The search for rebel interdependence

Abstract

The existing conflict literature tends to treat interdependence between rebel groups as a binary category: either groups are allied or unallied, fragmented or unified, interdependent or independent. Yet much of our qualitative knowledge suggests that interdependence is better understood as a matter of degree where certain groups exert a disproportionate influence over their counterparts. The challenge is how to identify the degree of interdependence in practice. As a solution, I conceptualize interdependence as a property of a system of interactions between rebel groups and government forces within and across borders. My approach is to model the entire system of interactions in order to test hypotheses related to the directionality of influence and the potential for military coordination between groups. I demonstrate the utility of this approach by examining the relationship between Pakistan and the two major factions which make up the Taliban organization – the Afghan and Pakistani Taliban. I analyze the triangular system with a vector autoregressive model and monthly time series data on violent actions initiated by each group from January 2008 to February 2013. The substantive findings support much of the received wisdom concerning Pakistan’s disparate relationship to both groups, which is characterized by antagonism with the Pakistani Taliban and collusion with the Afghan Taliban. The results also suggest that the claims of interdependence between the two Taliban groups have been overstated.

Keywords

civil war conflict processes insurgency interdependence rebel groups time series

Introduction

In 2001, US Special Forces and Northern Alliance rebels toppled the Taliban government in Afghanistan and pushed large numbers of Taliban fighters into the tribal regions of Northwest Pakistan. In the early years of the Afghanistan War, Pakistan adopted a relatively hands-off position toward Taliban activity along its border with Afghanistan. But in 2006, under pressure from the US government, Pakistan began a series of military offensives into the tribal regions. In response, several militant groups calling themselves the Pakistani Taliban began to carry out attacks within Pakistan. In late 2007, these groups coalesced into one entity, the Tehrik-e-Taliban Pakistan, and claimed allegiance with the Taliban organization. Since that time, the original Taliban movement is now commonly referred to as the Afghan Taliban.

What is the relationship between the Afghan and Pakistani Taliban? Are the two groups closely allied or relatively independent? To many observers, the rise of the Pakistani Taliban is an ominous sign of ‘Talibanization’ in Central Asia (Perlez, 2008). Najmuddin Shaikh, a retired head of Pakistan’s foreign service, warns that these groups have evolved into ‘a hydra-headed monster’ (Walsh, 2014). At the same time, other observers point out that the Afghan and Pakistani Taliban have dissimilar localized goals, which stem from Pakistan’s alleged collusion with the Afghan Taliban and antagonism toward the Pakistani Taliban (Shane, 2009). On balance, the relationship between the Afghan and Pakistani Taliban is a puzzle. As US General David Petraeus acknowledged in an interview: ‘it’s very difficult to parse and to try to distinguish between [these groups]. They support each other, they coordinate with each other, sometimes they compete with each other, sometimes they even fight each other’ (Bruno & Bajoria, 2010).

The ambiguity of the Taliban case is instructive for the broader literature on rebel interdependence. A wave of recent scholarship has studied the impact of rebel interdependencies on conflict outcomes (Nilsson, 2010; Cunningham, 2011; Akcinaroglu, 2012). Yet the way in which scholars have conceptualized rebel interdependence at the cross-sectional level does little to advance our understanding of the Afghan and Pakistani Taliban case. The reason is that the literature treats interdependence as a binary category: groups are either interdependent or independent. This view ignores the potential for varying degrees of influence, where some groups are more closely connected than others, as well as the possibility of directional influence, where some groups are dominant and others subordinate. Moreover, the binary view forces scholars to choose between studying either negative or positive interdependencies, when it is likely that both may be present.

The existing literature has also overlooked many of the inherent challenges of identifying interdependence empirically. In most conflict zones, data are relatively sparse and often contradictory. For the most part, scholars tend to infer interdependence from what little data are available, namely the public statements of rebel groups and the government. Yet this approach is prone to misspecification error, as both rebel groups and governments have incentives to mischaracterize the nature of their relationship. In sum, we are in the position of scholars who are certain that interdependence matters at the large-N level and yet we find ourselves unequipped to identify rebel independence in practice.

To move the literature forward, I first expand the binary definition of interdependence to encompass the potential for varying degrees of influence and directionality. I then create a framework that conceptualizes interdependence as a property of a system of interactions between rebel groups and government forces within and between borders. To characterize the conflict system, I draw upon the literature on superpower rivalry, which attempts to infer interdependence from what actors do rather than what they say (Ward & Rajmaira, 1992; Leng, 2000; McGinnis & Williams, 2001). I demonstrate the utility of this approach by using it to examine the relationship between the Afghan Taliban, Pakistani Taliban, and Pakistani military. I argue that the three actors form a triangular system of violence similar to the system outlined in Goldstein & Freeman’s (1990) model of US, Soviet, and Chinese relations.

The unclassified data from Afghanistan and Pakistan are sparse, but we do have access to monthly time series data on violent attacks initiated by each group from January 2008 to February 2013. I use these data to test for the presence of military coordination between the Taliban factions and to assess whether the two Taliban groups do, in fact, have a disparate relationship to Pakistan. My empirical strategy is predicated on modeling the dynamic properties of the system without making restrictive assumptions about the directionality and degree of influence between groups. I focus first on uncovering lagged relationships between the groups by estimating a reduced-form vector autoregressive model. After conducting tests of Granger causality, I then estimate a structural model that also incorporates the contemporaneous relationships between the actors in the triangular system. Impulse response functions are used to test for the nature of interdependence between the groups.

The empirical results demonstrate the value of moving beyond the binary conception of interdependence. There are clear signs of directionality and varying degrees of influence in the triangular system. The findings reveal that the Pakistani Taliban responds to the behavior of the Afghan Taliban in a manner consistent with a subordinate group, but this influence does not translate into meaningful military coordination. In addition, there is evidence that the Pakistani military decreases its military pressure in Northwest Pakistan when the Afghan Taliban is most vulnerable. This result is consistent with qualitative assessments of the conflict, which contend that Pakistan covertly supports the Afghan Taliban while publicly claiming to crack down on militants (Rashid, 2008). However, Pakistan’s support for the Afghan Taliban does not extend to the Pakistani Taliban. The results indicate that the Pakistani military and Pakistani Taliban are clear adversaries with both sides responding to attacks by the other in a reciprocal fashion. In sum, Pakistan’s disparate relationship to the two groups offers a compelling rationale for the lack of military coordination between the Afghan and Pakistani Taliban: there is little reason for the two Taliban groups to coordinate given their divergent attitudes toward Pakistan.

The article is structured as follows. First, I outline the historical background between the two Taliban groups. Second, I discuss the limitations of the current view of rebel group interdependence. Third, I explain my framework for thinking about rebel interdependence and outline testable hypotheses based on this approach. Fourth, I explain my empirical strategy, the data used in the analysis, and model fitting procedures. Fifth, I present the results. I conclude with a discussion of the implications of the findings.

History

After the USSR withdrew its military forces from Afghanistan in early 1989, the country descended into civil war between rebel mujahideen fighters and the Democratic Republic of Afghanistan. When the USSR collapsed in August 1991, the Soviet-backed governing coalition in Afghanistan lacked the military strength to counter the rebel advance and fell apart soon afterward. In the power vacuum that emerged, fighting broke out between competing rebel factions. The anarchic conditions of the civil war offered fertile ground for the Taliban movement. The group’s charismatic founder, Mullah Muhammed Omar, promised to create order by imposing a strict system of sharia law. According to Rashid (2008: 72), indigenous support for the Taliban arose from ‘the war weariness of the populace which stood ready to welcome any force that promised the disarming of the local brigands, the restoration of peace, the semblance of an honest administration, no matter how rough and ready the system of justice’. The Taliban seized Kabul by September 1996 and soon established control over most of the country.

When US Special Forces and the Northern Alliance pushed across Afghanistan in 2001, the senior Taliban and Al Qaeda leadership fled to the Federally Administrated Tribal Areas (FATA) in Pakistan (Scheuer, 2002). In large part, Pakistan’s tribal areas are the epicenter of Taliban activity. The FATA are an ideal headquarters for the Taliban because the tribes there are overwhelmingly Pashtun and Pakistan’s government has a history of marginalizing the local Pashtun population (Rashid, 2008: 273). The tribal areas are subject to the Frontier Crime Regulations, a draconian system of laws created by the British in 1901. As a consequence, Pashtuns within the FATA do not have the same political rights as in other regions of the country (Yusufzai, 2001). In fact, unless expressly decreed by the President, no law passed by Pakistan’s parliament applies to the FATA.¹ As one US diplomat remarked, the FATA are essentially ‘the Wild Wild West’.²

Pape & Feldman (2010) argue that the creation of the Pakistani Taliban was partly a by-product of Pakistan’s military incursions into Northwest Pakistan. Between 2002 and 2005, the Pakistani military never seriously

Table I.

Insurgent violence in Pakistan

Group	Number of attacks
Afghan Taliban	65
Sipah-e-Muhammad Pakistan	134
Lashkar-e-Jhangvi	342
Lashkar-e-Islam	393
Balochistan Separatists	2,127
Pakistani Taliban	7,241

Data range: January 2007 to January 2013.

challenged militants in the tribal areas of Northwest Pakistan. However, starting in 2006, Pakistan – under pressure from the US government – began a series of military offensives into the FATA which angered Pashtun tribespeople (see Pape & Feldman, 2010: 138–166). The situation further deteriorated in July 2007, when Pakistan’s military besieged a large group of fundamentalist militants inside the Lal Masjid (Red Mosque) in Islamabad. Over 100 people died and 250 were injured in the violence (Iqbal, 2007). The confluence of military incursions and the Lal Masjid crisis served as a catalyst for the unification of militant groups. On 14 December 2007, numerous militant groups came together to form the Tehrik-e-Taliban Pakistan (TTP). From the outset, the goals of the TTP were directly aimed at removing Pakistan’s military presence in Northwest Pakistan. The TTP declared that the Pakistani military had ten days to cease military activities in FATA and Swat province or risk a defensive jihad (Abbas, 2008).

As Table I shows, the Pakistani Taliban is responsible for the vast majority of insurgent violence in Pakistan. The Pak Institute for Peace Studies Database indicates that the Pakistani Taliban carried out 7,241 attacks in Pakistan from 2007 to 2013. In contrast, the Afghan Taliban carried out only 65 attacks in Pakistan during that same time period – and almost all of those attacks were against NATO convoys bound for Afghanistan.

The study of rebel interdependence

As a starting point for our investigation into the Afghan and Pakistani Taliban, it is useful to step back and consider how the literature on civil war has thought about the relationship between rebels groups more generally. Early work conceptualized civil war as a contestation between the government and a single rebel group. These dyadic studies of civil war tended to emphasize either government characteristics (Fearon & Laitin, 2003) or rebel attributes (Cunningham, Gleditsch & Salehyan, 2009) as explanatory variables. Needless to say, conflicts often involve more than one rebel group. Building upon this intuition, several scholars developed models that allowed for multiple government–rebel dyads within a single conflict (Harbom, Melander & Wallensteen, 2008; Nilsson, 2010).

While an improvement upon earlier work, the limitation of this multidimensional view is that each government–rebel dyad is assumed to be independent, which restricts the potential for interaction between rebel groups. More recent work has demonstrated the explanatory value of relaxing the assumption of independence between rebels. For example, Cunningham (2011) finds that governments are actually more likely to make concessions to internally divided rebel groups compared to unified groups. Infighting can also occur between rebel groups, as demonstrated by Fjelde & Nilsson’s (2012) study of rebel violence against other rebels. In addition, Akcinaroglu (2012) demonstrates that stronger ties between rebel groups are not sufficient to increase the probability of rebel victory.

With a few exceptions, the current literature tends to think about interdependence as a binary category; either groups are interdependent or independent.³ In part, this perspective stems from a tendency to equate interdependence with the presence of a formal alliance between groups. For example, many studies of rebel interdependence use the Uppsala Conflict Data Program (UCDP) Actor data, which includes a 0,1 indicator of whether a non-state actor entered into an alliance with another non-state actor. According to the UCDP coding rules, ‘When an actor is coded in Alliance, it ceases to exist on its own, as it together with another registered actor creates a new organization.’ According to this coding, rebel groups are either orthogonal to one another, or so intimately connected that they should be thought of as an entirely new entity.

We can reject the binary view of interdependence on three grounds. First, it restricts the potential for varying degrees of influence, in which some groups are more closely connected than others. If two groups claim allegiance, for example, we would like to be able to say something about the strength of that relationship compared to other groups. Second, the binary view ignores the potential for rebel groups to exert both negative and positive interdependences on one another. For example, pledging allegiance to a larger rebel organization may engender cooperation in the short term, but could also lead to intergroup competition in the long run if two groups end up fighting over recruits, scarce resources, or the spoils of war. Lastly, the binary view does not allow for directional relationships, where one group may influence another, but not vice versa. In most cases of civil war, we have good reason to suspect that some rebel groups are dominant and others subordinate.

Unfortunately, the deficiencies within the current scholarship cannot be entirely remedied by simply expanding our definition of interdependence. I argue that there are also inherent problems with the way in which scholars have gone about identifying rebel interdependence. In practice, determining whether two groups are interdependent is complicated by the data-sparse environment of civil war. As a result, scholars rely on news reports and published accounts of the conflict, which largely consist of public statements by the rebel groups themselves or government reports on their activity.

The problem with this approach is that there are good reasons to be skeptical of public accounts of the relationship between militant groups. For example, small militant groups have clear incentives to claim allegiance with a large group like the Taliban in order to boost local recruitment. And larger groups may have incentives to overstate their influence among smaller groups in order to project the outward appearance of a burgeoning, global brand, as in the case of the Islamic State in Iraq and Syria (ISIS). Furthermore, governments also have incentives to either lump groups together or split them apart. Akcinaroglu (2012: 889–890) aptly summarizes the difficulties of inferring interdependence from published accounts of the conflict: ‘Oftentimes, I confronted contradictory statements from book excerpts on whether the two groups I was interested in really had any cooperation or not, it was not rare for one author to claim so while the other one referred to such information as unfound[ed] rumors.’

In sum, we are faced with two challenges when determining whether rebel interdependence exists in practice. First, the available data are sparse and public accounts of the conflict are often contradictory. Second, the common approach of identifying interdependence based on statements from the government or rebel groups is prone to misspecification error, as the groups involved have incentives to distort, inflate, and otherwise mischaracterize the relationship.

All the aforementioned problems are evident in the Afghan and Pakistani Taliban case. As a result, the relationship between the Afghan and Pakistani Taliban remains a puzzle for policymakers and scholars. To move the literature forward, I outline a new approach to the study of interdependence between rebel groups. I begin by expanding the binary view of interdependence to include the idea of degree and directionality of influence. I then outline a framework for thinking about interdependence as a property of a system of interactions between rebel groups and government forces.

Conceptual approach

Rationalist scholars have argued that the defining feature of the international system is interdependence among states (Keohane, 1984: 122–123; Keohane & Nye, 1987; Milner, 1991: 81–85). The same logic can be usefully applied to conflict systems involving non-state actors. There are many different types of interdependence, but the most germane to conflict systems is the concept of strategic interdependence. According to Schelling (1960: 5), strategic interdependence is the idea that ‘the ability of one participant to gain his ends is dependent to an important degree on the choices or decisions that the other participant will make’. This implies that the utility functions of strategically interdependent actors are linked. In this context, we can think about multiple rebel groups as engaged in a mixed motive game, where both negative and positive interdependencies are possible. The interactions between rebel groups and government forces constitute an endogenous system, where the behavior of any single group is connected to the behavior of another by their linked utility functions.

As a practical matter, we must determine which actors are relevant to the conflict system. Within much of existing scholarship there is a tendency to focus on actors in the domestic sphere. Yet many conflicts feature a wide variety of rebel groups and terrorist organizations that operate across borders or have factions in neighboring countries, including the Afghan and Pakistani Taliban, ISIS, Rwandan Hutu (Interahamwe) militias, Boko Haram, the Kurdistan Workers’ Party (PKK), and the Sudanese People’s Liberation Army, to name only a few. Rebel groups that operate across borders can take advantage of sanctuaries in neighboring states and outside support from sympathetic foreign governments (Salehyan, 2007, 2010). The conflict system, therefore, consists of rebel groups and government forces within and between national borders.

The literature on superpower rivalry offers some practical advice on how to study strategic interdependence (Ward & Rajmaira, 1992; Leng, 2000; McGinnis & Williams, 2001). This scholarship is premised upon an inherent skepticism of the statements of great powers. Their solution to this problem is to analyze the systematic behavior of actors in the system in order to draw inferences about the nature of their relationship. In a conflict system, the most relevant behavior is violence initiated by rebel groups and government forces. We can leverage this behavior to gain insight into the connections between groups if we assume that interdependence within the system will manifest itself in patterns of violence. For example, interdependence could take the form of military coordination between two rebel groups, or reciprocal patterns of violence between a rebel group and government forces.

In general, there are two systematic components to each dyadic relationship in the conflict system. The first is directionality, which refers to whether one actor’s past behavior influences the current behavior of the other actor. Directionality can help us tease out the leaders and followers in the system by addressing the question of who is responding to whom. The second component is bilateral behavior, which reflects how actors respond to one another. The two most common forms of bilateral behavior are reciprocity and inverse response.⁴ It is important to point out that even if behavior is reciprocated, it need not be commensurate (Keohane, 1986: 6). Therefore, reciprocity and bilateral response can be used to characterize unequal relationships, which allows for variation between dominant and subordinate actors in the system.

In sum, this conceptual framework conceives of strategic interdependence as a property of a conflict system. In many cases, the system will have a transnational dimension as numerous rebel groups and terrorist organizations operate across borders. By assuming that strategic interdependence will influence behavior, we can tease out the connections between groups by examining the patterns of behavior within the system. These patterns can take the form of directionality, where one group changes its behavior based on the past actions of another, and bilateral response, where groups either reciprocate the behavior of another group or respond inversely.

To demonstrate the utility of this framework, I apply it to the Taliban case. I contend that the key to understanding the Afghan and Pakistani Taliban lies with their relationship to Pakistan. I propose that the three actors form a triangular system similar to the one outlined in Goldstein & Freeman’s (1990) model of US, Soviet, and Chinese relations. In the next section, I translate the narrative accounts of the Taliban case into testable hypotheses based on this framework.

Hypotheses

There are two competing accounts of the relationship between the two Taliban groups. The first is the ‘Talibanization’ narrative, which argues that the two groups are highly interdependent.

The Afghan and Pakistani Taliban present a strong prima facie case for interdependence based on their geographic proximity, shared history, and ideological similarity. The senior leadership of both groups resides in Northwest Pakistan, which provides ample opportunity for direct coordination. Furthermore, the historical ties between the two groups run deep: Mullah Omar appointed the TTP’s first leader, Baitullah Mehsud, to be Taliban commander in South Waziristan. In turn, Baitullah Mehsud pledged his allegiance to the Taliban organization, as did his successor, Hakimullah Mehsud (Khattak, 2012). Lastly, the two groups espouse a similar religious ideology based around Deobandi teachings and sharia law. This ideological overlap could foster a sense of common purpose within the broader Taliban movement where both groups have a mutual interest in supporting one another in order to bolster their shared ideology.

Two testable hypotheses emerge from the ‘Talibanization’ perspective. The first relates to the idea that the Pakistani Taliban is subordinate to the Afghan Taliban. If this is the case, the behavior of the Afghan Taliban is likely to be a major influence on the behavior of the Pakistani Taliban.

Talibanization hypothesis: The Pakistani Taliban reacts to past behavior by the Afghan Taliban.

Second, a major concern for policymakers is that the ideological connections between the Afghan and Pakistani Taliban translate into military coordination, potentially compounding the threat from these groups. Based on this logic, I hypothesize two potential patterns of militant group coordination. The first is Offense coordination, which implies that groups stage major offensives either contemporaneously or very close together. Coordinated offensives allow the two groups to leverage their combined forces in order to capture strategic assets such as towns or military outposts. And while force concentration has a clear military utility, it can also serve as a signal to adversaries about the strength of alliance ties between rebel groups. For example, coordinated offensives by the Afghan and Pakistani Taliban could signal resolve in regard to long-term goals such as creating a unified ‘Islamic Emirate of Waziristan’ (Shahzad, 2006).

Offensive coordination hypothesis: A surge in attacks by one Taliban faction leads to a surge in attacks by the other.

The second possibility is Offense–defense coordination where one group defends while the other launches a major offensive. Given the considerable geographical overlap between the two groups, when one group launches a major offensive there is likely to be shared territory that is relatively undefended. Thus, coordination between the groups could lead to a situation in which one group defends a particular region while the other attacks.

Offense–defense hypothesis: A surge in attacks by one Taliban faction leads to a reduction in attacks by the other.

The Talibanization perspective outlined above is not without its detractors. A competing account of the relationship calls into question the degree of positive interdependence between the two groups. According to this view, the two groups have little reason to work together because of a disagreement over localized goals. The source of contention between the groups rests on their vastly different relationship to Pakistan. On the one hand, the Pakistani Taliban’s raison d’être is a war against Pakistan’s military and government. Not surprisingly, the Pakistani Taliban explicitly targets members of Pakistan’s government, army, and police forces. As Hakimullah Mehsud remarked in October 2013: ‘Pakistan’s system is un-Islamic, and we want it replaced with an Islamic system. This demand and this desire will continue even after the American withdrawal [from Afghanistan]’ (BBC, 2013).

Two hypotheses emerge from this account of the animosity between the Pakistani Taliban and the Pakistani military. First, I expect that both antagonists are influenced by the past behavior of the other.

Adversary hypothesis 1: The Pakistani Taliban reacts to past behavior by the Pakistani military, and vice versa.

Second, I expect antagonists to react to one another in a reciprocal fashion, where attacks by one group lead to subsequent attacks from the other group.

Adversary hypothesis 2: A major offensive by the Pakistani military leads to an increase in attacks by the Pakistani Taliban, and vice versa.

In stark contrast, the Afghan Taliban is rumored to have close ties to elements of Pakistan’s military. For this reason, many observers argue that the Afghan Taliban does not share the Pakistani Taliban’s hostility towards Pakistan. As one Afghan Taliban commander put it, ‘Our aim was, and is, to get the occupation forces out [of Afghanistan] and not to get into a fight with a Muslim army’ (Shane, 2009). Another Afghan Taliban spokesman rejected any involvement with the Pakistani Taliban: ‘We don’t like to be involved with them, as we have rejected all affiliation with Pakistani Taliban fighters. […] We have sympathy for them as Muslims, but beside that, there is nothing else between us’ (Shane, 2009).

Pakistan’s government publicly maintains that it has severed ties with the Taliban and is fully cooperating with anti-Taliban efforts in Afghanistan, but few observers put much stock in that assertion. General McChrystal’s (2009) report on Afghanistan bluntly links Pakistan’s espionage agency, the ISI, to the Taliban: ‘Afghanistan’s insurgency is clearly supported from Pakistan. Senior leaders from the major Afghan insurgent groups are based in Pakistan, are linked with al Qaeda and other violence extremist groups, and are reportedly aided by some elements of Pakistan’s ISI.’ The US has accused Pakistan of allowing the Afghan Taliban to establish a base of operations in Northwest Pakistan from which to stage attacks into Afghanistan. This ‘safe haven’ for Afghan Taliban fighters has allowed the Afghan Taliban to operate in the region with impunity. Yet, since 2006, the Pakistani military has engaged in a series of major military incursions into Northwest Pakistan. The question is whether these incursions signal a ‘change of heart’, or whether they are merely token gestures used to cover up a continued policy of appeasement and collusion.

What are the observable implications of collusion? In my view, collusion implies the presence of two related behaviors. First, I expect that the Pakistani military pays close attention to the behavior of the Afghan Taliban when planning its own strategy.

Collusion hypothesis 1: The Pakistani military reacts to the past behavior of the Afghan Taliban.

Support for this hypothesis is not sufficient evidence of collusion, but it would establish that the Pakistani military is influenced by the behavior of the Afghan Taliban. To make the case for collusion, the behavior of the Pakistani military must also aid the Afghan Taliban. One implication is that the Pakistani military will scale back its attacks when it is convenient for the Afghan Taliban. The Afghan Taliban is most vulnerable after it launches a major offensive in Afghanistan because the tribal areas of Pakistan are relatively undefended. If collusion is present, then I expect a decrease in the intensity of Pakistani military operations in Northwest Pakistan when the Afghan Taliban launches a major offensive in Afghanistan.

Collusion hypothesis 2: The Pakistani military scales back its attacks on Northwest Pakistan following a major offensive by the Afghan Taliban.

Empirical strategy

The challenge of testing for interdependence is that each of the hypotheses above implies a different causal relationship. In this way, the choice of a particular structural model puts the cart before the horse if our goal is to assess the entire set of hypotheses. Therefore, we need an approach to modeling dynamic systems that does not treat the nature of interdependence as given, a priori, based upon the assumptions of a particular structural model. In other words, the inferential challenge of testing for independence is that ‘theory provides hypotheses but not enough knowledge about the structural (causal) relationships’ (McGinnis & Williams, 2001: 145).

Given these considerations, I adopt the vector autoregression (VAR) approach to modeling dynamic systems (Sims, 1980; Freeman, Williams & Lin, 1989; Sims, Stock & Watson, 1990). The advantage of the reduced-form VAR is that it places no a priori restrictions on the endogenous relationships between actors. Strictly speaking, the VAR model allows each series to be affected by lags of itself as well as lags of the other variables in the model. I then perform diagnostic tests to uncover the particular model that best characterizes the system.

Data

The data are time series of the number of violent actions initiated by each group per month from January 2008 to February 2013.⁵ Figure 1 presents the data used in the analysis. The violence is all group-initiated in order to capture purposeful actions by each group rather than

Figure 1.

The number of attacks by each group

incidents where another party initiated the attack. The level of violence is a clear choice for this analysis as it serves as a revealed preference, reflecting what groups do rather than what they say. This avoids the problem of trying to infer interdependence from group statements of allegiance, which can often be disingenuous.

The Afghan Taliban series is derived from unclassified ISAF reports on enemy-initiated attacks in Afghanistan.⁶ According to the ISAF methodology, ‘Enemy-initiated attacks are all enemy action (i.e. enemy-initiated direct fire, indirect fire, surface to air fire) and Explosive Hazard Events to include executed attacks only (i.e. IED Explosions and mine strikes).’ Potential or attempted attacks (i.e. IEDs found and cleared) are excluded as they may reflect activity months or even years earlier (Jacobson, 2011; ISAF, 2011). The attacks cover the full spectrum of targets – military, political, and civilian. The ISAF makes no distinction between ‘terrorism’ and ‘guerrilla’ tactics, which are often difficult to distinguish in wartime.

The Pakistani Taliban series was compiled from the Pak Institute for Peace Studies (PIPS) Digital Database on Conflict and Security.⁷ These attacks include militant activity which matches the coding criteria of the ISAF data series, including direct and indirect fire, explosive events, and suicide terrorism. I exclude attacks by Balochistan separatists, as well as other militant groups such as Lashkar-e-Islam, Lashkar-e-Jhangvi, and Sipah-e-Muhammad Pakistan. Like the Afghan data, the Pakistani series includes civilian, political, and military targets.

The Pakistani military series is the number of military offensives per month in Northwest Pakistan.⁸ According to the PIPS codebook, military offensives are ‘Large-scale operations launched by military and paramilitary forces against Islamist militants and separatist insurgents in Malakand Division, FATA and Balochistan to preserve law and order and the writ of the state.’ I exclude operations against Balochistan separatists as they do not fall under the umbrella of the Pakistani Taliban organization. It is important to underscore that, in contrast to the two Taliban series which reflect individual attacks, a military offensive represents a large-scale effort to purge an area of militants.

I proceed from the assumption that violence initiated by each group is a function of a unitary decisionmaking process. Some observers have questioned whether the insurgency in Afghanistan is part of a single organized group, or several. These observers argue that the Afghan Taliban is more like an umbrella movement composed of smaller organizational units (Giustozzi, 2008). However, the presence of smaller organizational units within the larger group does not violate the assumption above. Even within groups like the US military, division-level and brigade-level commanders are given a degree of autonomy over their actions while at the same time their overall activity remains a function of orders passed down from a centralized command structure at the top. Furthermore, the unitary actor assumption in regard to the Afghan Taliban is bolstered by qualitative accounts (Dorronsoro, 2009) and recent quantitative studies (Trebbi & Weese, 2015).

The internal cohesion of the Pakistani Taliban is more questionable than its Afghan counterpart. Qualitative accounts stress that the Pakistani Taliban is composed of multiple factions (Dorronsoro, 2009) and recently these factions splintered in the wake of Hakimullah Mehsud’s death. As a way to address these concerns, I focus on the 2008–13 time frame where the TTP was led by Baitullah Mehsud and Hakimullah Mehsud, two strong leaders who united the smaller groups under one banner, and where the group most closely exhibited a centralized command structure (see Shah & Johnson, 2008; Brumfield & Ng, 2014).⁹

Model

The reduced-form VAR model is parameterized as follows:

y (t) = α + \sum_{l = 1}^{L} β_{l} y (t - l) + ε (t),

where $y (t)$ is a vector of the three time series, $[y_{1} (t), y_{2} (t), y_{3} (t)]^{'}$ , where $y_{i} (t)$ is the number of attacks by group i during month t; α is a matrix consisting of a constant, seasonality variables, and exogenous regressors; the $β_{l}$ ’s are the coefficients for the lag terms, $y (t - l)$ ; and $ε (t)$ is the vector of the error terms for each series.

After fitting the model, I tease out the structure of the dynamic system using two time-series extensions: Granger causality and impulse response functions. Granger causality is a time-series notion of causality where one series is said to Granger cause another series if the lagged values of one series improve the ability to predict current values of the other series (Granger, 1969). In this way, Granger causality provides a good indication of ‘who leads and who follows?’

One limitation of the reduced-form VAR is that it ignores contemporaneous relationships between the time series. Because the data are aggregated monthly, there is good reason to believe that the current behavior of actors is also a function of the current behavior of other actors. To incorporate contemporaneous behavior, I estimate a structural VAR based on the Cholesky decomposition of the residuals. In order to achieve identification, I specify the following ordering of contemporaneous effects: Afghan Taliban → Pakistani Taliban → Pakistani military. This implies that the Afghan Taliban series affects the other two series contemporaneously and with a lag; the Pakistani Taliban affects the Pakistani military contemporaneously and the Afghan Taliban series with a lag; and the Pakistani military only affects the other series with a lag.¹⁰

Fitting the model

The goal of model fitting is to separate meaning patterns in the data from spurious associations that are the by-product of factors unrelated to strategic interdependence. I start from a simple, stripped-down model and then build in complexity by performing diagnostic tests and making decisions based on practical knowledge of the data. The final model used in the analysis is a VAR estimated in levels with a one-month lag. The Online appendix features additional information on a wide range of diagnostics, robustness tests, and a more comprehensive discussion of model specification. Below, I highlight two important modeling choices regarding seasonality and exogenous variables.

Seasonality

Qualitative accounts suggest that there is a fighting season in Afghanistan and Pakistan and this intuition is borne out in the data. In particular, the Afghan Taliban series exhibits clear signs of seasonality with violence peaking in the summer and dropping in the winter months. The cyclical structure of the time series at 12-month intervals is apparent when examining the autocorrelation and partial autocorrelation functions of the univariate series. If unaddressed, this seasonality is a potential source of spurious association between the time series.

Some analysts capture seasonality by including 12 lags in the model, but given the relatively small number of observations ( $N = 62$ ) in the time series, this option is not practical. To capture seasonal fluctuations, I test for a variety of deterministic components including linear and quadratic time trends, month indicators, a counter of months since January (and its squared term), cubic splines based around knots (quantiles), and sine and cosine functions (transformed to a 12-month periodization). Model comparisons based on BIC scores suggest that the sine and cosine periodization does the best job in capturing seasonality in these data, so I include the two terms in the model. The Bayesian information criterion (BIC) indicates a lag length of 1, while the Akaike information criterion (AIC) indicates a lag length of 12. It seems clear that the AIC is picking up on the seasonal nature of the data.¹¹

There is always a concern about overfitting the data when adding in deterministic components. However, in this case, models with seasonal terms perform much better in regard to stability and residual autocorrelation. Diagnostic tests show that a model without any seasonal component is not stable and there is clear evidence of residual autocorrelation at several lags including lag 12. Another valid concern is that the model results are somehow an artifact of the sine and cosine terms, but I find that the results are not sensitive to alternative seasonal specifications such as a counter of months since January (and its squared term). This robustness suggests that the results are not simply an artifact of a particular seasonal specification, and it reinforces our practical understanding of seasonality as a key feature of the data generating process.

Exogenous variables

Exogenous factors are another potential source of spurious correlation between the time series. To adjust for these associations, I include three exogenous variables based on practical knowledge of the conflict. The first is a measure of ISAF troop levels in Afghanistan, which could have an impact on the behavior of all three groups.¹² The troop number data are reported in the Brookings Institution’s Afghanistan Index (Brookings Institution, 2014).

There are good reasons to believe that ISAF troop numbers are exogenous to insurgent violence. First, troop levels are largely a function of the ISAF mandate established in the early stages of the war. Second, most changes in the troop levels correspond to political considerations in the United States and Europe. The complicated bureaucratic procedure necessary for troop increases implies weak correspondence to insurgent violence levels in the short term. In the long term, there may exist an endogenous relationship between troop levels and insurgent violence, but it is difficult to pick up on these long-run dynamics given the relatively small number of time points considered here.¹³

Another important exogenous factor is the 2010 Surge of US and NATO troops in Afghanistan. Based on BIC scores, I choose an operationalization that consists of a ‘ramp-up’ period from January 2010 to June 2010, corresponding to the increase in troop levels, and a

Table II.

VAR estimates

	Equation
Variable	Afghan Taliban	Pakistani Taliban	Pakistani military
$A T_{t - 1}$	0.600**	–0.023**	–0.012**
$P T_{t - 1}$	–1.310	0.480**	0.075
$P M_{t - 1}$	3.760	0.027	0.580**
sinetime	107.630	–24.610**	–11.660**
costime	–414.630**	–8.390	–10.160**
ISAF	0.006*	0.001	0.000
Surge	152.140	14.490	2.270
Mehsud	111.050	–31.780*	1.160
Constant	35.870	58.270**	6.390
$R^{2}$	0.920	0.590	0.720

**p < 1%, *p < 5%, ^† p < 10%.

flat period from July 2010 until July 2011, when the troop drawdown began. The surge entailed a major change in strategy and tactics, which makes it analytically distinct from the troop level metric.

The third exogenous factor is the August 2009 leadership change in the Pakistani Taliban. I operationalize the change as a step-function that takes values of 0 during Baitullah Mehsud’s tenure and 1 during the leadership of Hakimullah Mehsud. This measure is included to ensure that the results are not driven by factors related to the shift in leadership.

Results

Table II presents the estimation results.¹⁴ Given the concern of spurious results (Granger & Newbold, 1974), I perform a series of diagnostic tests on the model. The only potentially troubling result is the high $R^{2}$ value for the Afghanistan Taliban series. However, the residuals show no evidence of autocorrelation at lags 1 through 12 and the model satisfies the stability condition, which indicates that the data are covariance stationary (Lütkepohl, 2005: 25). Overall, the diagnostic tests support the conclusion that the results are not spurious.

Because the VAR is a system of equations, I conduct substantive interpretation of the results using Granger causality tests and impulse response functions.

Granger causality

Granger causality tells us whether the lagged values of a particular variable help predict the current values of

Table III.

Granger causality

Directionality			p-value
Pakistani Taliban	⇒	Afghan Taliban	0.319
Pakistani Taliban	⇒	Pakistani military	0.168
Afghan Taliban	⇒	Pakistani Taliban	0.016
Afghan Taliban	⇒	Pakistani military	0.003
Pakistani military	⇒	Pakistani Taliban	0.908
Pakistani military	⇒	Afghan Taliban	0.138

another series. Table III presents the results of Granger causality tests. The results show that the relationship between the Afghan and Pakistani Taliban is unidirectional: the Pakistani Taliban is responsive to the past behavior of the Afghan Taliban but not vice versa. This supports the conventional wisdom that the Afghan Taliban is the dominant group in the region. In addition, the directional component of the Collusion hypothesis is supported by the data: Afghan Taliban attacks Granger cause Pakistani military operations. This suggests that the Pakistani military changes its behavior in response to the Afghan Taliban. Lastly, the directional component of the Adversary hypothesis is not supported by the Granger causality tests. It appears that the lagged behavior of the Pakistani Taliban does not influence the Pakistani military, nor vice versa. However, this does not necessarily imply that the two groups are unresponsive to one another. As we will see more clearly in the subsequent structural VAR, the two series may be contemporaneously related.

Impulse response functions

Figure 2 depicts the orthogonalized impulse response functions, which depict a 12-month in-sample forecast of the effect of a hypothetical one standard deviation shock of one series on the behavior of another series. This shock can be likened to a major offensive or ‘surge’ in attacks by one of the groups.¹⁵

The results reveal three major findings. First, there is no indication of military coordination between the Afghan and Pakistani Taliban. Figure 2(a) indicates that a major offensive for the Afghan Taliban leads to only a slight decrease in Pakistani Taliban attacks. One month after the Afghan Taliban surge, there are three fewer Pakistani Taliban attacks. Cumulative impulse response functions (not pictured) indicate that the total decrease is around 16 attacks over eight months. The fact that the decrease occurs one month after the Afghan Taliban surge does not suggest offense/defense coordination, a scenario where a decrease in attacks is contemporaneous with the offensive. This decrease in attacks could be the result of a small number of Pakistani Taliban fighters crossing over to fight for the Afghan Taliban during major offensives. In any case, the results do not support the idea of widespread military coordination between the two groups. Figure 2(c) illustrates that there is no impact of a Pakistani Taliban surge on the behavior of the Afghan Taliban. This supports the idea that the Pakistani Taliban is the subordinate group in the relationship; the Afghan Taliban does not appear to be influenced by Pakistani Taliban behavior.

Second, while these data cannot provide definitive evidence of collusion, the results are consistent with the Collusion hypothesis. Figure 2(b) shows that a surge in Afghan Taliban attacks corresponds with a decrease in Pakistani military operations in the tribal areas. Specifically, a month after an Afghan Taliban surge, the Pakistani military carries out two fewer military operations in Northwest Pakistan. It is important to recall that these military operations are large-scale efforts, which are significantly more involved than a single attack. The decrease in military activity eventually returns to the mean level six months after an Afghan Taliban surge. Based on these results, it appears that certain elements of the Pakistani military scale back their military operations to decrease pressure on the Afghan Taliban, giving the group breathing room to carry out its attacks in Afghanistan with impunity. Interestingly, the Afghan Taliban responds to Pakistani military incursions with a noticeable uptick in attacks in Afghanistan, as evidenced in Figure 2(e). This suggests that, at least in the short term, attacks by the Pakistani military in Northwest Pakistan lead to more violence across the border.

Third, the antagonistic relationship between the Pakistani Taliban and Pakistani military is evident once we factor in contemporaneous levels of violence. Here, the impulse response functions are sensitive to the ordering of the variables, so I estimate the results from alternative orderings.¹⁶ Figure 2(f) is based an ordering where the Pakistani military → the Pakistani Taliban. The result illustrates that attacks by the Pakistani military lead to an increase in attacks by the Pakistani Taliban. Figure 2(d) is based on a Pakistani Taliban → Pakistani military ordering which shows that a Pakistani Taliban surge leads to an immediate increase of around four

Figure 2.

Impulse response functions

Pakistani military offensives that die out after six months.¹⁷ These findings show that the two groups respond in a reciprocal fashion to contemporaneous attacks by the other group.

Conclusion

In March 2015, Boko Haram pledged their allegiance to ISIS (BBC, 2015). As scholars, we face a very practical question: what does this mean? The answer is not readily apparent, but one thing is clear: we should not accept the public claims of rebel groups or governments as sufficient evidence of interdependence. Instead, we should treat these claims as testable hypotheses that merit further investigation into the systematic behavior of rebel groups. This article provides a framework for thinking about strategic interdependence as a property of a conflict system that spans national boundaries and includes rebel groups as well as government forces. Each actor in the system is mutually dependent on the actions of others, regardless of whether they are friend or foe. Within this context, we can tease out the nature of interdependence by examining the dynamic interactions between actors, such as whether antagonists engage in reciprocal attacks, or whether purported allies coordinate their military behavior.

The Taliban case demonstrates the value of thinking about strategic interdependence in this context. The empirical analysis reveals that there is little evidence of direct or tacit military coordination between the Afghan and Pakistani Taliban. The findings in regard to Pakistan’s relationship to both groups provide a cogent rationale for the lack of military coordination: the two Taliban groups have little reason to coordinate because of their disparate relationship to Pakistan. In this case, the analysis illustrates the relative importance of a cleavage in group goals compared to shared history, geographical proximity, and even ideological similarity. When such a disparity exists, counterinsurgency strategies that attempt to disaggregate insurgents may be particularly effective at fomenting discord between groups (see Kilcullen, 2005).

One of the most striking findings from this case concerns the relationship between the Afghan Taliban and Pakistani military. While the data cannot tell us whether the Pakistani military directly colludes with leaders of the Afghan Taliban, there is evidence that major offensives by the Afghan Taliban coincide with a suspicious decrease in the number of Pakistani military incursions into Northwest Pakistan. According to Rashid (2008), Pakistan plays a ‘double-game’ by covertly supporting the Afghan Taliban organization while outwardly appearing to crack down on militants. The empirical findings in this article indicate that Pakistan’s ‘double game’ involves considerable subtlety and nuance. At first glance, Pakistan’s military incursions into the tribal areas could be interpreted as bolstering the government’s claims of going after Taliban militants. But a closer analysis suggests that elements within the Pakistani military dial back pressure on the tribal areas when the Afghan Taliban is most vulnerable. In this regard, it appears that a subset of Pakistan’s military is careful to avoid jeopardizing their ties to the Afghan Taliban, which they view as a strategic asset in Pakistan’s long-standing conflict with India.

It is instructive to draw a parallel between the Taliban case today and Vietnam during the Cold War. In the 1950s and 1960s, US observers feared that the communist movement in Vietnam was evidence of strategic interdependence between Vietnam, the USSR, and China. It turned out that the Vietnamese brand of communism did not imply meaningful interdependence with the Soviets or the Chinese – Vietnam even fought a war with China in 1979. What was missing from the US assessment was careful attention to the localized goals of Ho Chi Minh and his movement, goals that ultimately clashed with other communist powers. The same logic exists in regard to the Taliban organization, which suggests that claims of interdependence should be met with careful inquiry into the underlying goals of the groups in question. While communism is no longer as powerful as it once was, transnational movements like the Taliban and ISIS have emerged to take its place, and many of the same questions we asked during the Cold War have returned again. The questions of whether rebel groups are interdependent and to what degree will continue to be relevant in the years to come.

Footnotes

Replication data

The dataset and do-files for the empirical analysis in this article, along with the Online technical appendix, can be found at .

Acknowledgements

The author thanks Bear Braumoeller, Christopher Gelpi, Alexander Thompson, and participants at the Program for International Security Policy Workshop at the University of Chicago and the 2014 Annual Meeting of the Midwest Political Science Association for helpful comments and suggestions.

Notes

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