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Reconsidering Social Capital: A Latent Class Approach
Ann L. Owen
Julio Videras
Hamilton College
Abstract
Social capital has proven to be a useful concept, but has not been well-measured in the
economics literature. We motivate and demonstrate the application of latent class models
to measure social capital, based on the idea that social capital is an unobservable
multidimensional construct. We explain and show the construction of latent classes that
measure an individual’s social capital using data from the General Social Survey. Our
method generates meaningfully different conclusions about the accumulation of social
capital than those obtained by previous research. We present evidence that higher income
influences social capital accumulation because of a higher opportunity cost of time. We
also find evidence of complementarities in social capital accumulation within an
individual’s peer group. Finally, we show that community heterogeneity influences the
likelihood that individuals adhere to certain social norms independent of their propensity
to participate in voluntary organizations.
1 Introduction
In the last few years, social scientists have used the concept of social capital to explain
how social norms and networks influence economic behavior and the outcomes of economic
policies.1 However, as many researchers have pointed out, the concept has been ill-defined and
imperfectly measured. Motivated by the fact that social capital is an unobservable
multidimensional construct, we propose a novel application of latent class models to the
measurement of social capital.
There are varying definitions and uses of the term social capital in the economics
literature. Sobel (2002) describes social capital as circumstances in which individuals can
benefit from group membership. The World Bank defines social capital on its web site as the
“norms and networks that enable collective action.” Other research focuses on trust among
individuals. Knack and Keefer (1997) found an important role for trust at the country level in
explaining economic growth, while, at the individual level, Karlan (2005) uses laboratory
experiments to measure trust, arguing that these experiments measure social capital and are
helpful in explaining individual behavior. However, Guinnane (2005) argues that trust is not a
useful concept because it cannot be separated from the quality of institutions. Durlauf and
Fafchamps (2004) discuss the many different definitions of social capital in empirical research
and assert that research on social capital is plagued by “conceptual vagueness.” Thus, the
concept of social capital has been broadly defined and measured, running the risk of becoming a
useless catch-all concept.
Rather than proposing another definition of social capital, we focus on two basic
components of the term to motivate our methodology. First, social capital is a multidimensional
concept: it embeds multiple manifestations of civic engagement as well as trust and fairness. A
useful measurement of social capital must account for as many of these dimensions as possible.
Second, unlike physical or human capital, social capital is not necessarily beneficial to society at
large (Durlauf and Fafchamps, 2004) – terrorist networks are one example. More generally,
individuals’ values and socio-economic characteristics can attract them to different networks that
have different effects on the economic system. An emphasis on the types of social capital is
important from the point of view of public policy since, as Durlauf and Fafchamps (2004) argue,
1 See for example, Easterly and Levine (1997), Golden and Katz (1999), Narayan and Pritchett (1999), or Guiso,
Sapienza and Zingales (2002) for a broad range of examples. Interested readers should also see Durlauf and
Fafchamps (2004) who provide a survey and critical analysis of this literature.
2
“it is social structures, not their consequences, which can be influenced by policymakers.” This
emphasis on the typology of social capital becomes important in empirical applications. Much
of the discussion about Putnam’s claim in Bowling Alone (2000) that civic engagement in the
United States has declined centers on how this concept is measured. Durlauf and Fafchamps
(2004) and Skocpol (2003) have argued that it is more appropriate to talk about changes in the
nature rather than the quantity of civic engagement. Thus, one must apply a methodology that
generates a typology of social capital that accounts for the different incentives that networks
provide and the various and even divergent effects that those networks might have on economic
outcomes.
We propose applying latent class models. This methodology approaches social capital as
a multidimensional concept that can embed both group membership and social norms. In two
examples that compare our approach to recent findings, we show that measuring social capital as
a multidimensional construct provides new meaningful insights about the determinants of social
capital. First, we replicate the models in Glaeser, Laibson, and Sacerdote (2002) and find results
that the authors’ theoretical model predicts but were unable to show empirically. Our second
application complements the research by Alesina and La Ferrara (2000) on the effects of
heterogeneity on the likelihood that a person belongs to one voluntary organization. Because our
methods incorporate social norms that Alesina and La Ferrara did not consider, our findings add
to the understanding of how community heterogeneity affects the type of social capital
individuals accumulate. Section 2 describes in more detail the differences in the empirical
approach and underlying theoretical motivation between this paper and Glaeser, Laibson, and
Sacerdote (2002) and Alesina and La Ferrara (2000).
Although many researchers agree social capital is a multidimensional concept, few have
applied multivariate methods. Sabatini (2005) uses principal components analysis to reduce a set
of indicators of social capital (including memberships) to a single variable. Paxton (1999)
applies confirmatory factor analysis to several indicators of trust. Our approach shares the same
motivation and strengths of these analyses because we use multiple indicators of social capital.
However, latent class models have some advantages over principal components analysis (PCA)
and factor analysis (FA). First, the results of FA and PCA are generally not unique as
researchers can rotate factor loadings to obtain a meaningful interpretation of the solution.
Latent class analysis, on the other hand, is model-based and there are formal criteria to decide on
3
the number of types of social capital that are present in the data. In addition, the interpretation of
latent classes is generally less arbitrary than the interpretation of principal components. More
importantly, PCA and FA assume that the observed indicators and the unobserved underlying
factors are continuous and normally distributed.2 However, it might be more reasonable and in
accordance with the theory to assume that social capital is a categorical variable and to
characterize individuals according to the type of social-capital class they belong to.3 Finally, this
method does not assume that the distinct components of social capital, civic engagement and
social norms of reciprocity, can be aggregated in an index. Indeed, our typology shows that
there are groups of individuals who hold norms of reciprocity but do not belong to voluntary
organizations.4
In what follows, we first discuss briefly the research by Glaeser, Laibson, and Sacerdote
(2002) and Alesina and La Ferrara (2000). We explain our empirical approach to measuring
social capital using latent class analysis and then discuss the results of latent class models. In
Section 5, we use the results of the latent class models in an estimation that mirrors that of
Glaeser, Laibson, and Sacerdote (2002) to demonstrate that our proposed approach generates
new insights about social capital formation. We then discuss the application of our methodology
to research by Alesina and La Ferrara (2000) on the effects of community heterogeneity. Section
6 summarizes the findings.
2 Related Literature
This section discusses how our research expands two well-known investigations on the
determinants of social capital at the individual level. Glaeser, Laibson, and Sacerdote (2002),
henceforth GLS, develop a model in which individuals invest time to accumulate social capital.
Their theory is an adaptation of human capital investment models. Some of the predictions of
2 Although a typology of social capital from FA or PCA can be obtained, the process is more arbitrary than that used
by latent class analysis. The researcher would need to calculate factor scores of each individual for each factor
loading. Then, the researcher would need to determine a cut-off point for the factor scores and cross-tabulate below
and above the cut-off point in order to obtain clusters of respondents. 3 It is important to note that although community involvement might be best understood as a categorical construct,
propensity to trust others and propensity to believe other people are fair might be better modeled as a continuous
factor. In our application, however, we only observe binary indicators for these social norms. Nonetheless, the
interpretation of the latent classes is based on the probabilities of responding affirmatively to the questions of
whether people can be trusted and other people are usually fair. 4 Knack (2002) argues that it is important to disaggregate civic engagement and generalized reciprocity. Knack
shows these two components have different effects on the quality of state governments.
4
the model are that social capital investment declines with the opportunity cost of time, age, and
mobility, and increases with the occupational returns to social skills and the level of social
capital in a community. Using the number of group memberships as a proxy for social capital,
the authors find support for many of their hypotheses. However, there are two key predictions
for which they are unable to find evidence. First, GLS find a positive association between
income and group membership, contrary to the prediction that higher wages should be associated
with less social capital because of the higher opportunity cost of accumulating it. Second, GLS
do not find evidence that social capital correlates within peer groups.
Alesina and La Ferrara (2000) also examine the determinants of individual social capital.
The focus of their paper is the effects of community heterogeneity. Noting that it is difficult to
measure social capital, Alesina and La Ferrara examine membership in voluntary organizations
only. The authors develop a model in which individuals prefer to interact with people from their
same racial, ethnic, and social-class group and utility from participating in a voluntary
organization depends on the composition of the organization and traveling costs. The key
prediction of this model is that increased community heterogeneity reduces participation in
mixed organizations. Empirically, Alesina and La Ferrara first estimate probit models of
membership in any organization. Secondly, they estimate the likelihood of participating in
specific organizations. The findings provide consistent evidence for the predictions of the
model: racial diversity, in particular, strongly reduces the likelihood of participation and the
effects are most marked for organizations that require frequent interactions.
While GLS measure social capital as the number of voluntary organization memberships
and Alesina and La Ferrara estimate a binary choice (membership or no membership in one
organization), we use latent class analysis to classify individuals into distinct types of social
capital using both memberships and indicators of trust and fairness. We argue that the number of
organizations an individual belongs to and whether or not a person belongs to a specific
organization are not as important as the nature of the social network an individual joins. One
reason is that the decision to join a specific group is not independent of the decision to join other
groups. Specific group memberships can be complements or substitutes and the economic
impact of not joining one particular group may be counterbalanced by joining a different group.
In formulating policy implications, it is important to investigate whether different types of social
capital influence economic decisions differently. We should expect that the socio-demographic
5
profile of individuals joining a union and a fraternal organization, for example, is different than
the profile of individuals joining literary and hobby clubs. Likewise, the economic impact of
social networks formed around labor unions and fraternal organizations is likely different than
the influence of networks of literary and hobby clubs. Thus, researchers need a categorical
variable that distinguishes among types of social networks and not just number of memberships.
Such typology can be constructed by applying latent class modeling to the usual indicators of
social capital.
Latent class models allow us to use trust and fairness in addition to voluntary group
membership to generate a typology of social capital. As GLS and Alesina and La Ferrara do, we
use data from the General Social Survey. We find peer-group effects that GLS predict in their
theoretical model but cannot identify empirically. We find results consistent with the hypothesis
that individuals with high opportunity cost of time choose classes of social capital with relatively
low time commitment and perhaps high monetary cost. Our results indicate that socio-economic
determinants sort individuals into types of social capital that vary in the nature of the social
capital class, but not necessarily in the number of memberships forming the classes. Extending
the findings in Alesina and La Ferrara, we also show that community heterogeneity influences
the likelihood that individuals hold specific social norms independent of their propensity to
participate in voluntary organizations. This finding suggests that focusing on a single component
of social capital can generate results that might not apply to the concept of social capital as a
whole.
The economic framework we adopt differs from that adopted by GLS because we view
the individual’s choice of social capital to be a decision about the type of social capital rather
than the amount of social capital. It also differs from the model by Alesina and La Ferrara
(2000) in that we do not assume the decision to participate in a given organization is independent
from membership in other organizations. Rather, the underlying theoretical framework of our
empirical analysis considers individuals who select a type of social capital in order to maximize
utility, given time and budget constraints. An individual joins a combination of groups and
organizations and adopts norms of behavior that others of the same class are also likely to join
and adopt. Different types of social capital provide different resources that individuals can use to
produce new goods for consumption or as consumption goods themselves. The individual’s
maximization problem can then be analyzed using the framework of discrete choice models.
6
In our empirical analysis, it is assumed that the individual chooses the type of social
capital that has the highest indirect utility among the set of all available types. We assume the
respondent’s utility can be decomposed into utility derived from observable characteristics and
the impact of all unobservable factors. Thus, the probability that the researcher observes the
individual choosing social class k over social class j is equal to the probability that the difference
in observable utilities obtained from membership in class k over membership in social class j is
greater than the difference in the unobservable components. The first step is to define the
alternative social capital structures individuals can choose from. We use latent class models to
derive a categorical construct that characterizes individuals as holding different (and exclusive)
types of social capital. Then, we assume the researcher observes the choice with error so that the
choice of social capital class can be analyzed in the context of a random utility model and
estimated via a multinomial logit model.
Although we believe our approach has many advantages, it also has limitations. Data
availability restricts us to considering the number of memberships rather than the strength of
engagement in groups when classifying individuals into different social capital groups. This
criticism is rightly levied at many empirical studies of social capital. To some extent, our
treatment of social capital - which incorporates social norms and group memberships as
indicators variables of the latent class - addresses to some degree this concern.
3 Using Latent Class Analysis to Measure Social Capital
In this section we motivate and describe latent class analysis. In Section 4, we apply this
methodology to eighteen questions from the General Social Survey (GSS) that are common
proxies for social capital: sixteen questions about membership in voluntary organizations and
two questions regarding whether people can generally be trusted and whether other people are
fair or try to take advantage of others.5
Latent class models are part of the family of generalized finite-mixture models. The
methodology is grounded in a probability framework that allows model testing and the
5 There is evidence that self-reported measures of trust might be weakly correlated with revealed measures of trust.
See Glaeser, Laibson, Scheinkman, and Soutter (2000) and Bellemare and Kroeger (2007). More recently,
Sapienza, Toldra and Zingales (2007) use experimental evidence to argue that these self-reported measures do reveal
beliefs that determine trust of others. Although measurement issues could affect the validity of some of our results,
an advantage of latent class models is that the methodology assumes the variables are indicators with errors of the
latent variable.
7
calculation of goodness-of-fit measures. Latent class analysis has been applied to several social
issues (see, for example, Patterson et al. 2002; and Biemer and Wiesen, 2002). In the economics
literature, researchers have applied latent class regression models to choice experiments in order
to estimate a person’s choice of alternative based on observable characteristics using attitudinal
variables as indicators of a latent variable. For example, Boxall and Adamowicz (2002) and
Greene and Hensher (2003) estimate latent regression models to the choice of a hypothetical park
and road type, respectively.6 Our approach is related but differs in that we estimate a latent
cluster model rather than latent regression models.
In particular, let i = 1,…, I, denote the respondents. For each individual we observe the
responses to eighteen questions denoted k =1,…, 18. 1ikY if individual i responds “yes” to
question k and 0ikY otherwise. An individual’s response pattern is the vector iY . We assume
a finite number of social capital classes denoted s = 1,…, S. The discrete latent variable X
represents the social capital class:
S
s k
iikii sXYPsXPYP1
18
1
).|()()( (1)
The prior probability of class membership is modeled as:
.)exp(
)exp()(
1' 0'
0
S
s s
si sXP
(2)
We estimate the models defined by equations 1 and 2, where class membership depends
on the responses to the 18 indicators of social capital. We first present and discuss the results
from these cluster models and then estimate multinomial logit models in which the dependent
variable is model class membership and the independent variables are socio-economic
characteristics.
It is possible to include observed variables (covariates) to help predict class membership.
Letting iz be a vector of T covariates, the probability )|( ii sXP z follows a multinomial logistic
regression model:
6 Clark, Etile, Postel-Vinay, Senik, and Van der Straeten (2005) and Morey, Thacher, and Breffle (2005) are other
examples.
8
S
s
T
t
ittss
T
t
itsts
ii
z
z
sXP
1'1
'0'
1
0
).exp(
).exp(
)|(
z . (3)
Although joint estimation of both class membership and the effects of the covariates
might decrease classification errors, we find that a model with covariates generates boundary
solutions and very large unexplained associations between indicators. We discuss these issues
further in Section 5.3. Nonetheless, in Section 5.1 we discuss robustness checks to the two-step
procedure that indicate our inferences are not likely to be affected by classification errors.
The conditional probability that an individual in latent class s responds “yes” to indicator
k is modeled as a logit equation:
,)exp(1
)exp()|1(
ks
ksiik sXYP
(4)
where ks is a free parameter and, consistent with the literature on latent cluster models, we
assume the conditional response probabilities do not depend on the covariates (Vermunt and
Magidson, 2005). We calculate posterior probabilities using Bayes theorem:
.)'|()'(
)|()()|(
'
s k iiki
k iiki
iisXYPsXP
sXYPsXPYsXP (5)
After calculating posterior probabilities, we assign each individual to the latent class for
which she has the highest posterior probability )(ˆ xP (empirical Bayes modal classification rule).
The resulting characterization of each individual as belonging to one of S classes constitutes our
typology of social capital. The probability of misclassification for each individual is defined as
)(ˆmax 1 xP . The estimated average of classification errors is (Skrondal and Rabe-Hesketh,
2004):
I
xPE
I
i
1)(ˆmax1
. (6)
Although equation 1 implies responses to the indicators are independent given latent class
membership, it is possible to relax this assumption of local independence by including direct
effects, that is, by combining any pair of dichotomous variables into one item and modeling the
four potential response patterns (0,0), (1,0), (0,1), and (1,1), as one multinomial response
(Skrondal and Rabe-Hesketh, 2004). For example, if we want to model a direct dependency
9
between item 2 and item 3, we modify equation 2 as follows (Vermunt and Magidson, 2005,
page 24):
.)exp(1
)exp()1,1(
2332
233232
ii YYP (7)
To identify the need for direct effects we use bivariate residuals: Pearson chi-squared
statistics divided by the degrees of freedom.7 Although the correlation between indicators given
class membership might be more complex, the models we estimate allow for pair-wise
correlations only. An alternative approach is to estimate models with more classes so that the
associations between some indicators can be explained better. In our application, this approach
generates additional classes too small to be meaningful without improving the model’s goodness-
of-fit.
The parameters of the models are estimated using maximum likelihood with the
likelihood function that is derived from the unconditional probability in equation 1.8 To evaluate
the goodness-of-fit of the models, we use the likelihood-ratio (LR) chi-square statistic that
compares the observed frequencies of the response patterns to the expected frequencies of the
model.9 Because of sparse tables, we apply bootstrapping to calculate the the LR chi-square
statistic.10
We estimate each model for 500 replication samples using maximum likelihood
estimates as starting values. We reject the model if the bootstrap p-value of the chi-square
statistic is smaller than .05 (Eid, Langeheine, and Diener, 2003). To select among models that
cannot be rejected, we use the minimum Bayesian information criterion (BIC). The criterion is
based on the log-likelihood of the model (LL) and accounts for the number of observations N
and parameters (Npar) to be estimated: BIC = -2LL + (logN)Npar.11
We also present the AWE
7 For each pair-wise combination of indicators, this statistic compares expected counts to actual counts in a two-way
table. Large residuals indicate that the model cannot explained well the association between those two indicators. 8 We use Latent GOLD to estimate the latent class models.
9 The Pearson statistic is usually defined as
jjjj een /)( 2 where n is the observed frequency of pattern j and e
is the expected frequency. The statistic is asymptotically distributed as a 2 distribution with degrees of freedom
equal to the number of response patterns minus the number of estimated parameters minus the number of categories. 10
Sparse tables occur when small and zero observed frequencies are common. With sparse tables, fit statistics such
as the test cannot be guaranteed to follow the assumed 2 distribution. 11
We also computed the Akaike information criterion (AIC = -2LL+2*Npar) and the consistent Akaike information
criterion (CAIC = -2LL+[log(N)+1]*Npar). The AIC favors models with larger number of classes, a tendency that
increases with the sample size. The CAIC favors models with fewer classes but this under-fitting declines with
sample size. In our application, both the BIC and the CAIC indicate a model with seven latent classes is the best
among the models that fit the data.
10
statistic that considers classification errors in addition to fit and parsimony.12
A common
problem estimating latent class models is the presence of local maxima. To address this
problem, we estimate each model using 500 different starting values.
4 Results of Latent Class Models
We apply latent class analysis to the responses to eighteen indicators by 14,527
individuals from the General Social Survey. Table 1 summarizes these variables. We choose
our sample to be identical to that used by Glaeser, Laibson, and Sacerdote (2002).13
Table 2
presents fit statistics from the latent class models. We present each model’s log-likelihood, the
associated BIC, number of parameters, bootstrapped p-value of the LR chi-square statistic,
classification error, and AWE statistic. The minimum BIC rule indicates that the best model
uses 8 classes. Once we select a model with 8 classes, we relaxed the assumption of local
independence. We model the response to the indicators with the largest bivariate residual as a
joint response and estimate the model. As the value of the AWE criterion shows, including one
direct effect (between membership in fraternal organization and membership in a Greek group)
improves the log-likelihood enough to compensate for the increase in parameters and
classification errors. However, when we repeated this process and add a second or third direct
effect, the AWE criterion increases, suggesting that the improved fit of the model is not justified
by the increase in parameters and classification errors. Because we are concerned the results of
the multinomial logit might be affected by misclassification, we choose the 8-class model with 1
direct effect as our preferred model.14
Table 3A presents class sizes (as a proportion of the total sample) and the conditional
response probability for each indicator, given latent class membership. As explained above, to
construct the classes, we calculate the probability of membership in each class for each
individual and assign them to the class for which they have the highest probability. We interpret
the classes by observing the differences in the patterns of these response probabilities. Table 3B
provides a summary of these characteristics.
12
The AWE criterion is defines as -2logLc+2(3/2+logN)Npar, where L
c represents the classification log-likelihood.
13 We thank Bruce Sacerdote for graciously supplying the data.
14 As we add more direct effects, the probability structure of the classes does not change qualitatively but
classification errors increase.
11
Class 1, the largest class (about 41 percent of the sample), corresponds to individuals
with very low probabilities of membership in any type of voluntary organization as well as low
probabilities of FAIR and TRUST. These individuals would have low levels of social capital by
any measure. Compared to individuals in latent Class 1, respondents in Class 2 are much more
likely to state they trust other people and believe other people are fair even though Class 2
individuals do not have high probabilities for group membership either. Descriptive statistics by
class show that individuals in Class 1 and 2 belong on average to .60 and .78 organizations,
respectively. However, only 36 percent of individuals in Class 1 believe people are fair and
fewer than 1 percent state people can be trusted while in Class 2, 86 percent of the individuals
believe other people are fair and 90 percent claim others can be trusted.
Individuals in Class 3 have the highest probabilities of FAIR and TRUST in the sample.
The probability that an individual assigned to Class 3 belongs to a professional organization is
relatively high, 55 percent. Individuals in Class 4 also have high and medium probabilities of
FAIR and TRUST. Among all individuals in the sample, individuals in Class 4 have the largest
probabilities of belonging to unions, veteran, and fraternal groups. Individuals in Class 5 have a
very high probability of belonging to a church organization. Respondents in Class 6 exhibit the
lowest probabilities of FAIR and TRUST but medium probability of membership in a church
group and relatively low probabilities of membership in school and sports groups. Individuals in
Class 7 show high probability of FAIR and medium probabilities of TRUST and memberships in
church and school organizations as well as relatively high probabilities of membership in youth
and sport groups. Class 8, with 3 percent of the individuals in the sample, corresponds to
individuals with high probabilities of group membership and high probability of trusting others.
Individuals in Class 8 are the most likely to belong to service, youth, school, hobby, literary,
fraternities, professional, political, and other organizations. The average number of memberships
in this latent class is 7.5. By most measures, individuals in Class 8 have high levels of social
capital.
Three conclusions are particularly interesting. First, FAIR and TRUST help to
distinguish individuals across classes in a nontrivial manner. Although the literature often
implies that trust is a consequence of social capital, we find that there are individuals who are
very likely to express trust but are unlikely to belong to any voluntary organization (individuals
12
in Class 2). On the other hand, we find that some individuals who are likely to belong to church
and other groups did not necessarily state other people are fair and can be trusted (Class 6).
Second, individuals with the same number of memberships are sorted into different types
of social capital. For example, of all individuals with three memberships who trust others and
believe people are fair, around 8 percent are classified in latent Class 2, 49 percent in Class 3, 20
percent in Class 4, 10 percent in Class 5, and 14 percent in Class 7. The probability structure of
these classes is different. Thus, despite the fact that all the individuals in these classes belong to
about three groups and hold the same social norms, their social networks are different. A key
dimension along which membership in these groups differ is that they may require different
levels of involvement of time and/or money. The importance of this last observation will
become apparent when we discuss the determinants of social capital formation.
Finally, examining the average number of group memberships by class also reveals that
simply adding number of memberships does not necessarily provide a meaningful measure of
social capital. For example, it is difficult to claim that individuals in Class 6 have more social
capital than individuals in Class 3. The results of the latent class model suggest that it is more
appropriate to conclude that individuals in Class 6 have a different type of social capital than
individuals in Class 3.
Table 4 presents the estimates of the β parameters in equation 4. We use dummy coding
for identification where the reference class is Class 1, the low social capital class. A positive
estimate for class s means that an individual in class s is more likely to answers “yes” to the
indicator than an individual in Class 1. In order to compare the magnitude of the effects we can
calculate the exponential value of the estimate and interpret the result as the odds of answering
“yes” in class s relative to the reference class. For example, the probability of membership in a
church organization is approximately 3.9 (or35.1e ) times higher in Class 3 than in Class 1. Table
4 also presents Wald statistics that suggest we can strongly reject the null hypothesis that each
estimate for a given indicator equals zero. Thus, all indicators discriminate between classes in a
statistically significant manner.
5 Using Latent Classes to Investigate the Determinants of Social Capital
In the previous section, we estimated latent classes that measure an individual’s social
capital. In this section, we compare the empirical results of Glaeser, Laibson, and Sacerdote
13
(2002) to results we obtain using the latent classes. We also apply our typology to the research
by Alesina and La Ferrara (2000) on the effects of community heterogeneity on individual social
capital. We show that the use of latent classes allows meaningful new insights about the
determinants of social capital. In Section 5.1 and 5.2, we estimate multinomial logit (MNL)
models where we use the social class typology discussed in the previous section as the dependent
variable and socio-economic characteristics as explanatory factors following the models by GLS
and Alesina and La Ferrara. In Section 5.3, we discuss an alternative approach in which we
estimate latent class models where the same socio-economic characteristics now influence the
prior probability of class membership.
5.1 Social Capital Formation: Results from Mutinomial Logit Model
We use the same independent variables used by GLS (descriptive statistics in Table 5)
and present the coefficients from multinomial logit estimation in Table 6. The specification in
these tables resembles a base specification of GLS in which they investigate how demographic
characteristics are associated with the number of group memberships.15
Before discussing the
results of the multinomial logit model, we note that a Hausman test strongly rejects the null
hypothesis that any pair of categories (that is, the latent classes) can be collapsed and that all
categories are indistinguishable with respect to the independent variables in the model. This test
supports the idea that the types of social capital we identified using latent class analysis are
distinct and economically meaningful.16
Examined directly, the coefficients in Table 6 have limited interpretive value. In Table 7,
we report the change in the odds ratio. For example, the first row of column 3 indicates that the
odds ratio of being in Class 1 vs. 2, Prob(Class 1)/Prob(Class 2), is .53 times larger when
education increases by one standard deviation. In other words, higher education levels reduce
the probability of being in Class 1 relative to Class 2. Similarly, the first row of column 5
indicates that Prob(Class 1)/Prob(Class 2) is 2.84 times larger when the respondent is black.17
15
We report results of only one of the several GLS specifications. We receive qualitatively similar results for all
other specifications reported in GLS. 16
A Hausman test also confirms that the assumption of the independence of irrelevant alternatives is valid. 17
These changes are calculated directly from the coefficients in Table 6. For example, the Class 2 – Class 3
comparison in Table 7 for the variable education is )(* educationstdbinchangee where the change in b is the difference
between the coefficients for education for classes 2 and 3 in Table 6. With a standard deviation for education of
3.15, the change in the odds ratio reported in Table 7 is e(.147-.5825)*3.15
=.3024.
14
In Table 7, we report only changes that are significant at the 10 percent significance level. Blank
cells represent insignificant changes.
The results in Table 6 and Table 7 indicate how individual characteristics sort people into
different types of social capital. Some interesting comparisons are between Class 1 and Class 2
and between Class 1 and Class 6. For example, the odds comparing Class 1 (low membership,
low trust group) and Class 2 (low membership, high trust group) indicate that individuals with
high levels of education and income are less likely to be in Class 1 than in Class 2, while being
black is associated with higher probabilities of being in Class 1 relative to Class 2. Higher
income and education are associated with higher probabilities of being in Class 6 (low trust,
relatively high membership in sport organization) relative to Class 1 (low trust, low
membership), but being married increases the probability of being in Class 1 relative to Class 6.
Education has a strong substantive effect. An interesting finding is that individuals with
higher levels of education are much more likely to be in Class 3 than in classes 5 or 6. These
classes are similar in terms of the number of memberships but Class 3 is defined by a higher
probability of membership in professional groups. Thus, there are socio-economic determinants
that sort individuals into different types of social capital classes that have very similar average
group memberships. Our results can also speak to the commonalities between the classes. For
example, individuals in both classes 1 and 6 have low values of TRUST and FAIR. The results
in Table 7 suggest that one demographic characteristic that sorts individuals into these two “low-
trust” classes is being black.
One of the hypotheses GLS obtain from the theoretical model is a negative association
between social capital and income: if individuals with high incomes have a high opportunity cost
of time, then they should belong to few groups. However, GLS find that there is a positive
association between social capital and income. Our typology of social capital sheds some light
on this issue. Some voluntary groups have high time commitments but low monetary costs
(church groups) while other groups (professional associations) have relatively low time
commitments and high monetary costs in the form of membership fees. If individuals do take
into account the opportunity cost of their time when accumulating social capital, then we should
see that higher-income individuals should be more likely to join social networks with lower time
commitments but higher monetary costs. Our results support this hypothesis. Comparing classes
3, 5, and 6, the odds that individuals are in Class 3, the class with the highest probability of
15
professional memberships, rather than in Class 5 or Class 6, increase with income. These results
are consistent with the fact that individuals consider the opportunity cost of their time in
decisions regarding social capital accumulation, a result that is impossible to uncover simply
using number of group memberships as a measure of social capital.18
These results are also
broadly consistent with the argument in Skocpol (2003) that elite Americans have shifted the
burden of civic engagement toward managed professionally-staffed organizations.
As we mentioned previously, individuals are assigned to classes based on a probabilistic
method and therefore there is some classification error in our dependent variable. As Table 2
indicates, as we increase the number of latent classes the models’ goodness-of-fit improves but
the classification error increases because there are more possible classes to which we assign
individuals. We would be concerned if that error was systematic and individuals with high levels
of classification error affected our conclusions. To investigate how robust the results are to
misclassification, we drop observations with maximum probabilities of class membership in the
bottom 25th percent (i.e., the probability of being assigned to their class is less than 56 percent).
Table 8 presents the results of the multinomial logit model for this sub-sample. The results are
very similar to those in Table 6. In terms of statistical significance, only three estimates become
insignificant, and qualitatively, we reach the same conclusions. Table 9 displays changes in odd
ratios based on the estimates in Table 8. Although some odds comparing classes become
insignificant while others are now significant at the 10 percent or better, overall, we can derive
the same inferences that we draw with the entire sample. In sum, these results suggest that class
membership misclassification is not affecting our conclusions.19
We turn now to another prediction of the theory that GLS were unable to support - that
the social capital of individuals should be positively correlated with the social capital of their
peer group because of interpersonal complementarities in social capital accumulation. In a
simple discrete choice framework, this phenomenon would occur if peer group membership in a
social capital class is an attribute of that class that yields utility or if selecting a social capital
18
Of course, like GLS, we can only comment on probabilities and cannot make a statement about causation. In fact,
in our theoretical framework and in that of GLS, social capital also influences income so we cannot emphasize the
interpretation of this result. We simply point out that our findings are at least consistent with a theory of social
capital accumulation that takes into account the opportunity cost of time. 19
We also estimate MNL models dropping individuals with a difference of 9.2 percent of lower between the largest
posterior probability and the second largest posterior probability (a difference of 9.2 percent is the 10th-percentile of
the distribution; the 25-percentile is 28.45 difference). We obtain very similar results qualitatively while in terms of
statistical significance these results are in fact stronger.
16
class that many peers also select reduces the cost of joining. Following GLS, we define an
individual’s peer group by geographic location (primary sampling unit) and religion. For
example, a peer group might be Baptists in Memphis or Catholics in Cleveland. We calculate
the average probability of membership in each class for that individual’s peer group, excluding
the specific individual and dropping observations for which there are less than five people in a
peer group. We then use the average probabilities of membership for the individual’s peer group
as an explanatory variable. The probabilities of peer group membership in each class vary by
both individual and class so that for each individual there will be a separate probability of peer
group membership associated with each class, in contrast to the other independent variables (age,
education, income, etc.) that do not vary by class for each individual. Therefore, rather than
estimating a multinomial logistic regression, we estimate a conditional logistic regression.
Omitted variables might create a spurious correlation between peer group values and
individual values. We follow GLS and instrument for peer-group membership probability with
the average education, age, marital status and income of the peer group. (In this estimation the
standard errors are bootstrapped.) Unlike GLS, even after employing instrumental variables
estimation we still find significant peer group effects, indicating that there are interpersonal
complementarities in social capital accumulation. Table 10 displays the results of the conditional
logit model. In the conditional logit model we estimate six coefficients for the individual-
specific variables (education, income, and so on) but only a single coefficient for the class-
specific variable (average class-membership probability). The positive statistically significant
effect of the class-membership probability for peer group is evidence that interpersonal
complementarities in social capital accumulation do exist. We believe that our stronger
empirical results are a direct consequence of our improved definition of social capital that
considers not just the number of groups, but the types of social capital individuals hold.20
5.2 Community Heterogeneity and Individual Social Capital
Alesina and La Ferrara (2000) also use GSS data to examine the determinants of
individual social capital. They focus on the effects of community heterogeneity. Alesina and La
20
The specification reported in Table 9 does not include state dummies because including them does not allow the
maximum likelihood estimation to converge. GLS do include state dummies in the IV estimations they report.
However the inclusion of state dummies is not driving the results: when we exclude state dummies from the IV
specification reported in GLS, we do not find materially different results for the coefficient on peer memberships.
Thus, the difference in results is not attributable to the exclusion of state dummies.
17
Ferrara first estimate probit models of membership in any organization. Then, to explore
whether heterogeneity affects differently the propensity to participate in organizations that have
different requirements in terms of interaction among their members, they estimate the likelihood
of participating in specific organizations. The authors find that racial diversity, in particular,
strongly reduces the likelihood of participation and that the strongest effects are for organizations
that require frequent interactions such as church groups and sports clubs.
In contrast to Alesina and La Ferrara (2000), we do not assume the decision to participate
in a given organization is independent from membership in other organizations. Because we
implicitly assume that individuals belong to a set of memberships and norms, our empirical
models investigate whether differences in the degree of racial and ethnic heterogeneity are
related to the type of social capital individuals choose. We use the sample whose descriptive
statistics are presented in Table 5 but we now add community-level variables following Alesina
and La Ferrara: the logarithm of the size of the MSA/PMSA where the individual lives (per
thousand people), the logarithm of median household income of the MSA/PMSA and the
logarithm of median household income squared, and two indices of racial and ethnic
heterogeneity of the MSA/PMSA where the individual lives. We also follow Alesina and La
Ferrara to construct these indices. We use 1990 Census data of five ethnic groups: (1) white, (2)
black, (3) American Indian, Eskimo, Aleutian, (4) Asian, Pacific Islander, and (5) other (that
mostly corresponds to Hispanics). We group ancestries into ten groups (see Alesina and La
Ferrara, 2000). The value of the indices can be interpreted as the probability that two individuals
selected at random belong to different racial (or ethnic) groups.
We estimate two multinomial logit models: one specification includes the racial index (as
well as the group shares that form the index), the second specification includes the ethnic index
(and ancestry groups shares as well). Table 11 presents the change in odds ratio for one standard
deviation increase in the racial and ethnic indices.21
We only present changes that are significant
at the 10 percent level or better (after clustering standard errors by MSA/PMSA). The results
indicate that the more heterogeneous the community is in terms of race, the probability that the
individual is assigned to the low social capital class is 1.13 higher than the probability that the
individuals is assigned to a class characterized by high levels of trust and fairness (Class 2). As
racial heterogeneity increases by one standard deviation, the probability that the individual is
21
Results of the multinomial logit models are available upon request.
18
assigned to Class 2 is .89 lower than the probability is assigned to Class 6, a class defined by the
lowest levels of TRUST and FAIR and medium probability of church membership. Our results
for the effect of ethnic heterogeneity are similar, but weaker. Greater ethnic heterogeneity sorts
people out of Class 2 and into the less trusting Class 5. The result that greater ethnic
heterogeneity sorts people out of the low trust Class 1 and into Class 5 does somewhat contradict
the patterns established by the other three coefficients, however, this result has weaker statistical
significance with a p-value of .08.
These results add new insights to those found by Alesina and La Ferrara. Racial
heterogeneity reduces the probability of holding beneficial social norms and we find similar, but
weaker, results when we explore the effects of ethnic heterogeneity. Overall, these results
suggest that community heterogeneity influences social capital accumulation by influencing trust
and perception of fairness in addition to its possible effects on willingness to interact with people
of different backgrounds.
5.3 Alternative Estimation Method for Social Capital
We have discussed the results when we apply multinomial logit models to the latent
classification from an 8-class model to examine how socio-economic characteristics influence
social capital. An alternative approach is to estimate jointly the latent classes and the effects of
observable characteristics on the prior probability of class membership. In this case, we modify
Equation 1 to indicate the influence of covariates:
S
s k
iikiii sXYPsXPYP1
18
1
)|()|()( z (1’)
where )z|( ii sXP is defined by Equation 3.
The joint estimation approach has the potential advantage of reducing classification
errors, however, we encountered issues in estimating this relatively complex model that urge
caution in interpreting the results. First, the bivariate residuals indicate that, in this specification,
there are very large unexplained associations between indicators which violate the assumption of
independence within classes.22
Second, when we attempt to address these associations by
including direct effects, we obtain boundary solutions which imply that we might not be able to
22
The largest residual, between FAIR and TRUST, is 324.75 (a residual over 1 indicates that the assumption of
independence of the indicators within latent class does not hold). Classification errors decrease by 7 percent.
19
find maximum likelihood estimates. Although we do not report detailed estimations results here,
we can draw the same inferences from these results: class sizes change but, overall, the
probability structure of the classes is very similar and the estimates of parameters for covariates
are very similar qualitatively to the estimates from the MNL model.23
Thus, we gain confidence
that the two-step approach we have discussed above generates robust and reasonable results. In
less complex applications with fewer covariates, we expect that the benefits of joint estimation of
latent class and the effects of observable factors on class membership would be more obvious
and unproblematic.
6 Conclusions
In this paper we motivate and demonstrate the use of latent class models to measure
social capital. The empirical treatment of social capital that we propose links more closely the
measurement of social capital with the concepts of social networks that underlie it. Latent class
analysis treats different kinds of social capital as being qualitatively different and is consistent
with an interpretation of social capital as an unobservable multidimensional construct. We show
that this new approach generates empirical results consistent with a theory of social capital
accumulation that the standard treatment of social capital could not reveal. Specifically, we
replicate the models in Glaeser, Laibson, and Sacerdote (2002). While Glaeser, Laibson, and
Sacerdote measure social capital as the number of voluntary organization memberships
individuals hold, we use latent class analysis to classify individuals into distinct types of social
capital using both memberships and indicators of trust and fairness. Using the same data, we
find peer-group effects that could not be identified previously. We also find results consistent
with the hypothesis that individuals with high opportunity cost of time choose networks with
relatively low time commitment and perhaps high monetary cost. Finally, we find that socio-
economic determinants sort individuals into types of social capital that vary in the nature of the
social network but not necessarily in the number of memberships forming the network.
We also apply this new measurement of social capital to the research by Alesina and La
Ferrara (2000) on the effects of community heterogeneity on social capital. Our results suggest
that racial heterogeneity affects social capital accumulation via its effect on the likelihood of
adhering to social norms of trust and fairness, independent of memberships in organizations.
23
All these results are available from the authors upon request.
20
Interestingly, once our multidimensional method accounts for trust and fairness, we do not find
as strong results for types of group membership as do Alesina and La Ferrara (2000). This result
is consistent with the idea that the link from heterogeneity to specific group memberships
operates through a channel created by trust and perceptions of fairness.
21
Table 1: Indicators (N = 14,527)
Indicator Description Percent
Fair = 1 if “people are fair” ( = 0 if “people try to take
advantage”)
59.72
Trust = 1 if people can be trusted 39.87
Church = 1 if membership in church organization 34.58
Service = 1 if membership in service group 9.72
Veteran = 1 if membership in veteran group 7.04
Union = 1 if membership in labor union 13.20
Political = 1 if membership in political club 3.97
Youth = 1 if membership in youth group 9.48
School = 1 if membership in school service 13.08
Farm = 1 if membership in farm organization 3.71
Fraternal = 1 if membership in fraternal group 9.40
Sport = 1 if membership in sports club 19.50
Hobby = 1 if membership in hobby club 9.31
Greek = 1 if membership in school fraternity 4.80
Nationality = 1 if membership in nationality group 3.30
Literary = 1 if membership in literary or art group 8.78
Professional = 1 if membership in professional society 14.70
Other = 1 if membership in any other group 10.43
22
Table 2: Model Selection: Fit Statistics
LL BIC(LL) Npar Bootstrap
p-value
Classification
Error
AWE
1-Cluster -94204.22 188580.95 18 <.001 .000 188807.46
2-Cluster -89510.47 179375.55 37 <.001 .087 186036.50
3-Cluster -88501.34 177539.36 56 <.001 .139 189068.38
4-Cluster -88116.64 176952.07 75 .2300 .203 193336.04
5-Cluster -87826.01 176552.88 94 ≈1 .208 194670.50
6-Cluster -87619.20 176321.37 113 ≈1 .215 195858.18
7-Cluster -87424.69 176114.45 132 ≈1 .275 198837.77
8-Cluster -87321.62 176090.38 151 ≈1 .279 200111.70
9-Cluster -87234.22 176097.67 170 ≈1 .282 200781.78
10-Cluster -87151.23 176113.79 189 ≈1 .283 202356.13
8-Cluster &
1 direct
effect
-87273.14 176003.01 152 ≈1 .284 200090.07
8-Cluster & 2
direct effects
-87244.50 175955.32 153 ≈1 .284 200322.78
23
Table 3A: Conditional Response Probabilities
Class1 Class2 Class3 Class4 Class5 Class6 Class7 Class8
Class Size .4079 .2268 .1110 .0728 .0470 .0648 .0398 .0300
Individuals 5,925 3,294 1,612 1,057 683 942 578 436
Fair .2950 .8835 .8936 .6784 .8356 .0040 .8174 .7646
Trust .0592 .7067 .7635 .4891 .4644 .0005 .5853 .5562
Church .1906 .1919 .4753 .3738 .9279 .5011 .5605 .7851
Service .0063 .0047 .2621 .2058 .0798 .1710 .1432 .6479
Youth .0081 .0001 .0458 .0368 .1580 .2837 .6497 .6615
School .0334 .0450 .2026 .0116 .2498 .3145 .4811 .7021
Sport .0774 .1139 .3007 .2123 .0755 .4230 .6824 .6426
Farm .0120 .0171 .0328 .0773 .0978 .0571 .0591 .1607
Hobby .0182 .0359 .2169 .1209 .1296 .2282 .1371 .3769
Literary .0069 .0123 .3161 .0207 .1246 .1942 .0754 .5847
Fraternal .0195 .0344 .1791 .3550 .0456 .1206 .0904 .3445
Greek .0016 .0147 .1882 .0191 .0033 .1111 .0368 .3314
Professional .0216 .0906 .5472 .0479 .0260 .2563 .1919 .6610
Veteran .0255 .0265 .0573 .3719 .0009 .0987 .0764 .1634
Political .0028 .0044 .1034 .0794 .0277 .0787 .0289 .3081
Union .1188 .0969 .0849 .3263 .0226 .1703 .2078 .1863
Nationality .0078 .0097 .0797 .0430 .0212 .0844 .0242 .2066
Other .0477 .0990 .1666 .1309 .2009 .1460 .0729 .2247
Mean group
membership
(std. dev.)
[min/max]
.598
(.709)
[0/3]
.781
(.755)
[0/4]
3.515
(1.331)
[1/8]
2.914
(1.123)
[1/9]
2.572
(.786)
[2/6]
3.577
(1.357)
[2/9]
3.753
(1.206)
[1/7]
7.50
(1.745)
[5/16]
24
Table 3B: Qualitative Characteristics of the Classes
Class Characteristics
Class 1 Low probabilities of FAIR and TRUST. Low probabilities of group membership. By
most measures of social capital, people in Class 1 would be considered to have low
social capital.
Class 2 High probabilities of FAIR and TRUST. Low probabilities of group memberships.
Class 3 High probabilities of FAIR and TRUST. Medium probabilities of memberships in
professional organizations and church groups.
Class 4 High probability of FAIR and medium probability of TRUST. Largest probabilities
of membership in unions, veterans, and fraternal groups.
Class 5 High probability of FAIR and medium probability of TRUST. Very high probability
of membership in church groups.
Class 6 Lowest probabilities of FAIR and TRUST. Medium probability of membership in a
church group. Relatively low probabilities of membership in school and sports
groups.
Class 7 High probability of FAIR. Medium probabilities of TRUST and memberships in
church and school organizations. Relatively high probabilities of membership in
youth and sport groups.
Class 8 High probability of FAIR and medium probability of TRUST. Largest probabilities
in service, youth, school, hobby, literary, fraternities, professional, political, and other
organizations. By most measures of social capital, people in class 7 would be
considered to have high social capital.
25
Table 4: Parameter Estimates for Indicators*
Cluster2 Cluster3 Cluster4 Cluster5 Cluster6 Cluster7 Cluster8 Wald Fair 2.89 2.99 1.62 2.49 -4.65 2.37 2.05 367.56 Trust 3.65 3.94 2.72 2.62 -4.85 3.11 2.99 786.38 Church .009 1.35 .930 4.00 1.45 1.69 2.74 399.06 Service -.301 4.02 3.71 2.61 3.48 3.27 5.67 325.52 Youth -4.40 1.77 1.53 3.13 3.88 5.42 5.47 359.93 School .311 1.99 -1.08 2.27 2.59 3.29 4.22 753.40 Sport .427 1.64 1.17 -.026 2.17 3.24 3.07 543.03 Farm .359 1.03 1.93 2.19 1.60 1.64 2.76 146.06 Hobby .695 2.70 2.00 2.08 2.77 2.15 3.48 378.04 Literary .583 4.19 1.11 3.02 3.54 2.46 5.31 428.81 Fraternal .558 2.12 3.30 .873 1.76 1.55 2.87 338.17 Greek 2.21 4.76 1.99 .690 4.21 3.05 5.35 143.19 Professional 1.51 4.00 .821 .190 2.75 2.37 4.48 393.74 Veteran .039 .844 3.12 -3.33 1.43 1.15 2.01 266.83 Political .463 3.73 3.44 2.33 3.43 2.38 5.08 207.74 Union -.228 -.374 1.28 -1.77 .420 .666 .529 133.36 Nationality .217 2.40 1.75 1.01 2.46 1.15 3.50 256.15 Other .786 1.38 1.10 1.61 1.23 .451 1.76 12.81
*All coefficients are statistically significant at the .01 percent level or better. Reference group is
Class 1 (no social capital class). A positive (negative) estimate means that individuals in that
class are more (less) likely to respond affirmatively to the corresponding indicator than
individuals in Class 1.
26
Table 5: Descriptive Statistics For Independent Variables
Variable Definition Mean Std. Dev.
Education Years Education 12.39 3.15
Log Income Log Annual Income 2.09 0.65
Income Missing =1 if income not provided 0.04 0.20
Black =1 if black 0.14 0.34
Female =1 if female 0.56 0.50
Birth Year Year of birth 1940.18 18.28
Married =1 if married 0.57 0.50
Babies Young children in household 0.26 0.59
Preteen Preteens in household 0.32 0.69
Teens Teenagers in household 0.24 0.59
South =1 if in south 0.34 0.47
East =1 if in east 0.20 0.40
West =1 if in west 0.19 0.39
Log of Population = log of population in PSU 3.43 2.17
Age 18-29 =1 if between 18 and 29 0.24 0.43
Age 30-39 =1 if between 30 and 39 0.23 0.42
Age 40-49 =1 if 40 to 49 0.16 0.37
Baptist =1 if Baptist 0.21 0.41
Methodist =1 if Methodist 0.10 0.30
Lutheran =1 if Lutheran 0.07 0.25
Presbyterian =1 if Presbyterian 0.05 0.21
Episcopalian =1 if Episcopalian 0.02 0.15
Other Protestant =1 if belong to other Protestant religion 0.14 0.35
Non Denominational Protestant =1 if non-denominational Protestant 0.04 0.19
Jewish =1 if Jewish 0.02 0.13
Catholic =1 if Catholic 0.25 0.43
Other Religion =1 if other religious affiliation 0.02 0.14
Race Racial heterogeneity of MSA/PMSA .25 .14
Ethnic Ethnic heterogeneity of MSA/PMSA .59 .10
Log med income Log median income of MSA/PMSA 10.29 .20
Size Log of population (in thousands) of MSA/PMSA 5.86 1.13
Total observations used in estimations: 13,926.
27
Table 6: Multinomial logistic regression for class membership
Class 2 Class 3 Class 4 Class 5 Class 6 Class 7 Class 8
Education .203**
(.010)
.583**
(.015)
.147**
(.015)
.252**
(.019)
.309**
(.016)
.250**
(.021)
.623**
(.023)
Log Income .195**
(.056)
.623**
(.104)
.656**
(.111)
.195*
(.112)
.298**
(.091)
.562**
(.157)
.537**
(.170)
Income
Missing
.407**
(.163)
.827**
(.319)
1.27**
(.304)
.324
(.313)
.757**
(.265)
1.00**
(.458)
1.09**
(.498)
Black -1.05**
(.093)
-1.23**
(.152)
-.334**
(.142)
-.860**
(.164)
.127
(.111)
-.966**
(.198)
.074
(.187)
Female -.006
(.049)
.235**
(.068)
-1.24**
(.079)
.907**
(.103)
-.092
(.076)
-.212**
(.094)
.174
(.113)
Birth Year -.023**
(.003)
-.019**
(.005)
-.023**
(.004)
-.025**
(.006)
.008
(.005)
.017**
(.007)
-.021**
(.008)
Married .041
(.054)
-.036
(.076)
.019
(.086)
.251**
(.102)
-.237**
(.085)
.330**
(.116)
-.182
(.125)
Age 18-29 .349**
(.138)
.026
(.194)
-1.19**
(.219)
-.257
(.255)
.071
(.229)
-.156
(.303)
.351
(.322)
Age 30-39 .293**
(.118)
-.006
(.163)
-.675**
(.178)
-.259
(.209)
-.024
(.193)
.185
(.247)
.047
(.266)
Age 40-49 .284**
(.098)
.152
(.135)
-.283**
(.142)
.021
(.171)
.052
(.165)
.476**
(.205)
.0141
(.224)
Base category is Class 1. Estimated with 13,926 observations. Standard errors are in parentheses.
**significant at the 5% level, *significant at the 10% level. Estimations also include, state dummies,
dummies for religious affiliation, regional dummies, log of population, and variables for babies, preteens,
and teens in the household.
28
Table 7: Change in Odds Ratio Odds Comparing
Column 1 –
Column 2
(3)
Education
(4)
Log
Income
(5)
Black
(6)
Female
(7)
Married
(8)
Age 18-
29
(9)
Age 30-
39
(10)
Age 40-
49
(1) (2)
Class1 Class2 .526 .882 2.84 .705 .746 .753
Class1 Class3 .159 .669 3.43 .790
Class1 Class4 .629 .655 1.39 3.47 3.27 1.96 1.33
Class1 Class5 .452 .882 2.36 .404 .778
Class1 Class6 .378 .825 1.27
Class1 Class7 .454 .696 2.63 1.24 .719 .621
Class1 Class8 .140 .707
Class2 Class3 .302 .758 .786 1.38 1.35
Class2 Class4 1.19 .743 .491 3.44 4.64 2.63 1.76
Class2 Class5 .858 .401 .809 1.84 1.74
Class2 Class6 .718 .309 1.32
Class2 Class7 .863 .789 1.23 .748
Class2 Class8 .266 .802 .326 1.25
Class3 Class4 .395 .407 4.39 3.36 1.95 1.54
Class3 Class5 2.84 1.32 .688 .512 .751
Class3 Class6 2.37 1.23 .256 1.39 1.22
Class3 Class7 2.85 1.56 .694
Class3 Class8 .879 .270
Class4 Class5 .718 1.35 1.69 .116 .792 .395
Class4 Class6 .601 1.26 .630 .316 1.29 .285 .522 .716
Class4 Class7 .722 1.88 .357 .732 .357 .423 .469
Class4 Class8 .223 .664 .243 .215 .486
Class5 Class6 .837 .373 2.72 1.63
Class5 Class7 .789 3.06 .635
Class5 Class8 .310 .802 .393 2.08 1.54
Class6 Class7 1.20 2.98 .567 .655
Class6 Class8 .371 .766
Class7 Class8 .308 .354 .680 1.67
For education and income, each cell gives the change in the odds ratio from a one standard deviation
increase in the selected independent variable. For dummy variables, each cell gives the change in the odds
ratio from an increase of 1 in the dummy variable. The odds ratio is defined as the probability of
belonging to the class in the Group 1 column divided by the probability of belonging to the class in the
Group 2 column. Only changes that are significant at the 10 percent level are reported. Blank cells
indicate the estimated change is not statistically significant.
29
Table 8: MNL for class membership, excluding observations with less than 56% probability of
membership
Class 2 Class 3 Class 4 Class 5 Class 6 Class 7 Class 8
Education .239**
(.012)
.648**
(.018)
.165**
(.019)
.285**
(.024)
.358**
(.019)
.271**
(.025)
.633**
(.025)
Log Income .281**
(.067)
.637**
(.123)
.718**
(.145)
.265*
(.150)
.422**
(.108)
.827**
(.207)
.573**
(.182)
Income
Missing
.533**
(.194)
.957**
(.381)
1.33**
(.402)
.190
(.446)
.903**
(.323)
1.67**
(.586)
1.13**
(.539)
Black -1.25**
(.117)
-1.36**
(.189)
-.252
(.185)
-.996**
(.212)
.100
(.128)
-.863**
(.239)
.179
(.200)
Female .047
(.057)
.278**
(.082)
-1.57**
(.109)
1.06**
(.132)
-.097
(.087)
-.314**
(.112)
.185
(.124)
Birth Year -.032**
(.004)
-.023**
(.005)
-.029**
(.006)
-.021**
(.007)
.009
(.006)
.015
(.009)
-.021**
(.008)
Married .063
(.063)
.008
(.091)
.054
(.112)
.507**
(.135)
-.109
(.098)
.341**
(.138)
-.122
(.138)
Age 18-29 .455**
(.162)
.0004
(.231)
-1.61**
(.307)
-.451
(.326)
.074
(.265)
.026
(.371)
.226
(.349)
Age 30-39 .417**
(.138)
-.039
(.195)
-.713**
(.228)
-.317
(.263)
-.079
(.223)
.365
(.303)
-.123
(.291)
Age 40-49 .406**
(.116)
.177
(.162)
-.550**
(.189)
.018
(.217)
.047
(.191)
.654**
(.255)
-.080
(.246)
Base category is Class 1. Estimated with 10,455 observations. Standard errors are in parentheses.
**significant at the 5% level, *significant at the 10% level. Estimations also include, state dummies,
dummies for religious affiliation, regional dummies, log of population, and variables for babies, preteens,
and teens in the household.
30
Table 9: Change in Odds Ratio, excluding observations with less than 56% probability of membership Odds Comparing
Column 1 –
Column 2
(3)
Education
(4)
Log
Income
(5)
Black
(6)
Female
(7)
Married
(8)
Age 18-
29
(9)
Age 30-
39
(10)
Age 40-
49
(1) (2)
Class1 Class2 .462 .833 3.51 .634 .659 .666
Class1 Class3 .124 .661 3.89 .758
Class1 Class4 .588 .627 4.82 5.00 2.04 1.73
Class1 Class5 .399 .842 2.71 .346 .602
Class1 Class6 .315 .760
Class1 Class7 .418 .584 2.37 1.37 .711 .520
Class1 Class8 .129 .689
Class2 Class3 .268 .794 .797 1.58 1.58
Class2 Class4 1.27 .753 .367 5.05 7.89 3.09 2.60
Class2 Class5 .863 .363 .641 2.48 2.09 1.47
Class2 Class6 .681 .258 1.19 1.64 1.43
Class2 Class7 .702 1.43 .757
Class2 Class8 .281 .238 1.72 1.63
Class3 Class4 4.75 .331 6.36 5.00 1.96 2.07
Class3 Class5 3.22 1.27 .457 .607
Class3 Class6 2.54 .233 1.46
Class3 Class7 3.38 .609 1.81 .717 .621
Class3 Class8 .215
Class4 Class5 .678 1.34 2.11 .072 .636 .314 .566
Class4 Class6 .535 1.21 .229 .186 .530 .550
Class4 Class7 .711 1.84 .284 .751 .195 .340 .299
Class4 Class8 .221 .649 .172 .159 .554
Class5 Class6 .789 .334 3.18 1.85
Class5 Class7 .694 3.96 .506 .529
Class5 Class8 .326 .308 2.40 1.88
Class6 Class7 1.33 .769 2.62 1.24 .638 .545
Class6 Class8 .413 .754
Class7 Class8 .311 .353 .607 1.59 2.08
For education and income, each cell gives the change in the odds ratio from a one standard deviation
increase in the selected independent variable. For dummy variables, each cell gives the change in the odds
ratio from an increase of 1 in the dummy variable. The odds ratio is defined as the probability of
belonging to the class in the Group 1 column divided by the probability of belonging to the class in the
Group 2 column. Only changes that are significant at the 10 percent level are reported. Blank cells
indicate the estimated change is not statistically significant.
31
Table 10: Conditional logistic regression for class membership Class 2 Class 3 Class 4 Class 5 Class 6 Class 7 Class 8
Membership
probability
of peer
group
1.03**
(.319)
1.03**
(.319)
1.03**
(.319)
1.03**
(.319)
1.03**
(.319)
1.03**
(.319)
1.03**
(.319)
Education .203**
(.015)
.586**
(.019)
.151**
(.019)
.263**
(.021)
.307**
(.026)
.256**
(.028)
.593**
(.035)
Log Income .141
(.092)
.507**
(.138)
.553**
(.142)
.133
(.127)
.282**
(.116)
.651**
(.253)
.379*
(.209)
Income
Missing
.410
(.255)
.548
(.416)
1.09**
(.431)
.160
(.382)
.802**
(.323)
1.39**
(.614)
.805
(.566)
Black -1.03**
(.132)
-1.25**
(.196)
-.414**
(.203)
-.742**
(.209)
.119
(.156)
-.866**
(.242)
-.033
(.211)
Female .008
(.068)
.263**
(.108)
-1.24**
(.112)
.888**
(.142)
-.079
(.119)
-.187
(.119)
.072
(.143)
Birth Year -.020**
(.005)
-.018**
(.006)
-.023**
(.006)
-.025**
(.006)
.008
(.006)
.015
(.009)
-.006**
(.0004)
Married .074
(.094)
-.007
(.112)
.069
(.115)
.229
(.141)
-.259**
(.127)
.327**
(.153)
-.214
(.166)
Age 18-29 .279
(.211)
.096
(.262)
-1.20**
(.319)
-.228
(.275)
.094
(.291)
-.089
(.396)
-.195
(.245)
Age 30-39 .236
(.185)
.027
(.229)
-.688**
(.213)
-.187
(.236)
.043
(.249)
.308
(.336)
-.308
(.207)
Age 40-49 .249
(.155)
.185
(.185)
-.204
(.210)
.136
(.223)
.064
(.209)
.527*
(.292)
-.216
(.189)
Estimated via instrumental variables estimation. Bootstrapped standard errors are in parentheses.
**significant at the 5% level, *significant at the 10% level. Estimations also include, dummies for
religious affiliation, regional dummies, log of population, and variables for babies, preteens, and teens in
the household. Peer groups are defined as religion by primary sampling unit cell (e.g., Baptists in
Memphis). Membership probability of peer group is the average probability of membership in a
particular class for the individual’s peer group, excluding the individual. Instruments for membership
probability of peer group were average age, education, income and marital status for the peer group.
32
Table 11: Change in Odds Ratio for a one standard deviation increase in independent variable
Odds Comparing Column 1 – Column 2 (3)
Race Index
(4)
Ethnic Index
(1)
Column 1
(2)
Column 2
Class1 Class2 1.13
Class1 Class5 .711
Class2 Class5 .709
Class2 Class6 .894
Each cell gives the change in the odds ratio that results from a one standard deviation increase in
the selected independent variable. The odds ratio is defined as the probability of belonging to
the class in the Group 1 column divided by the probability of belonging to the class in the Group
2 column. Only changes that are significant at the 10 percent level are reported. Blank cells
indicate the estimated change is not statistically significant. In addition to the variables in Table
7, these specifications include size of the MSA/PMSA, median household income and household
income squared (all in logs) and race group shares (column 3) and ancestry group shares (column
4).
33
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