3.1 Reciprocal trust

Throughout the analysis, we study the relation between the likelihood that a link between a pair of agents $i$ and $j$ forms and $RecipTrust_{ij}$ —a measure of reciprocal trust between $i$ and $j$ . We define $RecipTrust_{ij}$ as the sum of the amounts that $i$ and $j$ would have received in the role of the sender when interacting with each other in the trust experiment. To be precise, suppose that $i$ and $j$ interact in the trust experiment with $i$ as sender and $j$ as receiver, and let $EfTrust_{ij}$ be the total amount that $i$ would obtain in the experiment (i.e., the amount that heFootnote ¹⁷ would receive back from $j$ , computed using $i$ ’s sender strategy and $j$ ’s receiver strategy). $EfTrust_{ij}$ is large to the extent that $i$ sends a large amount to $j$ and $j$ , in response, returns a large amount to $i$ . This is the case because the amount that $j$ can send back to $i$ is limited by the amount that he receives from $i$ in the first place. $EfTrust_{ij}$ is thus a measure of $i$ ’s trust in an anonymous partner that he would see effectively reciprocated if that partner happened to be $j$ . $EfTrust_{ji}$ is defined analogously. Finally, we let:

\begin{equation*} RecipTrust_{ij} = EfTrust_{ij} + EfTrust_{ji}. \end{equation*}

We are able to compute $RecipTrust_{ij}$ for every pair of agents because we implemented the strategic version of the trust experiment: we asked each subject to specify the amount they would send as a sender and the amount they would return as a receiver in response to each possible received amount. $RecipTrust_{ij}$ captures how “productive” the partnership between $i$ and $j$ in the trust experiment would have been for the senders, assuming both individuals played the role of sender with the other as the receiver.Footnote ¹⁸

There are several other ways to define measures based on the data elicited in the trust experiment that capture the concept we aim to embody with $RecipTrust_{ij}$ . In Section 3.5, we present the results of our analysis using various alternative definitions. Three of these five alternative measures create different indices based on the rich behavioral data from the experiment, while the other two rely on survey-elicited measures of trust. These alternative constructions aim to assess whether our results stem from our particular way of collapsing trust game behavior into a one-dimensional index, or from the more general individual attributes that they encode.

For instance, it could well be that some pairs of individuals exhibit highly reciprocal return strategies but choose not to send—perhaps due to cautious priors—which they could easily overcome in face-to-face interactions. Such dyads might be well-positioned for relationship formation in repeated, non-anonymous settings. Our robustness checks, including those that isolate trustworthiness or use belief-based survey measures, aim to probe whether such subtleties meaningfully affect our conclusions. Our findings are consistent across all of them.

This robustness analysis is especially important given the absence of a detailed theory connecting trust as measured in experimental settings with the nuanced, dynamic processes behind real-world friendship formation.

We test whether pairs of individuals exhibiting higher reciprocal trust are more likely to form new connections. Starting a relationship, especially with someone unfamiliar, often comes at an initial personal cost—whether in terms of time, effort, emotional investment, or other intangibles. For such relationships to flourish and endure, the initial investment by one party should be mirrored by the other, creating a balance of give-and-take. This dynamic is similarly observed in trust experiments: a sender benefits from transferring money only if the receiver reciprocates. Consequently, pairs marked by elevated reciprocal trust comprise individuals who are not only open to vulnerability (akin to initiating friendships) but also predisposed to repay kindness rather than exploit it. Over time, these attributes may catalyze the development of genuine friendships.

Naturally, trust is intertwined with other traits like extroversion and sociability, which also play important roles in bond formation. There is no clear way of determining the extent to which these characteristics are integral to trust, as we measure it, or merely parallel to it.

Furthermore, because friendship formation is shaped by non-anonymous, repeated interactions, individuals’ capacities for particularized trust and trustworthiness are likely far more relevant than trust toward strangers as captured by the trust experiment or by standard survey questions.

In light of these limitations, our objective is primarily predictive: our research design allows us to assess whether pairs with higher reciprocal trust are more likely to form relationships, controlling for many variables that the existing literature identifies as strong predictors of link formation. This question remains important given the central role that trust and trustworthiness toward strangers play in prominent theories of social capital (e.g., Putnam, Reference Putnam1995) and in the functioning of a variety of market and nonmarket institutions.

3.2 Students’ characteristics, behavior, and networks

Students’ characteristics.   Table 1 presents summary statistics for the individual variables collected during both the first and second stages of the data collection process. The statistics reported refer to the sample of 55 students (1) who participated in the first stage, (2) who filled out the online survey we administered in the second stage, and (3) for whom we could obtain administrative data. Table 2 provides summary statistics for the administrative variables for the same sample of students. We proxy socioeconomic status with an administrative classification referred to as “estratificación socioeconómica” (socioeconomic stratification), which classifies residential real estates into six categories, ranging from 1 (corresponding to the poorest socioeconomic status) to 6 (corresponding to the richest one). The high school exit examination, officially referred to as the SABER 11 examination, is a standardized test administered to every graduating high school cohort in Colombia. This examination is similar to the SAT and ACT examinations in the United States, and its score ranges from 0 to 500.

Table 1. Summary statistics for the individual characteristics

Summary statistics under the “first stage” header refer to student characteristics obtained from survey questions asked on the “university welcome day,” immediately after the trust experiment took place. Summary statistics under the “second stage” header refer to characteristics obtained through survey questions administered at the end of the academic semester, immediately after eliciting the subjects’ social networks. The first stage summary statistics are based on a sample of 64 students who participated in the lab experiment during the first stage and for whom we have complete administrative data. The second-stage summary statistics refer to the sample of 55 students who participated in the first and second stages, and for whom we have administrative data.

Table 2. Summary statistics for the individual characteristics

This table reports summary statistics for the sample of 55 students who participated in the lab experiment, who filled out the online survey we administered in the second stage, and for whom we could obtain administrative data.

${ }^{\rm a}$ We proxy socioeconomic status with an administrative classification referred to as “estratificación socioeconómica” (socioeconomic stratification), which classifies residential real estates into six categories, ranging from 1 (corresponding to the poorest socioeconomic status) to 6 (corresponding to the richest one).

In our sample, most of the students come from wealthy families in Bogotá. Only for $34.5\%$ of the students’ socioeconomic status is 4 or less, and the average socioeconomic status is 5 out of 6. The average score obtained at the high school exit examination is about 400, which usually falls in the top percentiles of the country-level score distribution.

Table 3 presents a balance test indicating that the observable characteristics of the 55 students who participated in the lab experiment, completed the online survey administered in the second stage, and for whom we obtained administrative data are, on average, similar to those of the students for whom we have administrative data but did not complete the second stage.

Table 3. Balance tests: analysis sample vs. sample of students who did not complete the second stage

This table presents balance tests comparing the average observable characteristics between two groups of students: (1) the 55 students who participated in the lab experiment, completed the online survey administered in the second stage, and for whom we obtained administrative data, and (2) the students who participated in the first stage and for whom we have administrative data but did not complete the second stage of the data collection process.

${ }^{\rm a}$ Each unit represents two thousand pesos.

Students’ behavior in the trust experiment.   Figure 1 shows several summary statistics for the students’ behavior in the trust experiment. On average, the senders sent about half of his or her endowment of $COP \$ 20,000$ (Std. Dev. is $COP \$ 5,251.58$ ). Overall, our subjects’ behavior in the laboratory squares well with the literature.

Figure 1. Top: frequency of $RecipTrust_{ij}$ among the 1,485 dyads in our sample. Bottom left: frequencies of money sent (as senders) by the students in our sample. Bottom right: profiles of money sent back (as receivers) as a function of money received. The width of the line is proportional to the number of students that responded with that strategy profile. In all graphs, money is measured in units of two thousand pesos.

During the first stage of the data collection process (right after the trust experiment took place), we also asked survey questions aimed at measuring generalized (4.a and 4.b), and particularized trust toward friends (5.a and 5.c) and neighbors (5.e).Footnote ¹⁹ In Appendix B, we compare our lab-based trust measure with alternative measures obtained from the survey answers.

Figure 2. Survey- and turnstile-based networks.

This figure shows the networks involving the 1,485 dyads used in the baseline specification (Section 3.3). The left column shows survey-elicited networks (greeting, having lunch together, studying together, confiding in, and friendship). The center column displays short-term turnstile-based networks (August, September, October, and November 2017). The right column features long-term turnstile-based networks (2017-2, 2018-1, 2018-2, 2019-1, and 2019-2, where -1 denotes the first semester and -2 denotes the second semester).

Students’ networks. Figure 2 displays the survey-elicited networks, the short-term turnstile-based networks, and the long-term turnstile-based networks for the sample of 55 students who participated in both stages of the data collection process and for whom we could obtain administrative data.Footnote ²⁰ To be able to easily compare the results between the survey-elicited networks and the turnstile-based networks we treat the former as undirected, that is, we assume that the link between $i$ and $j$ exists only if both $i$ and $j$ acknowledged the relationship between them.Footnote ²¹ To compare the Tables 4, 5, and 6 display some summary statistics for the social networks. The average degree in the (survey-based) friendship network is 9.53, the average local clustering is 0.45, the global clustering is 0.39, and the average path length is 2.12.Footnote ²² The characteristics of the networks we retrieve square well with the literature (Jackson, Reference Jackson2010). In particular, they all exhibit high degrees of clustering and low average path lengths. The greeting network is denser than the other networks, the having lunch together and confiding in networks are sparser, and the studying together and friendship networks sit in between the two extremes. In all networks, there is one giant component, and the greeting network is connected. The average path lengths are similar across survey- and turnstile-based networks. The mean degrees and the clustering coefficients of the long-term turnstile-based networks are all within the range of the clustering coefficients observed in the survey networks. The short-term turnstile-based networks tend to have larger mean degrees and smaller clustering coefficients than the long-term turnstile-based networks. This pattern can be attributed to the construction of the short-term networks, which rely on a weaker definition of a link—individuals swiping in or out in close proximity only once within a given month. As a result, turnstile-based networks may mix elements of the underlying “true” relationships with a network arising from a more random Erdős-Rényi-like link formation process, which could contribute to both the higher mean degree and lower clustering. At the same time, this pattern is consistent with the idea that short-term networks capture relationships in formation, some of which do not persist long enough to become embedded in cohesive social structures that exhibit high clustering.

Table 4. Summary statistics for the survey-based networks

This table reports summary statistics for the survey-based networks. The number of observations is 1,485 dyads for each network.

Table 5. Summary statistics for the short-term turnstile-based networks

This table reports summary statistics for each of the short-term turnstile-based networks (August, September, October, and November 2017). The number of observations is 1,485 dyads for each network.

Table 6. Summary statistics for the long-term turnstile-based networks

This table reports summary statistics for the long-term turnstile-based networks (2017-2, 2018-1, 2018-2, 2019-1, and 2019-2, where suffix -1 denotes the first semester and -2 denotes the second semester).

3.3 Baseline specification

We test whether pairs of individuals exhibiting higher reciprocal trust are more likely to form new connections. We use LPMs to estimate the effect of $RecipTrust_{ij}$ on the presence or absence of relationships in our networks. In the following, we use capital letters for random variables, small letters for possible realizations, and bold letters for vectors. We assume that for, each unordered pair of subjects $\left \{ i,j \right \}$ , the probability that an undirected link between $i$ and $j$ forms is

(1) \begin{equation} Y_{ij} = \beta _0 + \boldsymbol{\beta }_1 (\boldsymbol{X}_i + \boldsymbol{X}_j) + \boldsymbol{\beta }_3 \boldsymbol{Z}_{ij} + \varepsilon _{ij}, \end{equation}

where $Y_{ij} = 1$ indicates that $i$ and $j$ have a relationship in the network in question, $\boldsymbol{X}_i$ and $\boldsymbol{X}_j$ are vectors of individual-level characteristics, and $\boldsymbol{Z}_{ij}$ is a vector of pairwise-level characteristics.Footnote ²³

If we were to assume that $\varepsilon _{ij}$ is independent of $\varepsilon _{k\ell }$ , for each $ij \ne k\ell$ , then we could estimate Equation (1) with a standard OLS regression. However, when observations $\left ( Y_{ij} \right )_{i,j = 1,\ldots ,N, i \ne j}$ correspond to the presence of links between $N$ individuals, it is generally unsafe to assume that unobservables are independent across pairs of individuals. Specifically, the unobservables of pairs that share a common individual are likely to be correlated. As a result, standard OLS regressions produce consistent point estimates but underestimate $p$ -values.Footnote ²⁴ Acknowledging the possibility of autocorrelation in the networks’ adjacency matrices, even after adjusting for observed traits, we lean toward a conservative approach that uses the dyadic-robust variance estimator (as detailed in Fafchamps & Gubert, Reference Fafchamps and Gubert2007 and Tabord-Meehan, Reference Tabord-Meehan2019) to refine standard errors.

We also add a battery of controls for several individual and pairwise characteristics. As for individual characteristics, we use information on sex, hometown, age, eye color, hair color, height, weight, whether wearing glasses, whether wearing tattoos, whether wearing piercings, number of siblings, score obtained at the high school exit examination.Footnote ²⁵ As for pairwise characteristics, we have information on whether the students reported knowing each other from before our intended socialization period, and the amount of time they spent together in the same classrooms during the first semester, as measured by the number of university credits that the students share.Footnote ²⁶ Moreover, for each individual characteristic $X$ and unordered pair of individuals $\left \{ i,j \right \}$ , we can also control for the presence of homophily in that characteristic, as defined by $\Delta X_{ij} \;:\!=\; |X_i - X_j|$ .

To ease the comparison of the effect of different covariates, we standardize each nonbinary variable by subtracting its average from the variable and dividing the result by the standard deviation of the variable.Footnote ²⁷ Thus, we can interpret the marginal effects in the regressions below as resulting from one standard deviation increases in the original variables.

3.3.1 Results

We estimate several LPMs using both the (survey-based) friendship network and the first-semester turnstile-based network. Specifically, for each of these two networks, we run three different models. First, we use only ${RecipTrust}_{ij}$ as an explanatory variable. Next, we introduce pairwise-level characteristics and homophily along individual characteristics as controls. Finally, we include both pairwise and individual-level characteristics as controls. We restrict our sample to the 1,485 dyads involving the subjects for whom we have complete first stage, second stage, and administrative data. We report the results in Table 7.

Table 7. Baseline regressions: survey-elicited friendship network and turnstile-inferred first semester network on reciprocal trust and various controls

This table reports three specifications of the linear probability model for the (survey-based) friendship network and the first-semester turnstile-based network. The first two columns display the results of a linear probability model using only ${RecipTrust}_{ij}$ as an explanatory variable. The next two columns introduce pairwise-level controls in the regression. The last two columns show the results of the specification that includes all individual-level controls, including the individual-level controls $X_i$ and $X_j$ used to construct the dyadic differences $\Delta X_{ij}$ included in the two middle columns to control for homophily in variable $X$ . For readability, we omit the coefficients associated with some controls (Section 1 of the Online Appendix reports the table including the coefficients associated with all the controls in the regression). Dyadic-robust standard errors are shown in parentheses.

The first two columns of Table 7 present the results of two LPMs that regress the (survey-based) friendship network and the first-semester turnstile-based network on the reciprocal trust between individuals $i$ and $j$ . In the last four columns, we introduce pairwise-level controls in the regression. First, we include a dummy variable indicating whether the students knew each other beforehand and their time of exposure in class. To account for the possibility that reciprocal trust may affect only pairs with significant exposure to each other, we include the interaction between individuals’ time of exposure and reciprocal trust. Additionally, we incorporate multiple variables reflecting differences in individual characteristics, which may be important due to homophilic motives. For readability, we omit the coefficients associated with some controls.Footnote ²⁸ Finally, the last two columns of the table show the results of the specification that includes all (pairwise- and individual-level) controls, including the individual controls $X_i$ and $X_j$ that we used to construct the dyadic difference $\Delta X_{ij}$ , which we included in the two middle columns to control for homophily in variable $X$ (for each $X$ ). Following the typical approach used in network regressions with undirected connections, we represent each individual’s level control as the sum of the values of the variable for both endpoints within the dyad under examination.

The first two columns show that the estimated coefficients of ${RecipTrust}_{ij}$ are nearly zero and statistically insignificant. In terms of magnitudes, a one standard deviation increase in reciprocal trust between $i$ and $j$ is associated with a 0.008 increase in the probability of a link between them in the survey-elicited network and a 0.006 increase in the turnstile-inferred network. Reciprocal trust remains insignificant even after introducing both pairwise-level controls (in the second two columns) and combined pairwise-level and individual-level controls (in the third two columns). The change in the sign of the point estimate of ${RecipTrust}_{ij}$ across specifications is unsurprising, given its proximity to zero. Regarding the controls, we find that prior acquaintance is a significant and substantial predictor of relationship formation. Specifically, if either subject indicates knowing the other from before, the likelihood of a link at the end of the first academic semester increases by between 0.33 and 0.36 in the survey-elicited network and between 0.52 and 0.54 in the turnstile-based network. This result demonstrates the persistence of friendships and the ease of befriending an already acquainted person. Additionally, when individuals spend more time together due to being assigned to the same classrooms, they are significantly more likely to form a link. A one standard deviation increase in time spent together due to being in the same class-sections increases the probability of a link by 0.07 in the survey-elicited network and by 0.09 in the turnstile-inferred network. Given the average densities of these networks are 0.18 and 0.13, respectively, these effects are substantial, resulting in a 40% and 70% increase in the probability of a link. These results align well with the evidence presented in Marmaros & Sacerdote, Reference Marmaros and Sacerdote2006, which finds that first-year students tend to interact and form long-term friendships with peers who are easily accessible. Additionally, the significant positive effect of exposure time on link formation probability supports Girard et al. (Reference Girard, Hett and Schunk2015)’s finding that students in the same study groups tend to form friendships among themselves.

Homophily in socioeconomic status is also significant. In the survey-elicited network, a one standard deviation increase in the difference between $i$ and $j$ ’s socioeconomic statuses decreases the probability of a link by 0.030–0.035. Given the average network density, this translates to a 20% decrease in the probability of a link. Although the estimates are noisier for the turnstile-inferred networks, resulting in only marginal significance, the magnitudes are similar ( $-0.022$ and $-0.021$ ). Similarly, homophily in hometown is a significant determinant of relationship formation. On average, if $i$ and $j$ both come from Bogotá or both come from outside Bogotá, they have a 0.03 to 0.09 higher chance of forming a link in the survey-elicited network. These findings are consistent with a large body of empirical evidence (McPherson et al., Reference McPherson, Smith-Lovin and Cook2001). Finally, we find that students $i$ and $j$ are less likely to be linked if they come from Bogotá. This is intuitive, as students from Bogotá likely already have an established network of friends in town, reducing their need to form new friendships.

Does the insignificance of reciprocal trust arise from a weak association with link formation or from high standard errors? To address this question, we analyze the power of our $t$ -test. Suppose the true partial correlation between $i$ and $j$ ’s reciprocal trust and the presence of a link between them, $\beta ^1_{\tau }$ , is 0.08, a magnitude comparable to that of the correlation between time of exposure and link formation. Given our sample size of 1,485 and the dyadic-robust standard errors of the estimated $\beta ^1_{\tau }$ from the OLS regressions (0.012 in the friendship network and 0.010 in the turnstile network), the probability of failing to reject the null hypothesis that $\beta ^1_{\tau } = 0$ is approximately zero in either case. More generally, given our sample size and standard errors, the minimum detectable partial correlation of reciprocal trust with the existence of a link, with 80% power, is about 0.034 in the friendship network and 0.028 in the turnstile network. These thresholds are slightly below the estimated effect of socioeconomic dissimilarity. Therefore, we can confidently assert that if the true effect of reciprocal trust on link formation probability is positive, it is very likely to be smaller than the impact of variables such as prior acquaintance, time of exposure, socioeconomic dissimilarity, and hometown dissimilarity.

3.4 Predicting relationship formation in the short term and the long term

Our analysis uses a one-semester period to define social ties, which aligns with Christakis (Reference Christakis2015)’s findings for U.S. colleges, which highlight a critical initial window of less than a month for forming acquaintances before relationships solidify. However, the dynamics at nonresidential institutions, such as the one we study, may differ significantly.

Given the potentially less intense socialization experiences at these universities, our ties may require prolonged acquaintance periods. As a result, reciprocal trust could become a relevant predictor of relationships later in their university journey, not necessarily by the end of the first semester. Alternatively, persistent classroom interactions and shared friendships could lead to gradual camaraderie among students. In this scenario, reciprocal trust would primarily influence relationships in the very early stages, potentially even shorter than our one-semester analysis period.

Figure 3. Coefficient estimates from the baseline regressions of the short-term turnstile-based networks on reciprocal trust and various controls.

This figure shows the estimated coefficients and 80% confidence intervals from the baseline regressions of the short-run turnstile networks on reciprocal trust and all the pairwise-level and individual-level controls. For readability and consistency, we report only the coefficient estimates and confidence intervals for the same controls shown in Table 7 (see Section 2 for further details).

For these reasons, we leverage the turnstile data to capture both short-term and long-term relationship formation: specifically, at one, two, and three months into the first semester, and then two through five semesters post-admission. Figure 3 shows the point estimates and 80% confidence intervals from the baseline regressions of the short-term turnstile data on reciprocal trust and all the pairwise- and individual-level controls. Figure 4 shows the point estimates and 80% confidence intervals from the baseline regressions of the long-term turnstile data on reciprocal trust and all the pairwise- and individual-level controls. For readability and consistency, we report only the coefficient estimates and confidence intervals for the same controls shown in Table 7. The coefficients are very similar to those presented in the third column of Table 7. In the short-run, our evidence indicates a negligible influence of reciprocal trust, with coefficients ranging narrowly between $-0.003$ and 0.005 during the September to November span. The August data reveals a slightly more pronounced coefficient at $-0.011$ , yet it pales in comparison to the coefficients linked with robust predictors of link formation—factors like knowing each other from before, time of exposure duration, gender, hometown, and differences in hometown.

Figure 4. Coefficient estimates from the baseline regressions of the long-term turnstile-based networks on reciprocal trust and various controls.

This figure shows the estimated coefficients and 80% confidence intervals from the baseline regressions of the long-run turnstile networks on reciprocal trust and various controls. For readability and consistency, we report only the coefficient estimates and confidence intervals for the same controls shown in Table 7.

3.5 Alternative measures of reciprocal trust, measurement error, and other robustness checks

The measure of reciprocal trust within dyads that we use in the baseline specification, ${RecipTrust}_{ij}$ , may be subject to measurement error or confounded by other factors. It might also be the case that the type of trust measured by the trust experiment (how much money a subject would endow another with, in the absence of commitment or punishment technologies) is not the type of trust that matters for approaching and interacting with strangers. We address this issue by constructing five alternative measures of reciprocal trust within dyads. Three of them rely on the same basic data as our measure of reciprocal trust stemming form the strategies of subjects as senders and receivers in the trust experiment. We use these alternative indices to assess whether our findings depend on the specific functional form that we use to define reciprocal trust. The final two measures rely on the two survey questions which inquire about subjects’ propensity to trust strangers. We begin by defining these measures and discussing how they are related among them and to our measure of reciprocal trust. We then present the results that we obtain by running our main specification using each of these alternative five measures and discussing how the results support our findings. Finally, we follow Gillen et al. (Reference Gillen, Snowberg and Yariv2019) and construct ORIV (obviously related instrumental variables) estimates of our coefficient of interest using the two final alternative measures of trust that rely on different data and that are therefore likely to meet main requirements of ORIV.

While trust in the trust experiment can only be measured by the amount of money sent, trustworthiness can be assessed in several ways. In Section 2, we measure the trustworthiness of an individual $i$ as the amount that he would send back to $j$ in response to the amount which they would receive from individual $j$ if $i$ was a receiver and $j$ was a sender. Our first alternative measure of reciprocal trust, which we refer to as $Exp1$ , is calculated as follows:

\begin{equation*} Exp1 = Exp1_{ij} + Exp1_{ji}, \end{equation*}

where $Exp1_{ij}$ is the amount of money sent by individual $i$ in the pair as a sender during the trust experiment plus the average amount of money sent back by individual $j$ as a receiver. The second alternative measure of reciprocal trust, which we refer to as $Exp2$ , is calculated as follows:

\begin{equation*} Exp2 = Exp2_{ij} + Exp2_{ji}, \end{equation*}

is calculated by summing the amount of money sent by individual $i$ in the pair as a sender during the trust experiment plus the average amount of money sent back by individual $j$ as a receiver conditional on receiving at least COP $10,000. This measure considers only the average amounts sent back by each individual in the pair as a receiver in the trust experiment, but only when they received more than half of the sender’s endowment. Our final measure of reciprocal trust, which we refer to as $Exp3$ , is calculated as follows:

\begin{equation*} Exp3 = Exp3_{ij} + Exp3_{ji}, \end{equation*}

where $Exp3_{ij}$ represents the amount of money sent by individual $i$ to individual $j$ as a sender in the trust experiment. This measure disregards trustworthiness entirely and considers only the amounts sent by each individual in the pair as senders in the trust experiment.

We also construct alternative measures of reciprocal trust based on subjects’ responses to survey questions about generalized trust, instead of their behavior in the trust experiment. The survey questions on generalized trust ask, on a 1–5 scale, to what extent the subjects agree with the following statements: (4.a.) One cannot trust strangers and (4.b.) When dealing with strangers, one should be careful and not readily trust them. These measures are less context-specific than the measure we build from the trust experiment, and could thus be argued to capture a more comprehensive dimension of trust. We let

\begin{equation*} Surv1 = Surv1_{i} + Surv1_{j}, \end{equation*}

where $Surv1_{i}$ is the negative value of student $i$ ’s answers to question 4.a. Finally, we let

\begin{equation*} Surv2 = Surv2_{ij} + Surv2_{ji}, \end{equation*}

where $Surv2_{i}$ is the negative value of student $i$ ’s answer to question 4.b.

Figure 5 shows the correlations between our baseline measure of reciprocal trust based on the students’ behavior in the trust experiment (defined in Subsection 3.1) and the five alternative measures of reciprocal trust defined above. Table 8 shows the results of running our baseline specification using the survey-based friendship network on each one of the five alternative measures of reciprocal trust, where we control for all pairwise and individual-level characteristics (analogous to Column (iii) in Table 7). Table 9 shows the results of running analogous regressions but using the first-semester turnstile-based networks. In 9 of the 10 specifications, the estimated coefficient of reciprocated trust is close to $0$ and not significant. The estimated coefficients on the measures of trust and the estimated coefficients on all the basic controls are very similar in all cases. In the specification that relies on $Surv2$ measure the estimated coefficient on trust is negative and significant and similar in magnitude to the estimated coefficient on Socioeconomic status $\Delta$ .

Figure 5. Correlations among our measure of reciprocal trust, the three alternative measures based on the lab data and the two alternative measures based on survey data.

Note: This figure shows the correlations between our baseline measure of reciprocal trust in dyads and the five alternative measures of reciprocal trust defined above.

Table 8. Robustness regressions: survey-elicited friendship network on alternative measures of reciprocal trust and various controls

This table presents the results of linear probability models regressing the (survey-based) friendship network on the reciprocal trust measures constructed using three alternative measures based on the lab data and two measures based on survey data, as described in Section C. All specifications include all pairwise- and individual-level controls. For readability, the coefficients associated with some controls are omitted. Dyadic-robust standard errors are shown in parentheses.

Table 9. Robustness regressions: first-semester turnstile-based network on alternative measures of trust and various controls

This table presents the results of linear probability models regressing the first-semester turnstile-based network on the reciprocal trust measures constructed using three alternative measures based on the lab data and two measures based on survey data, as described in Section C. All specifications include all pairwise- and individual-level controls. For readability, the coefficients associated with some controls are omitted. Dyadic-robust standard errors are shown in parentheses.

In what follows we rely on Gillen et al. (Reference Gillen, Snowberg and Yariv2019) to construct ORIV estimates of our main coefficient of interest. For that purpose we approach Reciprocal Trust, $Surv1$ and $Surv2$ as alternative imperfect measures of the underlying reciprocal trust in a dyad. $Surv1$ and $Surv2$ differ from our measure of reciprocal trust in that they aim to capture how trusting toward anonymous strangers the respondent is, but in contrast to our measure of reciprocal trust do not contain any information on her trustworthiness. The main assumption behind the validity of ORIV is that each of the alternative measures of reciprocal trust are valid instruments for the others in their relation to network formation. Specifically, each variable must be correlated with the other ones, and can only be related with link formation through the core underlying true measure of trust that they all share. Given that $Exp1, Exp2$ , and $Exp3$ , which we use above to explore the sensitivity of our results to the functional form, are constructed using the same data as Reciprocal Trust they and are not suitable instruments for ORIV.

Table 10 is analogous to Table 7 but estimating the model using ORIV and treating $RecipTrust$ , $Surv1$ , and $Surv2$ as alternative noisy measures of the same underlying feature. This estimation technique supports the paper’s main conclusion: there is no evidence that links are more likely to form among pairs with higher reciprocal trust. While some specifications show statistically significant reciprocal trust coefficients, they are consistently negative. Furthermore, these results can be understood by the fact that one of the instruments is $Surv2$ , which as shown in Table 8 is a negative a statistically significant predictor of links. Our results robustly show that trust, measured through both an experiment and survey questions, does not predict relationship formation among our subjects. Moreover, in the cases in which trust has a significant effect on relationship formation, this effect is negative. This evidence stands in opposition to our initial hypothesis that more trusting individuals should have a higher chance of forming relationships. We believe that there are ways in which our results can be rationalized besides concluding that trust does not matter for network formation among our subjects.

Table 10. Baseline regressions: ORIV with clustered standard errors

This table reports three specifications of the ORIV regressions for the (survey-based) friendship network and the first-semester turnstile-based network. The first two columns display the results using only ${RecipTrust}_{ij}$ as an explanatory variable. The next two columns introduce pairwise-level controls in the regression. The last two columns show the results of the specification that includes all individual-level controls, including the individual-level controls $X_i$ and $X_j$ used to construct the dyadic differences $\Delta X_{ij}$ included in the two middle columns to control for homophily in variable $X$ . For readability, we omit the coefficients associated with some controls. Standard errors clustered at the individual-level are shown in parentheses.

One possibility is that more trust is negatively related to some personality trait, for example, extroversion, that is in turn helpful in establishing new relations. Freitag & Bauer (Reference Freitag and Bauer2016) study how trust is related to Big Five personality traits. They find no evidence of relation between trust and extroversion. Moreover, trust is positively related to openness and agreeableness (traits potentially helpful in establishing relations).Footnote ²⁹

Late adolescents may value traits like dominance, charisma, or nerve when forming relationships with their peers. These traits could, in turn, negatively correlate with trust. This hypothesis stands in line with the literature on social status among adolescents. Parkhurst & Hopmeyer (Reference Parkhurst and Hopmeyer1998) distinguishes between sociometric popularity, representing the in-degree of an individual in a network, and perceived popularity, representing an individual’s reputation for being popular. Later studies (Hawke & Rieger (Reference Hawke and Rieger2013) and Franken et al. (Reference Franken, Harakeh, Veenstra, Vollebergh and Dijkstra2017)) also distinguish between the perception of being popular (popularity) and the perception of being well-liked (likability). The in-degree of adolescents is generally positively correlated with both likability and popularity. However, while likability is mostly related to prosocial behavior and traits, popularity is primarily associated with social dominance (Parkhurst & Hopmeyer, Reference Parkhurst and Hopmeyer1998) and correlates with physical aggression, relational aggression, and anti-social behavior (Cillessen & Mayeux, Reference Cillessen and Mayeux2004, LaFontana & Cillessen, Reference LaFontana and Cillessen2002, and Hawke & Rieger, Reference Hawke and Rieger2013). Popular adolescents are also described as manipulative, Machiavellian (Cillessen & Mayeux, Reference Cillessen and Mayeux2004) and hard to push around (Parkhurst & Hopmeyer, Reference Parkhurst and Hopmeyer1998). We hypothesize that while trust may be positively related to likability, it might have a stronger negative relationship with popularity, as adolescents may perceive trusting individuals as weak or naive. This hypothesis could explain why we find that trust does not generally predict (and sometimes negatively predicts) relationship formation among our subjects. One way to indirectly probe this hypothesis is by examining the possible heterogeneity in the correlation between reciprocal trust and link formation by gender under the assumption that traits like dominance are more valued by males than by females. Under this assumption we expect reciprocal trust to be more positively and strongly associated with link formation in dyads involving more females. Table C6 in Appendix C.6 shows the results from estimating a model analogous to or main one, but including a term capturing the interaction between the variable encoding the number of females in the dyad (0,1 or 2) and reciprocal trust. The estimated coefficients on the interaction term are positive and similar in magnitude to the reciprocal trust coefficients in all specifications, but are never statistically significant. While our research design was not developed in order to assess this kind of heterogeneity nor to evaluate if indeed there are differences in the valuation of traits like dominance in males and females in our sample, we include the results as an exploratory exercise as it is a promising approach for future research.

Other networks

We apply our baseline strategy to networks elicited using different survey questions: “greeting each other,” “having lunch together,” “studying together,” and “confining in each other.” Additionally, we complement our analysis by treating survey-elicited friendship network as a directed network in which it is possible that subject $i$ considers subject $j$ to be their friend but the friendship is not reciprocated. In all these specifications trust remains a poor predictor of network formation, and previous encounters, time of exposure, differences in socioeconomic status, and differences in the town of origin are key predictors of relationship formation. The details of these analysis can be found in Appendices C.2 and C.3.

Largest possible sample

We conduct the turnstile-elicited network analysis additionally including 15 subjects who did not participate in the second-stage survey. The results remain virtually unchanged. The details of these analysis can be found in Appendix C.4.

Individual network statistics and trust

In principle, the predictive power of individual or dyadic characteristics over network structure should express itself through the presence or absence of individual links, but the predictive power of individual characteristics can also be studied directly through regressions of individual network statistics on individual characteristics. The analysis in Appendix C.6 shows that individuals’ propensity to trust or to be trustworthy with respect to strangers does not predict individuals’ number of links, eigenvector centralities or betweenness centralities.