Social Capital and
Mobility: An
Experimental Study
Rationality and Society
XX(X):1-19
©The Author(s) 2022
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DOI: 10.1177/ToBeAssigned
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Ondřej Krčál, Štěpán Mikula and Rostislav Staněk 1
Department of Economics, Masaryk University, Czech Republic
Abstract
Theoretical models of local social capital predict that communities may find
themselves in one of two equilibria: one with a high level of local social capital
and low migration or one with a low level of local social capital and high migration.
There is empirical literature suggesting that immigrants who join communities high
in social capital are more likely to invest in local social capital and that the whole
community will then end up in the equilibrium with high local social capital and low
migration. However, this literature suffers from the selection of immigrants, which
makes the identification challenging. In order to test the causal influence of the initial
level of local social capital, we take the setup used in the theoretical models into the
laboratory. We treat some communities by increasing the initial level of social capital
without affecting the equilibrium outcomes. We find that while most communities
end up in one of the two equilibria predicted by the theoretical models, the treated
communities are more likely to converge to the equilibrium with a high level of local
social capital and low migration.
Keywords
Social capital, Integration, Equilibrium selection, Laboratory experiment
Introduction
Migratory movements are driven by a desire for a better future or simply by force.
Irrespective of their motives, migrants lose many of the social connections they had
0 1
Department of Economics, Masaryk University, Czech Republic
o
Corresponding author:
Ondrej Krcal, Faculty of Economics and Administration, Masaryk University, Lipov 41 a, 602 00 Brno, Czech
Republic
°Email: ondrej.krcal@econ.muni.cz
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2 Rationality and Society XX(X)
in their communities of origin and need to integrate into the social networks of their
receiving communities by investing in local social capital (SC).1
Investments in social
capital may yield considerable returns, as social capital has been shown to be correlated
for example with labour market outcomes (Freitag and Kirchner 2011) as well as with
physical and mental health (Costa and Kahn 2007; Folland 2007; d'Hombres et al. 2010).
Theoretical models of local social capital accumulation (David et al. 2010; Brauninger
and Tolciu 2011) have described individual investments in social capital as a function of
a community-level stock of social capital. Higher stock brings higher returns to those
who (a) previously invested and (b) stay in the community. These models typically
produce two stable equilibria: a community with high social capital and low mobility
(high-SC equilibrium) and a community with low social capital and high mobility (lowSC
equilibrium). The theory does not provide any guidance about which equilibrium a
particular community will end up in, or how that outcome depends on the initial level
of social capital in the community.2
In this paper, we address whether immigrants who
come into a community that is already high in local social capital are more likely to invest
more in that local social capital than immigrants who come into a community that is low
in local social capital.
Empirical evidence drawn from historical events following World War II suggests that
communities affected by migration may end up in one of the two equilibria described in
the theory.3
In the aftermath of the Second World War, ethnic Germans were expelled
from Central and Eastern European countries and forced to move to Germany and
Austria. Their expulsion resulted in a sudden inflow of 8 million people into West
Germany alone. These immigrants (expellees), who moved into established communities,
In line with Brauninger and Tolciu (2011), we define social capital as "a resource that actors derive from
specific social structures and then use to pursue their interests" (Baker 1990, p. 619), and we focus on the
geographical dimension of SC, which "arises from the fact that the value of social capital depends on the
physical distance between the location where an individual resides and the location where he possesses social
ties." (Brauninger and Tolciu 2011, p. 435) In our experimental design, we model social capital as an investment
whose return depends on the investment made by other community members. This approach is much closer to
the perspective on social capital represented by Nan Lin, who defines social capital as "investment in social
relations with expected returns in the marketplace" (Lin 2002, p. 19) than it is to Putnam's view of social capital
as "features of social life—networks, norms and trust—that enable participants to act together more effectively
to pursue shared objectives" (Putnam 1995, pp. 664-5). The crucial difference is that in our model, an individual
can benefit from social capital only if he/she contributes to it, while in Putnam's concept a community member
may benefit from a high level of social capital (e.g. because of efficient local political processes) without
contributing to it at all.
2
The model by Brauninger and Tolciu (2011) also includes a third unstable equilibrium at an intermediate
level of social capital; the authors postulate that once the social capital surpasses this intermediate level the
community will converge to the high-SC equilibrium, and vice-versa. However, the existence of this unstable
equilibrium depends on the assumption that individuals must commit to move or to stay in the community
before they realize the value of such a move. Unlike Brauninger and Tolciu (2011), our experimental design
does not require players to make the moving decision ex-ante and therefore our model includes only two stable
equilibria. Therefore, their argument about convergence is not applicable in our case.
3
The convergence to one of these equilibria is less likely if racial or ethnic differences prevent the immigrants
from investing or tapping into social capital available in local communities (Algan et al. 2010; Dancygier and
Laitin 2014).
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3
were similar to the domestic population of those communities in terms of language,
culture and human capital, but were substantially poorer (Bauer et al. 2013). Chevalier
et al. (2018) use municipality-level data from West Germany to show that the expellees
eventually succeeded in becoming politically integrated, with their higher taste for wealth
redistribution and preferences for different political parties disappearing in the mid-
1960s. The voter turnout in municipal elections, often used as a proxy for SC levels
(e.g. Knack 1992; Hotchkiss and Rupasingha 2021), converged even sooner, in 1950.
The expulsion of the ethnic German population did not only affect the receiving
communities in Germany and Austria. On the other side of the border, in what is now
the Czech Republic, the ethnic Germans had lived in the Sudetenland, a highly ethnically
segregated region close to the border, for centuries. Their expulsion emptied whole
municipalities and completely destroyed the region's local social capital. The empty
settlements they left behind were swiftly resettled by volunteers who sought to improve
their economic and social status by acquiring a house, a piece of land or a better job
(see e.g., Wiedemann 2016). These settlers were homogeneous in terms of language and
culture but they had little or no social connections prior to the resettlement. The new
communities they created therefore, presumably, had low initial levels of local social
capital. Guzi et al. (2021) show that the resettlement increased the population churn in
resettled municipalities and that this effect has persisted to the present day. They also
document that to this day the resettled municipalities still report lower voter turnout in
local elections and lower civic participation in local clubs - i.e., in local social capital.
The established communities in West Germany which experienced an inflow of
expellees maintained their high level of SC, while the municipalities in the Czech
Republic that suffered the destruction of their SC are still lower in SC. However,
the evidence that empirical research can deliver is limited due to the self-selection
of immigrants and their unobserved characteristics. Migration is typically a matter
of choice, and migrants are usually free to choose their country or municipality of
destination. The observed effects could be therefore driven by self-selection rather than
by the local social capital levels in the receiving communities. To tackle this concern, we
simulate the process of migration and investment in local social capital in a laboratory
experiment.
We propose an experimental design that follows theoretical models of local social
capital accumulation (David et al. 2010; Brauninger and Tolciu 2011). A community is
modelled as a group of experimental subjects, who make two choices. First, they decide
how much to invest in SC and second, they choose whether to stay in the community or
to move elsewhere. People who stay enjoy the return from their SC investments. People
who leave receive a reward (e.g. a better job or lower housing costs), but lose the benefits
of their local social network.
The experiment enables us to examine whether community members' choices and
the equilibrium the community ends up in depend on the community's initial level of
SC. A n exogenous shift in the initial level of SC is modelled through an investment
leader. This is a player who always invests as much as possible in local SC and never
leaves the community. Since returns from SC investment depend also on other players'
investments, the investment leader increases the lower bound return from SC investment
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4 Rationality and Society XX(X)
for the other community members. For this reason, we hypothesise that communities
with an investment leader are more likely to end up in the high-SC equilibrium than
communities without such a leader. Our experimental results confirm this hypothesis.
This effect is not due to the leader's impact on equilibrium payoffs; if anything the
introduction of the leader should lead to the opposite effect, because the leader does
not affect the payoff in the high-SC equilibrium, but increases the expected payoff in
the low-SC equilibrium. The leader impacts the search for an equilibrium, which is
modelled by repeating the same experimental game in the same group of players. Two
mechanisms are possible: the leader either impacts community members' expectations,
so that communities with a leader invest more and expect others to invest more, in the
first round of the game, or, alternatively the higher prevalence of the high-SC equilibrium
in leaders' communities may stem from players (with the same initial choices and
expectations) receiving higher payoffs in the treatment with the investment leader, and
therefore moving towards the high SC equilibrium in the second round of the game,
through feedback and learning. Our experimental results provide evidence in support
of the former explanation. We find that in the treatment with the investment leader,
community members expect others to invest more in SC, and invest more themselves, and
that this already happens in the first round of the game, before any feedback is given. This
finding suggests initial expectations about the behavior of other community members are
an important mechanism that can explain differences in communities' levels of social
capital and migration.
The rest of this study has the following structure: in the following section we present
the experimental design and formulate hypotheses, then we describe the experimental
procedures and data, and in final section we present and discuss the results.
Experimental design
Our experimental design consists of 10 rounds of a game that follows the logic of the
models of local social capital (SC) and mobility by David et al. (2010) and Brauninger
and Tolciu (2011). These models consider an individual living in two periods. In period 1,
individuals work and invest in their SC. At the beginning of period 2, some individuals
receive job offers from a company located in a different community. Workers who accept
the new jobs receive a mobility bonus but lose all their SC. On the other hand, individuals
who are not offered new jobs or who reject their offers do not receive any bonus but retain
their SC. The return the individuals derive from their SC depends not only on their SC
in period 2, but also on the SC of the other people living in the same community. So
their level of SC might provide a positive externality to other individuals in the same
community.
In our experiment, each community is inhabited by four players. At the beginning of
period 1, each player receives an endowment / = 80 C Z K 4
and chooses the amount to
invest in SC rn G (0,80). In period 2, three out of four group members receive new job
4
A t the time of the experiment, 1 USD equaled 23 Czech Crowns (CZK) and 1 EUR equaled 26 CZK. A
standard wage for an hour of unqualified student labor was approx. 100 CZK.
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5
offers. If they accept, they lose all their SC, i.e. Si = 0, but receive a mobility bonus b.
The size of the bonus is uncertain. There is a 10% probability of a bonus of 80 CZK, and
a 90% probability of a bonus of either 25 C Z K in the low-bonus treatment or 40 C Z K
in the high-bonus treatment.5
Participants see whether they get the 80-CZK or 25/40C
Z K bonus offer before deciding whether to accept or reject the offer. Players who either
receive no job offer or reject the offer received have a level of SC in period 2 of Si = rii.
The return from SC is calculated as the investment of player i times the rate of return as
determined by the sum of SC of other players in the group:
The payoff to each player equals I — rii + ri if they receive no offer or reject one, or
I — rii + b if they accept a job offer.
The game is repeated 10 times in partner matching, so the experiment consists of 10
consecutive rounds with two periods per round. The experiment investigates equilibrium
selection in a one-shot game as in David et al. (2010) and Brauninger and Tolciu (2011).
We repeated the game 10 times to facilitate learning by the players, and convergence of
the community to an equilibrium. At the end of period 1 of each round, players receive
feedback about the other players' investment. This information is anonymized to limit
reputation effects that might result from repeated interaction in partner matching (see
Figure 5 for the screen shown after period 1). At the end of each round, players also learn
how many players accepted job offers, the rate of return, the return from SC, and their
payoff in that round.
We look at how the initial level of SC influences the outcome. We implement a
novel procedure in which one of the community members is a computerized investment
leader. In the treatment with no investment leader (TO), all four players participate in
the experiment, and three of them receive job offers in period 2. In the treatment with
the investment leader (Tl), one group member, the investment leader, is played by a
computer algorithm that always chooses rii = 80, and never receives an offer in period 2.
In order to keep the same number of players without the job offer, all three "human"
players receive job offers with probability 1. The players are all made aware of the
existence and choices of the robot player in T l , as well as the fact that the three remaining
players will all receive job offers.
Both treatments lead to two subgame-perfect equilibria in pure strategies: In the
high-SC equilibrium, all players in a given group choose rii = 80, and do not accept
5
We varied the 90%-probability bonus to test the sensitivity of our results to the size of this parameter. We
expect that a higher bonus will encourage participants to accept job offers more frequently and discourage
investments in SC.
6
This formulation follows the logic of the model by Brauninger and Tolciu (2011), who see the rate of return
as a function of aggregate investment in the community. We offer one possible intuitive interpretation of the
formula: Suppose player i needs specialized assistance. If he/she asks members of her social network whether
they can help or know someone else who can, then the likelihood of receiving help depends not only on the
size of i's network, but also on the number of unique links her contacts have.
3=-i
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6 Rationality and Society XX(X)
any job offers. In the low-SC equilibrium, the players choose rii = 0, and accept job
offers. In both treatments the maximum payoffs in both equilibria is 160 CZK. While
any individual with 77.^ = 0 receives the maximum payoff with an exogenously given
probability, the payoff of any player with m > 0 depends on the other players' choices.
Since the expected payoff in a high-SC equilibrium exceeds that in a low-SC equilibrium,
players are motivated to invest in SC. The presence of an investment leader reduces the
risk of the investment, because it changes the support of the rate of return ^ . Compared
to the treatment without the investment leader (TO), where the rate of return ranges from
0 to 2, the lowest rate in T l equals 2/3, as the investment leader always has s = 80.7
This
reasoning leads to the following hypothesis:
Hypothesis 1. HI. A higher proportion of groups will converge to the high-SC
equilibrium in Tl than in TO. Hence investment and SC will be higher in Tl (investment
leader) than in TO, and the job acceptance ratio, which measures the share of subjects
that accepted the job offered to them in period 2, will be lower in Tl than in TO.
If we find support for H I , it would be interesting to see whether it can be attributed
to different ex-ante expectations or whether the presence of the investment leader affects
learning. To test these mechanisms, we elicit expectations about the investments that
other "human" players will make in each of the ten rounds. In the treatment with
no investment leader, players guess what the average investment chosen by the three
remaining players will be. In the treatment with the investment leader, they estimate the
choices the two remaining "human" players will make. In the results section, we also test
a second hypothesis, as follows.
According to the first mechanism, the presence of the investment leader with high
SC in T l affects players' expectations about their fellow players' investments, and
consequently affects their own investment choices. Hence, we test whether the treatment
affects the expectations measured in round 1, i.e. before players received any feedback,
and whether these ex-ante expectations explain the treatment differences in round 10
of the experiment. According to the second mechanism, the presence of the investment
leader affects learning. Participants may learn by comparing the end-of-round feedback
about the average investment choices of the other group members with their expectations.
We use these data to test whether participants in the treatment with the investment leader
'Let's assume no other player invests (SJ = 0) and all accept job offers (low-SC equilibrium). Then the return
to investment is equal to 2/3 in the treatment with the investment leader (Tl) and only equal to 0 in the treatment
without the investment leader (TO). While the best response in T l is still to invest 0 and leave, a lower average
contribution from other players is necessary to make positive investment worthwhile than in TO. Conversely, if
all other players invest and do not leave (high-SC equilibrium), the payoffs conditional on individual investment
are equal in both treatments (as the rate of return is equal to 2). Apart from the difference in lower bound of
the rate of return, our experimental design and procedures aimed to minimize the effect of the difference in the
number of human players (4 in TO and 3 in T l ) on individual player's incentives in both treatments. This is why
both treatments have the same number of group members and job offers, which leads to the same incentives
and payoffs assuming that the player who did not receive the job offer in the treatment without the investment
leader invests fully. Furthermore, participants are not informed about the identity of other participants in their
group, they usually do not know each other, and they are not allowed to communicate during the experiment.
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7
react differently to expectation errors compared to participants in the treatment without
the investment leader.
Hypothesis 2. H2. The expected investment by other "human" players is higher in Tl
(investment leader) than in TO.
Experimental procedures and data
The experiment was conducted in November 2018 at the Masaryk University
Experimental Economics Laboratory (MUEEL) in Brno, Czech Republic. In total,
we recruited 324 student subjects using hroot (Bock et al. 2014). Our participants
provided informed consent when they registered to our database as potential subjects.
The experiment environment was programmed in zTree (Fischbacher 2007). At the
beginning of the experiment, an experimenter read the instructions aloud, while students
followed on paper copies (see Appendix for the experimental instructions). At the end
of the experiment, one round was randomly selected for payment. Subjects received
their payoffs from that round and an additional bonus of 30 C Z K if the difference
between the estimated and actual average investment was less than or equal to 5 CZK.
Each experimental session contained a second part, administered after this experiment,
which is not related to this paper. The whole experimental session which included this
experiment (Experiment 1) and Experiment 2 containing money-burning games took
approximately 70 minutes. Participants did not get any information about Experiment
2 before Experiment 1 was over. The average payoff for the whole session equaled 280
CZK. The average payoff for Experiment 1 was 137 CZK.
We conducted 14 experimental sessions (each with 24 or 18 participants) with a total
of 324 participants: 7 sessions of TO with a total of 168 subjects (42 groups of four)
and 7 sessions of T l with a total of 156 subjects (52 groups of three). We also varied
the mobility bonus to test the robustness of our results: This was 40 C Z K in 8 sessions
(192 subjects, 56 groups) and 25 C Z K in 6 sessions (132 subjects, 38 groups). Table 1
shows that all four treatment combinations are balanced in terms of the proportion of
female subjects, age and the share of business studies students.8
Each session contained
10 rounds of the same game. In our analysis of the expectations and investments in the
first round, we take the choices of all 324 participants as independent. Once we are
interested in the outcomes in the last round, the independent observations are the 94
groups. Figure 1 presents the histogram of the group level average SC in round 10. It is
clear that most groups converged to one of the equilibria, i.e. the level of SC in period 2
equals either 0 or 80. Only 6 out of 94 groups have an average SC between 10 and 70.
The graph also shows that in line with Hypothesis 1 the relative share of groups in the
high-SC equilibrium is higher with the investment leader.
8
314 participants study at one or more schools at Masaryk University, the remaining 10 participants do not
study at Masaryk University. We counted all 209 students who study only business or combine business with
another field of study as 'Business studies students'. The other three most common fields of study among the
participants are medicine (39), social studies (21), and natural sciences (15).
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8 Rationality and Society XX(X)
Table 1. Descriptive statistics
Total
No investment leader
Low bonus High bonus
Investment leader
Low bonus High bonus
Subjects
Groups
324
94
72
18
96
24
60
20
96
32
Female
Mean age (St. Dev.)
Business studies students
52.8%
21.8 (2.1)
64.5%
52.8%
21.7 (2.3)
61.1%
53.1%
22.0 (2.0)
66.7%
55.0%
21.6 (2.0)
70.0%
51.0%
21.8 (2.0)
61.5%
30
20
10
Treatment
Investment leader
I No investment leader
20 40
Social capital
60 80
Figure 1. Histogram of group averages of SC in round 10 of the experiment.
Results
Our main results are summarized in Figure 2, which shows the group averages for SC
and job acceptance ratio in round 10 split by the value of the mobility bonus. The
job acceptance ratio measures the share of subjects that accepted the job offered to
them in period 2. In line with Hypothesis 1 the treatment increases SC and reduces
job acceptance. A lower mobility bonus increases the share of groups in the high-SC
equilibrium because it reduces the incentives to accept the job offer in period 2.
Table 2 tests Hypothesis 1. Column 1 shows the logit model explaining whether a
group converged to a high-SC equilibrium at the end of the experiment. Here we assume
that a group has converged to a high-SC equilibrium if the average level of SC exceeds
70, and to a low-SC equilibrium if it is below 10; we exclude the six groups whose
average SC was between 10 and 70. Columns 2-4 present OLS regressions of the group
averages of investment, SC, and the job acceptance ratio. In all the models, the treatment
with the investment leader changes the average size of the variable in the direction
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9
60
03
O
TO
O
O
CO 20
o-
Treatment
Investment leader
I No investment leader
high low
Mobility bonus
o 0 7 5
H
i
d)
o
Jj 0.50
Q.
O)
U
O
ro
-Q 0.25
o
o.oo-
Treatment
Investment leader
I No investment leader
high low
Mobility bonus
Figure 2. SC and job acceptance ratio in TO (no investment leader) and T1 for high and low
mobility bonus
predicted by H I by about 28% of the maximum value9
, and these changes are highly
statistically significant. As expected, a low mobility bonus moves all the variables in the
same direction as the investment leader. This is because the low bonus makes players
less likely to accept job offers, and therefore more likely to invest in social capital and
converge to the high-SC equilibrium.
We can see that participants end up in a different equilibrium in the treatments with and
without the investment leader. In the following analysis, we provide some evidence on the
process by which a community converges to an equilibrium. We investigate two possible
mechanisms. First, we test whether the presence of the investment leader changes ex-ante
expectations about other players' behavior. Then we study whether our treatments affect
the learning process (i.e. reactions to feedback) during the 10 rounds of the experiment.
9
The average marginal effect of the treatment with the investment leader in the logit model is 0.285. The
maximum level of investment and SC is 80.
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10 Rationality and Society XX(X)
Table 2. Treatment effects in the last round
Dependent variable:
High-SC equilibrium Investment Social capital Job acceptance
logistic OLS OLS OLS
(1) (2) (3) (4)
Investment leader 1.400*** 21.224*** 22.008*** -0.283***
(0.494) (7.227) (7.391) (0.092)
Low mobility bonus 1.177** 19.201** 20.053*** -0.262***
(0.488) (7.322) (7.487) (0.094)
Constant -1.705*** 14.539** 11.971 * 0.858***
(0.464) (6.220) (6.360) (0.080)
Observations 88 94 94 94
R2
0.140 0.144 0.153
Adjusted R 2
0.121 0.126 0.135
Log Likelihood -52.200
Akaike Inf. Crit. 110.400
Residual Std. Error (df = 91) 34.802 35.588 0.445
F Statistic (df = 2; 91) 7.422*** 7.681*** 8.231***
Note: S.E. in parentheses. Significance: *p<0.1; **p<0.05; ***p<0.01
Table 3 shows treatment differences between expectations and investment decisions
in round 1 of the experiment. The players had not received any feedback about the
other players' choices, so the independent observations are their individual choices. This
allows us to control for individual characteristics: age and dummy variables for gender
and all 22 combinations of their fields of study. The table provides evidence in support of
Hypothesis 2. The treatment with the investment leader increases both expectations about
the average investment of the other "human" players in the group and actual investments,
both by roughly similar values. Interestingly, Table 3 shows that the low mobility bonus
has no impact on expectations or levels of investment.
Table 4 provides additional evidence about the impact of players' initial expectations
on the equilibrium in round 10. This table adds first-round expectations to the models
from Table 2. The players' initial expectations have a positive and highly significant
impact on the share of groups that end up in high-SC equilibrium in round 10. This
shows that the initial expectations triggered by the presence of the investment leader are
important for reaching a high-SC equilibrium.
The equilibrium selection might be impacted by differences in learning, too. We use
the following empirical strategy to test the presence of this mechanism. For rounds 2-10
we estimate regressions
Yi = p0 + 0! * SRP + f32* SRP * LMB+
f33 * SRP *IL + f34* LMB + /35*IL + a.
Yi shows how individuals update their beliefs or how they adjust their investments.
It is calculated as the difference in the beliefs or investments reported in the current
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11
Table 3. The effect of treatment on expectations and investment choices in round 1
Dependent variable:
Expectations Investment
(1) (2)
Investment leader 8.321*** 9.465***
(2.309) (3.172)
Low mobility bonus -1.751 1.607
(2.364) (3.248)
Age 0.095 -0.663
(0.615) (0.845)
Female -5.355** -4.607
(2.356) (3.237)
Field of study Yes Yes
Observations 324 324
R2
0.139 0.084
Adjusted R 2
0.067 0.007
Residual Std. Error (df = 298) 20.232 27.797
F Statistic (df = 25; 298) 1.924*** 1.097
Note: S.E. in parentheses. *p<0.1; **p<0.05; ***p<0.01
Table 4. Initial expectations determine equilibrium type
Dependent variable:
High-SC equilibrium Investment Social capital Job acceptance
logistic OLS OLS OLS
(1) (2) (3) (4)
Investment leader 0.498 10.195 10.494 -0.141
(0.565) (7.003) (7.127) (0.089)
Low mobility bonus 1.389*** 21.498*** 22.451*** -0.292***
(0.557) (6.668) (6.786) (0.085)
Initial expectation 0.094*** 1.214*** 1.268*** -0.016***
(0.025) (0.269) (0.274) (0.003)
Constant -5.658*** -34.078*** -38.783*** 1.487***
(1.246) (12.164) (12.380) (0.155)
Observations 88 94 94 94
R2
0.299 0.309 0.313
Adjusted R 2
0.276 0.286 0.290
Log Likelihood -42.434
Akaike Inf. Crit. 92.868
Residual Std. Error (df = 90) 31.602 32.161 0.403
F Statistic (df = 3; 90) 12.788*** 13.412*** 13.645**
Note: S.E. in parentheses. Significance: *p<0.1; **p<0.05; ***p<0.01
and the previous round. The variable SRP measures surprise which is equal to the
difference between the actual investment behavior of other group members shown in
the feedback after the previous round and the belief about the average investment elicited
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12 Rationality and Society XX(X)
in the previous round. The levels of the variable SRP do not differ substantially between
treatments. The mean surprise in periods 2 and 3 where most of the convergence takes
place (over 75 % of groups reached an equilibrium in period 4) is not statistically different
(mean differences 1.38, p-value 0.74 in period 2; mean difference=5.57, p-value 0.14 in
period 3). The variables LMB and IL are indicator variables for low mobility and for
the treatment with the investment leader.
Panel A in Figure 3A documents the effect of surprise (SRP) on beliefs in the next
round: The upper figure shows that higher than expected investments from the other
group members lead to upward updating of beliefs in all 9 rounds. More importantly,
the interaction between surprise and both treatments (investment leader, low mobility
bonus), as shown in the following two figures, is not significantly different from zero in
most rounds. This suggests that learning does not differ between the treatments. Panel B
presents similar patterns for investment behavior. Learning that others invested more than
expected induces more investment in the subsequent round, but the process is similar in
treatments with and without the investment leader, as well as in treatments with high and
low mobility bonus. The analysis does not provide any evidence that subjects' reactions
to feedback are influenced by the presence of the investment leader or the size of the
mobility bonus.
In sum, the analyses suggest that the different dynamics observable in the treatments
with and without the investment leader should be attributed to participants' reactions
to different initial expectations about the other players' actions, and not to different
reactions to feedback.
Conclusion
This paper has studied how the initial level of social capital in a community influences
the integration of new inhabitants. The theoretical models of local social capital
accumulation (David et al. 2010; Brauninger and Tolciu 2011) show that the community
may end up in one of two stable equilibria (a high-SC or a low-SC equilibrium), but do
not study the factors that determine which of these outcomes will materialize. The use
of data from observational studies is problematic, because the results can be driven by
self-selection or subjects' unobserved characteristics. For these reasons we have used a
laboratory experiment to address our research question.
We have found that experimental communities that include an investment leader,
who invests highly in SC and never moves, are more likely to end up in the highSC
equilibrium. In addition, we provide some evidence of the process by which a
community converges to an equilibrium. We find that the presence of an investment
leader increases ex-ante expectations about other inhabitants' SC investments. Beyond
ex-ante expectations, the treatment effect could also have been influenced by learning,
i.e. how participants react to end-of-round feedback information about the choices their
group members made. We find that the difference between expectations and feedback
do explain how participants react in the following round, but that this reaction does
not differ among treatments. We also find that once participants initial expectations are
included in our main regression, the treatment effect due to the presence of the investment
Prepared using sagej.cls
13
C I
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gi
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CO
gi
TJ
X
F
SRPxLMB
•
--
r ' —
SRPxLMBSRPxLMBSRPxLMBSRPxLMBSRPxLMB
Panel A: The effect of surprise (SRP) on updating beliefs
1 cc
0.75
C 5C
C 25
C CC
i
! 0.5
GO
s
GO
s
GO
s
GO
s
GO
s
GO
s
a C
D
-c -C
B
CO
X
X
J1 J
CO
X
X
1[
1t
CO
X
X
r~
SRPxL
1
SRPxLSRPxLMB
1 1
Panel B: The effect of surprise (SRP) on investment adjustment
Figure 3. We estimate regression
Yi = 0o + f3i * SRP + /32* SRP * LMB + #$ * SRP *IL + /34* LMB + /35*IL + ei
for rounds 2-10. Yi is equal to the difference in beliefs (Panel A) or investments (Panel B)
between the current and previous round. Variables LMB and IL are indicator variables for
low-mobility-bonus and investment-leader treatments. SRP measures how surprising the
previous observation was as the difference between the average investment made by the
other players in the previous round and the players beliefs in the previous round. The graph
plots 95 % CI. Errors are clustered at the group level.
Prepared using sagej.cls
14 Rationality and Society XX(X)
leader disappears. We therefore do not confirm any learning effect in our main results.
Hence, in this paper, we have not only shown that the presence of inhabitants committed
to investing in local SC positively influences the outcome of the integration process,
but have also documented the role of community members' ex-ante expectations in this
process.
Studying the integration processes in the laboratory does not only come with benefits,
such as the exogenous assignment to treatment groups and possibility of measuring
expectations, but also brings some limitations. These are primarily related to the external
validity of laboratory experiments (Levitt and List 2007a,b). There are clear limits about
what can be learned about real-life integration processes from a laboratory experiment
featuring a stylized game with low stakes. A complementary source of data, which
could help establish the current findings as a robust phenomenon, would be natural
experiments in which immigrants are randomly allocated to municipalities or regions
with different initial levels of social capital. For example, Marten et al. (2019) use
exogenous assignment in Switzerland, where refugees with subsidiary protection have
to live and work in their exogenously selected canton for at least five years, to provide
complementary evidence on the effect of social networks on labor market outcomes. They
find that refugees randomly assigned to locations with higher concentrations of refugees
of the same nationality are more likely to be employed three years later. However, random
allocation typically occurs at the level of regions (rather than municipalities), which are
unlikely to differ substantially in local social capital. Even if the variation in social capital
was sufficient, it would be hard to disentangle the effect of social capital from that of other
factors correlated with social capital. We therefore consider the laboratory experiment a
valuable method for addressing this important research topic.
Acknowledgments
Financial support from the Czech Science Foundation through Grant GA18-16111S is
gratefully acknowledged. This output was also supported by the NPO "Systemic Risk
Institute" (LX22NPO5101).
References
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589-625.
Bauer TK, Braun S and Kvasnicka M (2013) The economic integration of forced migrants:
Evidence for post-war germany. The Economic Journal 123(571): 998-1024.
Bock O, Baetge I and Nicklisch A (2014) hroot: Hamburg registration and organization online tool.
European Economic Review 71: 117-120.
Brauninger M and Tolciu A (2011) Should i stay or should i go? regional mobility and social
capital. Journal of Institutional and Theoretical Economics JITE 167(3): 434-444.
Prepared using sagej.cls
15
Chevalier A, Eisner B, Lichter A and Pestel N (2018) Immigrant voters, taxation and the size of the
welfare state. IZA discussion paper (11725). U R L h t t p s : / / f t p . i z a . o r g / d p i 1725 .
pdf.
Costa D L and Kahn M E (2007) Surviving andersonville: The benefits of social networks in pow
camps. American Economic Review 97(4): 1467-1487.
Dancygier R M and Laitin DD (2014) Immigration into europe: Economic discrimination, violence,
and public policy. Annual Review of Political Science 17: 43-64.
David Q, Janiak A and Wasmer E (2010) Local social capital and geographical mobility. Journal
of Urban Economics 68(2): 191-204.
d'Hombres B, Rocco L , Suhrcke M and McKee M (2010) Does social capital determine health?
evidence from eight transition countries. Health Economics 19(1): 56-74.
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Economics 10(2): 171-178.
Folland S (2007) Does community social capital contribute to population health? Social Science
& Medicine 64(11): 2342-2354.
Freitag M and Kirchner A (2011) Social capital and unemployment: A macro-quantitative analysis
of the european regions. Political Studies 59(2): 389^-10.
Guzi M , Huber P and Mikula S (2021) The long-term impact of the resettlement of the sudetenland
on residential migration. Journal of Urban Economics 126: 103385.
Hotchkiss JL and Rupasingha A (2021) Individual social capital and migration. Growth and
Change 52(2): 808-837.
Knack S (1992) Civic norms, social sanctions, and voter turnout. Rationality and Society 4(2):
133-156.
Levitt SD and List JA (2007a) On the generalizability of lab behaviour to the field. Canadian
Journal of Economics/Revue canadienne d'economique 40(2): 347-370.
Levitt SD and List JA (2007b) What do laboratory experiments measuring social preferences reveal
about the real world? Journal of Economic perspectives 21(2): 153-174.
Lin N (2002) Social capital: A theory of social structure and action, volume 19. Cambridge
university press.
Marten L , Hainmueller J and Hangartner D (2019) Ethnic networks can foster the economic
integration of refugees. Proceedings of the National Academy of Sciences 116(33): 16280-
16285.
Putnam RD (1995) Tuning in, tuning out: The strange disappearance of social capital in america.
PS: Political science & politics 28(4): 664-683.
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1945-1952. Prague: Prostor.
Experimental instructions (translation from Czech)
Introduction [same for TO and T1]
Welcome to the experiment. The aim of the study is to understand how people make
decisions in certain situations. You will be able to earn money for your participation in
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16 Rationality and Society XX(X)
the experiment, depending on your decisions and the decisions of the other participants
in the experiment. You will receive payment at the end of this session in cash and in
private. Other participants will not be informed about your payment.
Do not communicate with other participants during the entire experiment, do not use
a mobile phone or other electronic devices except the computer at which you are seated,
and pay your attention exclusively to the experiment. In case of disobedience, you will be
excluded from the experiment without any payment. If you have a question while reading
the instructions or later during the game itself, please raise your hand and the research
assistant will come to you and answer the question.
Today's session consists of two parts. We will refer to them as Experiment 1 and
Experiment 2. We will now read the instructions for Experiment 1. Please listen carefully.
Experiment 1 [TO]
Experiment 1 consists of 10 identical rounds. In each round, you will play in a group with
three other players who will be randomly selected from the participants in the experiment
in this room. You will not receive any information about the identity of the players in
your group throughout the experiment. The composition of the groups remains the same
during experiment 1.
Each round of the experiment consists of two periods. In period 1, you will receive 80
CZK, from which you can invest 0 to 80 C Z K in the so-called social capital. In period 2,
three randomly selected members of your group will receive an offer to receive a bonus
of 40 C Z K (25 CZK) [in the low-bonus treatment], or 80 CZK. If they accept this offer,
they get a bonus, but their social capital is lost. If they do not accept it, their payment
from this round will depend on their level of social capital and also on the social capital
of the other members of the group. We will explain everything in detail in the following
text.
Period 1: A l l players in the group choose their investment in social capital in round 1.
You can invest any amount from 0 to 80 C Z K in social capital. If in period 2 you do not
receive a bonus offer or do not accept, then the amount invested equals the level of your
social capital.
The return on social capital is calculated as your social capital * rate of return. The
rate of return depends on the level of social capital of the other three members of the
group and is calculated as the sum of the social capital of the other three members of the
group /120. The rate of return ranges from 0 if the social capital level of the other players
is zero, to 2 if the social capital level of the other two players is 80 (a total of 240).
In period 1, we will also ask you to tell us how much you think, on average, the other
players in the group invest in social capital.
At the end of period 1, you will find out how much other players have invested in
social capital and which player did not receive the bonus offer. The order of the players
will be random for this information and will be drawn again in each round. Therefore,
you will not be able to track how a particular player made decisions in each round of the
experiment.
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17
Period 2: Randomly selected three of the four players in the group will receive an offer
to receive a bonus. The bonus has a value of 40 C Z K (25 CZK) with a 90% probability
and a value of 80 C Z K with a 10% probability. If the player accepts the offer, then his
social capital is lost, i.e. the level of his social capital is zero. In this case, the player in
period 2 will receive a bonus of 40 C Z K or 80 CZK, and his return on social capital is
zero. If the player does not accept the offer, then (s)he receives a return on social capital
in period 2.
Payoffs The player's payoffs from each round are therefore calculated as follows:
1. The player invests x in social capital and does not receive the offer. The player gets
the rest of the amount, i.e. 80 — x CZK, and the return on social capital, which is
calculated as x* rate of return. The rate of return is given as the sum of the social
capital of the other three members of the group/'120. Social capital of the other
players is equal to their investment if they did not receive the offer or rejected it,
and 0 if they accepted the offer.
2. The player invests x in social capital and receives and rejects the offer. In that case,
his payment is the same as in the previous point.
3. The player invests x in social capital, receives an offer of 40 C Z K (25 CZK) and
accepts it. The gets the rest of the amount, i.e. 80 — x CZK, and a bonus of 40
C Z K (25 CZK). In total, (s)he receives 80 - x + 40 C Z K (25 CZK).
4. The player invests x in social capital, receives an offer of 80 C Z K and accepts it.
The gets the rest of the amount, i.e. 80 — x CZK, and a bonus of 80 CZK. In total,
(s)he receives 80 - x + 80 CZK.
At the end of each round, you will find out how many of the other players accepted the
bids, what was the rate of return, what was the income from social capital and what was
your payoff in that round.
Out of 10 rounds of experiment 1, one round will be drawn at random and the amount
you earned in this round will be paid to you. If your estimate in the given round was 5
C Z K or less from the actual average invested amount of the other two players in your
group, then you will get an additional 30 CZK.
Experiment 1 [T1]
Experiment 1 consists of 10 identical rounds. In each round, you will play in a group
with one computer player and two other players who will be randomly selected from the
participants in the experiment in this room. You will not receive any information about
the identity of the players in your group throughout the experiment. The composition of
the groups remains the same during experiment 1. The computer player uses the same
strategy throughout the experiment, which is common knowledge to all players.
Each round of the experiment consists of two periods. In period 1, you will receive 80
CZK, from which you can invest 0 to 80 C Z K in the so-called social capital. In period 2,
all three members of your group will receive an offer to receive a bonus of 40 C Z K (25
CZK) [the low-bonus treatment], or 80 CZK. If they accept this offer, they get a bonus,
but their social capital is lost. If they do not accept it, their payment from this round will
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18 Rationality and Society XX(X)
depend on their level of social capital and also on the social capital of the other members
of the group. The computer player will never receive an offer. We will explain everything
in detail in the following text.
Period 1: A l l players in the group choose their investment in social capital in period 1.
You can invest any amount from 0 to 80 C Z K in social capital.
If in period 2 you do not accept the bonus offer, then the amount invested equals the
level of your social capital. A computer player always invests 80 C Z K in social capital
and never receives an offer, so his level of social capital is always 80.
The return on social capital is calculated as your social capital * rate of return. The
rate of return depends on the level of social capital of the other three members of the
group (i.e. the computer player and two other players) and is calculated as the sum of
the social capital of the other three members of the group /120. Because the computer
always has a social capital level of 80, the rate of return ranges from 2/3 (80/120) if the
social capital level of the other two players is zero, to 2 if the social capital level of the
other two players is 80 (together with the computer player would therefore be a total of
240).
In period 1, we will also ask you to tell us how much you think, on average, the other
two players in the group (i.e. everyone but you and the computer player) invest in social
capital.
At the end of period 1, you will find out how much other players have invested in social
capital. The order of the players will be random for this information and will be drawn
again in each round. Therefore, you will not be able to track how a particular player made
decisions in each round of the experiment.
Period 2: A l l players except the computer player will receive an offer to receive the
bonus in period 2. The bonus has a value of 40 C Z K (25 CZK)) with a 90% probability
and a value of 80 C Z K with a 10% probability. If the player accepts the offer, then his
social capital is lost, i.e. the level of his social capital is zero. In this case, the player in
period 2 will receive a bonus of 40 C Z K (25 CZK) or 80 CZK, and his return on social
capital is zero. If the player does not accept the offer, then (s)he receives a return on
social capital in period 2.
Payoffs The player's payoffs from each round are therefore calculated as follows:
1. The player invests x in social capital and rejects the offer. The player gets the rest of
the amount, i.e. 80 — x CZK, and the return on social capital, which is calculated
as x* rate of return. The rate of return is given as the sum of the social capital
of the other three members of the group /120. Social capital of the other players
is equal to their investment if they did not receive the offer (computer player) or
rejected it, and 0 if they accepted the offer.
2. The player invests x in social capital, receives an offer of 40 C Z K (25 CZK) and
accepts it. The gets the rest of the amount, i.e. 80 — x CZK, and a bonus of 40
C Z K (25 CZK). In total, (s)he receives 80 - x + 40 (25) CZK.
3. The player invests x in social capital, receives an offer of 80 C Z K and accepts it.
The gets the rest of the amount, i.e. 80 — x CZK, and a bonus of 80 CZK. In total,
(s)he receives 80 - x + 80 CZK.
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19
Kolo 1 z celkového počtu 10
[Round 1 out of 10]
Nyní se budete rozhodovat, kolik zalnvestovat do společenského kapitálu
[You will choose now how much to invest in social capital]
Váš majetek je 80 Kč.
[Your endowment is 80 CZK.]
Kolik od 0 do 80 Kč chcete investovat do společenského kapitálu? I
[How much, from 0 to 80 CZK, do you want to invest in social capital?]
Kolik si myslíte, že investovali v průměru ostatní (kromě Vás)?
[What do you think is the average investment of other players (excluding you)?]
Figure 4. Screenshot 1 - investment choice
At the end of each round, you will find out how many of the other players accepted the
bids, what was the rate of return, what was the income from social capital and what was
your payoff in that round.
Out of 10 rounds of experiment 1, one round will be drawn at random and the amount
you earned in this round will be paid to you. If your estimate in the given round was 5
C Z K or less from the actual average invested amount of the other two players in your
group, then you will get an additional 30 C Z K .
Screenshots
Each round consisted of three screens: investment choice, choice to accept or reject the
job offer, and feedback. The screens in Figures 4, 5, and 6 were shown to participants
who received job offers and were selected to the treatment without the investment leader.
The experimental environment was in Czech. The English translation in square brackets
was not part of the original screens.
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20 Rationality and Society XX(X)
Informace o všech hráčích Vaší skupiny: [Information about all players from your group:]
Náhodně zvolený hráč: 25
Náhodně zvolený hráč: 0
Náhodně zvolený hráč: 60
Náhodně zvolený hráč: 80
[Randomly selected player: 25]
[Randomly selected player: 0]
Nedostal nabídku [Randomly selected player: 60 Did not receive the offer]
[Randomly selected player: 80]
(Pořadí hráčů se losuje v každém kole znovu.) [(The order of players is randomly drawn in each round.)]
Váš příspěvek na společenský kapitál byl 0.0 Kč.
[Your contribution to social capital was 0.0 CZK.]
Průměrný příspěvek ostatních hráčů na společenský kapitál byl 55.0 Kč.
The average contribution to social capital of all other players was 55.0 CZK.]
Dostali jste nabídku, ve které získáte bonus 25 Kč.
[You received an offer. If you accept, you will receive a bonus of 25 CZK.]
Tuto nabídku můžete přijmout nebo odmítnout.
[You may accept or reject the offer]
Kdyžji přijmete, Vaše výplata bude 105.0 Kč.
[If you accept, your payoff will be 105.0 CZK]
Kdyžji odmítnete, Vaše výplata bude minimálně 80.0 Kč (pokud všichni ostatní přijmou nabídku), maximálně 80 0 Kč (pokud nikdo nepřijme nabídku)
[If you reject the offer, your payoff will be at least 80.0 CZK (if all other players accept the offer), 80.0 CZK at most (if no
other player accepts the offer.)] V a š e r o z h o d n u t í j e
[Your choice is]
odmítnout nabídku [reject the offer]
přijmout nabídku I [accept the offer]
Figure 5. Screenshot 2 - job offer
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21
Kolo 1 z celkového počtu 10
[Round 1 out of 10]
Výsledky kola 1
[Results of round 1]
Váš počáteční majetek byl 80 Kč.
[Your endowment was 80 CZK.]
Vaše investice do společenského kapitálu byla 80 Kč.
[Your investment in social capital was 80 C Z K ]
Míra výnosnosti společenského kapitálu ve Vaší skupině byla 0.72.
[The rate of return of social capital in your group was 0.72.]
Jelikož jste nedostali nabídku, získáváte příjem ze společenského kapitálu 57.3 Kč.
[Since you did not get the offer, you receive income from social capital of 57.3 CZK.]
Jeden z Vašich spoluhráčů přijal nabídku
[One other player accepted the offer.]
Váš celkový příjem z kola 1 je 57 Kč.
[Your total income in round 1 is 57 CZK.]
[Continue]
Figure 6. Screenshot 3 - feedback
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