Democracy, Wealth, Distance, and Time: A Parsimonious, Predictive, and Policy Relevant Model of Transnational Terrorism

Transcription

1 Democracy, Wealth, Distance, and Time: A Parsimonious, Predictive, and Policy Relevant Model of Transnational Terrorism Christopher Gelpi Duke University Nazli Avdan Oxford University Paper prepared for presentation at The Annual Meeting of the American Political Science Association August 29 Septeber 2, 2012 New Orleans, LA This is a draft. Please do not cite without permission. Comments are welcome and can be sent to the authors at gelpi@duke.edu Abstract: Which variables are most effective in predicting terrorist attacks, and how well do our statistical models forecast transnational terrorism? We seek to address these questions by analyzing data on transnational terrorist incidents from 1968 to We rely on receiver operating curves (ROC) as a diagnostic tool to assess forecasting ability of various models of terrorist activity. Our analyses yield four central conclusions. First, our model of transnational terrorism provides a fairly strong basis for forecasting attacks at least at the (relatively broad) level of the country-year. Second, while the overall forecasting capacity of this model is fairly strong, the model is also highly redundant in a predictive sense. That is, many of the variables appear to provide similar information in terms of identifying terrorist attacks. Third, four sets of variables stand out as providing the greatest leverage in predicting future terrorism: distance, wealth, democracy, and a history of terrorist violence. Collectively, these variables perform about as well as a more broadly specified model in forecasting terrorist attacks out of sample. Finally, these results suggest that policy makers would do best to focus on wealth and democracy when thinking broadly about how to reduce the incidence of transnational terrorist attacks.

2 Introduction Since the attacks of September 11, 2001, international relations scholarship has witnessed growing interest in transnational terrorism. Terrorism imposes monumental costs on affected countries and generates economic and political repercussions that reach well beyond the tragic costs of each particular attack. These costs bring great policy relevance to the problem of understanding terrorism, and make it especially important that we develop the ability to predict terrorist attacks (Young and Findley 2011). Expanding research into terrorism has improved our understanding into the determinants and consequences of terrorism. Nevertheless, the increased attention to the topic has also yielded controversies and inconsistent findings (Gassebner and Luechinger 2011; Krieger and Meierrieks 2011). The lack of robust empirical findings on what causes terrorism may be attributable to differences in methodological design, explanatory variables, the terror dataset employed, the estimation technique, the time period considered, among other factors. This problem of model dependence substantially inhibits our ability to make policy relevant statements about risks of terrorism because our advice may depend on arbitrary modeling choices that will not generalize outside of the sample of cases used in a particular study. Our intention in this paper is not to arbitrate among these contradictory modeling choices, but rather to develop a robust predictive model of terrorism that can help us to identify the risk factors associated with terrorist activity that can avoid the problems of model dependence. Following the logic of Ward et al (2010), we contend that forecasting ability is an important characteristic of policy relevance. For example, whereas a burgeoning body of literature estimates the average effects of variables like democracy on the incidence of terrorism, much less attention has been paid to the policy relevance of relying on democracy as an indicator of the risk of terrorism. Does knowing the regime type of the potential target and base states actually help us to predict when transnational terrorist attacks will occur? Which variables are most effective in predicting terrorist attacks? And how well do our statistical models forecast transnational attacks?

3 We seek to address these questions by drawing upon recent innovations in the analysis of multilateral international behavior (Poast 2010). More specifically, we employ an empirical framework that allows us to model the flows of terrorist activity from terrorist bases in multiple states toward targets in other states. We analyze data on transnational terrorism incidents from 1968 to 2007, drawn from the ITERATE database (Mickolous et al. 2007). Relying on receiver operating curves (ROC) as a diagnostic tool to assess forecasting ability, we show that democracy in the targeted state, the minimum level of democracy of origin states, and Gross Domestic Product (GDP) of the target in conjunction grant the greatest leverage in predicting transnational terrorism. Moreover, we show that a simple model relying on these four factors does a reasonably good job of predicting most transnational terrorist attacks, although there obviously remains room for improvement. Most importantly, our forecasts are restricted to the country-year level. While predictions of terrorist attacks at this level of aggregation may be relevant to broad strategic approaches to counter-terrorism, more fine-grained data and theories of terrorist activity would be necessary to provide operational forecasts about the specific timing and location of attacks. Nonetheless, our paper makes a significant contribution in moving beyond an explanatory framework toward a predictive one. Basing policy recommendations on probabilistic statistical summaries may be misleading insofar as the results from these analyses do not transfer beyond the sample analyzed (Ward et al. 2010). Importantly, the statistical significance of a variable is not necessarily equivalent to its predictive capacity. In fact, statistically significant variables may degrade the predictive power of a model (Gill 1999). As a result, in order to avoid policy prescriptions that depend on erroneous models, scholars need to identify the most important predictors of transnational terrorism. Our paper serves as a step toward accomplishing this goal. The rest of the paper proceeds as follows. The first section engages in a discussion of predictive ability from a policy standpoint. The second section draws on empirical literature on terrorism to construct the statistical model we employ in generating our forecasts. The third section provides an

4 overview of data and variables, followed by empirical analysis. Finally, we recapitulate our findings and conclude with suggestions for future scholarship. Predictive Ability and Policy Relevance As is the case with civil and interstate conflict (Ward et. al. 2010), the bulk of quantitative scholarship on transnational terrorism relies on testing the statistical significance and generating the predicted marginal impact of variables thought to be theoretically relevant. In this framework, one or more variables are found to be statistically and substantively significant, leading scholars to proclaim these factors as important determinants of terrorism. This approach is not surprising given that many scholars of conflict shifted attention to political violence in the wake of the 9/11 attacks (Young and Findley 2011). Undoubtedly, this literature is invaluable in explaining the whys and hows of terrorism, but it runs into problems when generating insights into the when and where. There are several ways in which studies that rest on statistical significance may lead us astray. First, the study of conflict behavior including transnational terrorism often involves using complex multivariate statistical models to analyze highly rare events. Sparse data coupled with a wide parameter space implies that estimated marginal effects for particular individual variables may be based on extrapolations of the model to thinly populated areas of the sample or may be based on highly implausible counterfactual scenarios that take a large number of collinear variables and hold all but one of them constant while varying the other. This issue has been termed the curse of dimensionality by demarchi (2005) as well as the authoritarian Canada problem by King and Zeng (2007). Second, many estimates of marginal effects are generated within a particular sample without concern for whether the model generalizes well outside of the estimation sample (Beck et. al. 2000; demarchi et. al. 2004). Statistical significance loses its import to the extent that it is dependent on the idiosyncrasies of a particular dataset and as such does not convey information about other samples. This is especially important in terms of policy relevance for statistical models, since the policy utility of such models inherently depends on out-of-sample performance.

5 Third, highly complex models of rare events may lead to a problem of overdetermination. Given the very large number of cases in many conflict datasets, variables may easily generate a statistically significant association with the relatively rare incidents of conflict even if they are highly collinear with other variables in the model. Generating separate estimated marginal effects in this context is misleading in terms of its ability to help us predict conflict because each variable provides relatively little independent information about the dependent variable. While each variable may have a large estimated (hypothetical) marginal effect, the model may predict conflict just as accurately without one or more of these variables because the information provided by other variables yields the same forecast. Consequently, we examine the explanations of terrorism by evaluating their effectiveness in forecasting terrorist attacks. The act of making policy is at its core a matter of forecasting. Policy makers must use available information to make predictions about the likely behavior of both potential allies and adversaries. Moreover, the forecasts made by policy makers will always be generalizing beyond the sample of available cases from which to make predictions. Thus traditional measures of in-sample fit and predicted effects may not be relevant for understanding cases outside the estimation sample. In sum, in accordance with Ward et al. (2010), we believe that an analysis of out-of-sample forecasting provides a better guide toward developing policy relevant models of conflict both because it ensures robust causal inference (Beck et. al. 2000; demarchi et. al. 2004; Jenke and Gelpi 2012) and because it identifies the key sources of independent information necessary to identify and predict the onset of conflict. A Model of Transnational Terrorism We develop our model of transnational terrorism based on a combination of both target and origin country characteristics that we expect will influence flows of transnational terrorism. Target traits refer to characteristics of the state in which a transnational terrorist attack occurs, while origin traits refer to characteristics of the network of states from which a transnational terrorist attack is

6 launched. We focus on traits identified in the baseline model of transnational terrorism employed by Gelpi and Avdan (2012). We have grouped these traits into sets of arguments about the sources of transnational terrorism, and our analysis will evaluate the contribution that each of these groups of arguments makes to our ability to forecast transnational terrorist activity. Distance We expect that terrorism will be facilitated by physical proximity between states. Because terrorist organizations frequently lack the ability that states have to project violence over distance such as ships and aircraft we expect terrorism to have a pronounced predictive impact on the flow of transnational terrorism. While we may be familiar with al-qaeda s 2001 attack on the United States from a great distance, this is an exception rather than the norm. The expectation that terrorism occurs in short range is buttressed by the literature. If we view transnational terrorism as bilateral activity between origin and target states, the logic of the gravity model widely applied in modeling capital and trade flows between states travels readily to flows of political violence (Blomberg and Hess 2008). Simply put, the gravity model predicts distance to negatively affect terrorism. A complementary perspective emphasizes spatial contagion such that proximity to countries that are exporters of terrorism makes the production of terrorism on a state s own soil more likely (Krieger and Meierrieks 2011; Midlarsky et al. 1980). Terrorist activity may be geographically concentrated also through the diffusion of tactics, weapons, and recruitment among terrorist groups across a network of states (Heyman and Mickolus 1980). Refining this argument, Braithwaite and Li (2007) have documented that terrorist attacks are more likely when states are located in terrorism hot spots neighborhoods consisting of proximate states in which violent activity abounds. Similarly, Drakos and Gofas (2006) empirically show that terrorist assaults are determined by location in certain world regions. Consistent with this literature, we expect distance to exert a non-linear effect on terrorism, with the natural log of distance functioning as an important predictor.

7 Power and Alliances : Military alliances may be important predictors of terrorism assaults to the extent that they mirror common security interests between states (see, for example, Bueno de Mesquita 1981; Bremer 1992; Crenshaw 2001; Dreher and Gassebner 2008). The nature of the relationship between interstate common security interests and the flow of transnational terrorism may be shaped by the relationship between the terrorist organization and the government of the origin states. In situations where a government is providing safe haven for a terrorist organization, we might expect a negative relationship between alliance ties and terrorism for a combination of reasons. For example, terrorist groups may share common goals and interests with states allied to their patron, and even in the absence of such common interests, host governments will discourage terrorists from targeting their allies. In situations where terrorist organizations are in conflict with the government of the origin state, on the other had, we may see an increase in terrorist activity toward the origin state s allies especially if those allies are providing support to the host state (Addison and Murshed 2005). The transference of terrorism abroad to allies increases with power differentials between origin and target states (Neumayer and Plumper 2010). Integral to this effect is the assumption that terrorist organizations are strategic actors that capitalize on targeting militarily powerful allies to bolster support for their cause, gain visibility, and gain influence against their own governments. Targeting the nationals of powerful allies grants terrorist organizations leverage back home, especially if allies provide military support to base country governments (Neumayer and Plumper 2011). This is congruent with the view of terrorism as a weapon of the weak (Crenshaw 1981; Lake 2002; Pape 2003) whereby terrorism is the preferred tool to achieve goals than the direct application of military force (Pape 2003). In addition, very powerful states tend to have security interests and a military presence that encroach upon the interests and activities of many smaller states. Savun and Phillips (2009) extend this argument to proclaim that the foreign policy behavior of democracies renders them particularly vulnerable to terrorism. Accordingly, we include alliances and power differentials between origin and target states in our predictive model of terrorism.

8 Rivalry: Diehl and Goertz (2001) identify enduring interstate rivalries as the source of preponderance of military conflict between states. States sometimes use terrorist groups as tools to pursue their foreign policy goals when the direct use of violence may be costly or unsuccessful. The exploitation of terrorism as a less costly vehicle to advance foreign policy interests is particularly likely in the context of rivalry if we consider that rival states generally mobilize all available resources to confront their opponents and so are more likely to support terrorist activity as part of this effort. In particular, the non-hierarchical structuring of transnational terrorism endows non-state actors with a distinct upper hand over states (Sandler 2003). Terrorists ability to form cross-border networks confers on them an asymmetrical advantage over states, rendering terrorism an attractive (and less costly) avenue through which sponsor states pursue aggressive goals without engaging in conventional warfare. More recently, Conrad (2011) has built on this argument to demonstrate that terrorism proxies for interstate violence. Using a monadic level of analysis, he shows that involvement in rivalries correlates positively with being targeted in attacks of terrorism. Extending this argument to the dyadic framework, Findley et al. (2012) show that rivalry increases the risk of terrorism within pairs of states. The rationale behind their argument is that it is less costly for states to clandestinely support terrorist groups than to engage in military attacks against target states. If policies are unpopular at home such as in the case of UK s support of Loyalists in Northern Ireland, terrorism affords plausible deniability. Alternatively, if terrorist goals are congruent with popular support, it allows the government to avoid international limelight. Furthermore, terrorism can compensate for strategic military weakness, as illustrated by Iran s support of Hezbollah and Hamas against Israel. Thus to the degree that rivalries tap into past conflict history between states, we expect rivalry to be an important predictor of transnational terrorism. Colonial and Ethnic Ties: Colonial experiences have a powerful and lasting effect on governance and levels of civil violence within states (Wilkinson 2008), and an enormous literature has developed around the impact of ethnicity and ethnic ties on violence (see, for example, Fearon and

9 Laitin 2003; Chandra and Wilkinson 2008, Toft 2010). The legacy of colonialism may shape the relationship between the developing and the developed world in a variety of ways. With regard to terrorism, the decolonization process left in its wake unresolved grievances that may provide a motive for transnational terrorism. Moreover, the economic and social ties that continue to bind colonies and their former occupiers may facilitate carrying out such attacks. Similarly, several studies have identified the treatment of ethnic diasporas in target states as a potential trigger for terrorism. While no consensus exists on the exact mechanism by which ethnic divisions encourage terrorism, ethnic, religious, and/or linguistic fractionalization are associated with greater frequency of terrorist incidents. Conversely, countries with homogeneous populations experience less terrorism (Basuchoudhary and Shughart 2010; Tavares 2004). An ancillary argument is that terrorism flows from the periphery to the metropole because Western countries constitute attractive targets and hold strategic value (Neumayer and Plumper 2009). 1 By targeting powerful states in the metropole, terrorist leaders seeking political change at home strategically seek media attention and global reach. Accordingly, we include colonial and ethnic ties between target countries and origin states as potential predictors of terrorism. Democracy: Students of terrorism have invested considerable intellectual resources into pinpointing the linkage between democracy and terrorism. Empirical scholarship is replete with conflicting findings, pointing to statistically significant negative, positive, or nonlinear effects that are sensitive to model specification (Gassebner and Luechinger 2011; Piazza 2008). Theoretically, scholars have proposed two countervailing arguments: on the one hand, increased liberties and a permissive institutional environment facilitate terrorist activity by decreasing the price of violence (Eubank and Weinberg 1994). At the same time, democracies lack the coercive tools to prevent or retaliate against political terror (Crenshaw 1981; Eubank and Weinberg 1994, 1998, 2001; Eyerman 1998; Schmid 1 Neumayer and Plumper test Huntington s clash of civilizations argument by examining whether terrorism flows across civilizational fault lines. They argue that strategy and not ideology is central to understanding terrorist activity targeting Western states.

10 1992). A second mechanism is that the institutional constraints on the executive branch of the target state will increase the risk of a terrorist attack (Li 2005). Adding more nuance to the institutional constraints argument, Young and Dugan (2011) argue that the central characteristic in democracies that invites terrorism is the number of veto players. By decreasing the likelihood of policy change, proliferation of veto players translates into a higher frequency of terrorism. 2 Third, democracies may also be prone to violence due to a crowding-out effect whereby dissatisfied groups resort to extreme measures to get their demands across to the government (Chewoneth 2010). Additionally, democracies constitute soft targets for terrorism due to casualty intolerance; the expectation that democratic leaders will more readily offer concessions to terrorist demands increases the probability of violence against them (Pape 2003; 2006). More recently, Savun and Phillips (2009) have challenged the literature that locates democratic vulnerability in institutional traits by surmising that what attracts transnational terrorism is aggressive foreign policy behavior of democracies. In sum, while pointing to different mechanisms, the majority of studies expect democracy to increase the risk of terrorism. On the other hand, a smaller contingency of scholarship expects democracy to diminish terrorist violence. The theoretical underpinning of this expectation is that democracies discourage terrorism by providing non-violent alternatives for pursuing policy change and expressing grievances (Eyerman 1998; Gassebner and Luechinger 2011). Thus, the extension of civil liberties in democratic states allows for legitimate channels of political participation and obviates the desire to engage in violent dissent, lowering the probability of terror in democratic states (Li 2005). Another implication is that well-established democracies rather than democratizing states witness fewer terrorist attacks because they are able to grant stable and recognized channels for grievances to be resolved (Eyerman 1998). Analogously, Walsh and Piazza (2010) have proposed that respect for physical integrity rights counters terrorism and that conversely violation of these rights incites terrorism by reducing 2 This argument applies to both homegrown and foreign terrorism. The distinction between homegrown and foreign terrorism is not the same as between domestic and transnational because the coding of terrorism is done according to the nationality of perpetrators and not the nationality of targets. Thus attacks include all those that take place within target s territory, whether the terrorists are homegrown or foreign.

11 international and domestic willingness to aid in counter-terrorism efforts. Thus, it is the behavior of democracies vis-à-vis their publics and not their institutional features that directly mitigates terrorism. Alternatively, Choi (2010) contends that legitimately held rule of law protects democracies from terrorism by allowing citizens to convey their discontent peacefully. To the extent that rule of law provides an effective conflict resolution mechanism, democracies experience fewer incidents of domestic and transnational terrorism. More recently, scholarship has stressed the importance of distinguishing between the effects of democracy according to perpetrator and target characteristics (Gassebner and Luechinger 2011; Krieger and Meierrieks 2011; Young and Findley 2011). In this vein, Blomberg and Hess (2008) dissociate the effects of globalization in net importers (targets) and net exporters (origins) of political violence. In a similar spirit, Krueger and Laitin (2008) examine the impact of GDP per capita and democracy in host and origin countries, additionally comparing the effects of terrorism according to location of attack and nationality of victims. Similarly, Blomberg and Rosendorff (2009) evaluate the simultaneous effect of democracy in source and origin states. An emerging conclusion from the recent literature is that democratic institutions in the target countries increase transnational terrorism while they decrease terrorism in the source countries. Dyadic studies of terrorism attempt to remedy the drawbacks of employing the state as the unit of analysis: whereas monadic approaches shed light on state-level characteristics that attract or repel terrorism, they fail to account for the transnational nature of terrorism (Young and Findley 2011). Gelpi and Avdan (2012) extend this strain of the literature by not only differentiating between origin and target democratic traits but also recognizing that terrorism is spread across a set of origin countries. This offers a novel way to fully account for the transnational nature of terrorism by modeling it as a multilateral process. Their framework recognizes the possibility that terrorist organizations may relocate operations from one source country to another. Furthermore, the authors identify more precise mechanisms by causally linking particular attributes of democracy in origin and target states to terrorist activity in the k-adic network. In particular, they find that political competitiveness in target states

12 increases the probability of terrorist incidents whereas civil liberties dampen terrorist activity in origin states. Accordingly, we include democracy in origin and target states in our forecasting model. GDP: Democracy and wealth may function in tandem to incentivize terrorism. In fact, scholarship has found it difficult to tease apart the independent effect of economic development on terrorism (Krieger and Meierrieks 2011). This is unsurprising considering that higher levels of economic development coincide with democratic governance (Przeworski and Limongi 1993). Economic wealth may correlate with high institutional quality, rendering wealthy democracies attractive targets for terrorism (Eyerman 1998; Li 2005). If terrorism functions as a weapon of the weak (Gassebner and Luechinger 2011; Lake 2002), it is more likely to flow from poorer countries toward powerful wealthy states. Krueger and Laitin (2008) find for example that whereas oppression correlates with terrorism in source states, the targets of attacks are often countries that bask in economic wealth. Consistent with this argument, attacking wealthy states is more lucrative for terrorist organizations because attacks against these countries will deliver more media coverage (Eyerman 1998). Alternatively, terrorists seeking agenda-setting discretion over the economy stand to gain more from targeting states with greater economic resources (Blomberg et al. 2004). In particular, dissidents are more likely to resort to terrorism than to attempt to overthrow the government in richer countries with sound institutions given the higher cost of rebellion in well established states with strong standing armies. Although this argument does not discriminate between domestic and transnational terror, it follows the notion of terrorism as a less costly form of political violence wielded against wealthy states with good institutions. Thus, we predict GDP and democracy together to increase the risk of terrorist incidents. Peace Years: Previous research on dyadic cross-sectional time series data has demonstrated the importance of controlling for the temporal dependence of these data (Beck, Katz, and Tucker 1998). More precisely, in parallel to spatial proximity effects, temporal proximity is an important determinant of terrorism incidents (Krieger and Meirrieks 2011). Put differently, terrorism exhibits a strong self-

13 perpetuating nature (Midlarsky et al. 1980). It is more profitable for terrorist organizations to maintain terrorist campaigns than to undertake isolated incidents. This set of variables provides a useful substantive baseline for evaluating the importance of other predictors of terrorism relative to a simple model that says that terrorist will occur in the future where it has occurred in the past. Data We test our hypotheses on a sample of directed k-ad-years from 1968 to 2007 developed by Gelpi and Avdan (2012). Each k-ad-year identifies one state as the target of attack and the set of base countries from which the flow of terrorist violence originates. For a full description of the coding procedures used for creating this dataset see Gelpi and Avdan (2012). Analyzing pairs of actors in a dyadic framework has long been the most common empirical approach for the study of interstate conflict, and this approach has recently spread to include the study of transnational violence like terrorism. While important tools for analyzing dyadic data where outcomes are interdependent across the observational units such as spatial lags and network models have been developed for the analysis of conflict data (Ward and Gleditsch 2002; Simmons et al. 2006; Franzese and Hays 2007; Warren 2009; Neumayer and Plumper 2010), the k-adic framework addresses a conceptual problem that is distinct from and prior to the problem of non-independence across dyads (Poast 2010). Network models assume a causal process in which the data are generated through the interaction of pairs of nodes in a network (e.g. dyads) but the outcomes across these dyadic interactions are interdependent (Beck, Katz, and Tucker 1998; Franceze and Hays 2007). Thus if an outcome is generated by more than two actors in a network, then the true probability of outcome will be incorrectly estimated by employing a dyadic framework. The k-adic approach, on other hand, is designed to target the inferential bias that accrues from splitting phenomena that are multilateral in nature into dyadic components. Thus we believe that a k-adic rather than dyadic unit of analysis is conceptually most appropriate for capturing the transnational nature of terrorist organizations. One defining feature of many terrorist

14 networks is their ability to organize across a set of base countries and to utilize these states as bases for training, mobilization, and for launching attacks (Sandler et al. 2009). This characteristic of terrorist organizations implies that transnational terrorist attacks are often multilateral events that involve 3 or more countries. Since data generation process (DGP) for transnational attacks inherently multilateral, dyadic models of these attacks will be inherently misspecified, and a k-adic approach to analyzing these data is necessary in order to avoid biased inferences (Poast 2010 ). 3 Poast (2010) develops a method for generating k-adic observations from dyadic data by building on King and Zeng s (2001) sampling procedure that generates a dataset that includes all observations in which the dependent variable takes on the value of one and a random sample of k-ads in which the dependent variable takes on a value of zero. 4 We employ King and Zeng (2001, (see also Tomz et. al. 1999) rare event logit estimator to adjust for bias resulting from differential sampling rates for the zero and one observations on the dependent variable. 5 Gelpi and Avdan (2012) develop a dataset of 224,201 k-ad-year observations with 1,565 incidents of transnational terrorism. The data include a relatively large number of different target states. Specifically, they identify 126 different targets of transnational terrorist attacks between 1968 and The most frequently targeted states include France (136 incidents), the United States (90 incidents), Lebanon (81 incidents), and Britain (72 incidents). Israel is the target of somewhat fewer transnational attacks than one might expect (34), because attacks launched from the West Bank and Gaza count as domestic rather than transnational since those territories are not recognized as independent states. Two thirds of these terrorist incidents involve violence flowing from a single base state to a target. Nearly 25% of the attacks, however, involved two distinct base states, while about 8% of the 3 This type of bias is distinct from other types identified in the literature as pertaining to dyadic analyses. For a discussion of other types of bias with dyadic data, see Beck and Katz 2001; Green et al. 2001; Signorino The corresponding Stata ado file for creating k-adic data from dyadic datasets (kadcreate) can be found at 5 We use the prior correction method to adjust for oversampling of incident k-ads. For the purposes of this paper and in the absence of knowledge about the true proportion of ones in the population, we take the default prior correction option of setting the correction weight to zero. Additionally, we employed the probability weights generated after running kadcreate in order to adjust for differences in sampling of groups of differing sizes.

15 attacks involved three or more base states as the source of the terrorist attack. This distribution illustrates the utility and importance of the k-adic empirical framework for studying a multilateral activity like transnational terrorism. A dyadic perspective on these attacks would appear to misspecify the data generation process for approximately one-third of transnational terrorist attacks. Our dependent variable is the occurrence of incidents of terrorism against the target state by a group operating in the base states of the k-ad during a given year. Gelpi and Avdan (2012) code the occurrence of incidents from the International Terrorism: Attributes of Terrorist Events (ITERATE) data from (Mickolus et al. 2007). ITERATE codes the presence of a terrorist attack based on sources such as Reuters, Associated Press, United Press International, Foreign Broadcast Information Services (FBIS), Daily Reports, and major US newspapers. To qualify as a transnational terrorist incident, an attack must reach across national boundaries either through the nationality of its perpetrators, its location, the nationality of its victims, the mechanics of resolution, or the ramifications of the incident (Mickolus et al. 2007). If a terrorist attack was recorded against a target state in a given year from any of the bases in the k-ad, the incident variable was coded as 1, and 0 in the absence of an attack. Gelpi and Avdan (2012) code identities of base countries according the identity of the terrorist organization specified by ITERATE as culpable for a particular incident. They compiled a list of base countries for terrorist organizations from the Global Terrorism Database (GTD), Terrorism in Western Europe, Events Data (TWEED), and the National Consortium for the Study of Terrorism and Responses to Terrorism (START) (LaFree 2010; Elgar 2004). 6 Gelpi and Avdan (2012) code independent variables for k-ads based on the weakest link assumption (Oneal and Russett 1997; Poast 2010). That is, ordinal variables such as the democracy score and interval variables such as distance between the target and the bases are set to equal the minimum and/or maximum of the score for the base state countries. Dichotomous variables such as ethnic or colonial ties take on the value of 1 if the corresponding dyadic variable for any of the target country-base country pairings equals 1. 6 The profile database can be accessed at

16 As discussed above, Gelpi and Avdan s baseline model of transnational terrorist activity includes numerous distinct theoretical arguments about the origins of transnational terrorist activity. In order to analyze and compare the policy relevant impact of these different arguments some of which may be reflected in several variables in the model we divide these correlates of terrorism into conceptual groups of arguments about the sources of transnational terrorist activity. Distance: We test arguments about the impact of distance on the flow of transnational terrorism by calculating the log of the minimum distance between the target and any one of the base states. Data on distance was derived from the EUGene data management program (Bennett and Stam 2000). Power and Alliance: We test the impact of arguments about power and alliances through a combination of several variables. First, we record the Great Power status of both target and base states according to the Correlates of War dataset on system membership. We code the Great Power status of the target state as a dummy variable with a value of 1 when the COW identifies the target as a Great Power. Similarly, we record the Great Power status of the potential base states as a dummy variable with a value of 0 for k-ads in which none of the potential bases are Great Powers. If any of the base states in the k-ad is a Great Power, we record a value of 1. Next, we measure the impact of alliance ties based on the Correlates of War dataset on alliances. Specifically, we record a value of 1 if the target has a COW alliance of any kind (defense pact, entente, or neutrality pact) with any of the base states. We record a value of 0 otherwise. Consistent with Gelpi and Avdan (2012) we allow the impact of alliance ties to vary across the Cold War and Post-Cold War eras by interacting the alliance dummy variable with a dummy variable marking the Post-Cold War era. Rivalry: Our evaluation of the impact of interstate rivalries on the flow of transnational terrorism is based on Goertz et al. s (2006) revised dataset on enduring rivals. Goertz et. al. (2006) code interstate disputes that were not isolated conflicts and exhibited spatial consistency and involved the military use of

17 force are coded as rivalries. 7 We code our dummy variable with a value of 1 if the target state was involved in an enduring rivalry with any of the base states during a particular year. Colonial and Ethnic Ties: Our estimation of the policy relevant impact of colonial and ethnic ties on the forecasting of transnational terrorism is also based on the impact of a combination of variables. We measure colonial history with a dummy variable that is coded 1 if any of the target country base dyads share a colonial past (Alesina and Dollar 2000). And we rely on Huth and Allee s (2001) dichotomous measure for ethnic ties in a dyad and update this measure to This k-adic measure of ethnic ties equals 1 if any of the base countries possess ethnic co-nationals in the target country. Consistent with Gelpi and Avdan (2012), we allow the impact of ethnic ties to vary across the Cold War, Post-Cold War, and Post-9/11 historical eras. Democracy: We test the importance of wealth and democracy for predicting terrorist attacks with a combination of three variables. We measure the wealth of the target state as the log of the gross domestic product (GDP) of the target state. We measure the democracy of both target and base states with scores from the Polity IV Project (Marshall and Jaggers 2000). As has become standard in the literature for the use of Polity data, we measure the overall level of democracy in both target and base states by subtracting the autocracy score from the democracy score. This procedure yields a variable ranging from -10 (representing extreme autocracy) to 10 (full democracy). For the target state we measure overall democracy with this Polity IV democracy score, and for the base states we record the minimum democracy score among all of the bases. Peace Years: We control for the temporal dependence of transnational terrorism within our k- adic dataset by accounting for the number of years since the most recent terrorist incident from any of the 7 In alternate models that we do not present here, we also employed a Militarized Disputes Dummy from the MIDs dataset. We rely on the Goertz rivalry measure because it is less vulnerable to problems of endogeneity.

18 bases occurred in the target state. In order to allow for a flexible and robust functional form for the impact of time, we transform this variable into a cubic spline. Analysis We examine the importance of each of these sets of variables by evaluating their effectiveness in forecasting terrorist attacks. demarchi, Gelpi, and Grynaviski (2004) demonstrate the importance of relying on Receiver Operating Characteristic (ROC) curves when evaluating a model s ability to forecast. Specifically, the use of ROC curves accounts for the arbitrary assumptions inherent in logit or probit estimations of the constant term in the statistical model so that the comparison of forecasts can be robust across all possible thresholds for predicting failure (i.e. violence). Previous work on interstate conflict has sometimes relied on classification tables of outcomes based on a 0.5 predicted probability of conflict or war (Huth 1988, Beck, King and Zeng 2000). However, the arbitrary nature of threshold estimation for probit and logit models makes the use of any single cutoff criterion for classifying cases generally inappropriate (Greene 1997; p ; King and Zeng 2001; p and Swets 1988; p ). ROC curves provide one solution to the problem of arbitrary thresholds, as they are designed to evaluate the trade-offs between false-positive and false-negative errors in forecasting (Swets 1988). These curves plot the proportion of positive cases correctly predicted against the proportion of negative cases correctly predicted. Thus each point on the ROC curve reflects the balance of false-positive and false-negative errors in prediction for a single threshold used for prediction. The area below each point on the curve represents the proportion of true negatives for that threshold, while the area above the point indicates the proportion of false positives. Similarly, the area to the left of a point on the curve corresponds to the proportion of true positives for a given threshold, while the area to the right of the point represents the proportion of false negatives. The critical quantity of interest for comparing ROC curves is the estimated area underneath the curve, which varies between 0 and 1. A value of 1 indicates a model that perfectly predicts every case,

19 while a value of 0 reflects a model that is exactly wrong in every case. 8 However, since one can obtain a value of 0.5 by predicting the outcomes at random, an area of 0.5 provides a more useful baseline for comparison as a null model rather than 0. Importantly, because ROC curves account for all possible thresholds of prediction, greater areas under the curve indicate a model s ability to better forecast without reliance on arbitrary thresholds. Finally, we can test whether estimated areas under an ROC curve differ statistically from one another by estimating a 95% confidence interval around each curve. Results We begin with the replication of Gelpi and Avdan s (2012) baseline model results. The coefficient estimates for this model are displayed in Table 1. This model identifies a large number of statistically significant relationships between a wide variety of independent variables and the incidence of transnational terrorism. Specifically, the models indicates that distance, Great Power status, alliances, inter-state rivalries, colonial and ethnic ties, wealth, and democracy all can have a statistically significant impact on the probability of a transnational terrorist attack. Table 1 About Here This baseline model confirms many expectations from the literature regarding the sources of transnational terrorist attacks, but how robust are these variables in terms of actually forecasting attacks, and which variables contribute the most leverage to those forecasts? In order to address these questions, we divided the Gelpi and Avdan data into a training set and a test set based on draws from a uniform random distribution ranging from 0 to 1. All cases assigned a value of 0.9 or lower were assigned to the training set and those assigned a value greater than 0.9 were assigned to the test set. The training set contained 201,844 cases and 1,404 attacks, while the test set contained 22,196 cases and 161 attacks. We generated out-of-sample forecasts by estimating coefficients for each of our models on the training set and then using those coefficients to predict the outcomes in the test set. 8 The latter result would still reflect perfect (if rather odd) discrimination between positive and negative cases.

20 To illustrate the interpretation of ROC curves for evaluating and comparing forecasts, Figure 1 displays the estimated ROC curves for the two baseline comparison models that we use in our analysis: Gelpi and Avdan s baseline model, and a model of terrorist attacks based solely on the peace years variables. The vertical axis in Figure 1 depicts the proportion of true positive outcomes (i.e. terrorist attacks) that are correctly predicted by each model at each possible forecasting threshold. This is known as the specificity of the model. The horizontal axis displays the proportion of true negative outcomes (i.e. non-attacks) that are incorrectly predicted by each model. This measures the false positive rate (or selectivity) of each model. The ROC curve for a perfect forecasting model would be a vertical line along the Y-axis going from 0 to 1 and then extending horizontally across the X-axis from 0 to 1. This result would indicate that the model correctly predicts 100% of the true positive outcomes without mispredicting any of the true negative outcomes. The area underneath (i.e. below and to the right of) this curve would be 1.0. Figure 1 About Here The black line in Figure 1 depicts the ROC curve for the Gelpi and Avdan baseline model when estimated on the training set and forecast onto the test set outcomes. The dark grey line in Figure 1 depicts the ROC curve for a model that forecasts outcomes in the test set solely from a model based on the analysis of peace years in the training set. Finally, the light grey line depicts the ROC curve that would result if one randomly assigned probabilities of an attack to each case. The black line representing the baseline model is clearly above and to the left of the dark grey line representing the peace-years model. Both models are capable of correctly predicting about 25% of the terrorist attacks without generating many false positive predictions. At this point, however, the peace-year model begins making a substantial number of false positive predictions in order to continue increasing the number of correct positive forecasts. The baseline model, on the other hand, can correctly predict nearly 75% of transnational terrorist attacks while only generating a false positive rate of about 10%. The peace-years only model generates a false positive rate of nearly 50% in order to accurately predict the same proportion of terrorist attacks.

21 However, the selectivity of the baseline model begins to drop off as well as if we ask it to predict more than 75% of the attacks. In order to push the true positive rate near 90%, for example, the model generates a false positive rate of about 25%. Once we seek to push the true positive rate near 98% there is once again little difference between the baseline and peace-years models. In this case, both models must accept a very high false positive rate in order to correctly predict the last few terrorist attacks. Not surprisingly, baseline model forecasts more accurately than the peace-years only model, and this accuracy is reflected in the greater estimated area underneath its ROC curve. As the legend in Figure 1 indicates, the estimated area underneath the ROC curve for the baseline model is , while the area underneath the ROC curve for the peace-years model is Figure 2 displays the estimated area underneath the ROC curve for the baseline model as well as a number of additional estimates that drop different variables from the baseline model. The circles reflect the estimated area under the ROC curves, while the vertical bars represent the 95% confidence intervals around those estimates. Since one can generate an area of 0.5 under the ROC curve by guessing at random, Figure 2 compares estimated areas under the ROC from 0.5 to 1. To the extent that each variable (or set of variables) contributes significantly to the ability of the baseline model to forecast attacks, we will observe a decline in the estimated area under the ROC when that variable is excluded from the model. Figure 2 About Here As noted above, the Gelpi and Avdan (2012) baseline model yields an area under the ROC curve of 0.88, which indicates that the model is fairly robust in forecasting out of sample. In fact, the out-ofsample area under the ROC does not differ significantly from the in-sample fit of 0.90, and also compares favorably with the forecasting abilities influential models of both inter-state disputes and civil wars. Jenke and Gelpi (2012), for example, demonstrate that Bennett and Stam s (2004) comprehensive Behavioral Origins of War model of militarized disputes generates an area under the ROC curve of 0.88 when used to forecast out of sample. Similarly, Ward, Greenhill and Bakke (2010) demonstrate that Collier and Hoeffler s (2004) model of civil war yields and area under the ROC curve of 0.82, while

22 Fearon and Laitin s (2003) model of This latter result is not much better than the forecasting ability of the peace-years only model displayed in Figure 1. Thus results suggest that the Gelpi and Avdan (2012) baseline model provides a very useful starting point for evaluating the contributions that different variables make to our ability to forecast terrorist attacks. 9 The next estimate in Figure 2 depicts the forecasting abilities of the baseline model when we remove distance between the target and base states from the estimation. Not surprisingly, the area under the ROC curve drops, but the decline is relatively modest. Specifically, the area under the ROC curve for the model without distance is This estimated difference is not quite statistically significant at the 0.05 level. Thus while distance is generally regarded as having a very substantial impact on the flow of terrorist activity, the model does not perform significantly worse without it. The next three estimates reflect the forecast of the baseline model with variables capturing power and alliance variables, inter-state rivalry, and ethnic and colonial ties. The areas under the ROC curve with each of these sets of variables excluded from the model are 0.88, 0.87, and 0.89 respectively. None of these forecasts approach being statistically significantly different from the baseline model. In fact, the areas under the ROC curve actually increases slightly when the power and alliance variables or the ethnic and colonial tie variables are excluded from the model. Thus while Great Powers are statistically significantly more likely to become the targets of terrorism, this information does not help us to predict terrorist attacks above and beyond the other variables in the baseline model. Similarly, while the Gelpi and Avdan (2012) model shows that ethnic or colonial ties or the existence of an inter-state rivalry between the target and base states increases the probability of a terrorist attack, the model is equally capable of forecasting terrorism without this information. 9 Consistent with concerns raised by Jenke and Gelpi (2012), we estimated out of sample forecasts across the three historical eras identified in the Gelpi and Avdan dataset. We found considerably greater cross-temporal stability for the Gelpi and Avdan model of terrorism as compared to the Bennett and Stam (2004) model of militarized disputes. Specifically, estimating the Gelpi and Avdan baseline model on a training set restricted to the Cold War era did not yield a substantial drop in the area under the ROC curve when forecast onto a test set based on post-9/11 cases. Stability of the model between the Cold War and the Post-Cold War ( ) era yielded slightly varying results depending on the test set drawn. But the drop in area under the ROC curve was not statistically significant.