Audience Costs and the Dynamics of War and Peace
∗
Casey Crisman-Cox
†
Michael Gibilisco
‡
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 replying on proxy variables, e.g., 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, incentiviz-
ing the country to stand firm and coercing its opponent to back down. Nonetheless, the
results demonstrate that larger audience costs would result 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 article are available on the
American Journal of Political Science
Dataverse within the Harvard Dataverse Network, at
doi:10.7910/DVN/XBNJD9
.
Word Count:
8,651
∗
Thanks to Scott Abramson, Rob Carroll, Kevin Clarke, Allan Dafoe, Mark Fey, Tasos Kalandrakis,
Brenton Kenkel, Bethany Lacina, Sergio Montero, Jack Paine, Keith Schnakenberg, and Curt Signorino for
helpful comments and suggestions. Earlier versions of the paper 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.
†
Washington University in St. Louis. Email:
c.crisman-cox@wustl.edu
‡
California Institute of Technology. Email:
michael.gibilisco@caltech.edu
1 Introduction
Audience costs—or the costs leaders pay from backing down before their opponents in in-
terstate disputes—are ubiquitous in international relations. Scholars use them to explain a
variety of phenomena including crisis bargaining, war duration, economic sanctions, and the
democratic peace. This prominence has sparked two fervid debates: Do audience costs exist
and how would we know? Specifically, the former question asks to what extent are leaders
punished for backing down (e.g., Snyder and Borghard 2011; Tomz 2007), while the latter con-
cerns the appropriate methodology for answering such a question (e.g., Kurizaki and Whang
2015; Partell and Palmer 1999; Schultz 2001).
Two substantial impediments prevent progress in either debate. First, since Fearon’s
(1994
a
) canonical paper, researchers traditionally proxy audience costs using democracy scales
such as polity2, and these measures often determine case-selection in qualitative studies and
independent variables in quantitative ones (Partell and Palmer 1999; Snyder and Borghard
2011). Nonetheless, analyzing the quality and strength of different proxies has proven difficult
(Levy 2012; Slantchev 2012). Scholars 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 increases in au-
dience costs may discourage a given country from initiating disputes if the country expects
its opponents to repeatedly stand firm in the future (Kurizaki and Whang 2015; Prins 2003;
Weeks 2012). On the other hand, 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 interaction (Schultz 1999). Thus, when countries internalize the long-term
strategies of their opponents, their unobservable strategies create a time dependence between
current escalation decisions and the expected path of future conflict, confounding the rela-
1
tionship between audience cost measures and dispute initiation. Such dynamic considerations
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 dispute 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 is merely transitory.
In this paper, we address these issues head-on by structurally estimating a dynamic game
of crisis escalation. As in Fearon (1994
a
), we model audience costs as a parameter capturing
the (dis)utility a country receives when it backs down from a dispute before 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 audience costs using country-specific fixed effects, which do not depend on
a priori
determined variables, and we select the audience costs (along with other parameters and
equilibria) that maximize the likelihood of the observed data. Specifically, we fit the model to
Militarized Interstate Dispute Incident Profiles (MID-IP) data that record escalation decisions
at the monthly level between 1993–2007 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 dominates 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% directed
dyads. In the estimated equilibria, audience costs serve as a commitment device: they tie the
hands of their respective countries, thereby encouraging them to stand firm and coercing
their opponents to back down in disputes. 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. The
coercion effect appears in 75% of directed dyads, where increasing a country’s costs results in
its opponent conceding more often. Although the two 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 analyses (Clark and Nordstrom 2005; Prins 2003; Weeks
2
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 observations.
Second, we use the model to address a substantive puzzle: do higher audience costs lead
to more or less conflict worldwide? On the one had, 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 dominates 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 identical 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.
Third, we test the hypothesis that standard proxies for audience costs correlate with our
estimates and find that they are fair, but underwhelming, first approximations. Although
regime types are important predictors, other systemic and domestic factors influence audience
costs. For example, the existence of an interstate rival attenuates the penalties leaders face
for backing down in a dispute. Democracies with rivals have, on average, audience costs
that are roughly similar to autocratic regimes with legal provisions for executive removal
(e.g., China), suggesting that democratic voters may provide leaders 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 debates concerning audience costs, our
framework produces implications for the wider international relations literature. We find that
trading partners and joint democracies are less inclined to enter wars, while 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 escalation, but in
3
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.
2 Modeling Audience Costs and Disputes
We follow the lead of Fearon (1994
a
, p. 582) and define audience costs as the (dis)utility
a country receives from backing down in an international dispute before its opponent. In a
similar vein, Slantchev (2012) 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. . . ”(p. 377). As discussed below, 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 side steps two theoretical explorations that have developed since Fearon’s seminal work. In
one development, scholars often interpret audience costs as the punishment leaders receive
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, however, as other theories require both initiators and
targets to receive costs for backing down (Fearon 1994
b
; Kurizaki 2007; Schultz 2001). This
latter approach is appropriate when “crisis diplomacy takes place before domestic audiences
on both sides” (Kurizaki 2007, p. 545).
In the second development, researchers have considered endogenous audience costs, allow-
ing them to grow over the dispute’s duration or be products of strategic choices (Fearon 1994
a
;
Leventoglu and Tarar 2005). Yet previous empirical work, including both reduced form and
structural approaches, treat audience costs as fixed and not being subject to strategic choices.
In this paper, we adopt the simplified conceptualization, where audience costs are country
1
In experiments, audience costs refer to the disapproval leaders create when then say one thing but do
another (Tomz 2007).
4
specific and do not depend on the historical evolution of disputes. This helps simplify 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. Thus,
long-term expectations influence whether countries incur 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 investigate their determinants in a post-estimation exercise. This approach has several
advantages. Most prominently, we avoid introducing an avenue of omitted variable bias into
the analysis, which is likely to arise because audience costs originate from several highly corre-
lated factors (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. Similarly,
fixed effects reduce the potential for separation that may arise from modeling audience costs
as functions of highly collinear variables.
Because we adopt a structural approach, our endeavor 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
assumption. Second, the two theoretical models differ considerably. 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 incur audience costs once. We estimate a dynamic
model with simultaneous choices, where countries are infinitely lived. Third, a draw back
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).
5
from using the crisis-signaling model to study interstate conflict is that the analysis almost
certainly requires a very specific dataset from Schultz, Lewis and Zucco (2012) covering the
inter-war period (1919–1939). In contrast, our model is more flexible with its informational
requirements, and we use the standard MID-IP dataset, covering a more contemporary period
(1993–2007). Finally, although the two models are quite different, both may admit multiple
equilibria under certain payoffs. Standard estimation techniques, e.g., Signorino (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.
3 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
6
=
i
its opponent. Time is discrete and indexed by
t
= 1
,
2
,....
In each period
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 information, unknown to opponent
j
, that country
i
has about the
costs/benefits of taking particular actions in period
t
. The variable
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
= 3 a state of 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
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.
6
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 begins
with the two countries in a state of war (
s
t
+1
i
= 3). We denote country
i
’s private information
about action
a
i
in period
t
as
ε
t
i
(
a
t
i
). The private information,
ε
t
i
(
a
t
i
), is independently and
identically distributed type I extreme value across actions, players, and states, which are
standard distribution and independence assumptions in these types of games.
Let
θ
denote a vector of relevant structural parameters to be estimated. Country
i
’s per-
period payoff against country
j
is given as
u
ij
(
a
t
,s
t
;
θ
) +
ε
t
i
(
a
t
i
), where
u
ij
is
i
’s deterministic
utility and
ε
i
is
i
’s (stochastic) private information. 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
δ
t
−
1
[
u
ij
(
a
t
,s
t
;
θ
)
+
ε
t
i
(
a
t
i
)
]
,
where
δ
∈
[0
,
1) denotes a common discount factor.
5
We endow
u
ij
with the following functional form:
u
ij
(
a,s
;
θ
) =
x
ij
·
β
(
s
)
︸
︷︷
︸
state-specific
payoff
+
z
i
·
κ
(
a
i
)
︸
︷︷
︸
action-specific
payoff
+
α
i
I
[
a
j
≥
s > a
i
]
︸
︷︷
︸
country-specific
audience cost
+
γ
(
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
·
β
(
s
), from being in state
s
with country
j
, where
x
ij
is a vector of dyad-specific variables
and
β
(
s
) a vector of associated coefficients. Dyadic variables could be directed, e.g., military
4
Unilateral escalation is common in the crisis and conflict literature (Fearon 1994
a
; Kurizaki and Whang
2015; Schultz 2001).
5
Notice we do not include
δ
in the parameters to be estimated. Without additional structure, it is
difficult to identify
δ
in these types of models, and previous papers traditionally assume a fixed discount factor
throughout. Here, we fix
δ
= 0
.
9.
7
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
·
κ
(
a
i
),
where
z
i
is a vector of country-specific variables and
κ
(
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 boarder 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
interpretation: while the U.S. 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 normalization that
β
(1) =
κ
(1) = 0, that is, the payoffs
x
ij
·
β
(
s
)
and
z
i
·
κ
(
a
i
) are relative to the baseline payoffs for the peaceful state and action, respectively.
The last two components in a country’s utility function depend on the actions of its
opponent. The parameter
α
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
continues or escalates the current
level of conflict (
a
j
≥
s
) and
i
backs down (
a
i
< s
), then
i
incurs cost
α
i
. Intuitively, this
means that countries never acquire audience costs when in peace or if their opponents do
not escalate/maintain the current conflict. Essentially, countries receive audience costs when
they deescalate the dispute before their rival, although size of the audience costs are fixed
throughout the dispute.
9
The
γ
(
s
) parameters are state-specific values measuring how
i
’s
cost of escalation varies with
j
’s actions in state
s
. When
γ
(
s
)
>
0,
i
’s cost of escalation
6
The payoff
x
ij
·
β
(
s
) may represent country
i
’s expected utility from some lottery with an outcome that
does not affect future payoffs. In the war lottery, where
p
ij
represents a probability of victory,
π
ij
the benefit,
and
c
ij
the cost, the war-state payoff takes the form
x
ij
·
β
(3) =
p
ij
π
ij
−
c
ij
.
7
Although we operationalize the costs of the crisis- and war-level actions in a similar manner, these actions
entail more differences because they transition the game to strategically different states. This setput is rich
enough to uncover differences once the model is taken to data.
8
This may appear to be non-standard n because these costs of escalation are not considered in previous
models, but this subsumes the case in which the coefficients
κ
(
a
i
) are zero.
9
We could accommodate the possibility 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
. This involves
estimating an additional 2
,
148 parameters describing equilibrium play. Instead, we allow both countries to
incur audience costs in disputes as in Fearon (1994
a
), Kurizaki (2007), and Schultz (2001).
8
(
a
i
>
1) decreases when
j
escalates in state
s
. Similarly, when
γ
(
s
)
<
0,
i
’s cost of escalation
increases when
j
escalates. Thus,
γ
(
s
) represents other strategic incentives as to why a country
does not escalate a conflict independently of audience costs including potential second-strike
(dis)advantages. For example, if
i
receives a large benefit in state
s
when its opponents attacks
first, e.g., support from an international community, then
γ
(
s
) would be negative.
We characterize Bayesian-Nash equilibria in stationary Markovian strategies (equilibria,
hereafter) as is standard in these games. Consider
i
’s net-of-shock expected utility from
choosing action
a
i
in state
s
, denoted
v
i
(
a
i
,s
), and let
v
i
denote the vector of expected utilities
for country
i
. Because
ε
i
is 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)
As in Signorino (1999), the expected utilities,
v
i
, are endogenous to equilibrium play. Unlike
most previous work, a closed-form solution for these values does not exist due to game’s infinite
horizon and simultaneous moves. In Appendix A, we demonstrate that profile
v
= (
v
i
,v
j
) is
an equilibrium if and only if it satisfies a system of 18 smooth equations, Φ(
v
;
θ
) =
v
.
In Appendix B, we analyze an equilibrium for 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 incentives and arises in a setting where both countries may incur audience
costs. In the subsequent sections, we the fit the model to data and examine whether this
relationship holds given our estimated equilibria.
9
4 Empirical Strategy
4.1 Constrained Maximum Likelihood
We estimate the model using a full-information constrained maximum likelihood estimator
(CMLE), as advocated by Su and Judd (2012). The estimator has significant advantages over
other methods (Aguirregabiria and Mira 2007; Hotz and Miller 1993). 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
equilibrium choice probabilities, which is particularly important 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 superscript
k
hereafter. We use data that can be summarized as a list
{
X,Z,Y
}
.
Here
X
and
Z
are matrices of ordered-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 action profiles for each dyad, i.e.,
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
̄
θ
denote the true vector of parameters. For each dyad
k
, we assume the data
Y
k
were generated from a
single
equilibrium, ̄
v
k
, i.e., Φ
k
( ̄
v
k
;
̄
θ
) = ̄
v
k
.
While multiple equilibria potentially exist in the game between the countries
i
k
and
j
k
, the
procedure requires that
Y
k
comes from only one of these. Let
v
= (
v
1
,...,v
D
) denote the
vector 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)
which is a standard multinomial log-likelihood summed over dyads, time periods, and players.
10
One drawback of the CMLE is that the procedure requires solving a constrained optimization problem,
which may be difficult to implement using standard statistical software. Appendix C describes how our
implementation overcomes these problems.
10
With a slight abuse of notation, the CMLE estimates, (
ˆ
v
;
ˆ
θ
), solve the following constrained
optimization problem:
max
(
v
;
θ
)
1
T
L
(
v
|
Y
)
subject to Φ
k
(
v
k
;
θ
|
X,Z
) =
v
k
, k
= 1
,...,D.
(4)
Standard results on Lagrange multiplier tests, found in Silvey (1959), guarantee that the
CMLE is consistent in
T
and characterize the estimator’s asymptotic distribution. Consis-
tency 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 con-
straint parameters. We still gain leverage by pooling information across dyads when
T
is
sufficiently large, however. We relegate further estimation details to Appendix C, and Ap-
pendix D contains a Monte Carlo illustrating the properties of the CMLE on datasets of
similar size to the one we construct in this paper.
4.2 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 what 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 recorded action are
on the standard 22-point scale, which we use to form the three levels of hostility countries
can take against each other. 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’ is recorded
if the country commits an action that is between a threat and an attack (MID-IP actions
1-15).
11
Table 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%
Caption:
The middle column displays the probability distribution over the possible transitions, and the
far-right column presents the conditional distribution in each state.
We follow Whang, McLean and Kuberski (2013) and construct the dataset in two steps.
First, to avoid selection 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
define 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 periods each;
approximately 95
.
4% of observed states are peace while 97% of actions are peace-level. Table 1
records the nine different types of possible transitions and provides preliminary evidence that
countries condition their behavior on the state variable of interest. That is, the conditional
distribution of transitions changes substantially 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, fix the strategies of the two actors in all periods such that they place
positive probability on every action in every state. Increasing
i
’s audience costs (
α
i
moves to
−∞
) has two effects. First,
i
’s expected 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 positive probability. Second,
i
’s expected utility of playing the
12
peace action (
a
i
= 1) in a dispute (
s >
1) will change as well, but the direction will depend
on
j
’s strategy. If
j
is likely to stand firm, then
i
’s utility of playing peace will decrease as it
expects to subsequently incur audience costs. In contrast, if
j
is likely to play the peaceful
action, then
i
’s utility may increase as
i
would prefer to deescalate the dispute, transitioning
the to a peaceful state without audience costs.
These dynamics have two important implications. First, we cannot identify a country’s
audience cost parameter if it has never been in a dispute with another country in the data,
although we do not require that it initiates or backs down in a dispute. Including such a
country, e.g., Costa Rica, would lead to separation because its contribution to the likelihood
function will be strictly increasing as its audience cost parameters become more negative.
11
Second, the above discussion highlights the importance of equilibrium analysis because it
fixes the strategies of both players, thereby ignoring the indirect effects of audience costs
through the equilibrium conditions. As demonstrated below, equilibria often times produce
comparative statics that diverge from the the previous paragraph’s naive predictions.
To isolate the effects of audience costs, we also control for other reasons why countries initi-
ate 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
γ
(
s
), while the latter are captured by including constants in
x
ij
and
z
i
. In addi-
tion, we include other control variables common to the interstate conflict literature. At the
dyadic-level, we use the minimum democracy level in the dyad (Polity IV database), the logged
capability ratio (CINC scores from the Correlates of War database), and the square-root of the
trade interdependence, where country
i
’s interdependence on country
j
is the sum of exports
and imports between
i
and
j
divided by
i
’s GDP. Trade data comes from the COW dyadic
trade data (Barbieri, Keshk and Pollins 2009), supplemented by data from Gleditsch (2002).
GDP data is from the Penn World Table (PWT) 8.0, supplemented with data from the World
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.
13
Bank and the UN. For the variables associated with country specific costs, we include logged
GDP per capita (from PWT) and logged military personnel per capita (from COW).
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 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 and the observed states and actions. See Appendix E for more details.
5 Audience Costs
Figure 1 presents the estimated country-specific audience costs and their 95% confidence
intervals, sorted by magnitude.
12
Even though the parameters
α
i
can take on any value in
estimation, all estimates are negative, suggesting that leaders are punished for backing down.
The countries with the ten largest (most negative) audience costs are mostly democracies, but
notable exceptions exist to the idea that democracy and audience costs are synonymous. Many
autocracies and anocracies exhibit substantial 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
anocracies (
p < .
05), but a test finds no difference between the latter two groups.
Although democracies have larger audience costs than autocracies on average, several ex-
ceptions to this trend are involved in historically salient and persistent conflicts. For example,
North and South Korea have similar audience costs as South Korea’s audience cost is very
moderate (less negative) compared to other advanced democracies. One reason for this is that
South Korea exists in a state of perpetual siege, suggesting that voters are more willing to
12
Point estimates in table format can be found in Appendix F.
14
Figure 1:
Country-specific audience costs, labeled with three-letter COW codes.
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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
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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
15
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 analyze the degree to which our estimated audience costs match the the-
oretical predictions regarding autocratic regime types in Weeks (2008, 2012).
14
In the case of
Weeks (2008), we consider personalist, single-party, and military autocracies, and from Weeks
(2012), we consider 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, 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 conventional levels.
5.1 The Effects of Audience Costs
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) initiate 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 backing down and initiating a conflict. We aggregate trends across individual
dyads rather than constructing an “average” 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 correlating our audience
cost estimates with the observed equilibrium choice probabilities in a reduced-form analysis.
13
Other explanations for South Korea’s moderate audience costs include its dependence on U.S. military
support and lack of Wartime 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 (
p <
0
.
01) among democracies.
14
Although only the former deals explicitly with audience costs, both generate predictions about the political
costs leaders face from domestic audiences.
16
Table 2:
Marginal effects of audience costs across dyads.
Marginal Effect of
α
i
→−∞
↑
Pr(
i
Backs Down)
22%
↑
Pr(
j
Backs Down)
75%
↑
Pr(
i
Initiates)
81%
↑
Pr(
j
Initiates)
16%
↑
Pr(Peace)
65%
Caption:
Percentages denote the proportion of directed dyads where increases in audience costs (toward
−∞
) increase the probability of backing down, initiating conflict, and the long-term probability of peace.
The probabilities, and their associated derivatives, are formally defined in Appendix B.
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, consider 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 frequency
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 audience costs increase. Likewise, larger
audience costs for 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 previous work (Fearon 1994
a
; Kurizaki
and Whang 2015; Partell and Palmer 1999; Uzonyi, Souva and Golder 2012).
Next, we examine the effects of audience costs on conflict initiation. Counter to intuition,
larger audience costs embolden leaders into initiating disputes with greater frequency. 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
17
and Whang 2015; Prins 2003; Schultz 1998; Weeks 2012). Nonetheless, 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 commitments. Essentially, when country
i
has larger audience costs, it more likely commits to standing firm in the subsequent dispute,
as in the hand-tying effect described above. Furthermore, these larger audience costs coerce
i
’s opponents to back down, as in the coercive effect described above. Countries internalize
these advantages 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 attempt to exploit their enhanced
credibility by becoming more aggressive.
Conversely, in 84% of dyads,
j
becomes less likely 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
disputes, and, as a result,
j
is relatively disadvantaged and will more likely concede. Thus,
j
avoids this relative weakness by initiating less, that is, increasing
i
’s audience costs deters
opponent
j
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 directed dyad’s probability of peace in the long run.
15
Simple
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
15
The long run probability of peace comes from the dyad’s invariant (stationary) distribution. We describe
this in Appendix B. In Appendix K, we provide evidence that equilibrium play has converged to its invariant
distributions in most dyads.
18
makes both sides more peaceful, while 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 dominant effect of audience costs is
their deterrence value: countries tend not to initiate disputes against countries with higher
audience costs, leading to more peace in the long run.
5.2 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 country’s polity2 score, Bueno de Mesquita et al.’s (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
there are 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),
16
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 proxies are all
significant and correlate in the expected direction. Because Kurizaki and Whang’s (2015)
audience cost measures are a linear function of polity2 scores, imputing audience costs using
their coefficient estimates with polity2 scores from our data, i.e., mean polity2 between 1993–
2007, will produce an correlation coefficient (0.18) identical in magnitude to that of polity2
in Table 3. Furthermore, the relationship between a free press and the strength of audience
16
Thompson and Dreyer (2012) 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 threating enemies”
(p. 11).
19
Table 3:
Correlates of audience costs.
Spearman’s
ρ
t p
-value (one-sided)
Polity2
-0.18 -2.04
0.02
W
-0.13 -1.49
0.07
Free Press
-0.13 -1.43
0.08
Elected Executive
-0.20 -2.29
0.01
Executive Removal
-0.14 -1.51
0.07
Executive Constraints
-0.09 -1.04
0.15
Rivalry
0.32
3.78
0.00
USG’s ACC
-0.25 -2.34
0.01
costs matches the theoretical predications 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
components. 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 if a country has a
polity2 score greater than or equal to –4.
17
Among autocracies, 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 –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
17
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.
20
Figure 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
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 U.S. 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 attenuates their magnitude.
Countries with polity2 scores larger than –4 but 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 average 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, i.e., 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,
21
such as Indonesia and Cambodia. Audience costs in these regimes are the lowest on this half
of the regression tree, indicating the importance of domestic institutions, besides democracy
levels, to constrain leaders. When non-autocratic regimes neither directly elect their chief
executive nor have a free press, then they have audience costs with those that are comparable
to autocrats. For example, Bangladesh with a polity score of six (until 2007) has an audience
cost of
−
1
.
9, rivaling the least constrained of autocrats.
5.3 Illustrative Examples
To illustrate these findings, we examine two salient conflicts in greater detail. First, we
consider substantive effects 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.
18
The graph illustrates the pacifying effects of audience costs. As both costs
become more severe (move towards
−∞
), the likelihood of peace in the long run increases. A
roughly two unit change in both cost parameters produces an eight 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 1990s and 2000s. After Kim Dae-jung assumes the presidency—
representing the first peaceful transfer of power to an elected opposition party—South Korea
finishes its democratic consolidation, and there is an unprecedented push towards 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.
19
Our analysis suggests that such
a shift would make North Korea less likely to initiate a dispute, i.e., the deterrent effect of
18
Multiple equilibria exist in each dyad, which complicates counterfactual experiments. Thus, we cannot
just vary the parameters, compute a new equilibrium, and compare choice probabilities under the old and
new parameters values. Doing so would not guarantee 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 contains more details.
19
Figure 1 could be interpreted as the effect of an unexpected and exogenous change in audience cost
parameters on the equilibrium probability of peace, an interpretation we maintain throughout.
22
Figure 3:
Audience costs and long-run peace: North-South Korea
−12
−11
−10
−12
−11
−10
0.88
0.90
0.92
North Korea AC
South Korea AC
Pr(Peace)
audience costs. When this interstate rivalry re-solidifies in the early 2000s, we expect 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 becomes more likely to initiate a dispute as South Korea’s
audience costs move from –13 to –10, i.e., the range in Figure 3. In contrast, the probability
of that South Korea initiates remains effectively unchanged. Matching this assessment, from
the mid-2000s onward there have been a rash of North Korea initiations (Lavelle 2015).
In another case, Figure 4 graphs the effects of audience costs on the conflict between
Lebanon and Israel. 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 prob-
ability of peace decreases by approximately 2 percentage points. This prediction has some
anecdotal support: Israel’s 2006 invasion of Southern Lebanon occurred during a period where
23
Figure 4:
Audience costs and long-run peace: Israel–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)
Wolf (2016) argues that the Israeli parliament was particularly fractured and unable to inflict
audience costs on the prime minister (p. 431). During this time, Israeli leadership faced lower
audience costs due to poor coordination among opposition 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 (toward
−∞
) 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 effect does not dominate in the data—
see Table 2—it appears in 35% of directed dyads. Upon further inspection, we find that larger
audience costs for Lebanon discourage both sides from initiating disputes,
but
the disputes
that do erupt, endure for longer periods. Specifically, adjusting Lebanon’s audience cost over
the range listed in Figure 4 increases conflict duration by three to four months on average.
24