Audience Costs and the Dynamics of War
and Peace
Casey Crisman-Cox
Texas A & M University
Michael Gibilisco
California Institute of Technology
Abstract:
We estimate audience costs and examine their substantive effects on the evolution of interstate disputes by using
an infinitely repeated and dynamic game of crisis escalation. Unlike past efforts, our approach estimates country-specific
audience cost parameters without relying on proxy variables, such as democracy measures. Contrary to intuition, increases
in a country’s audience costs encourage it to initiate disputes in equilibrium because the costs serve as a commitment device
during the subsequent crisis, incentivizing the country to stand firm and coercing its opponent to back down. Nonetheless,
the results demonstrate that larger audience costs would resul
t in more peace worldwide, as they also discourage potential
opponents from initiating disputes. Beyond regime type, we find that a free press, provisions for executive appointment or
removal, and historical rivalries are also important determinants of audience costs.
Replication Materials:
The data, code, and any additional materials required to replicate all analyses in this arti-
cle are available on the
American Journal of Political Science
Dataverse within the Harvard Dataverse Network, at
https://doi.org/10.7910/DVN/XBNJD9.
A
udience costs—or the costs leaders pay from
backing down before their opponents in inter-
state disputes—are ubiquitous in international
relations. Scholars use them to explain a variety of phe-
nomena, including crisis bargaining, war duration, eco-
nomic sanctions, and the democratic peace. This promi-
nence has sparked two fervid debates: Do audience costs
exist, and how would we know? Specifically, the for-
mer question asks to what extent are leaders punished
for backing down (e.g., Snyder and Borghard 2011;
Tomz 2007), whereas the latter concerns the appropriate
methodology for answering such a question (e.g., Kur-
izaki and Whang 2015; Partell and Palmer 1999; Schultz
2001).
Two substantial impediments prevent progress in ei-
ther debate. First, since Fearon’s (1994a) canonical arti-
cle, researchers traditionally proxy audience costs using
democracy scales such as polity2, and these measures of-
ten determine case selection in qualitative studies and
independent variables in quantitative ones (Partell and
Palmer 1999; Snyder and Borghard 2011). Nonetheless,
Casey Crisman-Cox is Assistant Professor, Department of Political Science, Texas A&M University, 400 Bizzell Street, College Station, TX
77843 (c.crisman-cox@tamu.edu). Michael Gibilisco is Assistant Professor of Political Science, California Institute of Technology, 1200
East California Boulevard, Pasadena, CA 91125 (michael.gilbilisco@caltech.edu).
Thanks to Scott Abramson, Rob Carroll, Kevin Clarke, Allan Dafoe, Mark Fey, Tasos Kalandrakis, Brenton Kenkel, Bethany Lacina, Sergio
Montero, Jack Paine, and Curt Signorino for helpful comments and suggestions. Earlier versions of the article also benefited from audiences
at the 2015 SPSA meeting, the 2015 PolMeth conference, the 2015 EPSA meeting, the 2016 APSA meeting, and the University of Rochester.
analyzing the quality and strength of different proxies
has proven difficult (Levy 2012; Slantchev 2012). Schol-
ars have yet to directly test the hypothesis that democratic
or authoritarian institutions covary with audience costs
because we lack a sufficient model for their measurement
independent of regime-type proxies.
Second, the substantive effects of audience costs on
conflict initiation are unclear due to two countervailing
effects. On the one hand, a broad literature argues that in-
creases in audience costs may discourage a given country
from initiating disputes if the country expects its oppo-
nents to repeatedly stand firm in the future (Kurizaki and
Whang2015;Prins2003;Weeks2012).Ontheotherhand,
larger audience costs may also encourage their country to
initiate a dispute if they simultaneously coerce opponents
to more quickly back down in the subsequent interac-
tion (Schultz 1999). Thus, when countries internalize the
long-term strategies of their opponents, their unobserv-
able strategies create a time dependence between current
escalation decisions and the expected path of future con-
flict, confounding the relationship between audience cost
American Journal of Political Science
,
Vol. 62, No. 3, July 2018, Pp. 566–580
C
2018, Midwest Political Science Association
DOI: 10.1111/ajps.12347
566
AUDIENCE COSTS AND THE DYNAMICS OF WAR AND PEACE
567
measures and dispute initiation. Such dynamic consid-
erations also affect the propensity for countries to back
down. For example, a country may be willing to back
down and incur a relatively large audience cost in a dis-
pute today only if it expects tomorrow’s peace to be stable
over the long run. In contrast, it would be less willing to
incur those costs if the peace were merely transitory.
In this article, we address these issues head-on by
structurally estimating a dynamic game-theoretic model
of crisis escalation. As in Fearon (1994a), we model au-
dience costs as a parameter capturing the (dis)utility a
country receives when it backs down from a dispute be-
fore its opponent by using an explicit game form. The
game is infinitely repeated, and countries fully anticipate
the expected evolution of conflict and the possibility of
incurring audience costs in equilibrium. We estimate au-
dience costs using country-specific fixed effects, which do
not depend on a priori determined variables, and we se-
lect the audience costs (along with other parameters and
equilibria) that maximize the likelihood of the observed
data. Specifically, we fit the model to Militarized Inter-
state Dispute Incident Profiles (MID-IP) data that record
escalation decisions at the monthly level from 1993 to
2007 by using a new constrained maximum likelihood
estimator developed by Su and Judd (2012) for dynamic
models. Three major results emerge.
First, contrary to prevailing intuitions, we find that
the second countervailing effect of audience costs dom-
inates in the data. That is, increasing a given country’s
audience costs encourages it to initiate disputes along the
path of play, an effect that emerges in 81% of directed
dyads. In the estimated equilibria, audience costs serve
as a commitment device: They tie the hands of their re-
spective countries, thereby encouraging them to stand
firm and coercing their opponents to back down in dis-
putes. We find the hand-tying effect in 78% of directed
dyads, where increasing a country’s audience costs forces
it to stand firm more frequently. Likewise, the coercion
effect appears in 75% of directed dyads, where increasing
a country’s costs compels its opponent to concede more
often. Although the hand-tying and coercion effects are
well studied in the literature, the finding that enhanced
audience costs incentivize countries to initiate conflicts
runs counter to previous findings in reduced-form analy-
ses (Clark and Nordstrom 2005; Prins 2003; Weeks 2012).
While audience costs and conflict initiation are negatively
associated in some of our estimated equilibria, this trend
appears in only a small minority of directed dyads.
Second, we use the model to address a substantive
puzzle: Do higher audience costs lead to more or less con-
flict worldwide? On the one hand, increasing a country’s
audience costs incentivizes it to stand firm and initiate
disputes. On the other hand, audience costs also coerce
opponents to back down. The peace-enhancing effects
dominate in the data; in two-thirds of directed dyads,
larger costs reduce the long-run probability that the dyad
enters a dispute. In 80% of undirected dyads, an identi-
cal increase in both countries’ audience costs results in a
higher propensity for peace in the long run. One reason
for these results is that audience costs have a deterrent
effect on dispute initiation. Countries avoid beginning
conflicts with opponents with enhanced audience costs
and the credibility that the costs entail.
Finally, we test the hypothesis that standard prox-
ies for audience costs correlate with our estimates and
find that they are fair, but underwhelming, first approxi-
mations. Although democracy and authoritarian regime
types are important predictors, other systemic and do-
mestic factors influence audience costs. For example, the
existence of an interstate rival attenuates the penalties
leaders face for backing down in a dispute. Democra-
cies with rivals have, on average, audience costs that are
roughlysimilartoautocraticregimeswithlegalprovisions
for executive removal (e.g., China), suggesting that demo-
cratic voters may provide leaders with some leeway when
they escalate disputes with rivals. Additionally, a free press
can strongly increase audience costs, confirming results
derived from the formal model in Slantchev (2006).
Finally, while the analysis primarily contributes to de-
bates concerning audience costs, our rich framework pro-
duces additional implications for the wider international
relations literature. We find that trading partners and
joint democracies are less inclined to enter wars, whereas
no such aversion to crises exists. Thus, a liberal peace
may prevent more hostile conflicts, but not lower-level
disputes. In addition, our results provide mixed support
for the two systemic theories of conflict in Braumoeller
(2008). In peace, the expectation of conflict deters escala-
tion, but in crisis and war, it encourages or spirals further
escalation. Such nuances offer one explanation as to why
conflicts cluster temporally and peace is self-enforcing.
Modeling Audience Costs
and Disputes
Wefollowthelead ofFearon (1994a,582)and defineaudi-
ence costs as the (dis)utility a country receives from back-
ing down in an international dispute before its opponent.
In a similar vein, Slantchev (2012, 377) defines the first
core premise of audience cost theory as “backing down in
a crisis makes [a country] suffer costs in addition to those
arising from conceding the contests.” As discussed below,
568
CASEY CRISMAN-COX AND MICHAEL GIBILISCO
this definition is tractable and permits identification from
standard event data on interstate disputes.
Although our conceptualization of audience costs
holds a prominent place in the literature, it sidesteps
two theoretical explorations that have developed since
Fearon’s seminal work. In one development, scholars of-
ten interpret audience costs as the punishment leaders re-
ceive from initiating a threat but failing to follow through
on it.
1
In this setup, audience costs only affect countries’
payoffs when they initiate disputes (Kurizaki and Whang
2015; Schultz 1998, 1999). Several exceptions exist, how-
ever, as other theories require both initiators and targets
to receive costs for backing down (Fearon 1994b; Kurizaki
2007; Schultz 2001). This latter approach is appropriate
when “crisis diplomacy takes place before domestic audi-
ences on both sides” (Kurizaki 2007, 545).
In the second development, researchers have consid-
ered endogenous audience costs, allowing them to grow
over the dispute’s duration or be products of strategic
choices (Fearon 1994a; Leventoglu and Tarar 2005). Yet
previous empirical work, including both reduced-form
and structural approaches, treats audience costs as fixed
and not being subject to strategic choices. In this ar-
ticle, we adopt the simplified conceptualization, where
audience costs are country specific and do not depend
on the historical evolution of disputes. This helps sim-
plify already complicated estimation and counterfactual
exercises, thereby serving as a useful starting point to
a problem in which theory has traditionally outpaced
empirics.
In addition, our framework treats countries as long-
lived actors, deciding whether to engage in conflict given
their opponent’s expected actions not only today but also
tomorrow. Long-standing theories, historical accounts,
and common intuitions maintain that countries and na-
tional leaders are strategic and forward-looking. Thus,
long-term expectations influence whether countries in-
cur audience costs. In a crisis, a country may be more
likely to back down and incur an audience cost today if
it expects a stable peace to emerge subsequently. In this
case, a country trades an immediate (audience) cost for
a delayed benefit (peace). Conversely, it would be less
likely to back down when the benefits of peace are more
fleeting.
Finally, we remain agnostic about the particular
mechanisms generating audience costs, but we investi-
gate their determinants in a postestimation exercise. This
approach has several advantages. Most prominently, we
avoid introducing an avenue of omitted variable bias into
1
In experiments, audience costs refer to the disapproval leaders
create when they say one thing but do another (Tomz 2007).
the analysis, which is likely to arise because audience costs
originate from several highly correlated factors including
democratic institutions, voter repressiveness, leader re-
moval, national honor, among others (Chiozza and
Goemans 2011; Dafoe and Caughey 2016; Levy 2012;
Smith 1998).
2
Instead, we treat audience costs as a
country-specific parameter to be estimated. In a simi-
lar vein, this fixed-effects approach reduces the potential
for separation that may arise from modeling audience
costs as functions of highly collinear variables.
Because we adopt a structural approach, our en-
deavor is most similar to Kurizaki and Whang (2015),
and we build upon their work in four ways. First, they use
polity2 to proxy audience costs by assuming the costs are
a linear function of democracy; we impose no such as-
sumption. Second, the two theoretical models differ con-
siderably. Kurizaki and Whang (2015) use a version of the
one-shot crisis-signaling model with sequential moves
from Lewis and Schultz (2003), in which initiators only
incuraudiencecostsonce.Inthispaper,weconstructady-
namic model with simultaneous choices, where countries
are infinitely lived, accommodating the long-term costs
and benefits of backing-down and standing firm. Third, a
drawback from using the crisis-signaling model to study
interstate conflict is that the analysis almost certainly re-
quires a very specific data set from Schultz, Lewis, and
Zucco (2012), which covers the interwar period (1919–
39). In contrast, the dynamic model is more flexible with
its informational requirements, and we use the standard
MID-IP data set, covering a more contemporary period
(1993–2007). Finally, although the two models are quite
different, both may admit multiple equilibria under cer-
tain payoffs. Standard estimation techniques (e.g., Sig-
norino 1999) do not account for this multiplicity, leading
to inconsistent estimates and incorrect counterfactuals
(Jo 2011). Our estimation strategy and counterfactual
exercises, however, avoid these issues.
Structural Model
In this section, we construct a dynamic game of crisis
escalation. Because estimation is our goal, we include
action-specific shocks that are private information and
allow payoffs to depend on observed covariates. Consider
two countries. We use
i
to denote an arbitrary country
and
j
=
i
its opponent.
2
As a result, we cannot compare our audience cost estimates to their
substantive effects on leader approval identified in the experimental
literature (Levy et al. 2015; Tomz 2007).
AUDIENCE COSTS AND THE DYNAMICS OF WAR AND PEACE
569
Consider two countries. We use
i
to denote an ar-
bitrary country and
j
=
i
its opponent. Time is discrete
and indexed by
t
=
1
,
2
,...
.Ineachperiod
t
, country
i
first observes a common state variable
s
t
∈{
1
,
2
,
3
}
and
a private state variable
ε
t
i
, which represents private in-
formation, unknown to opponent
j
, that country
i
has
about the costs/benefits of taking particular actions in
period
t
.Thevariable
s
t
represents the current level of
hostility, where
s
t
=
1 denotes that the countries are in a
state of peace,
s
t
=
2 a state of crisis, and
s
t
=
3astateof
war.
3
Each country then simultaneously chooses a level of
hostility against its competitor. Let
a
t
i
∈{
1
,
2
,
3
}
denote
country
i
’s action in period
t
, and a profile of actions is
a
t
=
(
a
t
i
,
a
t
j
). Here,
a
t
i
takes the values 1, 2, and 3, which
indicate peaceful, crisis-level (threat/demand), and war-
level (attack/invasion) actions, respectively.
The common state variable
s
t
evolves according to
past actions, and we assume escalation is deterministic
and unilateral, that is,
s
t
=
max
{
a
t
−
1
i
,
a
t
−
1
j
}
.
4
Thus, the
model captures situations in which a country declares
war (
a
t
i
=
3) on its opponent, and the next period be-
gins with the two countries in a state of war (
s
t
+
1
i
=
3).
We denote country’s
i
’s private information about the
cost of action
a
i
in period
t
as
ε
t
i
(
a
t
i
)
∈
R
.Theprivate
information,
ε
t
i
(
a
t
i
), is an independently and identically
distributed Type 1 extreme value across actions, players,
and states, which are standard distribution and indepen-
dence assumptions in these types of games.
Let
denote a vector of relevant structural parame-
ters to be estimated. Country
i
’s per-period payoff against
country
j
is given as
u
ij
(
a
t
,
s
t
;
)
+
ε
t
i
(
a
t
i
), where
u
ij
is
i
’s
deterministic utility and
ε
i
is
i
’s (stochastic) private infor-
mation. Given a sequence of action profiles, states, and
action-specific shocks
{
(
a
t
,
s
t
,
ε
t
i
)
}
∞
t
=
1
, country
i
’s total
payoff is the discounted sum of per-period utilities:
∞
∑
t
=
1
t
−
1
[
u
ij
(
a
t
,
s
t
;
)
+
ε
t
i
(
a
t
i
)]
,
where
∈
[0
,
1) denotes a common discount factor.
5
3
Hereafter, a
state
denotes the commonly observed level of hostility
s
t
, and we refer to the game’s actors as countries. We use the terms
dispute
and
conflict
interchangeably to refer to periods in which the
path of play resides in states 2 and 3.
4
Unilateral escalation is common in the crisis and conflict literature
(Fearon 1994a; Kurizaki and Whang 2015; Schultz 2001).
5
Notice we do not include
in the parameters to be estimated.
Without additional structure, it is difficult to identify
in these
types of models, and previous articles have traditionally assumed
a fixed discount factor throughout (Arcidiacono et al. 2016; Pakes,
Ostrovsky, and Berry 2007). Here, we fix
=
0
.
9.
We endow
u
ij
with the following functional form:
u
ij
(
a
,
s
;
)
=
x
ij
·
(
s
)
︸
︷︷
︸
state
-
specific
payoff
+
z
i
·
(
a
i
)
︸
︷︷
︸
action
-
specific
payoff
+
i
I
[
a
j
≥
s
>
a
i
]
︸
︷︷
︸
country
-
specific
audience cost
+
(
s
)
I
[
a
i
>
1]
I
[
a
j
>
1]
.
︸
︷︷
︸
spiral
/
deterrence
effect
(1)
Country
i
’s utility consists of four components. First,
it receives a state-specific payoff,
x
ij
·
(
s
), from being in
state
s
with country
j
,where
x
ij
is a vector of dyad-
specific variables and
(
s
) is a vector of associated co-
efficients. Dyadic variables could be directed (e.g., mil-
itary capability ratios) or undirected (e.g., minimum
democracy).
6
Second, regardless of the state, if country
i
chooses
action
a
i
,
i
pays some costs
z
i
·
(
a
i
), where
z
i
is a vec-
tor of country-specific variables and
(
a
i
) is a vector of
associated coefficients.
7
These costs of escalation capture
important transaction costs from declaring war, formally
threatening a opponent, or maneuvering military troops
to a border area.
8
Notice that
i
’s cost of action
a
i
does
not depend on characteristics of
j
. This independence is
an important identification assumption, but paired with
the state-specific payoff, this leads to a natural interpreta-
tion: Although the United States pays the same cost from
declaring war on Afghanistan and on Russia, it can still
possess a preference for being at war with Afghanistan
over being at war with Russia. We adopt the normaliza-
tion that
(1)
=
(1)
=
0; that is, the payoffs
x
ij
·
(
s
)
and
z
i
·
(
a
i
) are relative to the baseline payoffs for the
peaceful state and action, respectively.
The last two components in a country’s utility func-
tiondependontheactionsofitsopponent.Theparameter
i
is a country-specific value and measures
i
’s audience
costs. That is, if
i
and
j
are engaged in a dispute (
s
>
1),
j
continuesorescalatesthecurrentlevelofconflict(
a
j
≥
s
)
6
The payoff
x
ij
·
(
s
) may represent country
i
’s expected utility
from some lottery as the outcome does not affect payoffs or transi-
tions. In the war lottery where
p
ij
represents a probability of victory,
ij
the benefit of winning, and
c
ij
the cost of war, the war-state pay-
off takes the form
x
ij
·
(3)
=
p
ij
ij
−
c
ij
.
7
Although we operationalize the costs of the crisis- and war-level
actions in a similar manner, the model incorporates the possibility
that these actions entail more substantive differences. The two
actions transition the game to strategically different states, and they
generally produce diverging propensities for incurring audience
costs. This setup is rich enough to uncover empirical differences
once the model is taken to data.
8
This may appear to be a nonstandard modeling choice because
these costs of escalation are not considered in previous models, but
this version subsumes the case in which the coefficients
(
a
i
)are
zero.
570
CASEY CRISMAN-COX AND MICHAEL GIBILISCO
and
i
backsdown(
a
i
<
s
); then
i
incurs cost
i
. Intu-
itively, this means that countries never acquire audience
costs when in peace or if their opponents do not esca-
late/maintain the current conflict. Essentially, countries
receive audience costs when they de-escalate the dispute
before their rival, although size of the audience costs is
fixed throughout the dispute.
9
The
(
s
) parameters are
state-specific values measuring how
i
’s cost of escalation
varies with
j
’s actions in state
s
.When
(
s
)
>
0,
i
’s cost
of escalation (
a
i
>
1) decreases when
j
escalatesinstate
s
.
Similarly, when
(
s
)
<
0,
i
’s cost of escalation increases
when
j
escalates. Thus,
(
s
) represents other strategic
incentives as to why a country does not escalate a con-
flict independently of audience costs, including potential
second-strike (dis)advantages. For example, if
i
receives
alargebenefitinstate
s
when its opponents attack first
(e.g., support from an international community), then
(
s
) would be negative.
We characterize Bayesian-Nash equilibria in station-
ary Markovian strategies (equilibria, hereafter) as is stan-
dard in these games. Consider
i
’s net-of-shock expected
utilityfromchoosingaction
a
i
instate
s
,denoted
v
i
(
a
i
,
s
),
and let
v
i
denote the vector of expected utilities for coun-
try
i
. Because
ε
i
is a distributed Type 1 extreme value,
i
chooses
a
i
in state
s
with probability
P
(
a
i
,
s
;
v
i
)
=
exp(
v
i
(
a
i
,
s
))
∑
a
i
exp(
v
i
(
a
i
,
s
))
,
(2)
that is, equilibrium choice probabilities take the stan-
dard multinomial logit form. As in Signorino (1999),
the expected utilities,
v
i
, are endogenous to equilib-
rium play. Unlike most previous work, a closed-form
solution for these values does not exist due to the
game’s infinite horizon and simultaneous moves. In Ap-
pendix A in the supporting information (SI), we demon-
strate that profile
v
=
(
v
i
,v
j
) is an equilibrium if and
only if it satisfies a system of 18 smooth equations,
(
v
;
)
=
v
.
InAppendixBintheSI,weanalyzeanequilibriumfor
specific parameter settings to better illustrate the model’s
dynamics. A novel comparative static emerges: increasing
a country’s audience cost increases the probability that
the given country initiates a dispute along the path of
play. Schultz (1999) finds a similar result with a one-shot
signaling game, but our result does not require signaling
9
We could alter the model so that only initiators incur audience
costs by expanding the state space, where there are four dispute
states including crisis initiated by
i
and war initiated by
i
. Such
an extension involves estimating an additional 2,148 parameters
describing equilibrium play. Instead, we allow both countries to
incur audience costs in disputes, as in Fearon (1994a), Kurizaki
(2007), and Schultz (2001).
incentivesandarisesinasettingwherebothcountriesmay
incur audience costs. In the subsequent sections, we the fit
the model to data and examine whether this relationship
holds given our estimated equilibria.
Empirical Strategy
Constrained Maximum Likelihood
We estimate the model using a full information con-
strained maximum likelihood estimator (CMLE), as
advocated by Su and Judd (2012). Given our applica-
tion, this estimator has significant advantages over other
methods (Aguirregabiria and Mira 2007; Hotz and Miller
1993; Rust 1987). The procedure does not repeatedly
compute equilibria, a process that is further complicated
by the possibility of multiple equilibria. In addition, it
does not require consistent first-stages estimates of equi-
librium choice probabilities, which is particularly im-
portant for the rare-event nature of interstate disputes.
Finally, the CMLE avoids convergence issues that arise
when iterating two-step approaches (Egesdal, Lai, and
Su 2013).
10
We consider
D
dyads or games as described above.
We index dyads by
k
∈{
1
,...,
D
}
and include the super-
script
k
hereafter. We use data that can be summarized as a
list
{
X
,
Z
,
Y
}
.Here,
X
and
Z
arematricesofordered-dyad
and country-specific variables, respectively, which enter
the stage utilities through Equation (1). In addition,
Y
is
a collection of matrices detailing observed state and ac-
tion profiles for each dyad, that is,
Y
k
=
(
s
kt
,
a
kt
i
k
,
a
kt
j
k
)
T
t
=
1
,
and
T
is the total number of observed time periods. Let
̄
denote the true vector of parameters. For each dyad
k
, we assume the data
Y
k
were generated from a
single
equilibrium,
̄
v
k
,thatis,
k
(
̄
v
k
;
̄
)
=
̄
v
k
. While multiple
equilibria potentially exist in the game between the coun-
tries
i
k
and
j
k
, the procedure requires that
Y
k
comes from
only one of these. Let
v
=
(
v
1
,...,v
D
)denotethevec-
tor of all profiles of expected utilities. The log-likelihood
takes the following form:
L
(
v
|
Y
)
=
D
∑
k
=
1
T
∑
t
=
1
[
log
P
(
a
kt
i
k
,
s
kt
;
v
k
i
k
)
+
log
P
(
a
kt
j
k
,
s
kt
;
v
k
j
k
)]
,
(3)
10
One drawback of the CMLE is that the procedure requires
solving a constrained optimization problem, which may be dif-
ficult to implement using standard statistical software. Su and
Judd (2012) describe how researchers can use open-sourced, in-
dustrial software instead. Appendix C in the SI describes our
implementation.
AUDIENCE COSTS AND THE DYNAMICS OF WAR AND PEACE
571
which is a standard multinomial log-likelihood summed
over dyads, time periods, and players. With a slight abuse
of notation, the CMLEs, (
ˆ
v
;
ˆ
), solve the following con-
strained optimization problem:
max
(
v
;
)
1
T
L
(
v
|
Y
)
subject to
k
(
v
k
;
|
X
,
Z
)
=
v
k
,
k
=
1
,...,
D
.
(4)
Standard results on Lagrange multiplier tests, found
in Silvey (1959), guarantee that the CMLE is consis-
tent in
T
and characterize the estimator’s asymptotic
distribution. Consistency in the number of games or
dyads is not guaranteed, as there is an obvious incidental
parameters problem, where an additional dyad requires
estimating 18 new equilibrium constraint parameters.
We still gain leverage by pooling information across
dyads when
T
is sufficiently large, however. We relegate
further estimation details to Appendix C in the SI, and
Appendix D contains a Monte Carlo illustrating the
properties of the CMLE on data sets of similar size to the
one we construct in this article.
Data
We use the MIDs incident-level data known as MID-IP
4.01 (Kenwick et al. 2013) to define each dyad’s observed
path of play,
Y
k
. The data record actions taken by the
individual countries within interstate disputes between
1993 and 2010. These actions are then used to create
the state transitions. Dispute numbers determine which
country or countries the actions were taken against. In
our framework, a time period is a calender month because
approximately 50% of incident reports include no more
precise timing information. The actions recorded by the
MID-IP are on the standard 22-point MID scale, ranging
from no action to joining an interstate war. We use this
scale to form the three levels of hostility countries can take
against each other: war, crisis, and peace. We code a “war-
level” action if country
i
attacks or takes a more hostile
action against country
j
in period
t
(MID-IP actions
16–21). A “crisis-level” action is recorded if the country
commits an action that is between a threat and an attack
(MID-IP actions 1–15).
We follow Whang, McLean, and Kuberski (2013) and
construct the data set in two steps. First, to avoid selec-
tion bias, we fill in peaceful actions for all country-dyad-
months in which the MID-IP database does not include a
military incident (Huth and Allee 2002). Second, we de-
fine a set of “politically relevant dyads” that restricts the
sample to every dyad that has entered the MID-IP data.
Ultimately, the data contain 179 dyads with 180 time
T
ABLE
1 Distribution of Transitions in the Data
Transition
Percent of Data
Percent within
Each State
Peace
→
Peace
92.5
97.0
Peace
→
Crisis
1.82
1.91
Peace
→
War
1.09
1.14
Crisis
→
Peace
1.81
71.8
Crisis
→
Crisis
0.49
19.6
Crisis
→
War
0.22
8.62
War
→
Peace
1.09
53.6
War
→
Crisis
0.21
10.2
War
→
War
0.74
36.2
Note
: The middle column displays the probability distribution over
the possible transitions, and the rightmost column presents the
conditional distribution in each state.
periods each; approximately 95.4% of observed states are
peace, and 97% of actions are peace-level actions. Table 1
records the nine different types of possible transitions
and provides preliminary evidence that countries condi-
tion their behavior on the state variable of interest. That
is, the conditional distribution of transitions changes sub-
stantially across the observed states.
The model gains leverage on estimating audience
costs through two observable moments: the probability
with which a country (a) initiates disputes in peace and
(b) backs down within a dispute. To see this, hypothet-
ically fix the strategies of the two actors in all periods
such that they place positive probability on every action
in every state. Then increasing
i
’s audience costs (i.e.,
i
moves to
−∞
) has two important effects. First,
i
’s ex-
pected utility of initiating conflict (
a
i
>
1) once in peace
(
s
=
1) decreases because initiation certainly transitions
the game into a state in which
i
receives an audience cost
with a fixed probability. Second,
i
’s expected utility of
playing the peace action (
a
i
=
1) in a dispute (
s
>
1) will
change as well, but the direction of this change will de-
pend on
j
’s strategy. If
j
stands firm with a sufficiently
large probability, then
i
’s utility of playing peace will de-
crease as it expects to subsequently incur audience costs.
In contrast, if
j
is likely to play the peaceful action, then
i
’s utility of playing peace may increase, as
i
would prefer
to de-escalate the dispute, transitioning to a peaceful state
without audience costs.
These dynamics have two important implications.
First, we cannot identify a country’s audience cost pa-
rameter if it has never been in a dispute with another
country in the data, although we do not require that it
initiate or back down in a dispute. Including such a coun-
try (e.g., Costa Rica) would lead to separation because
572
CASEY CRISMAN-COX AND MICHAEL GIBILISCO
its contribution to the likelihood function will be strictly
increasing as its audience cost parameters become more
negative.
11
Second and more importantly, the above dis-
cussionhighlightstheimportanceofequilibriumanalysis.
Essentially, the discussion fixes the strategies of both play-
ers, thereby ignoring the indirect effects of audience costs
that will change
j
’s equilibrium strategy and therefore
i
’s expected utility calculations as well. As we demon-
strate below, the estimated equilibria can and oftentimes
produce comparative statics that diverge from the naive
predictions in the previous paragraph.
To isolate the effects of audience costs, we also con-
trol for other reasons why countries initiate a dispute
or back down. First, we control for the possibility of
second-strike (dis)advantages or a general preference for
peaceful actions and states. The former are controlled
for by the parameters
(
s
), whereas the latter are cap-
tured by including constants in
x
ij
and
z
i
. In addition,
we include other control variables common to the inter-
state conflict literature. At the dyadic level, we use the
minimum democracy level in the dyad, the logged ca-
pability ratio, and the square root of the trade interde-
pendence. We measure the minimum level of democracy
using the standard Polity IV database. Capability ratios
are computed as the ratio of CINC scores from the Cor-
relates of War (COW) National Material Capabilities 3.0
(NMC) dataset (Singer, Bremer, and Stuckey 1972). Trade
interdependence is measured in the usual fashion
(Gartzke 1998; Oneal and Russett 1997), where country
i
’s interdependence on country
j
is the sum of exports
and imports between
i
and
j
divided by
i
’s gross domestic
product (GDP). Trade data come from the COW dyadic
trade data (Barbieri, Keshk, and Pollins 2009), supple-
mented by data from Gleditsch (2002). GDP data are
from the Penn World Table (PWT) 8.0 (Feenstra, Inklaar,
and Timmer n.d.) and supplemented with data from the
World Bank and the United Nations. For the variables
associated with country-specific costs, we include logged
GDP per capita (from PWT) and logged military person-
nel per capita (from NMC).
We take the mean values over the course of the time
period in the study (1993–2007) to produce values in
x
ij
and
z
i
. While there is a legitimate concern that some of
these measures are endogenous to the conflict process
itself, the variables in the analysis show little change over
the time frame considered here. Even when these variables
do change, there is no correlation between these changes
11
In a similar vein, countries that only enter one dyad and one crisis
within that dyad (e.g., Ghana with South Africa) tend to have larger
standard errors associated with their audience costs.
and the observed states and actions. See Appendix E in
the SI for more details.
Audience Costs
Figure 1 presents the estimated country-specific audi-
ence costs and their 95% confidence intervals, sorted by
magnitude.
12
Even though the parameters
i
can take on
any value in estimation, all estimates are negative, sug-
gesting that leaders are punished for backing down. The
countries with the 10 largest (most negative) audience
costs are mostly democracies, but notable exceptions exist
to the idea that democracy and audience costs are synony-
mous. Many autocracies and anocracies exhibit substan-
tial audience costs (e.g., Turkmenistan and Belarus). This
offers some prima facie evidence in favor of arguments
suggesting that autocrats in weak states with real removal
threats face large audience costs. Despite this, preliminary
difference-in-means tests indicate that democracies have
larger audience costs than both autocracies and anocra-
cies (p
<.
05), but a test finds no difference between the
latter two groups.
Although democracies have larger audience costs
than autocracies on average, several exceptions to this
trend are involved in historically salient and persistent
conflicts. For example, North and South Korea have sim-
ilar audience costs, as South Korea’s audience costs are
verymoderate(lessnegative)comparedtootheradvanced
democracies. One reason for this is that South Korea ex-
ists in a state of perpetual siege, suggesting that voters are
more willing to give their leader free range to do whatever
she thinks is best to avoid a costly war.
13
A similar story
explains why Israel and India both have moderate—for
democracies—audience costs.
Finally, comparing across autocratic institutions, the
audience cost parameters vary in expected ways. We an-
alyze the degree to which our estimated audience costs
match the theoretical predictions regarding autocratic
regime types in Weeks (2008, 2012).
14
In the case of
12
Point estimates in table format can be found in Appendix F in
the SI.
13
Other explanations for South Korea’s moderate audience costs
includeitsdependenceonU.S.militarysupportandlackofwartime
operational control. The trend of smaller audience costs among
democracies with rivals holds more generally, however. Audience
costs and the number of rivals, as defined in Thompson and Dreyer
(2012), have a correlation coefficient of 0.34 among democracies,
which is significant at the p
<.
01 level.
14
Although only the former deals explicitly with audience costs,
both generate predictions about the political costs leaders face from
domestic audiences.
AUDIENCE COSTS AND THE DYNAMICS OF WAR AND PEACE
573
F
IGURE
1 Country-Specific Audience Costs, Labeled with
Three-Letter COW Codes
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
NAM
MON
EGY
VEN
BUI
MAA
SIN
RUS
BEL
UKG
SAL
GUY
PNG
POR
ZAM
INS
NTH
SLV
NIC
CAN
BHU
USA
PHI
ANG
KYR
HAI
SPN
HUN
LBR
COS
LIB
BOT
BLR
TAZ
RWA
FRN
ALG
ITA
SIE
GHA
GAM
CON
ARG
MLI
TOG
NIR
DEN
TKM
SWA
IVO
PER
LES
ECU
BRA
GUI
COL
SOM
SEN
HON
SUR
NOR
DOM
CYP
−40
−20
0
20
Audience Cost
Country
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
NEP
BNG
NIG
CAM
LEB
BEN
AZE
ARM
PAK
IND
CAO
DJI
SAU
SYR
MYA
YEM
IRQ
AFG
ALB
GRC
ERI
TUR
PRK
THI
ROK
BOS
VIE
GRG
ISR
JPN
BUL
LAT
QAT
POL
JOR
YGS
ZAI
CRO
CHL
SAF
RUM
TAJ
IRN
UKR
UGA
ZIM
KUW
SUD
MZM
CUB
LIT
ETH
MAL
UZB
MOR
MLD
CEN
CHA
CHN
KEN
AUL
GMY
−40
−20
0
20
Audience Cost
574
CASEY CRISMAN-COX AND MICHAEL GIBILISCO
T
ABLE
2 Marginal Effects of Audience Costs
across Dyads
Marginal Effect of
i
→−∞
↑
Pr(
i
Backs Down)
22%
↑
Pr(
j
Backs Down)
75%
↑
Pr(
i
Initiates)
81%
↑
Pr(
j
Initiates)
16%
↑
Pr(Peace)
65%
Note
: Percentages denote the proportion of directed dyads where
increases in audience costs (toward
−∞
) increase the probability
of backing down, the probability of initiating conflict, and the long-
term probability of peace. The probabilities, and their associated
derivatives, are formally defined in Appendix B in the SI.
Weeks (2008), we consider personalist, single-party, and
military autocracies, and from Weeks (2012), we con-
sider machine, junta, boss, and strongman. In both cases,
democracies are the excluded category. We uncover the
trends she hypothesizes in Table 8 in Appendix G in the
SI, where personalist and boss leaders have smaller (closer
to
+∞
) audience costs than democracies. Furthermore,
machines tend to have more intense audience costs than
democracies, but the difference is not significant at con-
ventional levels.
TheEffectsofAudienceCosts
What are the substantive effects of audience costs on the
evolution of interstate conflicts? We consider how changes
in audience costs affect countries’ propensity to (a) ini-
tiate disputes and (b) back down and receive audience
costs along the path of play. For each dyad, we com-
pute the marginal effect of making audience costs more
negative on each actor’s equilibrium probability of back-
ing down and initiating a conflict. We aggregate trends
across individual dyads rather than constructing an “av-
erage” dyad because there is no information concerning
what equilibrium such a dyad would play. Our exercise
is theoretical. It describes how the estimated equilibria
change as functions of audience costs rather than cor-
relating our audience cost estimates with the observed
equilibrium choice probabilities in a reduced-form anal-
ysis. As discussed above, the latter approach produces
misleading substantive effects, as it ignores the indirect
effects of audience costs through countries’ equilibrium
strategies.
Table 2 reports the percentage of directed dyads where
the marginal effect of more intense (negative) audience
costs on the indicated probability is positive. First, con-
sider their effects on a country’s likelihood of backing
down and receiving an audience cost. In 78% of directed
dyads, larger audience costs for country
i
decrease the fre-
quency
i
backs down along the equilibrium path of play.
This illustrates the hand-tying effect of audience costs,
where a country is less likely to concede a dispute as its
audiencecostsincrease.Likewise,largeraudiencecostsfor
country
i
increase the probability its opponent
j
backs
down along the path of play in 75% of directed dyads.
This is an indirect effect of audience costs through
j
’s
strategy, matching the coercive effects discussed in pre-
vious work (Fearon 1994a; Kurizaki and Whang 2015;
Partell and Palmer 1999; Uzonyi, Souva, and Golder
2012).
Next,weexaminetheeffectsofaudiencecostsoncon-
flict initiation. Counter to intuition, larger audience costs
embolden leaders into initiating disputes with greater fre-
quency. In 81% of directed dyads, as
i
’s audience costs
increase,
i
is more likely to initiate a dispute along the
path of play,
despite
the possibility that
i
might pay these
larger costs later. This finding runs counter to arguments
and empirics in other work, where authors find that larger
audience costs temper the propensity for countries to risk
conflict (Clark and Nordstrom 2005; Kurizaki and Whang
2015; Prins 2003; Schultz 1998; Weeks 2012).
15
Nonethe-
less, it provides the first empirical support for Schultz’s
(1999) prediction that increased audience costs result in
more crisis onsets. In some directed dyads, we find that
larger audience costs lead their respective countries to
initiate less, but this effect is not prominent, arising in
only 19% of observations.
The emboldening effect arises from credible com-
mitments. Essentially, when country
i
has larger audi-
ence costs, it is more likely to commit to standing firm
in the subsequent dispute, as in the hand-tying effect de-
scribed above. Furthermore, these larger audience costs
coerce
i
’s opponents to back down, as in the coercive ef-
fect described above. Countries internalize these advan-
tages when deciding whether to initiate disputes. Because
higher audience costs commit their respective countries
to stand firm and coerce their rivals to back down, they
also encourage countries to initiate disputes, as leaders at-
tempt to exploit their enhanced credibility by becoming
more aggressive.
Conversely, in 84% of dyads,
j
becomeslesslikely
to initiate disputes as
i
’s audience costs increase. This
effect arises for the same credibility concerns described
above. When
i
has larger audience costs, country
j
knows
that its opponent will more easily stand firm during
15
Previous work covering the 1993–2007 time frame uses standard,
reduced form regressions. Although Kurizaki and Whang (2015)
adopt a structural approach, they use data from 1919–1939.
AUDIENCE COSTS AND THE DYNAMICS OF WAR AND PEACE
575
T
ABLE
3 Correlates of Audience Costs
Spearman’s
t
p-value
(one-sided)
Polity2
−
0.18
−
2.04
.02
W
−
0.13
−
1.49
.07
Free Press
−
0.13
−
1.43
.08
Elected Executive
−
0.20
−
2.29
.01
Executive Removal
−
0.14
−
1.51
.07
Executive Constraints
−
0.09
−
1.04
.15
Rivalry
0.32
3.78
.00
USG’s ACC
−
0.25
−
2.34
.01
disputes, and, as a result,
j
is relatively disadvantaged
and will be more likely to concede. Thus,
j
avoids this
relative weakness by initiating less; that is, increasing
i
’s audience costs deters opponent
j
’s beginning new
disputes.
These results motivate a substantive question: Are
larger audience costs beneficial for peace? On the one
hand, raising a country’s audience costs encourages it to
initiate conflicts and stand firm in disputes. On the other
hand, larger costs also encourage opponents to back down
and not initiate new disputes. We calculate the marginal
effect of making audience costs more negative on each di-
rected dyad’s probability of peace in the long run.
16
Sim-
ple tallying demonstrates that in 65% of directed dyads,
increasing an actor’s audience cost results in more peace.
Specifically, in 38% of dyads, increasing either country’s
audience costs makes both sides more peaceful, whereas
both sides becomes more conflictual in only 8%. In the
remaining 54%, the effects are mixed. When we sum the
marginal effects of increasing both actors’ audience costs,
we find that in 80% of undirected dyads, the total effect is
an increase in peace. This analysis demonstrates that the
dominanteffectofaudiencecostsistheirdeterrencevalue:
Countries tend not to initiate disputes against countries
with higher audience costs, leading to more peace in the
long run.
The Correlates of Audience Costs
We explore the best proxies for audience costs by first
considering how well standard proxies associate with
the estimates in Figure 1. Table 3 reports the relevant
correlation coefficients. In particular, we consider a
16
Thelong-runprobabilityofpeacecomesfromthedyad’sinvariant
(stationary) distribution. We describe this in Appendix B in the SI.
In Appendix K, we provide evidence that equilibrium play has
converged to its invariant distributions in most dyads.
country’s polity2 score, Bueno de Mesquita and col-
leagues’ (2005) W, a dummy for free press from Freedom
House (Karlekar and Dunham 2012) and supplemented
by Li (2005), whether the executive is directly elected
(Regan, Frank, and Clark 2009), whether constitutional
provisions exist for executive removal (Regan, Frank, and
Clark 2009), a measure of executive constraints from the
polity2 data, the number of interstate rivals the country
has (Thompson and Dreyer 2012),
17
and a past proxy for
audience costs from Uzonyi, Souva, and Golder (2012),
which they call “audience cost capacity” (ACC).
The simple bivariate relationships suggest that many
of the standard proxies do a fair, but unimpressive, job
of capturing audience costs. The democracy-based prox-
ies are all significant and correlate in the expected di-
rection. Because Kurizaki and Whang’s (2015) audience
cost measures are a linear function of polity2 scores, im-
puting audience costs using their coefficient estimates
with polity2 scores from our data (i.e., mean polity2 from
1993 to 2007) will produce a correlation coefficient (0.18)
identical in magnitude to that of polity2 in Table 3. Fur-
thermore, the relationship between a free press and the
strength of audience costs matches the theoretical predi-
cations in Slantchev (2006). These relationships, however,
raise important questions about the appropriateness of
using any one variable to stand in for audience costs in
empirical work.
To analyze potentially more intricate relationships
between these proxies and audience costs, we consider
a regression tree. We include all the variables from
Table 3, except for executive constraints and ACC, which
are removed because they are composed of polity2 com-
ponents. Additionally, we add dummies for various types
of democratic electoral systems from Regan, Frank, and
Clark (2009). The output of the regression tree is shown
in Figure 2; values at each terminal node refer to the
average audience cost among classified countries and the
percentage of observations at the node.
According to this method, the best predictor of large
audience costs is whether a country has a polity2 score
greaterthanorequalto
−
4.
18
Amongautocracies,those
that do not have any institutions for executive removal
are the countries with the lowest audience costs. That is,
the truest of autocrats have an average audience cost of
17
Thompson and Dreyer (2012, 11) identify interstate rivals by
“avoid[ing] the conflict record and focus[ing] on who state decision
makers (or their historians) say are or have been their competitive
and threatening enemies.”
18
This is similar to Kurizaki and Whang (2015), who find that a
−
5
polity2 score is an important cutoff. In their case, it is the cutpoint
for whether audience costs exist. Here, it is the cutpoint that best
predicts high versus low audience costs.
576
CASEY CRISMAN-COX AND MICHAEL GIBILISCO
F
IGURE
2 Regression-Tree Predictors
of Audience Costs
Polity2
≥−
4
Any Rivals?
Executive Removal?
−
14
46%
Elected Executive?
−
17
21%
Free Press?
−
17
6%
−
11
4%
−
12
15%
−
8
.
1
9%
Yes
No
−
8 and include Saudi Arabia and Swaziland. In contrast,
those with legal provisions for executive removal (e.g.,
China and Vietnam) have larger costs, with an average
of
−
12.
Looking at democracies and anocracies (i.e., those
with a polity score above
−
4), the next most important
predictor—before any other domestic institution—is the
existence of an interstate rival. Countries in this group
include many powerful states, such as the United States
and Russia, as well as minor powers, such as Iran and
India. Thus, while democratic institutions are generally
associated with larger audience costs, having a rival atten-
uates their magnitude.
Countries with polity2 scores larger than
−
4but
without an interstate rival are split based on whether the
chief executive is directly elected. In countries where there
are direct elections, leaders face large costs, with an av-
erage of
−
17, which is substantial compared to the other
groups in the regression tree. Countries in this category
include a grab bag of strong and weak democracies, such
as France and Brazil. Notice that in countries without
direct elections of the executive, the existence of a free
press has the same effect as direct election; that is, a free
press can generate relatively large audience costs, again
confirming a result from the formal model in Slantchev
(2006). Countries at this node are mostly parliamentary
democracies.
The final node on the tree considers non-autocratic
countries without rivals, a directly elected executive, or a
free press. These countries tend to be weak democracies
and anocracies, such as Indonesia and Cambodia. Audi-
encecostsintheseregimesarethelowestonthishalfof
the regression tree, indicating the importance of domestic
F
IGURE
3 Audience Costs and Long-Run Peace:
North and South Korea
−12
−11
−10
−12
−11
−10
0.88
0.90
0.92
North Korea AC
South Korea AC
Pr(Peace)
institutions, besides democracy levels, to constrain lead-
ers. When non-autocratic regimes neither directly elect
their chief executive nor have a free press, then they have
audience costs comparable to those with autocrats. For
example, Bangladesh with a polity score of 6 (until 2007)
has an audience cost of
−
1.9, rivaling the least constrained
of autocrats.
Illustrative Examples
To illustrate these findings, we examine two salient con-
flictsingreaterdetail.First,weconsidersubstantiveeffects
from the North and South Korea dyad. Figure 3 graphs the
predicted probability of peace along the equilibrium path
of play as a function of each player’s audience cost.
19
The
graph illustrates the pacifying effects of audience costs. As
both costs become more severe (move toward
−∞
), the
likelihood of peace in the long run increases. A roughly
two-unit change in both cost parameters produces an
19
Multiple equilibria exist in each dyad, which complicates coun-
terfactual experiments. Thus, we cannot just vary the parameters,
compute a new equilibrium, and compare choice probabilities un-
der the old and new parameter values. Doing so would not guaran-
tee that the new equilibrium bears any resemblance to the estimated
one. To address this problem, we use a method from Aguirregabiria
(2012) that maps equilibria as locally continuous functions of data
or parameters. Appendix H in the SI contains more details.
AUDIENCE COSTS AND THE DYNAMICS OF WAR AND PEACE
577
F
IGURE
4 Audience Costs and Long-Run Peace:
Israel and Lebanon
−2.5
−3
−3.5
−4
−12.5
−12
−11.5
−11
0.40
0.45
0.50
0.55
Lebanon AC
Israel AC
Pr(Peace)
8 percentage point increase in the probability that these
countries are at peace.
Some of these trends appear when considering
how the relationship between the two countries evolved
during the 1990s and 2000s. After Kim Dae-jung assumed
the presidency—representing the first peaceful transfer
of power to an elected opposition party—South Korea
finished its democratic consolidation, and there was
an unprecedented push toward peace in the Sunshine
Policy (CNN 1998; Lee 2002). In this case, democratic
consolidation in South Korea may have increased
President Kim’s audience costs.
20
Our analysis suggests
that such a shift would make North Korea less likely to
initiate a dispute (i.e., the deterrent effect of audience
costs). When this interstate rivalry resolidified in the early
2000s, we would have expected South Korea’s audience
cost to become less intense. Notably, President Bush’s
“axis of evil” speech is frequently credited with helping
return this rivalry to saliency (Lee 2002; Paik 2002). Our
analysis suggests that North Korea would become more
likely to initiate a dispute as South Korea’s audience costs
move from
−
13 to
−
10, that is, the range in Figure 3. In
contrast, the probability that South Korea would initiate
a dispute remains effectively unchanged. Matching this
assessment, from the mid-2000s onward there has been
a rash of North Korean initiations (Lavelle 2015).
In another case, Figure 4 graphs the effects of audi-
ence costs on the conflict between Lebanon and Israel.
20
The substantive effects in Figure 1 could be interpreted as the
effects of an unexpected and exogenous change in audience cost
parameters on the equilibrium probability of peace. We maintain
this interpretation throughout this section.
Increasing Israel’s audience costs results in more peace,
but increasing Lebanon’s produces more conflict. To see
this, notice that if we were to fix Lebanon’s audience cost
and only decrease Israel’s by one unit, the dyad becomes
more hostile, where the probability of peace decreases by
approximately 2 percentage points. This prediction has
some anecdotal support: Israel’s 2006 invasion of South-
ern Lebanon occurred during a period when (Wolf 2016,
431) argues that the Israeli parliament was particularly
fracturedandunabletoinflictaudiencecostsontheprime
minister. During this time, Israeli leadership faced lower
audience costs due to poor coordination among opposi-
tion parties, and our analysis predicts a lower likelihood
of peace, matching the onset of the 2006 conflict.
In contrast, small increases in Lebanon’s audience
costs generate more conflict, where a unit increase (to-
ward
−∞
) results in a 10 percentage point decrease in the
predicted probability of peace. This comparative static is
an example where audience costs are positively correlated
with conflict in certain directed dyads. Although this ef-
fect does not dominate in the data—see Table 2—it ap-
pears in 35% of directed dyads. Upon further inspection,
we find that larger audience costs for Lebanon discour-
age both sides from initiating disputes,
but
the disputes
that do erupt endure for longer periods. Specifically, ad-
justing Lebanon’s audience cost over the range listed in
Figure 4 increases conflict duration by 3 to 4 months, on
average.
Additional Results
We note two important findings. First, we find a liberal
peace in war but not crisis.
21
Specifically, the estimates
suggest that as joint democracy levels and trade depen-
dence increase, the relative benefit from being in the war
state, compared to peace, decreases. However, we find
little support that democracies and trading partners avoid
entering crises with each other.
Second, we consider the spiraling/deterrence effects
of conflict (the
(
s
) coefficients) from the systemic theo-
ries of conflict in Braumoeller (2008). Note that
(P
EACE
)
<
0, which suggests that in peace, countries are playing
somethinglikechicken,andtheexpectationofconflictde-
ters reciprocation because
i
receives a strong additional
disutility from escalation when it expects
j
to escalate as
well. In contrast, the positive coefficients on
(C
RISIS
)
and (W
AR
) indicate that once countries are in a dispute, a
21
Appendix J in the SI contains additional substantive effects, in-
cluding the effect of joint democracy levels on the probability of
peace.