Abstract
This paper studies the dynamics of community formation when members differ substantially in their returns from voluntary local public good provision. Laboratory experiments are conducted to examine how agents relocate in response to both community provision and membership composition, as well as how the growth and stability of communities are dictated by moving costs and crowding. When the public good is congestible, such that returns are lower for larger populations, I find communities are characterized by instability, cyclical fluctuations in local provision, and a dynamic in which low demanders continually chase high demanders through locations. When congestion is eliminated, subjects with different returns do sometimes co-exist. Yet chronic, inefficient movement persists, suggesting that instability is driven by intrinsic preferences for community composition, as well as by sensitivity to congestion.
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Notes
See, for instance, Hudson (1980)’s application of the invasion-succession model to urban revitalization.
Florida and Melander (2007).
Hudson (1988) expands the invasion-succession model to include this second wave.
Likewise, trends similar to the cyclical pattern of neighborhood composition can be observed in other economic contexts. Karni and Schmeidler (1990) present a model of cyclical fashion trends in which consumers cycle through types of goods. In their model, members of a lower social class receive increasing utility from a good as more people consume it, while members of a higher social class receive utility that increases with the number of other high status users but decreases with the number low status users. Pesendorfer (1995) presents a model in which a monopolist introduces a redesigned good at a higher price as soon as the previous, discounted version becomes sufficiently popular. More desirable “high types” care more about matching with other high types than low types do and use the costly purchase of the new good as a means of coordinating with similar types.
At a broad level, the inability of a central authority to observe individual values for a public good is at the heart of the preference revelation problem, which results in under provision (Musgrave 1939; Samuelson 1954). In the specific context of linear public goods experiments, Ledyard (1995) suggests that heterogeneous returns have a negative effect on contributions (unless information is incomplete and participants only interact once). Fellner et al. (2011) find that, on average, subjects contribute less when individual marginal returns cannot be linked to individual behavior and less still if they are unaware of the distribution of returns. In a public goods game in which participants are aware of each player’s returns, Reuben and Riedl (2013) find that a punishment mechanism is used to enforce contributions proportional to returns.
For instance, Tiebout specifically references the desire of residents to have “nice” neighbors (Tiebout 1956, p. 418).
Throughout U.S. history, the ubiquity of this concern may be seen in limitations on the mobility of the poor in federal legislation, ranging from the Articles of Confederation, which excluded “paupers” from those who had the right to move freely between states, to the Personal Responsibility and Work Opportunities Reconciliation Act of 1996, which prevented newcomers from receiving welfare benefits beyond what they had been receiving previously for up to a year following their move (Donahue 1997).
In the typical public goods experiment, subjects receive an endowment in each period and, without discussion, choose how much to keep for private consumption and how much to contribute anonymously to the group. The total amount contributed is multiplied by a factor less than 1 and each subject receives this amount in addition to the portion of his endowment he kept for himself.
Experimental studies that have found sustained cooperation in groups formed of previously cooperative subjects include: Gunnthorsdottir et al. 2007; Rigdon et al. 2007; Gunnthorsdottir et al. 2010; Yang et al. 2007; Cabrera et al. 2012; Burlando and Guala 2005; Ones and Putterman 2007; and Gächter and Thöni 2005. An exception is Ockenfels and Weimann (1999).
The number of agents in the population is in line with the previous work on endogenous group formation reviewed in the previous section, which typically includes 9 or 12 agents. The limited number of locations used here is more restrictive than in these previous studies, which typically allow all participants to be in groups by themselves. However, all six locations are rarely used in this experiment (less than 1 % of observations) and thus the ability to form more communities likely would not have a large effect on the outcomes. Given the monetary incentives to form fewer groups, the availability of more locations could lead to more extreme results, in the form of lower efficiency and less stability.
The ratio of High and Low Types is held constant across all sessions and was chosen to be a (near) equal split, consistent with public goods experiments in fixed, heterogeneous groups. Populations that are homogeneous or that have a more extreme ratio of types might experience greater stability, as the incentives for “chasing” would be muted. However, this is not a question addressed by the current investigation, which focuses on populations with heterogeneous returns.
One CPG session was dropped because of a technical error, which caused no data to be recorded after the 27th period. One pilot CPG session was conducted that lasted 30 periods. Neither of these are included in the results reported in this paper, but are included in the data set. All of the pure sessions were conducted at Caltech, while the congestion sessions were conducted at both Caltech and Harvard. Every figure and table is reproduced with Caltech-only data in an appendix, available on request, which reveals no substantive changes or loss of significance.
The number of sessions, or populations of interacting participants, in each treatment compares favorably with other work on public goods games with endogenous group formation (e.g. Charness and Yang (2014); Ahn et al. 2008, 2009); Gunnthorsdottir et al. 2007) and Page et al. (2005) have three to seven sessions of interacting subjects per treatment).
Through pilot experiments it was determined that subjects who were provided with the full history never looked back more than two to three periods while choosing their location. Thus the available history was restricted to three periods to reduce clutter and confusion.
Taking each subject as the unit of observation, the difference in contributions between the High and Low Types is significant at less than the 0.01 level in both conditions using Wilcoxon rank-sum tests (\(Z=6.39\) for CPG and \(Z= 5.91\) for PPG). The differences remain significant at less than the 0.01 level if the session is taken as the unit of observation (\(Z= 3.49\) and \(Z=3.4\).)
See for instance: Isaac et al. (1984).
The difference in movement is significant if the unit of observation is the subject (\(Z=-5.101\), \(p<0.01\)) or the session (\(Z=-2.252\), \(p=0.024\)).
The average community size experienced by participants in the PPG condition is significantly higher if the subject is taken as the unit of observation (\(Z=9.43\)) or if the session is the unit of observation (\(Z=3.4\)). The average community sizes of 4 (CPG) or 7 (PPG) group members indicates that the groups formed are, on average, of similar size to those usually formed by experimenters in VCM experiments.
If either the individual or the session is taken as the unit of observation, \(p<0.01\).
This difference is significant at \(p<0.05\) (\(Z=-1.977\)).
Neither the sign nor significance of any estimates change if session-level random effects are included.
The decrease in contribution over time is significant for Low Types with individual fixed effects in both the CPG (\(p<0.01\)) and PPG (\(p=0.06\)) sessions.
These patterns are broadly consistent with the findings of Isaac et al. (1994) that participants with low MPCR (in homogeneous groups) respond positively to group size.
The difference between types in the provision of the community entered is significant at \(p<0.01\) in both the CPG and PPG sessions in Wilcoxon rank-sum tests, taking the individual subject’s average outcome over the session as the unit of observation. If session-level random effects are included the PPG sessions are different only at the \(p=0.03\) level and, if the session is taken as the unit of observation, \(p=0.14\). The difference remains significant at \(p<0.01\) in the CPG sessions.
The individual subject is the unit of observation and the variable considered is the difference in the size of the community entered vs. exited (not including the individual moving). The difference between types is significant at the \(p<0.01\) level in the CPG (\(\mathrm{Z}=-5.36\)) and PPG (\(\mathrm{Z}=-3.38\)) conditions. The difference is significant at the \(p<0.01\) in both conditions if session-level random effects are included. If the session-type is the unit of observation, the difference is significant at the \(p<0.01\) level in the CPG condition (\(\mathrm{Z}=-3.57\)) and at the \(p=0.07\) level in the PPG condition (\(\mathrm{Z}=-1.81\)).
At the individual level, the average contribution made by a participant in a high entry fee location is 11.7, compared to 5.8 in low fee locations. The effect of entry fee type on average contribution is significant at the \(p<0.01\) level (with each individual as the unit of observation and accounting for session effects) and holds even controlling for type. At the community level, average provision is 31 in populated high fee locations compared to 17.2 in other populated locations (\(p<0.01\) with session-level controls).
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I wish to thank Charles Plott, Leeat Yariv, Peter Matthews, Rod Kiewiet, John Ledyard, and Jean-Laurent Rosenthal, as well as two anonymous referees and the editor for their helpful comments, Meghan McKeown for lab assistance, and the Caltech Social Science Experimental Laboratory and the Harvard Decision Science Laboratory for their hospitality. Funding was provided by the Caltech Laboratory for Experimental Economics and Political Science and by Middlebury College.
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Robbett, A. Community dynamics in the lab. Soc Choice Welf 46, 543–568 (2016). https://doi.org/10.1007/s00355-015-0928-x
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DOI: https://doi.org/10.1007/s00355-015-0928-x