Multiplex Choices: Intra- and Inter-Network Dependencies
∗
and the Formation of Military Alliances
†
Oliver Westerwinter
†
Department of Political Science, University of St. Gallen
February 29, 2016
Version 1.5
Preliminary Draft Do not circulate or cite without the author's permission
Abstract
The formation, maintenance, and dissolution of international alliances is the result of strategic interaction among states. In this paper, I argue that states' alliance behavior is not only
aected by characteristics of individual states and dyads but also by the behavior of other
dyads in the international alliance network. I also maintain that patterns of cooperation in
other international networks, such as those constituted by states' shared memberships in intergovernmental organizations (IGOs), have inuence on how alliances are formed. In order
to estimate these within and cross-network extra-dyadic interdependencies, I use temporal
exponential random graph models. This allows to avoid the assumption of independence of
observations which underlies the vast majority of estimation techniques employed by international relations scholars and to directly model interdependence eects of triadic and higher
order within and across networks. I provide preliminary tests of my argument using data on
international alliances from 1950 to 1992. Results suggest that both within and cross-network
extra-dyadic dependencies exercise powerful inuence on states' alliance choices indicating
that strategic interaction does neither stop at the dyad nor at the network level of analysis.
Keywords: alliances, strategic interaction, interdependence, uncertainty, network analysis.
∗
I thank Paul Poast and Timm Betz for helpful comments on an earlier draft of the paper.
Introduction
Alliances are the result of interdependent choices of states. Particularly if they take the form of formalized, written agreements that include a commitment to use military force to support a partner
state in the event of a future conict, alliances are costly public signals that transmit information
about a state's intentions to cooperate in the case of military crises (Niou and Ordeshook, 1994;
Morrow, 1994, 1999; Fearon, 1997). As such, states' alliance behavior is likely to aect both the
expectations of the states directly involved in a military pact and the expectations of those that
remain outside of this cooperation. In other words, the political intentions that states signal with
their decisions to form and dissolve alliances do not only inform the expectations and behavior of
those with whom they form such pacts but have also the potential to shape the behavior of other
states that take notice of their actions.
Thus, states' alliance choices are unlikely to be shaped by factors at the actor and dyad level
of analysis alone but will also be determined by choices of other dyads in the international alliance
network.
For example, if two states,
relationships with
C
A
and
B,
have both a military pact with state
C,
their
can serve as channels through wich they can obtain strategic information
about each other's preferences and geopolitical interests which enables them to better estimate
whether the potential partner would be a useful ally in times of crisis. They can also use their ties
to the third party
C
to obtain information about the other's trustworthiness. This allows them to
update their beliefs about whether this state would be a reliable ally if its help is called upon in
the future. Such information about preferences and trustworthiness received from third parties are
likely to aect the alliance behavior of two states with respect to each other. Thus, dyads within
the international alliance network are unlikely to operate independently of each other.
Just as dyads within the alliance network are unlikely to be independent, it is also unlikely that
the alliance network forms and evolves independently of patterns of cooperation in other international networks, such as those constituted by joint memberships in intergovernmental organizations
(IGOs), preferential trade agreements (PTAs), or diplomatic exchanges. States that are, for example, closely linked through cooperative ties based on joined membership in intergovernmental
organizations that operate in the security area are experienced in interacting with each other in
2
security matters and possess detailed information about each other that allows them to estimate
each other's strategic interests more accurately than pairs of states that lack such cooperative
ties. They are also likely to develop a certain level of trust and form beliefs about each other's
trustworthiness based on repeated interactions in a cooperative context.
This information and
trust that stems from cooperative contexts other than military cooperation can have an impact on
whether or not two states decide to form, maintain, or abandon an alliance.
The interdependencies described above can cause severe diculties for statistical inference
about the determinants of states choices to form, maintain, and dissolve alliances because observations on states' alliance behavior violate the assumption of conditional independence that underlies
the vast majority of statistical techniques used by international relations scholars (Warren, 2010;
Cranmer and Desmarais, 2011). In addition, if interdpendencies within the alliance network as well
as interdependencies between the alliance network and other networks of cooperative international
ties are important drivers of states' alliances choices, then by omitting them from our theoretical
and statistical models of alliance choices we miss substantively important parts of the data generating process that underlies the pattern of alliance behavior that we observe across states and
over time. The result, an increased risk of misleading statistical inference (Dorussen, Gartzke and
Westerwinter, 2016). Therefore, in order to bring our models of alliance behavior technically and
substantively closer to what I argue in this paper is likely to be the data generating process at
work in the international system, researchers may want to take into account the complex pattern
of intra-network and inter-network dependencies at work in the international alliance system.
Students of alliances have so far largely ignored the interdependence of alliance choices. Models
have typically assumed independence of observations and applied case study methods or conventional statistical methods (Waltz, 1979; Walt, 1987; Siverson and Emmons, 1991; Snyder, 1997;
Simon and Gartzke, 1996; Lai and Reiter, 2000; Leeds, 2002; Gibler and Scott, 2006). While these
studies have made important contributions to enhancing our understanding of the determinants
of international military pacts, they miss most of the complexity constituted by intra- and internetwork dependencies within the alliance network. Recent works have made important rst steps
toward taking interdependence into account more systematically (Warren, 2010; Cranmer and Des-
3
marais, 2011; Cranmer, Desmarais and Menninga, 2012). Yet, while these works make important
rst contributions, they still leave critical aspects of the complex interdependencies at work in the
context of states' alliance choices underexplored. Most importantly, they ingnore the possibility of
inter-network dependencies and how these aect the formation of military pacts among nations.
In this paper, I argue that the concerns about strategic interaction that led researchers to
consider dyads in the rst place strongly suggest that looking exclusively at bilateral interactions
may be insucient to understand the full implications of strategic interaction (Smith, 1998; Signorino, 1999). Direct and indirect network ties among states can possibly serve as communication
infrastructure to obtain strategic information about possible alliance partners' preferences and
trustworthiness. More importantly, portfolios of network ties can serve as signals to convey information about the similarity of interests and resource needs which can trigger cooperation among
states with similar network tie portfolios. This in turn may have a positive eect on their likelihood
to form an alliance. In sum, complex interdependencies of extra-dyadic and higher order are likely
to operate within the international alliance network as well as between the international alliance
network and other international cooperative networks.
In order to empirically test this theoretical argument, I use temporal exponential random graph
models (TERGMs) as method of modeling state alliance choices (Cranmer and Desmarais, 2011).
This allows to avoid the assumption of dyadic independence and to directly model interdependence
eects of triadic or higher orders both within the alliance network as well as between the alliance
network and other international networks. Using data on international alliances from 1950 to 1992
from the Alliance Treaty Obligations and Provisions (ATOP) data set (Leeds, 2002), preliminary
ndings indicate that both intra- and inter-network interdependencies exert powerful inuence
over states' selection of alliance partners.
In what follows, I outline my theoretical argument about the complex interdependence of states'
alliance choices.
I then elaborate on my empirical strategy and the operationalization of the
variables I include in my models. Section four presents preliminary results using data on alliances
and states' joint IGO memberships.
Results suggest that states' alliance choices are driven by
both interdependencies within the international alliance network as well as by interdependencies
4
that operate between the alliance network and the security IGO network. A nal section briey
concludes.
Alliances, Strategic Interaction and Interdependence
Following previous work (Warren, 2010; Cranmer, Desmarais and Menninga, 2012), I argue that
extra-dyadic interdependencies arise in the alliance network because when deciding to form, maintain, or dissolve a military pact states do not only consider the characteristics of their partners
(e.g. political regime type, military power) and their relationship with them (e.g. bilateral trade,
shared language) but also what happens in other alliances. In an international environment where
accurate information about others' intentions and geopolitical interests is scarce and, hence, the
credible revelation of interests notoriously dicult, alliances serve as one way for states to publicly
represent their interests and allegiances (Fearon, 1994). Yet, because they are made in public these
signals are not limited to the states directly involved in an alliance but also inuence the expectations of actors external to the alliance which in turn can take that information into consideration
when making decisions about with whom they are going to ally. Thus, rather than being the result
of decisions in isolated dyadic bubbles (Warren, 2010), states' alliance choices are the result of
complex interdependencies that reach far beyond dyadic relationships.
Uncertainty about the reputation of potential allies is another mechanism that produces interdependency of alliance choices. Since information about states reputation and trustworthiness is
scarce and dicult to obtain in an anarchic international system, states have diculties arriving
at accurate assessments of how trustworthy a potential ally is and how likely it will honor its duties
in case of a future conict. One way to obtain such information is through other states with which
one is already allied and which are related to the state with which one considers establishing an
alliance. In other words, when considering the establishment of a new alliance with a state whose
reputation is unclear a state can use its relationship with another party who is also linked to this
state in order to obtain information about its credibility and trustworthiness. Thus, in terms of
network theory we would expect that transitivity is at work in the international alliance network
and shapes the presence and absence of alliance ties.
5
I develop this argument one step further and argue that in the same way as dyads within
the alliance network do not evolve independently of each another the alliance network itself does
not evolve independently of the patterns of cooperation and conict that occur in other networks
(Maoz, 2011, p. 39). States can, for example, use information gained from direct links of cooperation in intergovernmental organizations as a means to assess the reputation and trustworthiness
of a potential ally. If state
A
considers forming an alliance with state
B
with which it is directly
linked to in the network constituted by joint IGO memberships, it will use the knowledge it can
gain from state
state
B
B
through their joint IGO engagement to make a better decision about whether
is likely to be a good or bad ally. Similarly, if states
A and B
are structurally equivalent in
the IGO network, i.e. they are connected to similar groups of other states, this conveys information
about similarity of interests and trustworthiness and has therefore an aect on
whether or not to form a military pact.
A's and B 's choices
As a result, the international alliance network reects
intra-network as well as cross-network interdependencies that shape states' alliances choices and
therefore the structure of the global alliance network.
Bringing the dierent strands of the argument made so far together, I expect that states that
have an indirect communication channel within the alliance network are more likely to have a
formal alliance because the information they obtain through this channel about the preferences
and trustworthiness of potential allies help them to overcome uncertainties and problems of trust.
Likewise, everything else being equal two states that are directly connected in an international
cooperation network that is dierent from the international alliances network (e.g.
network of
IGOs) are more likely to have an alliance tie compared to two states that lack such a connection.
I hypothesize:
Hypothesis 1:
States that have an alliance with the same third party are more likely to have
an alliance.
Hypothesis 2:
States that have a direct tie in an international cooperation network dierent
from the international alliance network are more likely to have an alliance.
Despite their function as a communication infrastructure, direct network ties do not solve the
6
problem of strategic misrepresentation in the international system (Schelling, 1966; Fearon, 1995).
In a situation in which two states are bargaining over the formation and the terms of an alliance,
each of them has an incentive to present its interests and trustworthiness in such a way that allows
it to obtain the best deal possible, i.e. an alliance that is with respect to its terms and conditions
as close as possible to its idealpoint.
Given that the other state does not have access to this
private information, it has diculties to evaluate the accuracy of the communication it receives
from the possible partners. States are aware of this problem and therefore they will discount any
information they receive directly from a potential alliance partner. As a consequence, direct ties
in cooperation networks other than the alliance network might have not much of an informational
value and therefore not much of an eect on the likelihood of the formation of an alliance tie.
This problem may be mitigated when a third party is involved in the communication, although
it is not entirely resolved.
Rather than being directly connected through cooperative ties in a
network dierent from the international alliance network the states
linked through a third party
for information between
A
C.
and
A and B
This third party state can act as broker and transmission belt
B.
It may, for example, provide
A
with information about
geopolitical interests and record as a reliable partner which may help
suitable and trustworthy ally.
might be indirectedly
A
to assess whether
Yet, the problem continues to exist that now
C
(in fact, given that alliances are unlikely to be independent it is quite plausible that
benets its interests (Kydd, 2003).
A
and
B
is
might have an
interest in shaping whether and, if so, what form the military cooperation between
interest) and therefore misrepresent the information transferred between
B 's
B
A
C
and
B
takes
has such an
in a way that
This makes the realization of the potentially positive eect
of information transmission through indirect network ties on alliance formation dependent on the
preference prole of the third party
C
and should make it dicult to nd an unconditional eect
of third party ties on alliance formation.
A second way how states can make use of network ties within the alliance network and other
international cooperation networks to inform their alliances choices is to use patterns of network
ties as a signal that contains information about other states and their preferences (Spence, 1973;
Calvert, 1986). Students of alliances have frequently acknowledged that alliances are costly sig-
7
nals to alliance partners (Niou and Ordeshook, 1994; Morrow, 1994; Fearon, 1997). In addition,
alliances are also costly signals to states that are not directly involved in the alliance. The formation of a formal military pact between two states is often publicly visible to other states in the
international system.
Furthermore, states outside an alliance can obtain information about the
alliance by consulting various sources, such as international treaty depositories or databases. As
this information about individual alliances accumulates states obtain an overview of the overall
pattern of alliance relationships in the international system at a given point in time. The same
applies to the structure of networks of international cooperation based on joined memberships in
IGOs, preferential trade agreements, or dimplomatic exchanges. States can use their knowledge
about this pattern of alliance and other cooperative ties in order to obtain information about other
states' preferences and turstworthiness.
One way to use information about the overal structure of cooperation networks to obtain information about other states is to examine the portfolio of ties of other states and assess how similar
or dissimilar it is to one's own tie portofolio. By choosing their alliance partners or cooperation
partners more generally, states convey signals about the issues and geographic regions they care
about and what kind of alliance they prefer for what purposes. Other states can use this information that is implicitly contained in another state's tie portfolio to ascertain whether this other
state cares about similar or dierent issues and countries which in turn may help it to make a
decision whether or not to form an alliance with this state and what form this alliance should
take. Similarly, by comparing tie portfolios a state can also gain information about which other
countries already trusted a particular state as an alliance partner and use this as a diuse measure
of the trustworthiness of the state it considers forming an alliance with.
Importantly, other than direct or indirect communication through network ties, the signaling
function of patterns of network ties is more dicult to manipulate strategically and therefore less
subject to strategic misrepresentation.
The formation and dissolution of formal military pacts
incurs material and political costs to states and political leaders. In addition, negotiations over
the formation and the specic terms of an alliance can be lengthy. The same applies to joining and
leaving of IGOs to create new IGO ties or the creation and dissolution of PTAs. Assuming that a
8
state seeks to change its overall portfolio of alliance or other cooperative ties strategically in order
to signal preference compatibility or trustworthiness of a particular other state, this is likely to
involve the change of not only one but several network ties which multiplies the costs and resources
involved. Even if this state would nd it worth the investment it would still be dicult to time
such changes in a way that is conducive to conveying information to a particular other state at
a particular moment in time. In short, compared to communication via direct and indrect links,
manipulating the signals about preferences and trustworthiness implied in the portfolio of alliance
and other cooperative ties is less likely to be subject to strategic misrepresentation. As a result,
the similarity of portfolios of network ties should be a useful source of information in the context
of making decisions about the creation, maintenance, and dissolution of formal military pacts. In
fact, controlling for the similarity of states' portfolios of network ties should have a dampening
eect on the relationship between direct ties and the likelihood of alliance formation.
Hypothesis 3:
States that have similar portfolios of alliance ties are more likely to be allies.
Hypothesis 4:
States that have similar portfolios of ties in an international cooperation network dierent from the international alliance network are more likely to be
allies.
Empirical Strategy
I use temporal exponential random graph models (TERGMs) to examine the eect of intra- and
inter-network interdependencies on states alliance behavior (Hanneke, Fu and Xing, 2010; Cranmer
and Desmarais, 2011). TERGMs are an extension of the basic exponential random graph model
(ERGM) for the analysis of longitudinal network data. The ERGM is a general model for statistical
inference with network data (Robins et al., 2007; Lusher, Koskinen and Robins, 2013). ERGMs
are probability models for networks on a given set of actors with the response variable being the
probability of the observed collection of network ties. They allow modeling the network generating
process that underlies an observed pattern of relationships as a function of both exogenous actor
9
and dyad covariates and endogenous structural eects (e.g. the friend of my friend is my friend).
1
Importantly, the ERGM relaxes the assumption of conditional independence of observations
which is critical for conventional statistical analysis (Cranmer and Desmarais, 2011). In fact, one
of the primary advantages of ERGMs as opposed to the conventional regression framework is that
they allow for explicitly characterizing interdependencies among units. For example, with respect
to alliance choices researchers can employ the ERGM to investigate whether in addition to actor
and dyad covariates, such as regime type or trade dependency, extra-dyadic dependencies in the
alliance variable, such as the friend of my friend is my friend, shape states' alliance decisions. If such
endogenous interdependencies remain unmodeled, they can yield biased estimates of coecients
and inconsistent standard errors due to unobserved heterogeneity (Cranmer and Desmarais, 2011,
p. 67). Thus, using ERGMs to analyze the eects of intra and extra network interdependencies on
states alliances helps avoiding faulty inference on the variables of interest and allows for directly
modeling the complex relational interdependencies at work in the alliance network.
The general specication of the ERGM is given by the following equation:
exp(−
P (Ωm ) =
P (Ωm )
j = 1, . . . , k
Γmj ψj )
j=1
M
P
exp(−
m=1
where
k
P
k
P
,
Γmj ψj )
j=1
is the probability of the observed network,
Γm
that can be computed on the observed network,
parameters that describe the eect of the statistics in
denote the single elements in
Γ
by
Γmj .
variable which is hypothesized to aect
Γ
The statistics in
P (Ωm ).
(1)
is a vector of
Ωm ,
and
ψj
k
network statistics,
is a vector of
k
on the probability of observing
Γ
model
Ωm .
I
can include any possible explanatory
I estimate TERGMs for the international alliance
network using a bootstrap pseudolikehood appraoch (Cranmer and Desmarais, 2011).
1 The statistical approach pursued in this project, thus, goes beyond existing technical solutions to interdependence (e.g. Heagerty, Ward and Gleditsch, 2002) which tend to obscure rather than reveal substantively interesting
patterns of interdependence and can create their own problems (for a discussion, see Gartzke and Gleditsch, 2008).
10
Mesurement
The dependent variable in my models is the pattern of alliance relationships among states in a
given year
t.
from state
i
Let
Ω
to state
be an
n×n
matrix, where the element
j , (i, j = 1, . . . , n)
and
n

Ωn,n
ω
 1,1

 ω2,1


=
 ω3,1

 ..
 .

ωn,1
ωij
represents the relation directed
is the number of states in the network:
ω1,2 · · · ω1,n
ω2,2
ω3,2
.
.
.
ωn,2
Alliance ties are non-directioal and therefore



· · · ω2,n 


· · · ω3,n 
.

. 
..
.
.
. 

· · · ωn,n
ωij = ωji .
The elements of
Ω
can, therefore, be
formally dened as follows:
ωij = ωji =



1
if state


0
otherwise.
i
and state
j
had an alliance in year
t
(2)
A tie is included in the network if two states are allied, as reported by the Alliance Treaty Obligations and Provisions (ATOP) dataset (Leeds, 2002).
I focus on all types of formal alliances
as dependent variable in my main models. The results I present in the next section are similar
compared to models that use formal defense and oense pacts as dependent variable.
To test hypothesis 1, I examine whether we can observe triadic closure within the alliance
network (if state
i
has an alliance with state
k
and
j
has an alliance with
k,
then
i
and
j
are
also likely to have an alliance). To capture this eect I include a measure for the geometrically
weighted edgewise shared partner distribution (GWESP) proposed by Snijders et al. (2006) in
my TERGM models. GWESP is useful from a modeling perspective as it captures specic linear
combinations of an entire distribution of degree or shared partner statistics (Hunter et al., 2008,
p. 13). Importantly, GWESP is shown to work well in practice in overcoming model degeneracy
and producing models that t a wide range of data well (Goodreau, Kitts and Morris, 2009,
p. 111).
The expectation of triadic closure in the alliance network should result in a positive
11
coecient on the GWESP statistic.
Figure 1: Within-Alliance Network Triadic Closure
k
j
i
+
To investigate whether states' alliance choices are aected by the patterns of relationships in
other networks of international cooperation, I use data on security IGOs and IGOs more generally
and construct two independent variables. The rst variable is a simple measure of the strength of
a cooperative relationship in the security IGO network that captures the number of security IGOs
that two states have in common. Similarly, I construct a measure that captures the strength of
the relationship between two states based on their joined memberships in all IGOs. To measure
security IGO and IGO memberships I use data reported by Boehmer, Gartzke and Nordstrom
(2004). In accordance with the theoretical reasoning underlying hypothesis 2 I expect to observe
a positive coecient for this variable.
Second, I use the structural equivalence of two states in the alliance network as well as within
international cooperation networks other than the alliance network as measure for the similarity of
their network tie portfolios. Structural equivalence captures the degree to which two states have
similar portfolios of network ties to other states. I use a measure of structural equivalence that
is based on Euclidean distance. Two states that score low on this measure have similar portfolios
of network ties.
By contrast, high values on this variable refer to structurally disimilar states.
As indicated in gure 2, if states
k
i
and
j
are connected to the same set of other states (l and
in this case) they score low in terms of structural equivalence measured based on Euclidean
distance between network tie portfolios which makes them more likely to be allies according to my
theoretical argument. By contrast, if
i had, for example, connections to n, o, and p their structural
equivalence would be low which according to my argument would make them less likely to form
an alliance. Again, I construct two structural equivalence measures for each dyad, one based on
12
alliance ties and one based on security IGO ties and IGO ties more generally.
If hypothses 3
and 4 are supported, I expect to nd negative coecients for both structural equivalence within
the alliance network and of structural equivalence in the security IGO network and IGO network
more generally because this would suggest that states that dier with respect to their network
tie portfolios are less likely to have a formal alliance. In addition, the inclusion of the structural
equivalence measure should reduce the eect of direct network ties.
Figure 2: Structural Equivalence
l
l
j
i
k
+
m
k
g
To control for structural eects endogenous to the alliance network in addition to triadic closure,
I include a statistic that measures node popularity (number of times where two states
an alliance with the same state
k ).
i and j
have
I include this dependency in the alliance variable in my TERGM
specication as a 2-star statistic. The 2-star statistic counts the number of 2-stars in the alliance
network and includes this count as a statistic in
two dierent nodes
k
such that the ties
δik
Γ.
A 2-star is dened as a node
exist for all
k.
number of times path of connections of length 4 occur (e.g., the dyads
ik
or
jl).
and a set of
In addition, to more accurately capture
complex relations, I include a 4-cycle network statistic in my models.
direct ties, but there are no indirect ties like
i
This statistic counts the
ij , jk , kl,
and
li
all have
This statistic provides an added layer
of complexity in addition to the GWESP measure. This allows me to measure complex network
connections beyond the triad.
I also include a range of controls in my models. Previous work has debated whether political
regime type has a positive, negative, or no eect on states' likelihood to form an alliance (Siverson
and Emmons, 1991; Simon and Gartzke, 1996; Lai and Reiter, 2000; Gibler and Scott, 2006).
Using Polity IV data (Jaggers and Gurr, 1995), I include the absolute dierence between two
states' regime scores in order to capture the eect of regime type on alliance formation.
In addition, I control for revealed preference similarity using data on United Nations General
Assembly roll-call votes Gartzke (1998). Including a measure of preference similarity is important
13
for my analysis because it allows me to examine how much informational added value direct and
indirect network ties have in addition to and beyond measures of preference similarity. If network
ties were simply a dierent way to capture preference similarity as it would be if one argued
that states form network ties in the international system largely with states they share preferences
with, then including my network variables in a model together with a preference similarity measure
should lead to statistically non-signicant network eects.
Finally, I also include geographic distance, distribution of military capabilities, and bilateral
trade volume as additional econometric controls.
Results
Figure 3 plots the structure of the international alliance network in 1960, 1970, 1980, and 1990.
We can see that at all four points in time the alliance network consisted of a few densely connected
clusters that are only sparsely linked with one another.
Interestingly, the number of bridges
between the clusters seems to have increased over time so that overall the network became more
integrated. Furthermore, we can also observe that over time more and more states formed formal
alliances with others and established network ties.
Accordingly, the number of isolates in the
network decreased over time. In the remainder of the paper, I use TERGMs in order to examine
what determines these structural patterns in the evolution of the international alliance network.
Table 1 and gure 4 present TERGM results for the 1950-1992 international alliance network.
In both models, the network constituted by all types of alliances that existed in a given year is
the dependent variable. We can see that in both model specications the GWESP parameter has
a positive sign and is statistically signicant. It has also a substantively large eect. This lends
support to hypothesis 1. Substantively this means that there is a strong tendency towards triadic
closure in the international alliance network. In other words, if two states,
alliance with state
C,
A and B ,
have both an
this makes them more likely to also have an alliance with each other. The
substantively large coecient suggests further that the tendency toward triadic closure is both
strong and widespread within the network. Judging by gure 3, it appears that the international
alliance network has indeed several densely connected clusters and the the number of states that
14
Figure 3: International Alliance Network, 1960-1990
Alliance Network 1960
Alliance Network 1970
Alliance Network 1980
Alliance Network 1990
Note: Network plotted using a version of the Fruchterman Reingold algorithm.
are part of these clusters has increased over time.
The eect of structural equivalence in the alliance network (TERGM 1) is both negative and
statistically signicant. Everything else being equal, states that have dierent portfolios of alliance
ties are less likely to form an alliance.
Conversely, states that are similar with respect to their
alliance tie portfolios are more likely to have an alliance. This supports the hypotheses that states
that have similar portfolios of ties in the alliance network are more likely to have an alliance
with each other.
Importantly, this eect exists, although the model controls for states' overall
preference similarity using anity scores based on countries' United Nations General Assembly
voting behavior. This suggests that the signaling of strategic interests and trustworthiness which
I propose is associated with structural equivalence is indeed plausible.
TERGM 2 in table 1 conrms the negative relationship between the dissimilarity of states'
portfolios of network ties and alliance formation, i.e.
structurally more similar states are more
likely to be allies, for the international network constituted by joined membership in security
IGOs. At the same time, the estimation results of TERGM 2 also indicate that conditioning on
structural similarity in the security IGO network and the other variables in the model, direct
15
Table 1: TERGM Results
TERGM 1
Edges
GWESP (0.5)
Four-Cycle
Two-Star
SE Alliance
0.33
[−0.59; 0.87]
1.01∗
[0.92; 1.06]
0.02∗
[0.01; 0.03]
0.12∗
[0.11; 0.14]
−0.99∗
[−1.04; −0.92]
Security IGO
SE Security IGO
Log Distance
Anity (UNGA)
Log Trade
Dierence Regime
Capability Ratio
∗
−0.70∗
[−0.75; −0.63]
0.53∗
[0.29; 0.78]
0.45∗
[0.42; 0.49]
−0.04∗
[−0.08; −0.02]
1.26∗
[1.06; 1.59]
TERGM 2
∗
1.63
[0.50; 2.44]
1.11∗
[1.05; 1.17]
0.04∗
[0.04; 0.05]
−0.07∗
[−0.08; −0.06]
−0.09
[−0.33; 0.20]
−0.04∗
[−0.06; −0.02]
−0.93∗
[−1.00; −0.85]
0.35∗
[0.15; 0.68]
0.39∗
[0.35; 0.42]
−0.09∗
[−0.13; −0.06]
0.85∗
[0.59; 1.13]
0 outside the condence interval. Condence intervals are based on 1,000 bootstrap iterations.
connections via security IGOs have no eect on the presence of an alliance that is distinguishable
from 0. Together, these results provide preliminary support for hypothesis 4 and no support for
hypothesis 2. However, they are in line with the expectation that strategic information received
through direct communication channels are less eective in shaping states' alliance behavior than
information inferred from signals about private information implied by states' overall pattern of
relationships to other states.
Moreover, we can also see that in addition to a strong tendency toward triadic closure, there
is a also tendency toward clustering beyond the level of the triad as indicated by the positive and
signicant four-cycle parameter. The sign of the eect of the two-star parameter is not consistent
across model specications. Finally, all control variables have the expected sign and are statistically
16
Figure 4: Point estimates and 95% condence intervals for TERGMs 1 and 2
Coefficients TERGM 1
Coefficients TERGM 2
●
Edges
●
Four−Cycle
●
●
Two−Star
●
GWESP (0.5)
●
GWESP (0.5)
Four−Cycles
●
Edges
Two−Star
●
Security IGO
●
●
SE Alliance
●
SE Security IGO
●
Log Distance
Log Distance ●
●
Affinity (UNGA)
●
Log Trade
●
Difference Regime
●
−1
0
●
Log Trade
●
●
Difference Regime
Capability Ratio
−2
Affinity (UNGA)
1
●
Capability Ratio
2
−1.0
Point Estimates with 95% CIs
−0.5
0.0
0.5
1.0
1.5
2.0
2.5
Point Estimates with 95% CIs
Note: 95% condence intervals computed based on results from models 1 and 2 in table 1. Point
estimates and condence intervals marked in blue refer to statistically insignicant eects.
signicant.
Overall preference similarity as captured by the anity variable makes states more
likely to be allies, as do high volumes of bilateral trade, and asymmetrically distributed military
power. Geographical distance between two countries as well as dierence in their domestic regime
type, by contrast, have a negative eect on the likelihood of two states being allies. This provides
further plausibility to these preliminary results.
An additional empirical implication of my theoretical argument about the signaling of strategic
information through portfolios of alliance and other cooperative ties in the internationa system is
that states should be better able to estimate which potential partners in the international system
are likely to be good allies for their purposes and which are not based on the information that is
contained in the linking behavior of their potential partner. In other words, they should be less
uncertain about with whom they should ally and with whom not. Statistically, one implication
of this is that the error variance of a model that captures states' alliance relationships should be
negatively inuenced by the structural similarity of the portfolios of relationships of states. For
the measure of structural similarity/dierence based on Euclidean distance this implies that larger
17
dissimilarity should have a positive eect on error variance, while smaller dissimilarity should have
a negative eect.
I test this additional empirical implication of my theoretical argument using a heteroscedasticity
probit model where I estimate the eect fo structural similarity on both the conditional mean of
the distribution of alliance ties and its variance. The results of this analysis are shown in table
2.
We can see that as in the TERGM analysis both structural similarity in the security IGO
network and in the alliance network have the expected negative and statistically signicant eect
on states' likelihood of being allies. Furthermore, we can also see that in both models the variance
is positively inuenced by the distance based measure of structural equivalence. Specically, higher
structural dissimilarity is associated with higher variance. This provides additional plausibility for
the information and signaling mechanism that I propose operates through the similarity of states'
portfolios of ties in international cooperative networks.
Figure 5: Predicted Error Variance Heteroscedasticity Probit Models
5
10
15
15
10
5
Predicted Error Variance Alliance Choice
4
3
2
0
0
5
Predicted Error Variance by SE Security IGO
1
Predicted Error Variance Alliance Choice
Predicted Error Variance by SE Alliance
0
SE Alliance
5
10
15
20
SE Security IGO
Note: 95% condence intervals computed based on results from hetprobit 1 and hetprobit 2.
Conclusions
I argue that state alliance choices are not merely a function of actor and dyad covariates, but
are also aected by interdependencies both within the alliance network and between the alliance
and other international cooperation networks. Using TERGM models, I nd rst support for the
18
Table 2: Heteroskedasticity Probit Regression Estimates
Hetprobit 1
Hetprobit 2
DV: alliance tie
−0.557∗∗∗
(0.00890)
SE Security IGO
−0.630∗∗∗
(0.00721)
SE Alliance
Anity (UNGA)
0.121∗∗∗
(0.0174)
0.360∗∗∗
(0.0240)
Log Trade
0.239∗∗∗
(0.00217)
0.463∗∗∗
(0.00419)
Capability Ratio
−0.0462
(0.0306)
0.245∗∗∗
(0.0433)
Log Distance
−0.826∗∗∗
(0.00541)
−0.663∗∗∗
(0.00807)
Dierence Regime
−0.0322∗∗∗
(0.00147)
−0.0403∗∗∗
(0.00206)
5.111∗∗∗
(0.0495)
4.371∗∗∗
(0.0717)
Constant
DV:
lnσ 2
0.140∗∗∗
(0.00167)
SE Security IGO
0.101∗∗∗
(0.00148)
SE Alliance
χ2
Observations
40752.1∗∗∗
281, 471
18729.5∗∗∗
281, 471
Standard errors in parentheses.
+
p < 0.10,
∗
p < 0.05,
∗∗
p < 0.01,
19
∗∗∗
p < 0.001
relevance of intra-network and inter-network interdependencies as drivers of state alliance behavior.
Importantly, I nd a consistently strong negative eect of structural equivalence in both the alliance
network and the security IGO network on the probability of alliances. I also nd that structural
dissimilarity in the alliance and security IGO networks is positively associated with variance in the
conditional distribution of alliances which suggests that the information contained in states' overall
linking behavior can indeed be used by other states to inform their choices of alliance partners.
This analysis adds an important dimension to the complexity of interdependencies at work in the
international alliance network that has so far been underexplored by students of alliances. Future
steps will include the analysis of the goodness of t of the models that have been estimated so far
as well as the inclusion of other international networks (e.g. diplomatic missions, preferential trade
agreements) as operationalization structural equivalence in international cooperation networks.
20
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