Dyadic Effects, Relevance, and the Empirical Assessment of the Kantian Peace

ABSTRACT

Dyadic effects to a large extent account for the difficulty of explaining and predicting international conflict. In this study, I derive a statistical model to estimate unobserved dyadic effects in the dyadic analysis of conflict. The proposed model employs a hierarchical modeling approach to estimate dyadic effects, thereby avoiding the problems caused by the use of fixed effects models. Furthermore, it simultaneously addresses the important sample selection issue of identifying relevant dyads. I show that the estimation of dyadic effects significantly improves the model fit and generates several interesting findings. Substantively, this study makes an important contribution to the empirical evaluation of the Kantian peace. It argues that international organizations increase the likelihood of conflict of interest between member states but reduce the probability of militarized conflict. I demonstrate that the positive coefficient of international organizations in Oneal and Russett (1999) is biased in the positive direction. When the proposed statistical model is used, international organizations, together with trade and democracy, reduce the probability of conflict.

KEYWORDS:

• Dyadic effects
• hierarchical model
• international organizations
• Kantian peace
• relevance
• split population model

Acknowledgments

I would like to thank Kevin Clarke, Mark Fey, Hein Goemans, Michael Peress, Solomon Polachek, and Curtis Signorino for comments and suggestions.

Supplemental Material

Supplemental data for this article can be accessed on the publisher’s website.

Notes

¹ Only in a problematic politically relevant dyads sample and with the omission of the common control of temporal dependence in the dependent variable do international organizations reveal a constraining effect on conflict.

² One such attempt is in Ward et al. (2007) who introduce a hierarchical bilinear mixed effects model to estimate spatial dyadic interdependence.

³ Split population models are suggested in Beck and Katz (2001) and King (2001) as an alternative to the fixed effects modeling technique. However, in this case a split population model is used to identify relevant dyads instead of modeling unobserved dyad-specific heterogeneity.

⁴ Our familiar example is the data of militarized interstate dispute onset—an observation takes a value of 1 if a MID onset occurs and 0 otherwise.

⁵ Thus far, the presented split population model is equivalent to the one discussed in Xiang (2010).

⁶ Because I estimate individual intercepts in the selection equation, I do not estimate a common intercept due to model identification. In the outcome equation, I estimate a common intercept.

⁷ By assuming zero covariances, the proposed statistical model foregoes the opportunity to model any interdependence between the two equations. This result suggests that the proposed statistical model is inappropriate when our quantity of interest is interdependence between the two processes. Another consequence is that when interdependence is present and has a strong correlation coefficient, assuming zero covariances can potentially cause biased estimates in the two equations. Nonetheless, Xiang (2010) demonstrates that the correlation coefficient between the two equations is very weak (that is, it is equal to .083 and is statistically insignificant) based on his dyadic analysis of conflict.

⁸ Several existing studies also rely on Bayesian approaches to estimate split population models (or zero-inflated regression models). For example, Ghosh, Mukhopadhyay, and Lu (2006) introduce a zero-inflated power series model, and Agarwal, Gelfand, and Citron-Pousty (2002) discuss a hierarchical zero-inflated Poisson regression model.

⁹ Here I denote .

¹⁰ I implement this algorithm in C++ and link it to R.

¹¹ I choose this sample period for two reasons. First, the exchangeability assumption is difficult to justify for the longer time period that covers both the pre-Cold War and the Cold War periods. Second, the majority of observations are missing for the pre-Cold War years. This can cause a serious inference problem if the omission is nonrandom.

¹² In the proposed statistical model, the dependent variable is jointly determined by the relevance equation and the conflict equation. Because each of the three variables affects relevance and conflict in the same direction (for example, Contiguity increases both relevance and conflict), that variable’s expected effect in the conflict equation is captured by its estimated effect in the relevance equation to a large extent. This argument suggests that we can use a probit model when each independent variable affects relevance and conflict in the same direction. However, a simple probit model becomes insufficient when we have a variable that affects relevance and conflict in different directions (for example, International Organizations increases relevance but decreases conflict).

¹³ For example, he does not include the three Peace Year variables in the relevance equation based on the justification that the duration dependence in relevance differs from the duration dependence in conflict.

¹⁴ Model 2 is estimated by the Boolean probit model using the mlboolean command in Stata (Braumoeller 2003).

¹⁵ Model 3 is estimated through Bayesian simulation. I run 1.1 million iterations with the first 100,000 iterations discarded as the burn-in. Moreover, to avoid highly correlated values, I thin the chain by taking every 500th observation.

¹⁶ Future research can further explore how international organizations increase the probability of relevance among member states.

¹⁷ For trade, it is the 90% credible interval.

¹⁸ The six functions are “coercing norm breakers; mediating among conflicting parties; reducing uncertainty by conveying information; problem-solving…; socialization and shaping norms; and generating narratives of mutual identification” (1998:444–445).

¹⁹ Apart from its advantages, the disaggregated analysis has certain disadvantages. For example, measuring international organizations solely based on security-related international organizations is subject to the endogeneity problem, because war drives states to create and join security-related international organizations.

²⁰ The existing studies of the Kantian peace have adopted various research designs. The examples include omitting the variables that control for the temporal dependence, using wars or fatal MIDs instead of all MIDs as the dependent variable, and constructing alternative measures of international organizations. See footnote 3 of Pevehouse and Russett (2006) for a more detailed discussion of the literature.

²¹ Only 6,934 observations are retained in the estimation, which amount to 6% of the original data.

²² Oneal and Russett (1999) show that the Kantian peace is empirically supported based on the politically relevant dyads sample. However, they omit the variables that control for the temporal dependence in their analysis.

²³ This illustration does not suggest that the relevance equation is more important than the dyadic effects. Instead, it argues that even after we control for the dyadic effects in model 3, it is essential to estimate the relevance equation.

²⁴ I thank one reviewer for suggesting this point.

²⁵ This discussion suggests that since globalization has a significant impact on relevance, it is expected that relevance is to a large extent exogenous to state leaders’ decision making on war.

²⁶ Similarly, trade demonstrates an inverted U-shaped relationship, as illustrated in Xiang (2010) and suggested by this study. Since an overwhelming amount of empirical studies show that trade has a pacifying effect on conflict (Oneal and Russett 1999; Polachek 1980; Xiang, Xu, and Keteku 2007), it is likely that its threshold is reached, and increased trade will reduce conflict.

²⁷ A militarized interstate dispute occurred between Argentina and Japan in 1987.

²⁸ As previously mentioned, Pr(Conflict) is equivalent to Pr(Relevance)Pr(Conflict|Relevance) in a split population model.

²⁹ Figure 3 also shows that model 2 outperforms model 1 by a noticeable margin at the high values of the horizontal axis.

³⁰ Since their statistical model does not index time, we cannot include all years in their analysis. As a result, the samples of analysis are very different between their statistical model and the proposed statistical model.