10.1177/0022002702239511
JOURNAL
Reed
/ INFORMATION
OF CONFLICT
ANDRESOLUTION
ECONOMIC INTERDEPENDENCE
ARTICLE
Information and
Economic Interdependence
WILLIAM REED
Department of Political Science
Rice University
The pacifying effect of economic interdependence on conflict onset can be better understood in the context of “noisy” bargaining. Specifically, trading states bargain under less noisy conditions and, as a result,
are unlikely to engage in militarized conflict. Noise is introduced into a generic take-it-or-leave-it bargaining game in the form of nonspecific asymmetric information about the defender’s reservation value. Comparative statics show a positive monotonic relationship between variance in the noise term and the onset of
militarized conflict. The relationships among economic interdependence, variance in the noise term, and
conflict onset are evaluated with a Bayesian heteroskedastic probit model. Historical data are used to demonstrate that interdependence and uncertainty are related to each other and jointly related to the onset of militarized conflict. Uncertainty appears to be reduced by economic interdependence, and this leads to an
enhanced probability of agreement short of a militarized clash.
Keywords: conflict; militarized dispute; economic interdependence; uncertainty; Bayesian probit
The effect of economic interdependence on the onset of militarized conflict is a topic
of much interest among world politics researchers. Although some researchers continue to claim that trade may enhance the probability of war, most acknowledge that
trade decreases the likelihood of militarized conflict. At least two notions motivate the
hypothesized link between economic interdependence and militarized conflict. Some
scholars argue that economic interdependence makes conflict too costly. Thus, states
that are cognizant of the costs of a militarized clash choose to settle their differences
short of the use of force. Others claim that economic interdependence decreases the
probability of conflict by solving problems associated with asymmetric distributions
of information. That is, in a bargaining context, the reservation values of states engaging in high levels of bilateral trade are more or less transparent. This allows differences
to be settled peacefully, leading to more efficient transactions. Still others argue independently of the explanations based on costs or distributions of information. This line
of research suggests that the observed pacifying effect of economic interdependence is
nothing more than an artifact of unaccounted for time series dynamics.
AUTHOR’S NOTE: I am grateful to David Clark, Scott Gates, Doug Lemke, and Dan Reiter for their
comments. I also thank Kevin Clarke, Ashley Leeds, Cliff Morgan, Karoline Mortensen, Jiyoung Kwon,
Stephen Haptonstahl, Wonjae Hwang, and Randy Siverson for useful suggestions.
JOURNAL OF CONFLICT RESOLUTION, Vol. 47 No. 1, February 2003 54-71
DOI: 10.1177/0022002702239511
© 2003 Sage Publications
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Reed / INFORMATION AND ECONOMIC INTERDEPENDENCE
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I argue that trade may enhance the probability that states settle their disagreements
short of militarized conflict, because it serves to minimize distortion about the willingness of a target to give in to any specific demand issued by a dissatisfied challenger. It is
important to note that this claim is only subtly different from the “conflict is too costly
for trading states” notion. Because one of the parameters in the decision to use militarized force is the actors’utility for the costs of the conflict, the effect of costs is a crucial
component in the “information” explanation. Although an increase in the costs of conflict for either actor will decrease the probability of conflict, my claim is that economic
interdependence does not just result in increased costs. Rather, the effect of interdependence is most profound with respect to variation in the distribution of information
about the costs of conflict and other crucial parameters in the actors’ value functions.
That is, trade affects the costs of conflict in two independent ways. First, the costs of
conflict for trading states may be higher than for comparable nontrading states. Second, trading states have more precise information about their opponent’s costs than do
nontrading states. Although theoretically, these are different processes relating trade
to conflict, the empirical implications of these independent effects are observationally
equivalent. Trade should decrease the probability of conflict.
I construct a simple bargaining model to illustrate formally my argument. I evaluate
the credibility of the formal model with a Bayesian heteroskedastic probit estimator.
My results suggest that economic interdependence mitigates the effect of uncertainty,
and this leads to an enhanced probability of settlement short of militarized conflict. I
also show that trade is related to heterogeneity in conflict data. This heterogeneity is a
possible explanation for the null findings in some of the published papers that examine
the trade and conflict puzzle.
HETEROGENEITY AND CONFLICT ONSET
Previous empirical studies of international conflict model the onset of conflict
using special cases of generalized linear models for indicator variables (Maoz and
Russett 1993; Lemke and Reed 1996; Gartzke 1998; Oneal and Russett 1997; Beck,
Katz, and Tucker 1998). Unfortunately, these models are ill equipped to assess heterogeneity in conflict behavior that may be a function of economic interdependence and
make it difficult to evaluate claims relating bilateral trade to distributions of information.
One weakness of previous empirical studies of conflict onset is their assumption
that there is no observed heterogeneity in the conflict data. That is, all of the variation
in conflict behavior is assumed to be only a function of x i′β. Not only is this an unrealistic practical assumption, it is also at odds with international relations theory. Standard
empirical treatments pool together pairs of states as diverse as the United States and
Canada or India and Pakistan and assume the variation in their conflict behavior is
identical. Moreover, these models assume the variance in conflict behavior among
Western European dyads is the same as among African dyads (Lemke 2002). Not only
does this seem unreasonable intuitively, but there are strong theoretical reasons to
expect it is false. Bargaining models anticipate heterogeneous behavior as a function
of asymmetric information and the variance in the distribution of types of defenders. If
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bargaining theory is credible, I expect the variance of the error in the challenger’s estimate of the defender’s type to vary with economic interdependence. As the challenger
and defender trade less, the variance in the challenger’s estimate of the defender’s reservation value is greater. This leads to an enhanced probability of mistakes and a positive probability of conflict onset. A different specification is needed to address this
deficiency in the standard models. To evaluate my claims about variance in the challenger’s estimate of the defender’s expected value for conflict, I incorporate
heteroskedasticity in the probit model following a hierarchical specification.
Reparameterizing the standard model to explicitly incorporate heterogeneity allows
me to assess how variance in conflict behavior may be related to different levels of
trade.
To manage the computational costs of evaluating the reparameterized probit likelihood function, I analyze the conflict data with Bayesian tools. Other Bayesian applications in political science include articles by Western and Jackman (1994); Western
(1998); Schofield et al. (1998), Quinn, Martin, and Whitford (1999); Smith (1999);
King, Rosen, and Tanner (1999); and Jackman (2000b).1 The Bayesian approach
assumes the data are fixed and the parameters of interest vary. The goal is to compute
the probability density of the parameters of interest conditioned on the observed data.
This probability density conditioned on the data is called the posterior. The posterior
density summarizes the beliefs about the parameter of interest after observing the data.
It is also necessary to specify formally beliefs about the parameter of interest before
examining the data. Similar to the posterior, prior beliefs are expressed as a prior density. The parameter of interest is θ, and this parameter is assigned a prior π(θ). The
prior summarizes the beliefs about θ before examining the data. The prior can be
informed by theoretical expectations or by empirical patterns reported in past research.
Although there are conventions for assigning priors, ultimately the information contained in the prior is left to the analyst. In this application, the parameter θ contains
information about the relationship between economic interdependence and the emergence of conflict, and I assign diffuse priors to θ, such that the historical data dominate
the priors. Using diffuse priors usually refers to the practice of specifying a prior distribution with wide variance. Uninformative priors are flat, and as the variance of the
prior increases, diffuse priors approach uninformative priors. The model I use is x ~
f(x|θ), where x are the data and f(•) is a generic response function. This model is proportional to the likelihood function summarizing the information about θ from the data,
l(θ|x) ∝ f(x|θ). Using Bayes’s theorem gives the posterior distribution for θ,
π (θ x ) =
f ( x θ )π (θ )
∫
f ( x θ )π (θ )dθ
,
(1)
where π(θ|x) is the posterior density of θ.
For this specific application, I use the following model:
1. Several other papers are circulating: Andrew Martin (2000), Martin and Quinn (2000), Ward and
Gleditsch (2001), and Clarke (2001).
Reed / INFORMATION AND ECONOMIC INTERDEPENDENCE
57
yi i. i.~d Ber( pi ) ,
(2)
g( pi ) = x ′iβ + ε i .
(3)
where
I assign a subjective prior to β such that β ~ Normal(0, 104). That is, β is distributed
normally with a mean of 0 and variance 10,000, and I assign a χ2(r)/r prior to the variances where r = 4. This prior is consistent with outliers and approximates the logit
model. These priors are only marginally informative such that the data dominate the
prior. By utilizing Bayesian simulation (Markov Chain Monte Carlo [MCMC]), I am
able to make inferences based on the posterior.
I use the Gibbs sampler to obtain posterior samples.2 However, obtaining samples
directly from the posterior is difficult because of the presence of several integrals and
the probit function Φ in the likelihood. To overcome these difficulties, I use the auxiliary variable technique of Albert and Chib (1993).3 This approach allows me to augment the observed data with a quantity Z. From both the observed data and Z, it is possible to calculate the posterior density. I augment the data by introducing auxiliary
information zi where
1 if zi > 0
.
yi = 
0 if zi ≤ 0
(4)
Because the data are augmented with Z = (z1, z2, . . . ,zN), the likelihood is equivalent to
the standard linear model. As a result, this posterior is computationally manageable. I
ran 25,000 Gibbs samples to recover the posterior densities with a burn in period of
10,000 samples. The Gibbs sampler begins with initial values (β0, v0, ε0, Z0) and simulates the posteriors π(β|v, ε, Z, y), π(v|β, ε, Z, y), π(ε|Z, v, β, y), and π(Z|β, ε, v, y).4 The
general idea behind the estimation is to use the conflict data to find reasonable starting
values for the parameters. Next, these parameters are used to estimate the latent variable Z. Then the latent variable is used to estimate the parameters, and this is repeated.
This approach is useful for my problem because it provides me with a posterior for the
variance of each observation in the data file. The mean of these posterior densities can
be plotted to explore visually the relationship between variance and economic interdependence. Standard approaches simply assume the variance is constant and make such
exploratory analysis difficult.
2. See Jackman (2000a) for a discussion of the Gibbs sampler in a political science context. A more
general discussion may be found in Carlin and Lewis (1996) and Gelman et al. (1995).
3. For an alternate approach to modeling heterogeneity in the context of a probit regression, see
Alvarez and Brehm (1995).
4. See Smith (1999) for a discussion of estimating the posterior though data augmentation in the context of crisis escalation.
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TRADE AND CONFLICT
Returning to the substantive problem, the relationship between the onset of militarized conflict and economic interdependence is an important area in which research on
international bargaining may offer novel insights. This is an especially fertile area of
research because of the lively scholarly debate about the effect of economic interdependence on the onset of militarized conflict. Working within the liberal peace
research program, John Oneal and Bruce Russett (1997, 1999a, 1999b, 1999c, 2001)
have published several papers supporting the contention that trade promotes peace or
at least has a robust pacifying effect on the onset of militarized conflict. Moreover,
Oneal and Russett argue that the pacifying effect of economic interdependence holds
important clues about the observed peace between and among democratic states.
Democracy may reduce the probability of militarized conflict by indirectly increasing
the amount of economic interdependence (Russett and Oneal 2001). In related work,
Lisa Martin (2000) asserts that democratic states may be better equipped to foster economic interdependence because they are better able to make credible commitments
with respect to the terms of trade. In sum, economic interdependence allows for more
efficient bargaining.
Similar lines of inquiry claim that increased contact in the form of economic
exchange between states can decrease the probability of conflict. For example,
Deutsch et al. (1957) argue that trade can lead to the development of a sense of community, and this shared community may make conflict less likely. Moreover, Polachek,
Robst, and Chang (1999) claim that because states know conflict will distort the benefits from trade, trade deters militarized conflict. Put simply, the costs of conflict are
higher for trading states, and with greater costs, the expected value for militarized conflict is lower. Thus, ceteris paribus, trading states can expect to gain less from a militarized clash than would nontrading states and, as a result, are more likely to accept a bargained outcome short of militarized conflict. Yet it is also theoretically possible that
interdependence may enhance the probability of militarized conflict. With the prospect for economic gains from trade comes the possibility that failure to agree on the
terms of trade may result in the escalation of hostility. Therefore, depending on the
context of the transactions between states, interdependence provides an opportunity
for conflict that might not exist in the absence of international exchanges of goods and
services. Stated more formally, as the stakes of a militarized conflict increase, states’
expected value for conflict increases. This makes a bargained outcome appear less
attractive and enhances the probability of conflict.
Contributing to the richness of this research area, several sophisticated econometric
analyses of the relationship between trade and conflict have been conducted. Unfortunately, the results from these studies contradict each other. Much of the inconsistency
is attributable to the use of varied temporal domains, different statistical estimators,
and alternate measures of economic interdependence. The discrepancies are most
apparent in the work of Barbieri and Schneider (1999) versus Oneal and Russett
(1997). Whereas Barbieri and Schneider find that economic interdependence actually
enhances the probability of disputes and wars, Oneal and Russett report economic
interdependence decreases the likelihood of disputes. Barbieri and Schneider claim
Reed / INFORMATION AND ECONOMIC INTERDEPENDENCE
59
that economic interdependence increases the stakes of conflict, and as the stakes of the
conflict increase, so do states’ expected values for conflict. This makes conflict appear
more attractive when compared to a bargained outcome. It also should be noted the
consistency of the statistical results have been somewhat qualified by Beck, Katz, and
Tucker (1998). Specifically, Beck, Katz, and Tucker argue that trade has little effect on
the probability of militarized conflict once temporal dynamics are taken into account.
BARGAINING AND CONFLICT
The literature on bargaining and its various applications to the study of world politics has profoundly affected the scientific study of international interactions. Bargaining models are being used to better understand the onset of militarized conflict, the
process of conflict within a war, and the outcomes of war.5 This approach has also been
used to better explain the relationship between trade and conflict (Gartzke, Li, and
Boehmer 2001). I build on this important research by studying the effect of economic
interdependence on the probability of militarized conflict in the context of the bargaining framework. I use a simple bargaining model to evaluate the relationship between
the distribution of information, economic interdependence, and the onset of militarized conflict (see Figure 1). I show how interdependence might decrease the probability of conflict by increasing the costs of conflict (Oneal and Russett 1997). I also illustrate how interdependence can enhance the probability of conflict as it increases the
stakes of the contest (Barbieri and Schneider 1999). Moreover, to the extent that these
two effects are working against each other, null findings are anticipated by the bargaining model. Finally, I show how economic interdependence might decrease uncertainty,
lowering the likelihood of conflict. Thus, all of the notions that relate interdependence
to the onset of conflict can be represented in this overly simple formalization.
Restating my argument more formally, consider two risk-neutral actors with linear
utility functions where a status quo challenger makes a demand, x, and the defender
chooses to accept or reject the demand. If the defender accepts the challenger’s offer,
the challenger receives x and –x goes to the defender. If the defender rejects the challenger’s offer, conflict with stakes π occurs. In the event of such a conflict, the challenger prevails with some likelihood, p, and pays a cost of cC. Thus, the challenger’s
expected value for conflict is pπ – cC, whereas the defender’s expected value is –pπ –
cD. Because the challenger and defender would prefer to forgo the costs of conflict, ci,
the challenger selects a demand to make the defender indifferent between the utility for
the challenger’s demand and the expected value for militarized conflict. Setting –x
equal to –pπ – cD and solving for the optimal demand yields x* = pπ + cD. Thus, when
the challenger and defender know each other’s payoffs, and conflict is costly, the probability of conflict is zero. They are always able to settle on a bargain short of militarized conflict, avoiding the costs of such a contest.6
5. For a review of this emerging literature, see Reiter (2001).
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Figure 1:
A Simple Bargaining Game
Yet it seems more reasonable and is critical to my argument to assume the challenger is uncertain about the optimal offer (x* from above). I incorporate uncertainty
into the challenger’s decision by assuming the defender’s expected value for conflict,
as observed by the challenger, has some error, ε.7 I assume the error is known by the
defender but the challenger knows only the distribution from which ε is drawn. Thus,
the defender’s expected value for war is –pπ – cD + ε. In this application, the probability
of conflict is Pr(x > pπ + cD – ε), and solving in terms of the error gives Pr(ε > –x + pπ +
cD). This splits the population of defenders into two types. Those defenders with ε ≤ –x +
pπ + cD give in to the challenger’s demand, whereas defenders with ε > –x + pπ + cD
reject the demand in favor of a militarized clash. If the challenger underestimates the
defender’s expected value for conflict, it assumes that the defender is a low type ε. If
the defender is actually a high type ε, conflict occurs. Because the cumulative distribution function (CDF) can be used to express the probability of a variable being less than
or equal to some value, the probability of conflict is Pr(ε ≤ x – pπ – cD) ≡ F(x – pπ – cD).
Because the challenger is uncertain about the defender’s type, it is faced with a riskreturn trade-off. The larger the demand, the greater the potential payoff. However, at
the same time, the larger the demand, the greater the probability of conflict. The size of
the demand is related to the probability of conflict because increasing demands raise
the cut point, dividing defenders who prefer to fight and defenders who prefer to concede to the challenger’s demand.8 Formally, the challenger’s expected value for a
demand x is
E(x) = {F[x – pπ – cD](pπ – cC)} + {1 – F[x – pπ – cD]}x.
(5)
6. This result is consistent with several applications of the bargaining model that suggest uncertainty
is a necessary condition for the onset of conflict. For a general discussion of the implications of this model,
see Fearon (1995).
7. Although most applications assume an asymmetric distribution of information, two-sided uncertainty is perhaps more realistic. However, such a model would make the empirical analysis that follows
impossible. Therefore, I limit my formalization to asymmetric information.
Reed / INFORMATION AND ECONOMIC INTERDEPENDENCE
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The first expression in equation (5) is the product of the probability the defender fights
and the challenger’s expected value for conflict. The second expression in equation (5)
is the product of the probability the defender accepts the challenger’s demand and the
magnitude of the demand. The challenger’s problem is to maximize equation (5) with
respect to x. Solving this problem is straightforward:
∂E ( x )
= 1 − F [ x − pπ − cD ] + ( pπ − x − cC ) f [ x − pπ − cD ] = 0.
∂x
(6)
The second order condition is
–2 f [x – pπ – cD] + (pπ – x – cC) f ′[x – pπ – cD] < 0.
(7)
The optimal demand, x*, solves the first order condition (6) subject to the second
order condition (7).
COMPARATIVE STATICS
The model suggests some sharp expectations about the relationship between costs,
stakes, uncertainty, and the likelihood of militarized conflict. Specifically, the following implications are deduced from the model:
Proposition 1: A marginal increase in either the defender’s or challenger’s costs of conflict
will decrease the probability of conflict.
This is shown by differentiating the first order condition (6) and noting that marginal
increases in the defender’s or challenger’s costs of conflict have a negative effect on the
probability of conflict.
Because the costs of conflict affect how the challenger and defender view their
expected values for conflict, as the costs increase, the expected value for conflict
decreases, when compared to the utility for a bargained outcome. As a result, increases
in the costs enhance the chances that the defender will accept the challenger’s demand
in favor of a militarized clash and also decrease the size of the challenger’s demand.
This static is consistent with the claims of Oneal and Russett (1997) and generally supports the liberal position that relates trade to costs and subsequently less conflict.
Proposition 2: A marginal increase in the stakes of the conflict will increase the probability
of conflict.
This is shown by differentiating the first order condition (6) and noting that a marginal increase in the stakes of conflict has a positive effect on the probability of conflict. Because the stakes of the conflict affect how the challenger and defender view
8. For a discussion of the endogeneity of demands in a similar bargaining context, see Werner (2000).
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their expected return from a militarized clash, as the stakes increase, the states’
expected values for conflict increase, making a bargained outcome less attractive.
This static is consistent with the claims of Barbieri and Schneider (1999) and generally supports the notion that if interdependence increases the stakes of a conflict, it will
subsequently enhance the probability of a militarized clash. Moreover, it makes clear
how the claims of Oneal and Russett (1997) and Barbieri and Schneider are logically
consistent but likely work against each other in standard empirical tests of the trade
conflict puzzle.
VARIANCE IN DEFENDER TYPES AND CONFLICT
Most relevant for this study is the question of how changes in the variance of the distribution of types of defenders affect the probability of conflict.9 Specifically, consider
the effect of expanding or contracting the range of ε without changing the mean. Substantively, this amounts to increasing the noise in the challenger’s choice of the optimal
demand, which is equivalent to expanding the variance of ε. As the variance in the distribution of types of defenders expands, it is increasingly difficult for the challenger to
differentiate between defenders of low type ε from defenders of high type ε. What
effect does the variance in distribution of defender types have on the probability of
conflict? To assess the effect of incremental changes in the variance of the distribution
of types of defenders on the likelihood of conflict, I denote µ to be the mean of the distribution f(•) and assume ε is distributed in the interval [µ – σ(µ – a), µ + σ(b – µ)],
where 0 < a < b < 1, with a probability density function (PDF) h(•) and a CDF H(•)
defined by
1 
x −µ 
f µ +

σ 
σ 
(8)
x −µ 

H( x ) ≡ F µ +
.
σ 

(9)
h( x ) ≡
and
Using different values for σ gives a family of distributions all with the same mean but
with different higher moments. This allows me to assess the impact of variance in the
distribution of ε on the probability of conflict. For σ = 1, h(•) is equivalent to f(•). However, for σ > 1, h(•) is an expanded version of f(•); and for σ < 1, h(•) is a contracted version of f(•). A third proposition follows.
Proposition 3: An expansion of the range of ε will increase the probability of conflict.
9. Schultz (1999, 245) makes a similar argument about the relationship between variance in information and its relationship to domestic political institutions.
Reed / INFORMATION AND ECONOMIC INTERDEPENDENCE
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Increasing the variance in the distribution of types of defenders enhances the likelihood of conflict because it increases the differences among types in the expected outcome of conflict. This static is consistent with those presented in Wittman (2001) and
Bebchuk (1984). This result can be confirmed by rearranging equation (6) into the hazard rate. Manipulating the first order condition gives the hazard rate
f [ x − pπ − cD ]
1
.
=
1 − F [ x − pπ − cD ] x − pπ − cC
(10)
Substituting the expanded distribution H and h for F and f gives
h[ x − pπ − cD ]
1
=
σ.
1 − H[ x − pπ − cD ] x − pπ − cC
(11)
The proposition is proved by differentiating the first order condition, using h and H
instead of f and F, and noting that marginal increases in σ have a positive effect on the
probability of conflict.
To interpret the relationship between economic interdependence and the emergence of militarized conflict, it is important to consider how trade might be related to
the variance in ε. It seems reasonable to expect high levels of economic interdependence to be associated with an enhanced likelihood that trading states can better estimate each other’s reservation value. This is consistent, for example, with the claims
made by Deutsch et al. (1957) discussed earlier. As states are more engaged economically with each other, the variance in the noise parameter can be expected to shrink.
Likewise, pairs of states that do not trade are likely to be more uncertain about their
respective reservation values, and the range of ε can be expected to expand. It also
seems reasonable to expect the relationship between trade and uncertainty to be nonlinear where the informational returns from trade are marginally decreasing.
Following Wittman (2001), I formally incorporate this dynamic into the bargaining
model by assuming σ is a function of the level of economic interdependence. As pairs
of states trade less, σ increases, leading to greater uncertainty. Likewise, as trade
increases between two states, σ approaches zero, and the variance in the distribution of
types of defenders shrinks. Thus, ceteris paribus, I expect the probability of conflict
emergence to be greatest when there is little or no trade because of the negative relationship between economic interdependence and variance in the distribution of types
of defenders.
Hypothesis 1: Economic interdependence is negatively correlated with the variance or
uncertainty about the defender’s reservation point.
Hypothesis 2: Increases in variance or uncertainty about the defender’s reservation point
enhance the probability of militarized conflict.
The first hypothesis follows from the logic of liberal theories of world politics and
the expectation that σ is a function of economic interdependence. The second hypothesis is deduced directly from the bargaining model. To facilitate comparison with
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previous research, I use data from Oneal and Russett (1997) to evaluate the credibility
of these hypotheses. These data consist of observations on 20,990 pairs of states over
the time period between 1950 and 1985. The unit of analysis is the dyad year, and the
data contain information on 827 politically relevant dyads. Each dyad is observed once
for every year it appears in the data file. The dependent variable is the existence of a
militarized dispute. The coding of this dependent variable and the collection of the
militarized interstate dispute date are discussed in Jones, Bremer, and Singer (1996).
The crucial independent variable for this research is economic interdependence, as
indexed by Oneal and Russett. This variable increases as there is greater economic
interdependence between two states. Thus, drawing on past research and the logic of
the bargaining model, I expect the average effect of this variable to be negatively
related to militarized conflict. Measures of joint democracy, the distribution of capabilities, alliance membership, and territorial contiguity are included as controls. The
measurement of these control variables is discussed in Oneal and Russett and in Beck,
Katz, and Tucker (1998). I also include a spline to correct for temporal dependence
existing in the data, following Beck, Katz, and Tucker.
STATISTICAL ANALYSIS
The formal model suggests that the defender rejects the challenger’s offer if ε is
greater than pπ – x + cD. Therefore, the probability of militarized conflict is Pr(ε ≤ –pπ + x
– cD). Assuming that proxy measures can be found for the variables, it is possible to
rewrite the probability of conflict in statistical terms as a probit with the form Φ(–pπ +
x – cD) ≡ Φ(x′β). Using the standard normal cumulative distribution function to express
the probability of ε being less than or equal to x′β, the probit model is derived from the
bargaining model. This is simply the ε distribution evaluated at x′β. This of course
assumes ε is exogenous and symmetric. However, because the bargaining model suggests ε is endogenous and says little about the shape of its distribution, the probit model
is only loosely derived from bargaining theory. I explore the endogeneity problem
elsewhere (Reed and Hwang 2002). Although past research does not provide an
explicit formal justification for the statistical model, this is essentially the statistical
model used in the published studies that analyze the effect of interdependence on conflict onset.
To evaluate the credibility of the bargaining model, I assess the relationship
between economic interdependence and the variance in the distribution of types of
defenders. Essentially, the goal of the statistical analysis is to estimate the relationship
between economic interdependence and σ from equations (8) and (9) and is central to
evaluating the first hypothesis.
INTERPRETATION
My hypotheses deduced from bargaining theory anticipate the variance in the distribution of types of defenders to be greatest at low levels of economic interdepen-
Reed / INFORMATION AND ECONOMIC INTERDEPENDENCE
65
dence, and this increased variance enhances the likelihood of a militarized clash.
Therefore, the presence of heteroskedastic errors related to different levels of economic interdependence would be consistent with the expectations deduced from bargaining theory and would provide some support for my hypotheses and the bargaining
model. Thus, if I discover evidence of heteroskedastic errors related to different levels of
trade, the first hypothesis is deemed plausible. An observed relationship between interdependence and militarized conflict would suggest the second hypothesis is credible.
Results from the estimation are presented in Figure 2 and Table 1. I plot the means
of the posterior densities of the variance parameters against the economic interdependence variable in Figure 2. The mean of the posterior density for β is reported in the
first column of Table 1.
These mean values are comparable to conventional maximum likelihood estimates
and are consistent with previous research (Oneal and Russett 1997; Beck, Katz, and
Tucker 1998). I report the results from a standard maximum likelihood probit model in
the third column of Table 1 for comparison. Inspection shows the maximum likelihood
estimates and the means of the posterior distributions are similar. Past research that
reports a negative relationship between economic interdependence and militarized
conflict is confirmed. The mean of the posterior density of the trade variable is negative. As states trade more, the probability of militarized conflict decreases. The effects
of the control variables are also consistent with the empirical patterns reported in the
literature. Jointly democratic dyads are less likely to experience militarized conflict;
states that share a border are more likely to fight; states sharing an alliance, experiencing economic growth, and with a relatively unequal balance of military capabilities are
less likely to engage in conflict. These results are also consistent with the comparative
statics from the bargaining model with respect to the costs of conflict on the probability of a militarized clash. Liberal variables associated with costs, such as joint democracy and trade, pacify conflict.
I refer to Figure 2 to evaluate the credibility of my first hypothesis about the relationship between variance in the distribution of types of defenders and the level of economic interdependence. I plot the means of the posterior samples of vi against different
distributions of trade to assess the possibility that the posterior means of vi are a function of economic interdependence. The assumption of constant variance in the errors
and independence between the error and the explanatory variables can be evaluated
visually. The formalization suggests variance will increase as states trade less, and
increases in the variance will be associated with the onset of militarized conflict. Following past research that equates increasing uncertainty with greater error variance
(Downs and Rocke 1979; Alvarez and Brehm 1995), the relationship between trade
and variance in the distribution of types of defenders is informative. The figure shows
the plot of the mean of the posterior densities of the variances against the trade variable. Each plotted point is the mean of the draws from the posterior distribution of vi.
As pairs of states trade less, variance in the distribution of types of defenders and its
proxy, the mean of the posterior distributions for the variances, increase in magnitude.
These results suggest there is a great deal of volatility in the model as trade approaches
zero and that a strong positive correlation exists between less trade and greater variance in the distribution of types of defenders. This illustration provides support for the
66
JOURNAL OF CONFLICT RESOLUTION
Figure 2:
Trade and Information
first hypothesis. There appears to be a link between variance in the distribution of types
of defenders and trade. It is also important to note that the mean of the posterior distributions for the variances appears to come from a mixture distribution. One distribution
has a mean of approximately 1.8, whereas the other distribution has a mean around
1.35. An important next step in this research will involve constructing an empirical
model that not only incorporates the heterogeneity associated with economic interdependence but also accounts for the mixture in the distribution.
Because uncertainty formally results in a nonzero probability of conflict, conceptualizing uncertainty or asymmetric information as a relevant variable that is excluded
from the empirical model suggests excluded variable bias. Earlier work by Morrow
(1989) points to this problem, which is confirmed by Clark and Nordstom (2001), who
suggest a similar interpretation of the effect of uncertainty on the significance of
empirical research that relies on the relationship between the distribution of power,
regime type, and conflict onset. The same logic holds here. If uncertainty is correlated
with trade, it is difficult to make a precise estimate of the effect of interdependence on
conflict onset without first partialing out the effect of uncertainty. As a result, past
research that reports a weak pacifying effect of interdependence is qualified, and to get
a reasonable estimate of the effect of interdependence on conflict emergence, it is necessary to model this heterogeneity that is assumed away by the standard treatments.
Reed / INFORMATION AND ECONOMIC INTERDEPENDENCE
67
TABLE 1
Bayesian Heteroskedastic Probit of Dispute Onset
Variable
Trade
Capabilities
Joint democracy
Growth
Alliance
Contiguity
Intercept
Posterior
SD
MLE
SE
–1.58
–0.0001
–0.0048
–0.0019
–0.0645
0.1451
–0.4558
1.634
0.00002
0.0017
0.0029
0.0242
0.0262
0.0348
–5.11
–0.001
–0.024
–0.007
–0.186
0.380
–0.591
4.436
0.0002
0.004
0.005
0.044
0.044
0.047
Burn-in iterations = 10,000
MCMC iterations = 25,000
Observations = 20,990
NOTE: The mean and standard deviation of the samples produced by the Gibbs sampler are reported in the
first two columns. For comparison, maximum likelihood estimates (MLEs) and their standard errors appear
in the third and fourth columns. MCMC = Markov Chain Monte Carlo.
Not only is there a significant amount of unexplained heterogeneity in the data, the
heterogeneity is correlated with the level of trade. This result demonstrates that the
homogeneity assumption made by international relations researchers using traditional
logit or probit model is unrealistic. Because maximum likelihood estimators are
known to be inconsistent and the covariance matrix may be incorrect (Yatchew and
Griliches 1985) when the variance of the errors is heteroskedastic, the implications of
this analysis are quite broad. Specifically, research that does not address the relationship between the variance in the error and economic interdependence may be incorrect. Although I demonstrate a potential source of the heterogeneity, a much richer
model is needed to correct for the heterogeneity. Additionally, my results provide support for formal bargaining models of international interactions. Increases in the variance of the distribution of types of defenders appear to exhibit the expected effect of
creating the conditions for bargaining to break down, leading to the use of force to dictate the bargains.
CONCLUSION
My results suggest that a focus on traditional world politics explanatory variables
alone is insufficient. Instead, the distribution of information and its relationship to the
standard explanatory variables is a potentially important determinant of international
interactions. I illustrate the effect of information formally and provide a rational explanation for the relationship between economic interdependence and militarized conflict. Bargaining models suggest that if the absence of trade is associated with greater
variance in the distribution of types of defenders, the probability of conflict is greatest
between states with low levels of economic interdependence. The hypothesized link
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JOURNAL OF CONFLICT RESOLUTION
between uncertainty and economic interdependence is corroborated with historical
data analysis, which illustrates a correlation between the level of trade and uncertainty.
This suggests that as states become less economically dependent on each other, uncertainty about their opponent’s type is greatest. I argue that because uncertainty is necessary for conflict, this covariation at least partially explains the observed relationship
between economic interdependence and the onset of militarized conflict.
These findings offer important clues about the credibility of bargaining models of
international politics. The results I report provide tentative, but encouraging, support
for the use of a bargaining framework to understand international interactions. My
argument and results are consistent with others who utilize a bargaining framework
and suggest a much richer relationship between economic interdependence and the
probability of militarized conflict. Specifically, I find that asymmetric information and
greater variance in the distribution of types of defenders is related to trade, and I claim
that the often debated relationship between trade and militarized conflict may, at least
to some extent, be an artifact of the relationship between economic interdependence
and the distribution of information.
Furthermore, I show the logit and probit models frequently employed by international politics researchers may yield inconsistent parameter estimates as a result of the
heterogeneity present in international relations data, and I offer a Bayesian alternative
to the standard empirical models. Evidence is rapidly mounting to suggest heterogeneous data are the norm in international politics (Clark and Nordstrom 2002; BoxSteffensmeier and Zorn 2001; Lemke 2002). As a result, it is essential for future
research to recognize the threat that such heterogeneity poses for inferences about
international interactions. However, this study is not without its weaknesses. It is difficult to make a very sharp inference about the relationship between the variance in the
model and economic interdependence with the simple graphical illustration I present.
Moreover, the statistical model is likely overparameterized and is only identified
because of the priors. An important next step in this line of inquiry is to partition out the
variance in militarized conflict that is explained by information effects from the effect
of economic interdependence. This can be accomplished within the Bayesian framework and avoids the potential problem of overparameterization.10
10. For an example of this approach to a similar problem, see Gill and Meier (2002).
Reed / INFORMATION AND ECONOMIC INTERDEPENDENCE
69
APPENDIX
The first proposition is proved by differentiating the first order condition and noting that marginal increases in the costs of either actor decrease the probability of conflict:
∂F (conflict)
∂(1 − F (conflict))
= − f (conflict),
= f (conflict).
∂(defender' s costs)
∂(challenger' s costs)
The second proposition is proved by differentiating the first order condition and noting that
marginal increases in the stakes of the conflict increase the probability of conflict:
∂F (conflict)
= − pf (conflict).
∂(stakes)
The third proposition is proved by differentiating the first order condition, using h and H instead of f and F, with respect to σ:
∂(1 − H(conflict))
( total costs) h(conflict)
.
=−
∂σ
σ2 π
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