each institution’s marginal effect. In experimental economies, institutions may be changed one at a time, randomly (avoiding endogeneity), while maintaining an otherwise constant environment. Furthermore, institutions can be mixed and matched to create hybrids that do not naturally occur (e.g. dictatorships with a free press).
Our methodology can be applied to study the effectiveness of particular institutions in overcoming different sources of suboptimal growth, and we presume that different institutions are better suited to countering different sources of inefficiencies. The experiment here is focused on how institutions can overcome inefficiencies resulting from the existence of multiple equilibria in the economy. Our experimental environment consists of a dynamic macroeconomy with two stationary
Pareto-ranked competitive equilibria, first studied experimentally by Lei and Noussair (2003).
3 The environment is an extension of the optimal growth model of Ramsey (1928), Cass (1965), and
2 S ee Temple (1999), Islam (2003) or Durlauf and Quah (1999) for a discussion of empirical methodology and
3 results with regard to international comparisons of rates of economic growth.
See Plott and George (1990) for a experimental study of one-period markets in which there are two competitive equilibria.
2

Koopmans (1965), and is well understood theoretically.
4 The crucial extension of the
Ramsey/Cass/Koopmans model is a threshold externality in capital productivity – the existence of a level of aggregate capital at which capital productivity jumps sharply. This threshold creates two equilibria. The better equilibrium gives every agent higher consumption and higher utility (which in the experiment takes the form of dollar earnings to participants) than the worse equilibrium, which we call a technological poverty trap.
5 The parametric structure of the economy and the initial endowments are chosen so that the poverty trap is likely to be reached. Simple “institutions” are added to the economy, and their ability to extract the economy from the poverty trap is evaluated.
The first institution we consider is a highly stylized version of “freedom of expression” in which all agents are allowed to engage in communication, unrestricted in content, in a “chat room” before each investment period. In principle, communication can enable agents to coordinate investment to cross the capital threshold. Communication is also known to improve equilibrium selection in experimental coordination games (see e.g., Camerer, 2003, chapter 7). The recording of messages also allows us as economists to “eavesdrop” on what individuals are thinking, which is often insightful and surprising. The second institution is a highly stylized version of a democratic voting process, resembling voting for an “industrial policy”. In each round, two agents are chosen randomly to submit a proposal specifying the quantity that each agent will consume and invest. The citizen/agents vote for proposals and the one elected by the majority is automatically implemented. A third treatment combines the communication and voting treatments to see if they interact (e.g., agents might discuss the merits of different policies before voting or submitting proposals). The focus of our
4
A principal result of the Ramsey/Cass/Koopmans model (Ramsey, 1928; Cass, 1965; Koopmans, 1965) is that countries that have access to the same production technology converge toward a common income level even if their initial endowments of capital differ. Thus, relatively poor countries exhibit higher growth rates than richer ones. However, field studies have generally failed to support the hypothesis of convergence towards a common income level (Temple, 1999; Durlauf and Quah 1999; Islam, 2003). Indeed, the data are more consistent with the alternative hypothesis of club convergence (Baumol, 1986), which postulates that a small number of steady states exists, and that each country has a tendency to converge to one of them. Such a framework can explain the observed pattern over time of both an increase in income differences between the OECD countries and the developing world and a decrease in the differences within each of the two groups.
5
The absence of convergence can be explained with models with multiple competitive equilibria. Originally attributed to Rosenstein-Rodan (1943), the idea that multiple equilibria exist in macroeconomies has led to a variety of growth models with multiple equilibria. For instance, Azariadis and Drazen (1990) construct an overlapping generations model with two stable Pareto-ranked equilibria. In the inferior equilibrium, no agent trades with members of other generations. Murphy et al. (1989) build a model with synergies among industries, where each industry is profitable only if other industries operate. There are Pareto-dominant equilibria where all of the industries operate and dominated equilibria where none operate. Galor and Zeira (1993) and Banerjee et al. (2001) show that inequality and the resulting differential access to credit among members of the population can keep an economy in a Pareto dominated equilibrium. See Azariadis (1993) and Cooper (2002) for a detailed treatment of the principal analytical issues in growth models with multiple equilibria.
3

analysis is on whether these economies sink into the poverty trap or escape it, and whether communication, voting, and the combination of the two affect economic outcomes.
Since these experiments are the first to explore the effect of institutions on economic growth, we deliberately chose an environment familiar to growth economists, in the hope of initiating dialogue about what experimental data can tell us about growth. We also deliberately began with a simple setup that can be complicated in future experiments (a method used in all successful laboratory sciences). If we had started with a much more complicated design, we would be less likely to get reliable, clear results, and less likely to know which factors caused outcomes. Because the design is simple, the manner in which we create “free expression” and “democratic voting” is not intended to capture all the complexities of these institutions when they occur naturally. Furthermore, the fact that engaged readers of this article can probably imagine many different versions of these or other types of institutions worthy of study in this or similar environments is evidence that the general design can be fruitfully used as part of a research program , of which this paper is the start.
The next section describes the experimental economy, the theoretical predictions, and the procedures of the experiment. In section three the results are reported, and in section four, we provide a summary and ideas for future research.
We adopted the multiple equilibrium environment of Lei and Noussair’s (2003) 6 study. At the aggregate level, the economy may be thought of as populated by an infinitely-lived representative consumer with a lifetime utility given by: t
∞
= 0
( 1 +
) − t U ( C t
) , (1)
ρ is the discount rate, C t
is the quantity of consumption at time t , and U ( C t
) is the representative consumer’s utility of consumption. Alternatively, the expression in equation (1) may be thought of as the total value that an infinitely-lived group of agents receives from consumption. The economy faces the following resource constraint:
C t
K t + 1
A
F ( K t
)
(1
δ ) K t
, (2)
6 Lei and Noussair (2003) study an economy with the same parametric structure as the economies studied here.
That is, the values of the parameters given in table 1 are identical in their study and in ours. However, the two studies differ in that Lei and Noussair used double auction markets rather than call markets, described in section
2.3.5, to exchange output. They also do not include the insitutional structures, described in section 2.4, that serve as the primary focus of this study.
4

with
A =
⎧
⎨
⎩
A , if
A , if
K
K
<
≥
. (3)
δ is the depreciation rate, K t
is the economy’s aggregate capital stock at the beginning of period t , and
A is an efficiency parameter on the production technology. The value of A depends on the current level of capital stock in the economy. There exists a threshold level of capital stock, K
A has the value A and below which it has the value A , with A < A . The threshold can be interpreted as a positive externality in production, generated by a sufficiently large aggregate quantity of capital stock in the economy.
7 Table 1, lists the values of the principal parameters of the economy in effect during the experiment.
[Table 1: About here]
In the experiment, the aggregate production capability and the value of consumption of units of output are divided among five heterogeneous agents populating the economy. Each subject i is given an individual production schedule that outlines his or her ability to transform capital k t i
into output A * f i ( k t i ) . Each individual’s (discrete integer-valued) production schedule consists of two parts, corresponding to the individual’s component of the aggregate production function when the economy-wide level of capital exceeds the threshold (when K t
=
i k t i ≥ 31 ) and when it does not.
The marginal utility of consumption of agent i is a discrete approximation of v i ' ( c t i ) = 396 + 4 i − 20 c t i . The utility function for consumption is expressed in terms of an experimental currency called “Yen,” which is converted into US dollars at the end of the experiment at a predetermined exchange rate. Individuals’ utility and production functions were private information. The economy’s aggregate production and demand curves are shown in Figure 1.
[Figure 1: About Here]
2.2. Competitive equilibria
7 See Azariadis (1993) and Azariadis and Drazen (1990) for discussion of growth models with a threshold externality in production.
5

The economy is structured in such a way so that there exist two stationary stable rational expectations competitive equilibria (using the same parameters as in Lei and Noussair, 2003), which represent our primary benchmarks. One of these equilibria is also an optimal steady state. The optimal steady state is the outcome to which the economy would asymptotically converge were it under the direction of a benevolent social planner. Such as planner would choose C
1
, …, C
∞
to maximize (1), subject to (2), (3), and the constraints that C t
≥ 0, K t
≥ 0 and K t + 1
≥ ( 1 −
) K t
(gross investment in every period must be non-negative). Table 2 shows the values of the key variables in the Paretodominant equilibrium (the optimal steady state) 8 and the Pareto-dominated equilibrium (the poverty trap).
[Table 2: About here]
2.3. Procedures
2.3.1. General procedures
The experiment consisted of a total of 21 sessions. There were four different treatments in the experiment, and the four treatments differed from each other only in the institutional structures guiding activity in the economy. The environment is otherwise identical in the four treatments. The four treatments are called the baseline , communication , voting , and hybrid treatments. Each treatment will be described in more detail in the next subsection. Participants were undergraduate students at
Emory University, located in Atlanta, Georgia, USA, and at the California Institute of Technology, in
Pasadena, California, USA, and the sessions were conducted in dedicated experimental laboratories at the two universities. Subjects were paid an initial fee of either $5 or $10 for their participation, depending on the session and their role in the experimental economy. Their additional earnings from
8 The optimal equilibrium capital/consumption combination ( 45 , 70 ) has the property that from any initial level of capital stock K
0 level of K t
> 0, including K
0
= 9, the optimal sequence of consumption and investment decisions of a hypothetical benevolent social planner converges asymptotically to ( K t
, C t
) = (45, 70). At an initial capital
= 45, the optimal sequence is a constant level of capital and consumption of (45, 70). Thus, ( K t
, C t
) =
(45, 70) is an optimal steady state for our economies. At this optimal steady state, which is a Pareto-optimal competitive equilibrium for our decentralized economies, each agent consumes 14 units per period for an economy-wide total of 70 units of consumption, and the capital stock is distributed among the agents in the following manner: k
1 = 12 , k
2 = 9 , k
3 = 6 , k
4 = 8 , and k
5 = 10 , where k i is the equilibrium capital holding of agent i , yielding a total
5
=
1 k i
45 . At the Pareto inferior equilibrium agents 1 to 4 each consume 3 units and agent 5 consumes 4 units per period for a total consumption of 16. The allocation of capital stock in this equilibrium is of 9 units. k
1 = 1 , k
2 = 2 , k
3 = 1 , k
4 = 2 , and k
5 = 3 , yielding a total equilibrium capital stock
6

their activity in the economies described below ranged from $11.56 to $47.26. In all of the sessions, no subject had participated in a similar experiment previously, although some of the subjects had participated in other, unrelated experimental studies. The next three subsections briefly describe the experiment, and the instructions in the Appendix contain a more detailed explanation of the decision environment. Table 3 contains a list of the sessions, the date and location they were conducted, and the average earnings of participants during each session.
[Table 3: About here]
2.3.2. Timing within a session
Five subjects participated in each session, and were grouped together in the same economy.
At the beginning of each session, the experimenter distributed and read aloud the instructions for the experiment. The activity in each session consisted of several horizons of random length and each horizon consisted of a series of periods. The period of time defined by a horizon in the experiment corresponds to an infinite horizon in the theoretical model of section 2.1. In the experiment, a random ending rule was used to induce a decision situation equivalent to an infinite time horizon with discounting.
9 Under the assumption that subjects in the experiment are risk neutral in their final monetary payment, a constant probability of 20% of the horizon ending in each period is equivalent to an infinite horizon in which
= 0 .
25 . The experimenter implemented the ending rule by rolling a die to determine whether or not the horizon would terminate at the end of the current period. Thus, a horizon, which corresponds to the life of the economy in the theoretical model, is a distinct notion of time from an experimental session. Each session was composed of several horizons and the number of horizons in our sessions ranged from 2 to 8.
10 Table 3 lists the number and the lengths of the horizons that made up each session.
Each session was scheduled for a three-hour time interval for which subjects were recruited.
The instructions indicated that if the current horizon ended with more than 30 minutes remaining in the three-hour interval, a new horizon would be started with the same initial endowments of 5 units of capital and 10,000 Yen per person. The initial endowments for each horizon were independent of any activity in prior horizons. Restarting with the same initial values after an exogenous random ending has no distortionary effect on optimal decisions. If a horizon did not terminate by the end of the third
9 Other authors have used a similar rule to create the incentives of infinite horizon models in the laboratory. See for example Camerer and Weigelt (1993), Noussair and Matheny (2000), or Lei and Noussair (2002, 2003).
10 After the instructions were read, subjects participated in a three period practice horizon which did not count toward their earnings.
7

hour of a session, it would continue on another evening. Subjects would be free to return for that session and continue in their same roles at the point at which they left off. If a subject was unwilling or unable to return, a substitute would be recruited to replace him. The earnings of the substitute would be awarded to the original subject as well as to the substitute himself. This technique, first applied in Lei and Noussair (2002), preserves the incentive for subjects to behave as if they were to participate until the end of the horizon. In no session of our experiment was it actually necessary to continue the session on another day.
2.3.4. Timing within a period
The sequence of activities within each period for the four treatments is shown in Figures 2a –
2d. The figures also illustrate the differences among the four treatments. In all treatments, each period consisted of two decision stages. In stage 1, subjects participated in a market for capital. In stage 2, subjects chose how much of the capital to consume. In the baseline treatment, whose timing is illustrated in Figure 2a, the timing of events within a period were as follows. At the beginning of period t , production occurred automatically as the computer program mapped k t i , the capital stock that each individual held, into output ( c t i + k t+1 i ), according to the individual’s production function f i ( k t i ).
A market for output then opened. The trading rules in effect in the market are described in subsection
2.3.5. After the market closed and transactions were realized, agents chose the portion of their output to allocate to consumption c t i .
Before making their decisions, agents could use a simulator which allowed them to study, by submitting hypothetical consumption and investment scenarios, how their choice of c t i affected their utility of consumption u i
( c t i ), their remaining capital stock k t+1 i , and the quantity of output they would have at the beginning of the next period f i ( k t+1 i ) . The remaining unconsumed output of each individual, after her choice of consumption, became her k t+1 i . At the beginning of period t+1 , production occurred as k t+1 i was mapped into output ( c t+1 i + k t+2 i ), according to the function f i ( k t+1 i ), for all i .
The sequence of events in a period under the communication treatment was identical to the baseline treatment, except that before the market opened, subjects were allowed to communicate with each other. Each agent’s screen displayed a chat-room, which he could use to send and receive messages in real time. Communication was unrestricted in content and all agents could observe all messages. Figure 2b illustrates the sequence of events in the communication treatment.
In the voting treatment, shown in Figure 2c, the timing of events was identical to the baseline treatment except that in stage 2, subjects’ consumption and investment decisions were determined differently from the baseline and the communication treatments. Two agents were randomly chosen in each period to each submit a proposal specifying the quantity each agent in the economy would
8

consume for the period. A proposal consisted of a five-element vector of consumption levels, one element corresponding to each agent. Before submitting proposals, proposers received information indicating the current output held by each agent, after the market had closed for the period (they did not become aware of other agents’ utility or production functions, which remained private information at all times). The two proposals were submitted simultaneously and appeared on each agent’s computer screen. All agents were then required to vote in favor of exactly one of the two proposals. Majority rule determined the winning proposal; that is, the proposal that gained at least three of the five total votes was enacted. Each agent consumed the quantity of output specified under the winning proposal, and began the next period with the amount of capital allotted to her under the winning proposal.
Under the hybrid treatment, an opportunity for agents to exchange messages was available, as in the communication treatment. Thus, the first stage of the hybrid treatment was identical to first stage of the communication treatment. The second stage was identical to that of the voting treatment.
The sequence of events in a period of the hybrid treatment is shown in Figure 2d. The instructions for the baseline treatment are given in the Appendix.
[Figures 2a-2d: About here]
2.3.5. The Market
In our economies, each agent received an endowment of cash, which he could use for purchases and sales of output. The cash was not a fiat money, but rather was convertible to dollar earnings for the subject at a conversion rate that was known to the individual in advance, and thus the cash had intrinsic value. Since agents were not symmetric (i.e., their utility and production functions differred from each other’s), gains from trade existed from the exchange of output. During each period of each treatment, there was an interval of time during which a computerized call market for capital was in operation.
The call market operated in the following manner. In each period, all agents were required to submit demand schedules that specified limit prices for each unit of capital that they wished to purchase, and an aggregate demand schedule was constructed from the individual schedules. The aggregate supply schedule of output was constant, corresponding to a vertical supply curve, at the total amount of output in the economy for the current period K t
. The market-clearing price was determined by the intersection of aggregate demand and supply and equaled the lowest accepted bid, which was equal to the K t th highest bid among all players. Agents who submitted limit prices greater
9

than or equal to the market-clearing price received the units of capital. Any tie for the K t th highest bid was broken by allocating the last units to the tied marginal bidders randomly. When an individual had a net change in capital holding after the market process, the agent either (a) paid a per-unit price equal to the market-clearing price for each unit he purchased, or (b) received a per-unit price equal to the market-clearing price for each unit he sold.
In other words, the market reallocated output in the following manner. In period t each agent i submitted a demand curve d i t ( p ), where p was the price for output. An algorithm then calculated
Σ i d i t ( p ), and solved for the price p * at which Σ i d i t ( p *) = Σ i f i
( k t i
). Agent i ’s final allocation of output was equal to d i t ( p *). The net change in his holding of output was equal to d i t ( p *) – f i
( k t i
). Each agent i received a cash transfer of p *[ f i
( k t i
) - d i t ( p *)].
2.3.6. Initial Endowments and Agent Incentives
Each of the five agents received an initial endowment of five units of capital, so that aggregate initial capital, K
0
, equaled 25. The initial endowments were chosen so that the poverty trap would be likely to be reached in a decentralized market economy, in the absence of any additional institution to aid economic performance. The conjecture that the baseline treatment would converge to the poverty trap is based on the results of Lei and Noussair (2003), whose design was identical to the baseline treatment except that the market for output used double auction rather than call market rules. Each agent also received 10,000 units of experimental currency with which to make transactions. This cash endowment was sufficient to ensure that cash constraints were unlikely to be binding at any point in time.
Each agent’s earnings resulted from consumption as well as from sales of output in the market. In each period t , a player i ’s earnings, in terms of experimental currency, were given by u i
( c i t )
+ m i1 t – m i0 t , where u i
( c i t ) denotes individual i ’s earnings from consumption, and m i0 t and m i1 t denote i ’s cash holdings at the beginning and the end of period t , respectively. Over each horizon, individual i ’s earnings, in terms of experimental currency, were given by Σ t
[ u i
( c i t ) + m i1 t – m i0 t ], the total earnings in all of the periods making up the horizon, so that each individual had an incentive to hold some output in the form of investment to allow consumption or sales in future periods. A player also had an incentive to sell output if the price was high, in order to increase his end of period cash holdings, as well as an incentive to purchase output at low prices either to consume, to produce more output in future periods, or to resell at a higher price. Over an experimental session, a participant’s dollar earnings were equal to τ i
+ γ i
( Σ j
Σ t
[ u i
( c i t ) + m i1 t – m i0 t ]). j indexes the horizon within an experimental
10

session, γ i
is agent i ’s conversion rate from experimental currency to US dollars, and τ i
is agent i ’s fixed supplementary payment for his participation in the experiment.
11
2.4. Design
The four treatments in our experiment constitute a two-level two-factor experimental design, where the factors are the institutions of communication and of voting, and the levels are the presence and the absence of the institution. The treatments are compared with regard to output and welfare, with a focus on whether communication and voting increase the likelihood that the economy avoids the poverty trap and lead to higher levels of output and income.
The parameters were chosen with the purpose of making it probable that the economy would reach the poverty trap in the baseline treatment. The basis for this conjecture is the previous work of
Lei and Noussair (2003). They study a decentralized economy with the same parametric structure and find a strong tendency for the economy to converge to the poverty trap. The only difference between the economies that Lei and Noussair study and the baseline treatment reported here is that call markets to exchange output, whereas Lei and Noussair use continuous double auction market rules
(Smith, 1962). Thus, the data from the baseline treatment can also be used to test the proposition that the two different trading rules for exchanging output have no effect on aggregate behavior in the economy.
Our hypotheses are that both voting and communication increase welfare and lower the likelihood that the economy reaches the poverty trap. The basis for this assertion is that equilibrium selection in our economies presents a coordination problem. All agents can benefit if the Paretooptimal equilibrium is selected over the other equilibrium. Communication is known to improve equilibrium selection in normal form games, because it reduces strategic uncertainty. Agents are presumably more likely to play their component of an optimal equilibrium strategy profile, the more confident they are that others will also do so. Furthermore, the existence of institutions promoting communication between economic agents in field economies, such as free speech or a free press, has been associated with higher rates of economic growth (Barro, and Sala-i-Martin,1995; Barro, 1997).
An analogous effect here could manifest itself in two ways, either as a direct effect when it is added to the baseline treatment alone, or as a marginal effect in conjunction with the voting process.
11 γ i
and τ i
differed among agents, τ baseline treatment, γ i i
equaled $5 for players 1 and 2, and $10 for players 3, 4, and 5. In the
equaled 0.001 (1 unit of experimental currency = γ i and 0.002 for players 2,…, 5. In the other three treatments
2,…, 5.
γ i
US dollars for player i ) for player 1
equaled 0.0005 for player 1 and 0.001 for players
11

Similarly, in the voting treatments, the ability for an individual agent to propose a level of capital stock for each of the five agents and commit all five agents to the winning proposal provides a possible means to reduce the coordination problem arising from the existence of multiple equilibria.
In addition, democratic institutions in the field are positively associated with higher rates of economic growth (see Barro and Sala-i-Martin, 1995). Thus, the production-enhancing effect of the introduction of the voting procedure would be expected to appear in a comparison between the voting and baseline treatments as well as in a comparison between the hybrid and the communication treatments.
3.1 General Overview of the Data
Figures 3 – 6 below illustrate the dynamics of aggregate consumption behavior, C t
, in each session of the four treatments. Each chart illustrates the time series of the variable for one of the sessions, and each figure corresponds to one of the treatments. Each unit along the horizontal axis corresponds to one period of the session. The dashed horizontal lines are the optimal equilibrium and the poverty trap levels of consumption C *
H
=70 and C *
L
=16 units, respectively. The discontinuities in the time series of period consumption represent the beginning of new horizons. In general, consumption can also be viewed as a reasonable, though noisy, measure of welfare. Consumption and earnings, which are in each period t given by u ( c t
), are highly correlated. Analogous data for aggregate capital stock K t
are depicted in Figures 7 - 10.
[Figures 3 – 10: About Here]
Overall, for the baseline treatment, the poverty trap is a powerful attractor. Figure 3 shows that in four of five sessions, consumption and total output remain close the poverty trap level. Figure
7 shows that in one of these four sessions, EmoryB3, the economy invests sufficiently in capital to surpass the threshold of 31 units in the first horizon, but it is unable to attain the threshold level of capital for the remainder of the session. In one session, CaltechB2, capital stock surpasses the threshold in two different horizons, but there is an interval of three horizons in between, when the economy operates close to those of poverty trap. The data show that avoidance of the poverty trap in early periods or horizons does not guarantee successful avoidance in later periods or horizons. Thus, in the absence of institutions that facilitate coordination, our economies seem unable to successfully avoid or exit the inferior equilibrium. The baseline data are highly consistent with the data that Lei and Noussair (2003) report.
12

To parsimoniously characterize behavior in the economies we estimate equation (4). The equation facilitates a description of the asymptotic behavior and provides a test for convergence to equilibrium for the individual economies that make up the experiment.
Y jt
B
1
1 t
B
2 t
1 t
ε j
ν jt
(4)
In this regression, Y jt
is the dependent variable of interest, either the total utility U ( C t
) = ∑ i u i
( c i t ) actually realized in the economy, or the economy-wide capital stock K t
= ∑ i k i t , at time t . t is the period number within a horizon, j indexes the horizon within a session, and the B’ s are the coefficients to be estimated. The coefficient Β
2
is the point at which the dependent variable Y jt is estimated to be converging for the session, and the equation is estimated separately for each session. We will refer to the estimate Β
2
as the convergence value of the dependent variable for the session. We will say that the dependent variable is converging to a particular level, such as an equilibrium prediction, if the convergence value Β
2
is not significantly different from that level.
12
Since there is considerable heterogeneity in welfare and capital levels across horizons within sessions, we account for horizon-specific disturbances when estimating convergence levels. We use a random-effect specification in which each horizon is assumed to have a random effect on the dependent variable. Tables 4 and 5 contain the maximum likelihood estimates of the convergence values for the dependent variables of total capital and total welfare of the economy, respectively. The estimated convergence values of capital and welfare are also illustrated in Figure 11. Each point corresponds to one session and the shaded lines through each point represent the 95% significance intervals. The dotted lines represent the competitive equilibria, with the equilibrium in the lower left indicating the poverty trap and that in the upper right indicating the optimal equilibrium. 13
[Insert Tables 4 and 5 and Figure 11: About here]
There are several patterns that emerge from the analysis of the baseline sessions, which confirm the visual impression from the graphs in Figures 3 and 7. The first is that the economy is
12 These regressions are related to those in Noussair et al. (1995, 1997) to study convergence of experimental international economies. However, unlike in Noussair et al. (1995, 1997), to reflect the idea that these economies with multiple equilbria have multiple reasonable attractors, the convergence values here are allowed to differ by session.
13 In order to test the relevance of estimating the maximum-likelihood random-effect model, we compared our model to an OLS model using the Hausman specification test. The resulting chi-square statistic was significant at the 5 percent level for 19 out of 21 estimations, where each estimation corresponds to one session. This supports the hypothesis that the maximum-likelihood random-effect model is the better specification for equation (4).
13

unable to surpass the threshold level of capital in all but one of the sessions, CaltechB2, which shows large standard errors. In addition, there is a strong tendency for the data in the baseline treatment to converge to one of the equilibria, and this is usually the poverty trap. Four of the five convergence values are not significantly different from the poverty trap level of 9 at the 5% level. A similar pattern holds for the welfare of the economy shown in Table 5.
14 Three out of five economies have convergence values that are below the poverty trap level of 5856 and small standard errors. Moreover, one of these sessions, EmoryB2, is not different from 5856 at the 5% level of significance. All are significantly different from the optimal equilibrium welfare of 18060. Thus, as we had initially expected, the baseline treatment converges to the poverty trap, representing a welfare loss of over two-thirds of the welfare that would be attained at the optimal equilibrium.
As depicted in Figures 4 and 8, in the communication treatment, outcomes are more variable across sessions than in the baseline treatment. Although the economies have an identical parametric structure, and the members of the different economies are drawn from the same population, they follow very different trajectories from each other for reasons that are completely endogenous. The behavioral differences between the communication and the baseline treatments illustrate that institutions can and do alter both the expected income of an economy as well as the variability of outcomes across sessions. Figure 4 shows that two the sessions, CaltechC2 and CaltechC3, consistently surpass the threshold level of capital and move towards a consumption level close to the optimum. Two other sessions, EmoryC3 and CaltechC1, remain near the poverty trap level of consumption. In one of the remaining two sessions, EmoryC1, the economy is moving close to the optimal steady state in the last of the two horizons of the session. Finally, one session, EmoryC2, exhibits behavior that is difficult to categorize, but is highly variable from one period to the next.
The convergence values of capital and welfare for the communication treatment in tables 4 and 5 support the same conclusions. For capital, the pattern that arises from the regression supports our observations from the charts of Figure 8. The communication sessions exhibit variable outcomes, but each estimated coefficient for a session, except for EmoryC1, has a small standard error. This indicates a strong tendency toward convergence to some level of capital stock within a session, but with considerable heterogeneity across different sessions. Capital stock, in three of the six sessions, converges to levels not significantly different from the poverty trap. With regard to welfare, EmoryC1
14 Although session CaltechB2’s estimated convergence value for capital is not different from 45 (the optimal steady state level), its welfare convergence value is not different from 5856 (the poverty trap). The same happens in session EmoryC1 of the communication treatment. This seeming contradictions can be explained by the existence of high variability in economic behavior within those two sessions.
14

converges to levels not different from the poverty trap level, and two of the sessions, CaltechC2 and
CaltechC3, converge to levels not different from the optimal equilibrium of 18060.
As shown in the charts of Figures 5 and 9, the voting treatment exhibits more variance within sessions than either the baseline or the communication treatments. The reason for an increase in the variance appears to lie in the centralized nature of decision making. In contrast to the baseline and communication treatments, where decentralized decision-making on the part of individuals determines consumption and investment choices in each period, in the voting treatment investment and consumption decisions are made by majority choice from a small and changing set of alternatives. This results in large swings in economic activity from period to period. Indeed, in only one of the sessions, EmoryV2, does consumption remain consistently close to the poverty trap level.
The convergence value estimates in the voting treatment typically have higher variances than those in the baseline and communication treatments. This suggests that the voting treatment generates larger fluctuations from one period to another, even asymptotically. Three of the sessions show convergence values for capital that are not significantly different from the steady state at the 5% level of significance. However, with respect to the welfare estimates, in three out of the five sessions the convergence values are not different from the poverty trap levels. This seeming contradiction is the result of the centralized way whereby both capital and consumption are allocated among subjects.
Indeed, a closer look at the individual data shows that some proposals reflect a preference for a high level of current consumption with the minimal requirement that aggregate capital surpass the threshold; and the majority of the subjects will, at times, vote in favor of such proposals, resulting in suboptimal levels of welfare. Individual behavior in the voting treatment is considered in more detail in subsection 3.6.
A similar pattern of highly variable activity exists in the hybrid treatment. As in the voting treatment, it appears that the voting process impedes convergence to equilibrium, because consumption and capital decisions are made by a changing subset of the subjects in a centralized fashion. However, in contrast to the other three treatments, in the hybrid treatment the economy reliably escapes the poverty trap. As shown in the session charts of Figure 6, every session contains late horizons that are characterized by consumption levels closer to the optimal equilibrium than to the poverty trap. In addition, as Figure 10 illustrates, the levels of capital are consistently in excess of the threshold of 31 from period four onward in all the sessions.
The estimated convergence values for capital and welfare confirm the impression that
Figures 6 and 10 convey. As shown in Table 4, the hybrid treatment estimates for capital stock levels are on average higher than in the other treatments. Two sessions, EmoryH1 and EmoryH2, attain
15

levels not different from the optimal equilibrium. A similar result applies to total welfare. As shown in Table 5, all convergence values exceed the poverty trap level and in two sessions, EmoryH3 and
CaltechH1, the values are not different from the optimal steady state levels at the 5% level of significance. However, as in the voting treatment, the estimates have high standard errors. Finally, in contrast to all of the other treatments, all convergence values are significantly different from the poverty trap value.
Thus, to summarize our observations, in the absence of institutions that would resolve the coordination problem, our economies converge to the poverty trap. The introduction of voting or communication, or both simultaneously, improve outcomes when measured by either output or welfare. The hybrid treatment is the most conducive to allowing the economy to surpass the threshold and exit the poverty trap. In the voting and hybrid treatments, a subset of agents can dictate the consumption and investment decisions of the economy, this process appears to solve the coordination problem of how to avoid the inferior equilibrium, and the existence of communication renders the process more effective. As we describe in section 3.6, communication improves both voter and proposer decisions. However, the voting process also distorts the economies in a manner that introduces additional variance from one period to the next, making the behavior of the economy less stable than under the systems in which individuals make their own consumption and investment decisions. On the other hand, whereas communication in the absence of voting imposes no such distortions, it is not fully effective as a coordinating mechanism for exiting the poverty trap, perhaps because the lack of commitment to investment levels prevents the total elimination of strategic uncertainty.
3.2 Treatment Effects
Figures 3 – 10 reveal that although the economies begin each horizon with the same initial endowments, production technology and consumption incentives, the different institutions generate very different economic behavior. To further consider how the different institutional treatments affect outcomes in our economies, we conduct Mann-Whitney rank sum tests of the differences in both economic output and welfare between treatments, maintaining the conservative assumption that each session is a unit of observation. The total output of the economy in period t is equal to the value of F ( K t
) = Σ i f i
( k i t ) the economy realizes in period t . The total welfare in period t is defined as U ( C t
) =
Σ i u i
( c i t ). We use the average observed value of total output and welfare by period to achieve comparability between sessions containing different number of periods. Under this period weighting assumption, each period of activity receives equal weight in the calculation of the average, regardless
16

of the length of the horizon that includes the period. Table 6 shows the results of the MW tests under the null hypothesis of no difference between treatments.
[Insert Table 6: About here]
With regard to the output of the economy, we fail to reject the hypothesis that the baseline and communication treatments are equal at the 5% level. However, we are able to reject the hypotheses that (a) the baseline and voting treatments and (b) the baseline and hybrid treatments, yield the same output, with baseline yielding lower output in both cases. There is no difference between the communication and the hybrid treatments, or between the voting and the hybrid treatments.
15 Thus, voting has a positive impact on output when there is no free expression, but its marginal impact is attenuated when free expression exists. It appears that there is some redundancy in the two instruments, although the application of both together achieves outcomes that are no worse than each instrument separately.
With regard to overall welfare, we find rather similar patterns as for output. The only treatment differences that are significant at the 5% level are those between the baseline and voting treatments, the baseline and hybrid treatments, and the voting and hybrid treatments. Communication and voting improve welfare significantly, regardless of whether or not the other institution is present.
The next subsections present an exploratory analysis of empirical patterns in our data.
3.3 Inefficiencies
There are three types of allocative inefficiency that can appear in the experiment. The first is what we will call the output gap , a lower actual production level than the highest possible production given the quantity of capital currently residing in the economy. An output gap occurs in a period because the economy’s capital at the end of the period is allocated among agents in a suboptimal manner (i.e., other than to the individuals with the highest marginal products for capital). The output
15
We also use horizon weighting as an alternative means of testing these hypotheses. Under horizon weighting , each horizon receives equal weight in determining a session average. To calculate the average value of a variable in a session under horizon weighting, we calculate the average value by period within a horizon, and then calculate the average of the resulting horizon averages. The result of this calculation is taken as the average value of the variable for the session. Under horizon weighting, similar results are obtained as under period weighting. We fail to reject the hypotheses that the baseline and the communication ( z = 1.095, p = .14), the communication and hybrid ( z = .548, p = .29), the voting and hybrid ( z = .522, p = .30), and the communication and voting treatments ( z = .365, p = .36), yield identical output. However, we find that voting leads to higher output than under the baseline treatment, rejecting the null hypothesis of no difference ( z = 2.193, p = .01). We also reject the hypothesis of equality of output in the baseline and the hybrid treatments ( z = 2.611, p = .005).
17

gap is calculated as ( F* ( Σ i k i t ) - Σ i f o ( k i t ))/ F* ( Σ i k i t ), where F* ( Σ i k i t ) is the maximum possible production possible with capital stock Σ k i t , were it to be allocated among agents to maximize total output. Σ i f o ( k i t ) is the actual production observed. The output gap equals on average 39.0%, 31.6%, 34.4%, and
27.7% in the baseline, voting, communication and hybrid treatments, respectively. An institutional structure in which subjects can exchange information and also vote for alternative proposals, i.e., the hybrid treatment, is the least inefficient in terms of allocating capital across subjects. However, the differences between treatments are small, suggesting that these institutions are not geared to reducing the output gap, and inviting an inquiry into which institutions might be effective in reducing this source of inefficiency.
A second type of inefficiency is consumption inefficiency . The value of a given amount of aggregate consumption is maximized when the units are allocated to individuals in order of their marginal utility of consumption. If a unit can be transferred from an individual to another, who has a higher marginal utility for the unit than its current owner, the original allocation is inefficient. The consumption inefficiency can be measured as the ratio ( U ( C t
) – Σ v i o ( c i t ))/ U ( C t
), where Σ v i o ( c i t ) is the actual total value of consumption that individuals achieve in period t , and U ( C t
) is the optimal level.
This loss is greatest in the hybrid treatment (8.6%), followed by the communication and the voting treatments, (6.4% and 6.2%, respectively), and lowest in the baseline (4.9%). The relatively good performance of the baseline treatment on this measure may be due to the stronger tendency for convergence to a stationary competitive equilibrium, albeit the poverty trap, in the baseline than in the other treatments. The stability that accompanies strong convergence to equilibrium makes it easier for individuals to discern the price of capital and therefore to correctly apply the optimal decision rule of consuming until the marginal utility of consumption equals the price of capital.
We term the third type of inefficiency as dynamic inefficiency , which results from suboptimal allocations to investment and consumption. Let V ( K t
) be the value of the economy’s capital stock in period t , assuming that the economy behaves like a benevolent social planner, making optimal decisions from period t onward. This value is calculated in the following manner. Suppose the economy from period t onward is directed by a benevolent social planner choosing aggregate levels and individual allocations of capital and consumption to maximize total welfare. Then, there is an optimal sequence of capital stock levels from period t on, and the market value of a unit of capital under this assumption can be calculated for each current level of capital stock. The market value in period t is equal to the marginal utility of consumption in period t along the economy’s optimal trajectory. Let V ( K * t
) be the value of the optimal quantity of capital stock given the current level of output and V ( K t
) be the value of the total level of capital generated from the individual agents’ actual
18

choices in period t and assuming optimal decisions for the economy thereafter. The level of dynamic inefficiency in period t is defined as ( V ( K * t
) - V ( K t
))/ V ( K * t
). This measure shows considerable differences among treatments. In the baseline treatments, the level of dynamic inefficiency averages
21.99%. In the voting and communication treatments, the inefficiency is 12.81% and 12.27%, respectively. In the hybrid treatment, the average value of the measure is 5.01%. The hybrid treatment has the lowest dynamic inefficiency, and this effect reflects its greater success in escaping the poverty trap compared to the other treatments, and its ability to move the economy relatively close to its optimum level of capital.
16
We also consider the price efficiency of the markets for output. Figures 12-15 show the time series of the market price for capital in each session of the four treatments. We ask whether market prices satisfy rational expectations. To do so, we calculate the value for each unit of output assuming the entire economy behaves optimally from the current period onward. This per-unit value is given by
V* ( K t
)/ K t
. The square-shaped markers in Figures 12-15 illustrate these theoretical predictions given the actual capital stock in each period t for each session. The figure shows that actual prices and rational expectations predictions are positively correlated.
[Figures 12 -15: About Here]
3.4. How do the economies avoid the poverty trap?
The market mechanism that we have introduced in our economies appears to be an effective institutional structure for reaching a competitive equilibrium. However, an economy with multiple
Pareto-rankable equilibria poses an additional challenge for the market. To operate efficiently, the market must not only locate an equilibrium, but it must also select the optimum from a set of equilibria.
In the baseline treatment, the difficulty of this challenge is apparent. The market alone, in conjunction with an initial endowment below the threshold level of capital stock, is only able to surpass the threshold in a small minority of instances. However, the additional institutions of communication and voting increase the likelihood that the economy surpasses the threshold. When both are present as in the hybrid treatment, the economy surpasses the threshold with some consistency in every session. In this subsection, we explore the manner in which the economy successfully surpasses the threshold in the various treatments we have studied.
16 The chat-room transcripts in both the communication and the hybrid sessions contain no explicit attempts to reduce output gap or consumption inefficiency.
19

In the baseline treatment there were only two episodes in which the capital stock of the economy surpassed the threshold level of 31. Two instances occurred in session CaltechB2, in the first and fifth horizons. The other episode occurred in the first horizon of session EmoryB3. All three episodes were essentially single-handed efforts in which one agent accumulated a large amount of capital while the other four held small quantities. This unilateral investment was apparently not viewed as profitable, since similar behavior was not attempted consistently later in the sessions. Thus, when the economy successfully exited the poverty trap in the baseline treatment, it was not through coordination but rather because one individual reduced his own consumption by a sufficient amount to enable the economy to exit the poverty trap.
In the communication treatment, the exchange of messages facilitates coordination and thereby makes it more likely that the threshold is surpassed. However, communication does not guarantee that the economy escapes the poverty trap. In two sessions, the economy failed to surpass the threshold at any time. In the periods in which the threshold was surpassed for the first time in a session, communication always followed a specific pattern. One player would suggest that players not consume at all or consume very small quantities in the current period, and one or more players (and in all but one instance two or more players) would indicate agreement. Then, after successfully passing the threshold, the next period was characterized by acknowledgement of the successful coordination.
Below we present a typical dialogue in a period in which the threshold was surpassed for the first time in a session in the communication treatment. In the EmoryC1 dialogue, agent 4 takes the initiative of convincing other players to keep capital. Player 2 expresses support for the initiative.
Player 1 is suspicious, although he does make the required investment. Player 3 then indicates support for the strategy in period 2 after player 4 announces the group’s success. With all players now in agreement, the economy remains above the threshold for the remaining periods of the horizon.
Similarly, in EmoryC3, the dialogue shows four of five players indicating support for not consuming in period 1. Then, in period 2, players congratulate each other for their successful coordination.
Example 1: Horizon 2, Communication treatment, Session EmoryC1
Period 1
(player 4)>HOLD K for a round
(player 2)>once again...lets keep all our k...nobody consume this round
(player 4)>is that good player 1 and 5
(player 1)>we say that every round and no body does it
(player 5)>we only have a few min. left
(player 4)>just do it for the first round and we all will have a lot more to use
Period 2:
20

(player 4)>SEE!
(player 3)>good work
(player 2)>wanna do it again?
(player 3)>let's let it keep growing
Example 2, Horizon 3, Communication, Session EmoryC2
Period 1:
(player 5)>NOBODY CONSUME
(player 1)>DONT CONSUME
(player 4)>lets get this show on the road...move quick
(player 5)>JUST THE FIRST ROUND, ITS WELL WORTH IT
(player 1)>lose a lil...make a lot
(player 3)>HOW
(player 2)>by not consuming
Period 2:
(player 1)>GOOD JOB
(player 4)>well done
(player 5)>THAT A WAY TO DO IT
Figure 16a displays the capital stock held at the end of each period and the number of individuals who either proposed or agreed on a decision to keep capital above the threshold level during the period. The figure shows that, when the economy was below the threshold, a majority agreement to coordinate was always necessary, but not sufficient, for the economy to surpass the threshold (in session EmoryC1, the majority agreement occurred in the horizon preceding the one in which the threshold was surpassed). In the two sessions in which the threshold was never surpassed,
EmoryC3 and CaltechC1, there was no expression of majority support for attempting to surpass it at any time.
In the hybrid treatment, communication did not typically follow the same pattern as in the communication treatment. Indeed, in only six of fifteen instances in which the threshold was surpassed and in only two of five instances when it was surpassed the first time, was there a majority agreement that proposers should increase the capital stock. The voting process on its own provides the device to coordinate decisions to surpass the threshold, making communication to some extent redundant. This is because one proposer, along with majority approval after the proposal is submitted, is sufficient to coordinate the economy’s activity. The majority does not have to express a desire to invest more for the coordination problem to be solved. Indeed, in the hybrid treatment, there were sometimes expressions of a desire to consume a large quantity in the current period rather than attempting to hold more capital. This type of message likely did not occur in the communication treatment because subjects were always free to consume as much as they wanted. Figure 16b shows
21

the number of agents who proposed or agreed on keeping capital above the threshold along with the amount of units kept at the end of each period in the hybrid treatment.
[Figures 16a and 16b: About Here]
In both the voting and hybrid treatments, when the economy was below the threshold and there were two proposals to bring it over the threshold, agents usually chose to vote for the one that crossed the threshold by closer to the minimum amount required. In only 1 of 10 such instances in the voting treatment did the proposal that specified holding more capital defeat the one with less capital proposed. This one instance was a pair of proposals in which an alternative that proposed an aggregate level of capital stock of 32 defeated one proposing 31. Similarly, in the hybrid treatments, in none of the eight instances in which the threshold was crossed did the proposal with the higher capital stock win. The winner was always 31, which was a powerful attractor for the voting process.
However, the submission of a proposal with aggregate capital stock above the threshold while the economy was below it, did not guarantee that the economy would surpass the threshold. When the economy was below the threshold and exactly one proposal exceeded the threshold, it won its vote in
12 of 21 (57.1%) instances in the voting treatment. This increased to 9 of 11 (81.8%) instances in the hybrid treatment. Thus, communication improves voting decisions in this regard. In the baseline and the communication treatments, there was not a single instance in which an economy surpassed the threshold and later fell below it in the same horizon. In contrast, there were two such instances in the voting treatment and two more in the hybrid treatment. While the coordination achieved in the voting or hybrid treatments requires fewer agents, it is also less durable than under the communication treatment.
3.5. The content of communication
The content of communication is of potential interest, since, as we have seen, the content of messages affects the behavior of the economies. To render an analysis of communications tractable, we have divided the comments into three categories that we believe to be the most relevant in affecting behavior. These categories are: “Don’t consume”, “Keep K (general)”, and “Specific proposal for investment”. The first category consists of proposals suggesting zero consumption for all traders. The second category is a general statement that more capital should be held. The third category includes specific suggestions such as “everyone hold on to 7”, and “everyone try to keep 9-
10”. Table 7 summarizes the content and timing of messages. To study which of the categories affect
22

investment behavior, we construct a random effect model. Each period t of a given session constitutes an observation and the data are pooled for all of the sessions making up a treatment. The dependent variable is the total number of units of capital K t
allocated for investment in the economy. The independent variables are the total output of the economy in period t and dummy variables for the three categories of messages listed above. The dummy variables take on a value of 1 in periods in which the corresponding category of message is articulated and a value of 0 otherwise. Each session and each horizon is assumed to have a random effect.
Table 8 shows the results of the regressions for the communication and hybrid treatments.
Under the communication treatment, general suggestions to hold capital do not affect the levels of investment. However, the specific proposals to consume zero or that specify exact levels of investment do increase average capital stock. Specific detailed messages are more effective than general ones in solving the coordination problem that exists in the communication treatment. Under the hybrid treatment, none of have proposals have significant effects on the level of investment. The economy attained high levels of investment without the exchange of substantive suggestions in the hybrid treatment.
[Table 7 and 8: About Here]
3.6. Voter and proposer behavior: What is proposed and what do people vote for?
In this subsection we explore voters’ and proposers’ choices. We take each individual voting decision as a unit of observation and identify four relevant variables that can potentially explain individual voting behavior. Our first variable is “higher consumption for the voter;” a dummy variable taking on a value of 1 if the proposal subject votes for gives him more consumption than the competing proposal. This captures the behavior of individuals who myopically favor proposals that give them higher current consumption, which is immediately converted into earnings.
The second dummy variable is “Closer to the myopic optimum consumption.” This variable, intended to capture a plausible form of rational voting, is constructed in the following manner. We calculate a myopically optimal level of consumption. Because an individual can allocate output to either capital or consumption, at an optimum in which a positive quantity of output is assigned to each use, the marginal value of each use must be equal. Therefore, it is optimal for an individual to consume until the marginal utility of consumption equals the expected future price of capital. For the calculation, we suppose that the expected future price of capital is equal to the average price in the current period. This seems to be a reasonable supposition for the beliefs of individuals in the
23

experiment. The variable “closer to myopically optimal consumption” equals 1 if an individual votes for the proposal that yields him a value of consumption closer to the optimum compared to the other proposal, and equals 0 otherwise.
The variable “More equal investment schedule” is the third regressor. An equal investment schedule does not yield more equal earnings, since subjects have different utility and production schedules. However, subjects may have a preference for holding a similar amount of capital in each period, viewing the holding of capital as a form of contribution to group welfare. Indeed, in some of the communication transcripts, subjects proposed that all agents hold 7 units of capital stock. Finally,
“Vote for my own proposal” is our last variable. This is a dummy variable taking on a value of 1 if the individual voted for a proposal that he submitted himself, and zero otherwise. It is reasonable to expect that those who propose an investment schedule would want their proposals to be implemented.
We use a random-effects logit model to estimate the coefficients, incorporating both horizonspecific and session-specific disturbances. A dependent variable is 1 when a subject votes for proposal 1 and 0 otherwise. Table 9 displays the results. The results in both the voting and the hybrid treatments show that “Higher consumption for the voter” and “Vote for own proposal” are the only factors that can explain voting decisions.
[Tables 9 and 10: About Here]
The proposals reflect a considerable degree of rationality on the part of proposers, and sufficient resistance to the temptation to propose a large own consumption. There is no tendency for proposers to submit proposals that yield themselves more consumption than at the myopic optimum or even more consumption than the other agents. The data are shown in table 10. Compared to the myopic optimum, agents propose more consumption for themselves an average of 26.2% of the time in the voting treatment and 23.6% of the time in the hybrid treatment. Proposers gave themselves higher consumption that all of the other four agents in 21.3 and 23.3 percent of instances in the voting and hybrid treatments respectively (this fraction would equal 20 percent if each of the five individuals were equally likely to have the highest consumption level). In addition, proposals give the proposing individual greater consumption than the group average in 46.8 percent of instances in the voting and
48.7 of instances in the hybrid treatment (this fraction would equal 50 percent if there was no bias in favor of higher own consumption).
Communication appears to improve proposer decisions. In voting treatment, there are 18 proposals (8.3% of all proposals) that render a higher consumption than the myopic optimum for the
24

proposer, and also lower the investment level below the threshold. These proposals impose a permanently lower income on the economy, including the proposer, because of a desire to increase current consumption. In contrast, in the hybrid treatment, where communication is allowed at the beginning of each period, there are only 3 such cases (2% of all proposals). Another interesting pattern is shown in Table 11. This table contains the number and percentage of proposals that would keep the economy above the threshold or would pull aggregate capital below 31. In all voting sessions, when the economy-wide capital is above 31, 33% of the proposals would pull K t
below the threshold. This is in contrast to the hybrid sessions, where only 17% of the proposals, conditional on current aggregate capital exceeding 31, would bring K t
below the threshold. In addition, when the economy is below the threshold, only 36.4% of the proposals in the voting treatment would bring the economy’s capital over the threshold. In the hybrid treatment, however, this percentage increases to
68.9%. Overall, the communication among members of the group appears to help individuals to formulate proposals that are better for the group. The communication possibility present in the hybrid treatment improves voter and proposer decisions relative to the voting treatment principally by its mere existence and the contact between agents it creates (voters and proposers are exposed to any messages others which to send in reaction to their decisions), rather than by providing specific recommendations to voters and proposers.
[Table 11: About here]
In this paper we introduce a laboratory methodology for studying the effect of institutions on economic growth. Our first conclusion is that is feasible and productive to do so. Experiments allow the actual behavior of the economy to be compared with the theoretically optimal path. They permit a focus on economies with specific characteristics, such as those with multiple equilibria, where institutions can be compared while keeping the environment constant. This allows the researcher to focus on solutions for specific sources of suboptimal growth. In the case of this project, we have chosen the coordination failure that is due to the existence of multiple rational expectations equilibria.
The experimental economies include aspects of behavior not present in most modern macroeconomic models, such as the direct and interaction effects of the decision biases, trembling hand errors, strategic uncertainty, and cooperative motives that influence human behavior. The experiment allows observation of such behavioral elements as they interact with different economic environments and institutions such as markets and political processes and generate patterns of
25

behavior that have implications on output and welfare. Behavioral phenomena that might cause an economy to operate below its optimum and institutions that might correct different types of economic failure might be identified. We view this study as a first step towards bringing experimental economic methods to bear on issues of macroeconomic policy and economic development.
In this study, we observe clear effects of institutions on income and on the ability to avoid a poverty trap. The economies of the baseline treatment tend to converge to the poverty trap of the economy, which is not a surprising result since the parameters were chosen to make this a likely outcome for the baseline treatment. The data from the baseline treatment indicate that while an appropriately organized market institution reliably reaches a competitive equilibrium, additional institutions may be required to help select the optimal from among several equilibria. We identify two institutions, communication and voting, which when applied together, are sufficient to enable the economy to extricate itself from a poverty trap.
Both the availability of communication, a highly stylized version of free expression, and the voting process, a highly stylized democratic process, improve output and welfare on average over the level achieved in the baseline treatment. The task faced in our economies with multiple equilibria is a specific type of coordination of activity among agents. When applied alone, communication and voting each have some advantages over the other. The communication treatment promotes coordination, presumably because it reduces strategic uncertainty about others’ investment decisions, but does not guarantee that successful coordination occurs. It increases the probability that the economy will exit the poverty trap, and in cases where this is successful, the economy then tends to move in the direction of the optimal equilibrium. There is little variance in outcomes from one period to the next once the threshold has been crossed, as the prices in the market help guide the economy smoothly toward its optimum. On the other hand, a consensus is required that it is desirable for the economy to cross the threshold, and if this consensus is not reached, the economy tends to fall into the poverty trap.
The existence of the voting process also increases the likelihood that the poverty trap is escaped. Although the voting process is characterized by significantly higher output and welfare than the baseline treatment, the variance of outcomes and the fluctuations from one period to the next are greater. The coercive nature of the voting process means that a lower degree of consensus in favor of high investment is required than in the communication treatment and that strategic uncertainty in investment decisions is eliminated, making it easier to exit the poverty trap. However, the voting process fails to converge to stable outcomes, but rather generates greater variability in capital stock levels than communication.does. This may be due to the changing identity of proposers. This
26

possiblity that could be studied by allowing individuals to remain in the role of proposers for multiple periods, with re-election possibilities one method of doing so. The variability may also be due to the fact that individual investment levels are determined by a centralized process rather than decided upon by those who hold private information about their own utility of consumption and marginal product of capital.
When the communication and voting processes are both in effect in the hybrid treatment, output and welfare are greater than in the other treatments. This is the only treatment, in which the economy surpasses the poverty trap in every session. Thus, we find that a particular implementation of “democracy” promotes growth and welfare in our economies, and this is effect is more reliable when citizens of the economies can engage in free expression. Adding communication improves voter and propser decision making, and the voting process improves the effectiveness of communication, perhaps by further reducing strategic uncertainty.
Our inferences are obviously specific to economies with the particular structure we have studied. As with theoretical modeling, both the environment and the institutions are very simple compared to those that are naturally occurring. The level of generality of any empirical patterns observed in this or any other study of this type must be determined with an accumulation of evidence beyond a single study. The structure of the economy here was intentionally chosen to have the structure of a well-known theoretical model. However, it is straightforward to add features of macroeconomies that are of interest to economists, such as the possibility of endogenous growth, multiple interacting economies with an international structure, multiple sectors in the economy, incomplete property rights, and a wider array of government fiscal, monetary, or regulatory policy options. Institutions that are successful at producing wealth in one environment can be implemented in another to test their robustness. Indeed, different political systems such as dictatorship, indirect democracy, socialism, and anarchy can be implemented, their performance measured, and their properties studied.
We may find that certain institutions are highly suitable for economic environments with a particular structure but not others. For example, in an economy with a single rational expectations competitive equilibrium, decentralized markets alone may be very effective in guiding the economy to close to its optimum, and a voting process may introduce undesirable fluctuations in economic activity. However, as our data here suggests, in an economy with multiple equilibria, the same minimal institutional structure may lead to a suboptimal equilibrium, and supplemental institutions appear to be required to select optimal equilibria. The cost of the variability the voting process introduces does not offset the benefit from increasing the likelihood the poverty trap is avoided. More
27

generally, different institutions may be particularly effective in combating different causes of suboptimal economic activity. The search for such institutions need not be restricted to those that are naturally occurring. In the laboratory, new institutions that theory and economic intuition suggest may promote economic growth can be designed, tested and refined.
Acemoglu, Daron, Simon Johnson and James Robinson, “The Colonial Origins of Comparative
Development: An Empirical Investigation,” American Economic Review , December 2001, 91(5),
1369-1401
Azariadis, Costas and Allan Drazen, “Threshold Externalities in Economic Development,” Quarterly
Journal of Economics , May 1990, 105(2), 501-26.
Azariadis, Costas, Intertemporal Macroeconomics , Cambridge, MA: Blackwell, 1993.
Banerjee, Abhijit,Fr Dilip Mookherjee, Kaivan Munshim and Debraj Ray, “Inequality, Control
Rights, and Rent Seeking: Sugar Cooperatives in Maharashtra,” Journal of Political Economy ,
2001, 109, 138-90.
Barro, Robert J. and Xavier Sala-i-Martin, Economic Growth , New York: McGraw-Hill, 1995.
Barro, Robert J., Determinants of Economic Growth: A Cross-Country Empirical Study , MIT Press,
1997.
Baumol, William J., “Productivity Growth, Convergence, and Welfare: What the Long-Run Data
Show,” American Economic Review , 76(5), December 1986, 1072-85.
Camerer, Colin and Keith Weigelt, “Convergence in Experimental Double Auctions for
Stochastically Lived Assets,” in D. Friedman and J. Rust, eds., The Double Auction Market:
Institutions, Theories, and Evidence , New York: Addison-Wesley, 1993, 355-96.
Cass, David, “Optimal Growth in an Aggregative Model of Capital Accumulation,” Review of
Economic Studies , July 1965, 32(3), 233-40.
Cooper, Russell, “Estimation and Identification of Structural Parameters in the Presence of Multiple
Equilibria”, working paper, Boston University, 2002.
Durlauf, Steven and Danny Quah, “The New Empirics of Economic Growth,” in John Taylor and
Michael Woodford, eds., Handbook of Macroeconomics , Amsterdam, New York and Oxford:
Elsevier Science, North-Holland, 1999, 235-308.
Galor, Oded and Joseph Zeira, “Income Distribution and Macroeconomics,” Review of Economic
Studies , January 1993, 60(1), 35-52.
Islam, Nazrul, “What Have We Learned from the Convergence Debate? A Review of the
Convergence Literature,” Journal of Economic Surveys , July 2003, 17 (3), 309-362.
Knack, S., and P. Keefer, “Does Social Capital Have an Economic Payoff? A Cross-Country
Investigation”, Quarterly Journal of Economics , 112, 1251-1288.
Koopmans, Tjalling C., “On the Concept of Optimal Economic Growth,” in Pontifical Academy of
Sciences, The Econometric Approach to Development Planning , Amsterdam: North-Holland,
1965, 255-87.
Lei, Vivian and Charles Noussair, “An Experimental Test of an Optimal Growth Model”, American
Economic Review , Vol. 92, no 3, June 2002, pages 549-570.
Lei, Vivian and Charles Noussair, “Equilibrium Selection in an Experimental Macroeconomy”, working paper, Emory University, 2003
Murphy, Kevin M., Andrei Shleifer, and Robert W. Vishny, “Industrialization and the Big Push,”
Quarterly Journal of Economics , May 1989, 106(2), 503-530.
28

Noussair, Charles N. and Kenneth Matheny, “An Experimental Study of Decisions in Dynamic
Optimization Problems,” Economic Theory , March 2000, 15(2), 389-419.
Noussair, Charles, Charles Plott, and Raymond Riezman , “An Experimental Investigation of the
Patterns of International Trade”, with Charles Plott and Raymond Riezman, American Economic
Review , June 1995, pages 462-491.
Plott, Charles and Glen George, “Marshallian vs. Walrasian Stability in an Experimental Market,”
Economic Journal , May 1992, 102, 437-460.
Ramsey, Frank P., “A Mathematical Theory of Saving ,” Economic Journal , December 1928, 38, 543-
59.
Rosenstein-Rodan, Paul, “Problems of Industrialization of Easter and Southeastern Europe,”
Economic Journal , 53, June-September 1943, 202-211.
Sachs, Jeffrey and Andrew Warner (1995), “Economic Reform and the Process of Global
Integration,” Brookings Papers on Economic Activity , 1995:I, 1-118
Smith, Vernon “An Experimental Study of Competitive Market Behavior,” Journal of Political
Economy , 1962, 70, 111-137.
Smith, Vernon and Arlington Williams (1982), “The Effect of Rent Asymmetries in Experimental
Double Auction Markets”, Journal of Economic Behavior and Organization, 3(1), 99-116.
Temple, Jonathan, “The New Growth Evidence,” Journal of Economic Literature , March 1999,
37(1), 112-56.
Theil, H., 1967, Economics and Information Theory , North Holland, Amsterdam.
29

Table 1: Parameters of the model
U ( C t
) : economy-wide utility function
F ( K t
) function
: economy-wide production
A: production-efficiency parameter
: threshold level of capital stock
: discount rate
: depreciation rate
400 C t
− 2 C t
2
AK t
0 .
5
A
A
= 7 .
88 ; if K t
= 16 .
771 ; if K t
31
0.25
1
<
≥
31
31
30

Table 2: Values of variables in equilibrium
Variable
Capital (K)
Consumption (C)
Price (P)
Welfare (U)
Optimal Steady State
45
70
118
18,060
Poverty Trap
9
16
334
5,856
31

Table 3: Session information for all treatments
# of periods per horizon, h:
(h1, h2, h3, …hi)
Baseline
EmoryB1
EmoryB2
EmoryB3
CaltechB1
CaltechB2
03/22/04
03/24/04
04/07/04
07/08/04
07/12/04
5
6
6
4
6
(4, 7, 2, 2, 7)
(3, 3, 7, 2, 1, 4)
(5, 2, 1, 3, 4, 4)
(4, 4, 7, 6)
(2, 3, 3, 2, 3, 1)
Avg.
earnings
in Yen
Avg. earnings in $ §
25,343
23,801
28,678
22,274
17,007
39.24
36.84
47.26
34.80
26.87
Communication
EmoryC1 03/22/04 2
EmoryC2
EmoryC3
CaltechC1
CaltechC2
03/23/04
04/01/04
07/15/04
07/19/04
5
4
5
5
(7,
(8, 1, 3, 5, 2)
(3, 7, 6, 4)
(6, 1, 1, 2, 4)
(3, 4, 1, 3, 6)
CaltechC3 10/07/04 4 (11, 2, 5, 2)
Voting
19,848 16.06
27,607
23,458
14,219
33,060
52,170
23.57
19.26
11.56
28.64
44.24
EmoryV1
EmoryV2
EmoryV3
CaltechV1
03/24/04
03/27/04
04/01/04
07/13/04
4
6
5
7
(11, 5, 3, 3)
(6, 2, 1, 2, 5, 5)
(1, 5, 1, 7, 4)
(6, 2, 4, 2, 1, 3, 5)
CaltechV2 07/14/04 8 (3, 4, 8, 2, 1, 3, 1,2)
Hybrid
EmoryH1 06/01/04 2
EmoryH2 09/01/04 3
EmoryH3 09/01/04 4
CaltechH1
CaltechH2
08/03/04
08/04/04
5
3
(4,
(8, 2, 4)
(4, 4, 7, 4)
(5, 8, 2, 2, 2)
(2, 9, 2)
36,767
25,750
37,355
35,963
31.05
21.86
32.27
30.85
31,330 25.66
17,202 27.15
23,102
37,190
48,015
22,045
18.74
31.27
42.66
18.72
32

Table 4: Convergence Estimation Results for Capital
Random-Effects MLE
Optimal Eq. Capital = 45, Poverty Trap Capital = 9
Baseline
At the5% level, convergence value significantly different from:
Optimal Eq. Poverty Trap
EmoryB1 11.29 2.45 No
EmoryB2 10.95 3.12 No
EmoryB3 18.65 6.41 No
CaltechB1 13.14 2.87 No
CaltechB2 33.34 6.46 No
Communication
EmoryC1 47.05 21.99 No No
EmoryC2 28.81 5.64
EmoryC3 10.49 1.11 No
CaltechC1 10.74 2.60 No
CaltechC2 55.83 3.10
CaltechC3 54.86 1.33
Voting
EmoryV1 56.47 9.44 No
EmoryV2 13.74 1.54
EmoryV3 59.96 8.53 No
CaltechV1 41.59 5.92 No
CaltechV2 35.96 3.96
Hybrid
EmoryH1 31.08 11.38 No No
EmoryH2 45.05 2.74 No
EmoryH3 74.32 7.98
CaltechH1 32.37 1.70
CaltechH2 35.55 3.40
33

Table 5: Convergence Estimation Results for Welfare
Random-effects MLE
Treatment
Baseline
Coefficient
Opt. Eq. Welfare = 18,060, Poverty Trap Welfare = 5,856
B
2
Error
At the 5% level, convergence value significantly different from:
Optimal Eq. Poverty Trap
EmoryB1
EmoryB2
4,436
4,336
428
918
EmoryB3 9,910 1,824
CaltechB1 3,729 653
No
CaltechB2 9,536 2,364 No
Communication
EmoryC1 3,406 596
EmoryC2 10,430 2,311
EmoryC3 4,444 389
CaltechC1 3,406 596
CaltechC2 18,576 1,888 No
CaltechC3 19,952 902 No
No
Voting
EmoryV1 11,118 1,857 No
EmoryV2 4,885 411 No
EmoryV3 14,969 1,920 No
CaltechV1 13,006 2,294
CaltechV2 8,933 2,031 No
Hybrid
EmoryH1 11,867 3,108
EmoryH2 11,900 1,088
EmoryH3 17,341 1,709 No
CaltechH1 20,697 1,273 No
CaltechH2 12,031 2,267
34

Table 6: Rank-sum tests of differences in output and welfare between treatments
(output)
Communication Voting Hybrid
Baseline z =1.10, p p =0.01
Communication p = 0.36
Voting
(welfare)
Communication Voting z =2.61, p =0.005 z =0.91, p =0.18 z =1.15, p =0.13
Hybrid
Baseline z =0.91, p =0.18 z =2.19, p =0.01
Communication p = 0.36
Voting z =2.61, p =0.005 z =1.28, p =0.1 z =1.78, p =0.03
35

Table 7: The content of communication, all sessions, communication and hybrid treatments
Session Time Observed (Horizon, Period)
EmoryC1 Don't Consume (H1, 5), (H2, 1)
Keep K (general) (H1, 1), (H1, 6), (H1, 7), (H2, 1), (H2, 4)
Specific Proposal (H2, 2), (H2, 3)
EmoryC2 Don't Consume (H1, 2), (H2, 1), (H3, 1), (H4, 1), (H5, 1), (H5, 2)
Keep K (general) (H1, 1), (H1, 2), (H5, 1)
EmoryC3 Don't Consume (H4, 3)
CaltechC1 Don't Consume (H1, 2), (H1, 3)
Keep K (general) (H1, 2), (H1, 3), (H1, 4), (H1, 5)
Specific Proposal (H1, 1), (H2, 1), (H4, 1)
CaltechC2 Don't Consume (H1, 2), (H1, 3), (H2, 2)
Keep K (general) (H1, 2), (H1, 3), (H2, 2), (H2, 3), (H4, 2)
Specific Proposal (H1, 3), (H2, 1), (H2, 3), (H3, 1), (H4, 2)
CaltechC3 Don't Consume (H1, 1), (H2, 1)
Keep K (general) (H1, 1), (H1, 4)
EmoryH1 Keep K (general) (H1, 3), (H1, 4), (H2, 1)
EmoryH2 Keep K (general) (H1, 2)
EmoryH3 Don't Consume (H1, 1), (H3, 2), (H4, 1)
Keep K (general) (H1, 1), (H2, 2), (H2, 3), (H4, 3)
CaltechH1 Keep K (general) (H1, 1), (H1, 3), (H1, 4), (H1, 5), (H2, 1), (H2, 2)
Specific Proposal (H2, 5), (H2, 6), (H2, 7), (H3, 1), (H3, 2), (H4, 1), (H4, 2), (H5, 1)
CaltechH2 Keep K (general) (H2, 2), (H2, 4), (H3, 2)
36

Table 8: The Effect of Communication Content on Capital Stock Level,
Results of Random-effect GLS Estimation
Dependent Variable = Economy-wide Capital Stock Level
(Communication) R 2 (overall)=0.86
Total K in the Economy
Don't Consume
Estimated coefficient
0.46
6.99
Std Error
0.02
2.28
p>|z|
0.00
0.00
Keep K (general)
Specific Proposal
1.13
4.32
2.18
2.53
0.61
0.09
Constant 1.71
(Hybrid) R
1.50
2 (overall)=0.54
0.25
Total K in the Economy
Don't Consume
Keep K (general)
Specific Proposal
Estimated coefficient
0.34
8.02
-5.12
-5.95
Constant 14.87
Std Error
0.04
7.04
3.37
4.46
3.96
p>|z|
0.00
0.25
0.13
0.18
0.00
37

Table 9: Influences on voting decisions, Random-effects logit estimation
Dependent Variable = 1 if Individual Votes for Proposal, and = 0 otherwise
Voting Sessions Estimated coefficient Std Error p>|z|
Higher own C
Higher own K
Closer to the myopic optimum C
Equal investment
Vote for own proposal
Constant
Hybrid Sessions
0.62 0.23 0.01
-0.07 0.23 0.75
0.00 0.02 0.91
0.13 0.20 0.51
2.69 0.36 0.00
-0.80 0.30 0.01
Higher own C
Higher own K
Closer to the myopic optimum C
Equal investment
Vote for own proposal
Constant
0.68 0.24 0.01
-0.02 0.26 0.95
-0.02 0.02 0.29
-0.34 0.25 0.18
1.32 0.28 0.00
-0.26 0.33 0.44
38

Table 10: Percentage of proposals that render a higher consumption to proposer than at the myopic optimum and than that allotted to any other individual
Higher than Myopic
Optimum
Higher than Any Other
Individual
Voting Sessions
EmoryV2 10
EmoryV3 25
CaltechV1 13
CaltechV2 17
14%
43
14
9
27
Hybrid Sessions
EmoryH1 10
EmoryH2 61
EmoryH3 21
CaltechH1 3
CaltechH2 23
Percentages rounded to the nearest integer
15
21
26
29
19
39

Table 11: Percentage of proposals above and below the threshold when the economy-wide K
≥
31
Proposal is above threshold Proposal is below threshold
Voting Sessions Percentage
EmoryV1 73%
EmoryV2 0
EmoryV3 86
CaltechV1 76
CaltechV2 63
Total 63
Percentage
27%
100
14
24
37
37
Hybrid Sessions
EmoryH1 81
EmoryH2 96
EmoryH3 82
CaltechH1 84
CaltechH2 84
Total 82
Percentages rounded to the nearest integer
19
4
18
16
36
18
40

220
200
180
160
140
120
100
80
60
40
20
0
0
Figure 1: Aggregate Production and Demand Functions.
Discontinuous increase in input-output productivity when aggregate capital stock reaches 31.
Aggregate Production Function Aggregate Demand Function
25 50 75
Units of Input
100 125 150
450
400
350
300
250
200
150
100
50
0
0 20 40
Units of K
60 80 100
41

Period t begins
Stage 1
Trading in call market
Transfer k t
into output (c t
+k t+1
)
Period t begins
Figures 2a-2d: Timing within a period
Stage 1
Trading in call market
Chat is allowed
Transfer k t output (c t
into
+k t+1
)
Period t begins
Stage 1
Trading in call market
Transfer k t
into output (c t
+k t+1
)
Period t begins
Baseline
Period t ends
Stage 2
Allocation of output to c t
Communication
Period t ends
Stage 2
Allocation of output to c t
Voting
Period t ends
Stage 2
Propose allocation of output to c t
Vote for a proposed allocation
Hybrid
Period t ends
Period t+1 begins
Determine if horizon ends
Determine if horizon ends
Chat is allowed
Transfer k t+1
into output (c t+1
+k t+2
)
Period t+1 begins
Determine if horizon ends
Transfer k t+1
into output (c t+1
+k t+2
)
Period t+1 begins
Transfer k t+1
into output (c t+1
+k t+2
)
Period t+1 begins
Stage 1
Trading in call market
Chat is allowed
Transfer k t
into output (c t
+k t+1
)
Stage 2
Propose allocation of output to c t
Vote for a proposed allocation
Determine if horizon ends
Chat is allowed
Transfer k t+1
into output (c t+1
+k t+2
)
42

80
60
40
20
0
Figure 3: Observed and Equilibrium Aggregate Consumption, Baseline Treatment
C* optimal = 70, C* inferior = 16
§
Emory B1 Emory B2
80
60
40
20
0
Data
Time
C* optimal C* inferior
Data
Time
C* optimal C* inferior
80
60
40
20
0
Emory B3
80
60
40
20
0
Caltech B1
Data
Time
C* optimal C* inferior
Data
Time
C* optimal C* inferior
Caltech B2
80
60
40
20
0
Time
Data C* optimal C* inferior
§= Each data point represents a period in a horizon. Horizons are separated by spaces. For instance, in the
Baseline Emory session 1, the first horizon had four periods
43

Figure 4: Observed and Equilibrium Aggregate Consumption, Communication Treatment
C* optimal = 70, C* inferior = 16
Emory C1
Emory C2
80
60
40
20
0
Data
Time
C* optimal C* inferior
80
60
40
20
0
Data
Time
C* optimal C* inferior
Caltech C1
Emory C3
80
60
40
20
0
Data
40
20
0
80
60
Data
Time
C* optimal
Caltech C2
Time
C* optimal
C* inferior
C* inferior
80
60
40
20
0
80
60
40
20
0
Data
Data
Time
C* optimal
Caltech C3
Time
C* optimal
C* inferior
C* inferior
44

Figure 5: Observed and Equilibrium Aggregate Consumption, Voting Treatment; C* optimal = 70, C* inferior = 16
Emory V1
Emory V2
80
60
40
20
0
80
60
40
20
0
Data
Time
C* optimal C* inferior Data
Time
C* optimal C* inferior
Emory V3
Caltech V1
80
60
40
20
0
80
60
40
20
0
Data
Time
C* optimal C* inferior
Data
Time
C* optimal C* inferior
Caltech V2
80
60
40
20
0
Data
Time
C* optimal C* inferior
45

Figure 6: Observed and Equilibrium Aggregate Consumption, Hybrid Treatment; C* optimal = 70, C* inferior = 16
Emory H1
Emory H2
80
60
40
20
0
80
60
40
20
0
Data
Time
C* optimal C* interior Data
Time
C* optimal C* inferior
Emory H3
Caltech H1
80
60
40
20
0
80
60
40
20
0
Data
Time
C* optimal C* inferior Data
Time
C* optimal C* inferior
Caltech H2
80
60
40
20
0
Data
Time
C* optimal C* inferior
46

Figure 7: Observed and Threshold Level of Capital, Baseline Treatment, All Horizons and Sessions
Emory B1
Emory B2
80
60
40
20
0
'
80
60
40
20
0
K stock
Time
Threshold K stock
Time
Threshold
Emory B3
K stock Threshold
Caltech B1
K stock Threshold
Time
Caltech B2
K stock Threshold
Time
Time
47

40
20
0
80
60
Figure 8: Observed and Threshold Level of Capital, Communication Treatment, All Horizons and
Sessions
Emory C1 Emory C2
80
60
40
20
0
80
60
40
20
0
Time
K stock Threshold K stock
Time
Threshold
Emory C3
Caltech C1
80
60
40
20
0
80
60
40
20
0
K stock
Time
Threshold
K stock
Time
Threshold
Caltech C2
Caltech C3
80
60
40
20
0
K stock
Time
Threshold K stock
Time
Threshold
48

Figure 9: Observed and Threshold Level of Capital, Voting Treatment, All Horizons and Sessions
80
60
40
20
0
80
60
40
20
0
Emory V1
K stock
Time
Threshold
Emory V3
K stock
Time
80
60
40
20
0
Threshold
Caltech V2
\
K stock
Time
80
60
40
20
0
80
60
40
20
0
Emory V2
K stock
Threshold
Time
Threshold
Caltech V1
K stock
Time
Threshold
49

Figure 10: Observed and Threshold Level of Capital, Hybrid Treatment, All Horizons and Sessions
Emory H1
Emory H2
80
60
40
20
0
80
60
40
20
0
Time
K stock Threshold K stock
Time
Threshold
80
60
40
20
0
Emory H3
80
60
40
20
0
Caltech H1
K stock
Time
Threshold
Caltech H2
80
60
40
20
0
K stock
Time
Threshold
K stock
Time
Threshold
50

Figure 11: Convergence Values and 95% Confidence Intervals for Capital Stock and Welfare, All
Sessions and Treatments
Baseline
Voting
25000
25000
20000
20000
15000
15000
10000 10000
5000
0
0 20 40 capital
60 80
5000
0
0 20 40 capital
60 80
Hybrid
25000
20000
15000
10000
5000
0
0
Communication
20 40 capital
60
25000
20000
15000
10000
5000
0
0 80 20 40 capital
60 80
51

Figure 12: Observed Prices and Theoretical Predictions, Baseline Treatment
Emory B1 Emory B2
1000 1000
500
0
500
0
Observed Prices
Time
Theoretical Prediction Observed Prices
Time
Theoretical Prediction
Emory B3 Caltech B1
1000
1000
500
500
0
Observed Prices
Time
Theoretical Prediction
Caltech B2
0
1000
Observed Prices
Time
Theoretical Prediction
500
0
Observed Prices
Time
Theoretical Prediction
52

1000
Figure 13: Observed Prices and Theoretical Predictions, Communication Treatment
Emory C1
Emory C2
1000
500
500
1000
0
Observed Prices
Time
Theoretical Prediction
Emory C3
1000
0
Observed Prices
Time
Theoretical Prediction
Caltech C1
500 500
1000
0
Observed Prices
Time
Theoretical Prediction
Caltech C2
1000
0
Observed Prices
Time
Theoretical Prediction
Caltech C3
500
0
Observed Prices
Time
Theoretical Prediction
500
0
Observed Prices
Time
Theoretical Prediction
53

Figure 14: Observed Prices and Theoretical Predictions, Voting Treatment
Emory V1 Emory V2
1000
1000
500
500
1000
0
Observed Prices
Time
Theoretical Prediction
Emory V3
1000
0
Observed Prices
Time
Theoretical Prediction
Caltech V1
500 500
0
Observed Prices
Time
Theoretical Prediction
0
Caltech V2
1000
Observed Prices
Time
Theoretical Prediction
500
0
Observed Prices
Time
Theoretical Prediction
54

1000
Figure 15: Observed Prices and Theoretical Predictions, Hybrid Treatment
Emory H1 Emory H2
1000
500 500
1000
0
Observed Prices
Time
Theoretical Prediction
Emory H3
1000
0
Observed Prices
Time
Theoretical Prediction
Caltech H1
500 500
0 0
Observed Prices
Time
Theoretical Prediction
Caltech H2
Observed Prices
Time
Theoretical Prediction
1000
500
0
Observed Prices
Time
Theoretical Prediction
55

Figure 16a: Economy’s Capital Stock and Number of Agents Communicating a Willingness to
Coordinate Investment, Communication Treatment
Communication (Emory session 2)
Communication (Emory session 1)
K stock Threshold
100
80
60
40
20
0
2
3
0
0 0
3
4
1
Time
5
2
1
0
0
1
100
80
60
40
20
0
1
2 1 0 0
0
0 0
1
3
3
0
2
0
0
0
0
3
2
T ime
Communication (Emory session 3)
100
Communication (Caltech session 1)
K stock Threshold
80
60
40
20
0
0
0
0
0
0 0
0 0 1
0
0
0 0 0
0
0
0
1
0
0
Time
100
80
60
40
20
0
2
2
3
4
2
0
1 0 3
2
0 3
0
0
Time
Communication (Caltech session 2) Communication (Caltech session 3)
100
80
60
40
0
4
5
4
4
3
20
5
0 0
0
0
0
0
0
0
0
0
0
Time
100
80
20
0
60
40 5
0
0
3
0
0
0
0
0
0
0
4
0
0
0
0 0
0
0
0
T ime
56

Figures 16b: Economy’s Capital Stock and Number of Agents Communicating A Willingness to
Coordinate Investment, Hybrid Treatment
80
60
40
20
0
0
0
Hybrid (Emory session 1)
K stock Threshold
0
0
1 0
0
0
1 1
Hybrid (Emory session 2)
100
80
60
40
20
0
0
1
0
1
0
0 0
0
0
0
0
0
0
0
T ime Time
Hybrid (Emory session 3)
100
80
60
40
2
0
0 0
0
1
3
0 1
0
20
0
0
0
0
0
2
1
1
0
0
T ime
Hybrid (Caltech session 1)
K stock Threshold
100
80
60
40
20
0
5
5 5
5
5
5 4 0
0 5 5 5 5
5
5
4
5
4
0
Time
Hybrid (Caltech session 2)
100
80
60
40
20
0
0 0
0
2
1
1
2
2
1
0
0
0
1
T ime
57