Cartography of Crisis: Diffusion of Insurgent Violence As A Strategic Process

Transcription

1 Cartography of Crisis: Diffusion of Insurgent Violence As A Strategic Process Jesse Hammond October 11,

2 1 Introduction In the year 1999, war was beginning in Liberia. Rebel forces dissatisfied with the authoritarian rule of President Charles Taylor, many of them armed and trained in the First Liberian civil war that had ended two years earlier, launched a sustained military assault on the Taylor regime from bases on Liberia s northern border. During the next three years, violence spread steadily through the northern and central areas of the country, culminating in a prolonged siege of the capital, Monrovia. After thousands of deaths and tens of thousands of people fleeing the country to refugee camps in neighboring Guinea and Sierra Leone, the war ended in the triumph of rebel forces and the exile of Charles Taylor to Nigeria in late These are all historical facts that can be found in any account of the Second Liberian Civil War. What significantly less is known about, however, is the process by which civil wars like this one spread. How do insurgent forces choose their targets? Why do some civil wars spread to embroil entire states in violence, while others are confined to outlying regions? These are crucial questions in the 21st century, where civil war and substate violence have come to the fore as primary issues of human security (Sambanis 2002). Thus far, scholars have largely focused their efforts on predicting the onset (Fearon & Laitin 2003), duration (Collier et al. 2004), and termination (Gartner & Bercovitch 2006) of civil war. However, these efforts tends to black-box the actual conflict processes that go on during civil conflicts. I argue that, while such work is absolutely valuable, it is also important to understand the dynamic processes that govern how, when and why violence happens during civil war. This is because these processes have an enormous affect on the characteristics of a conflict wars that spread quickly and cover large swathes of a country are likely to result in more death and destruction than those that spread slowly or are confined to outlying regions. It is possible to explain and predict the diffusion processes of violence during civil war by focusing on the strategic decision-making process of insurgents regarding the use of costly violence at a given place and time. Violence is neither random nor uniformly distributed instead, it is the result 2

3 of rational, utility-maximizing insurgents choosing to use costly violence at locations and times where it will be most effective. Understanding the systematic factors underlying civil war violence can help policy-makers construct institutions that can minimize the catastrophic effects of conflict, and can help national and international counter-insurgency forces better focus their efforts and protect the civilian population. 2 Background: Space Matters Conflict can be studied at a variety of analytical levels. Most common in international relations scholarship is to use the state level of analysis treating geopolitical entities as the primary units allows for many useful assumptions to be made and is a cornerstone of modern international relations theory. This level of analysis has been carried over to the study of sub-state violence, with scholars using state-level variables to explain and predict civil war onset and duration (e.g. Fearon & Laition 2003, Collier & Hoeffler 2004). However, sub-state violence is by definition a localized phenomenon, and can be affected by factors that aggregated state-level measurements cannot capture. The use of state-level variables poses major challenges in drawing strong inferences about civil war dynamics. This is because studying local-level phenomena using state-level variables overaggregates, leaving open the possibility of committing ecological fallacies drawing erroneous conclusions about individual-level data from aggregated variables (King 2002). One common example of overaggregation is the treatment of terrain. Despite strong theoretical grounding and case-study evidence that rough or forested terrain can be important factors in civil war violence, in that insurgent forces can use them as natural strongholds in evading incumbent forces, empirical analyses of the role of terrain have been mixed (e.g. Fearon & Laitin 2003, Raleigh et al 2010). This is entirely unsurprising, however terrain is meaningless unless it is being used by insurgent forces. This means that potential insurgent populations must be located in or near mountainous terrain for it to matter, and therefore 3

4 the effects of terrain type are highly localized. Using state-level measurements are too broad to capture these local nuances, rendering them useless in studying what is clearly a local-level phenomenon. Recently, there has been some movement toward using disaggregated data to study civil war dynamics. With the compilation of new data sets including many local-level variables, it is becoming increasingly possible to study civil war at the substate level. This influx of new data has allowed scholars to ask a variety of new questions about where civil wars are more likely to break out (Buhaug 2010, Weidmann 2009), where violence will occur (Hegre & Raleigh 2009, Buhaug & Gates 2002), and how much of a state will be directly involved in violence over the course of a war (Buhaug & Rod 2006). These works all share the same broad finding: that violence in civil war is spatially dependent the distribution of violent events is strongly affected by geographically varying factors. Given that civil war is an explicitly intra-state phenomenon, the finding that violence is not randomly located is both intuitive and extremely important, both for scholars and for policy-makers. Structural characteristics that vary within states render certain locations more vulnerable to insurgent contestation of power, and because many of these characteristics are empirically measurable, this represents a new avenue of scholarship for civil war scholars. One particularly interesting new avenue of study is conflict diffusion. A key contribution of this study is the addition of an explicitly temporal component to the study of where and why violence occurs. This is the key difference between distribution and diffusion: examining the distribution of violence leaves out time, only examining the overall conflict zone of a given civil war (Buhaug & Rod 2006). However, temporal dependence is crucial for measuring and predicting violence events that occurred yesterday can be useful in predicting reoccurence today. Including time allows for a much more specific analysis, measuring how violence forms clusters in time as well as space. This means that a much more specific analysis can be conducted that can pick up variation in how the conflict zone shifts and grows or contracts over time. 4

5 With new georeferenced conflict data and the increasing inclusion of geographic imaging system (GIS) technology into the study of political science, it is becoming possible to track the spread of violence from day to day and week to week, and to understand the factors governing how quickly violence spreads and where it spreads to during a conflict. In many ways, this field of study is similar to the study of conflict dispersion where violence will be seen over the whole course of a civil war but diffusion research explicitly takes temporal dynamics into account: not just where violence occurs, but when it occurs, and where it is likely to occur next. The use of GIS, while still fairly new to the study of political science, is widely used in other fields where spatial relationships are crucial, such as epidemiology (Krieger 2003), criminology (Ratcliffe & Mccullagh 1998), and urban planning (Dai et al. 2001). Geographic imaging systems provide scholars with a powerful and flexible way to explicitly measure spatially-dependent relationships, and the increasing availability of satellite-based or georeferenced data sets allows for highly accurate and disaggregated measures of concepts like population density, distance, and terrain. Using GIS in conjunction with existing theory and mathematical techniques can help political scientists model relationships using accurate real-world data, and allow presentation of these relationships in a clear, intuitive fashion. Given that my theory deals with diffusion processes that are highly spatially dependent, GIS technology is an ideal conduit for the measurement and presentation of these concepts. Previous work on conflict diffusion has pushed the field forward significantly, but still lacks theoretical depth. Much of the most sophisticated diffusion modeling has been done by political geographers (O Loughlin 2010, O Loughlin et al. 2010, O Loughlin & Raleigh 2007, O Loughlin & Witmer 2010), and despite its methodological sophistication, this work remains primarily descriptive in nature patterns of diffusion are measured well, but theoretical motivation for diffusion is weak. On the other hand, recent work by political scientists using georeferenced conflict data has been theoretically richer, but methodologically crude in its measurement of spatial and temporal dependence, and generally limited to one state or 5

6 region (Raleigh & Hegre 2009, Zhukov 2010, Chojnacki & Metternich 2008, Urdal 2008). My contribution builds on both these previous bodies of work by combining a stronger theoretical model with more sophisticated operationalization and mathematical models to gain greater leverage on the diffusion process. Furthermore, by using an expanded cross-national data set, I can strengthen the inferences drawn from this analysis. A larger sample means that I can make a stronger case for my findings being universal, capturing underlying elements of insurgent violence that are common to many sub-state conflicts. 3 Theory: Diffusion as a Strategic Process What motivates insurgents to use violence at the times and locations they do? One existing explanation is that violence is used to control territory. This view regarding territory is common in international relations theory (e.g. Huth 1998) as well as a large body of work on substate violence (e.g. McCall 1969). Under this view, territorial control is an end unto itself control of geographic space directly translates into political power. Violence, then, is a tool used to contest control of geographic space. This is embodied in the classic Maoist theory of revolution, dictating that insurgents work to seize control of the countryside in order to cut off state power and establish a parallel state of insurgent dominance (Zedong 1969). Should this be the case, one would expect violence to concentrate in rural, isolated areas, at least in the early stages of insurgency, and only move to urbanized population centers toward the end of war. However, large-scale empirical studies have done little to explicitly test this theory of civil war violence. This analysis provides such a test, examining whether this theory of rural insurgency and territorial motivation holds in modern-day civil conflicts, and can therefore be used to explain the diffusion patterns of insurgent violence. Recent empirical work has had some success in describing and predicting the overall spatial distribution of insurgent violence (e.g. Raleigh & Hegre 2009, Urdal 2008), but the theoretical motivation for these models has often been slim. Hypotheses abound as to where 6

7 insurgents will use violence, linking insurgent activity to natural resources, mountainous terrain, highly rural or highly urbanized areas, military bases, densely or sparsely populated locations, and so on, but many scholarly works neglect to specify any underlying motivation for these hypotheses. Recent work has attempted to bring some unifying theoretical underpinnings to insurgent behavior by explicitly applying rational-choice theory (Cornish & Clarke 1986) to the study of civil war violence, bringing in tools and techniques from similar bodies of work in criminology literature and finding preliminary support for the idea that insurgents are rational actors with measurable motivations (Townsley et al. 2008). Thus, I explicitly assume rationality on the part of insurgent actors. Violence in civil war, then, is instrumental insurgents do not expend resources and personnel on random endeavors, but choose targets based on the efficacy or rate of return of violence, as well as the constraints imposed by geographic and topographic factors that make it easier or more difficult to export violence to a new location. In so doing, my theory accounts for temporal variation in insurgent activity by modeling the risk of insurgent violence as a function of both insurgent utility and target accessibility. These utility and accessibility variables are related but distinct, and taking both types of variables into account is necessary to properly model diffusion processes. I define strategic variables as characteristics of a given location that affect that location s attractiveness as a target to insurgents. I term these strategic variables because violence is the outcome of a strategic process rational, utility-maximizing insurgents with limited resources are more likely to use violence against targets where it will be most effective and has the highest likelihood of success. These factors vary from location to location, meaning that they are spatially heterogeneous and therefore different locations may have higher or lower strategic value. However, many of these variables are static over time (or change so slowly as to make no difference in my analysis) and therefore do little to explain temporal variation in patterns of insurgent violence. To explain both spatial and temporal patterns of violence, it is necessary to take acces- 7

8 sibility into account. These variables measure the ability of insurgents to export violence to a given location, and therefore are dynamic over time as the front of violence shifts, the ability of insurgents to commit violent acts at new locations changes. The risk of a given location experiencing violence, then, is partially a function of that location s proximity to previous violence, as well as the level of intensity of violence in the immediate region. Therefore, these variables are highly dynamic, and help predict the risk of a given location experiencing violence at a specific time. To model diffusion, it is necessary to separate strategic value from accessibility, but also to take both of these concepts into account. Strategic variables are useful in predicting why some locations are (ceteris paribus) more likely to experience violence than others, but do not take into account the real-world constraints facing insurgents seeking to export violence. Only examining the role of strategic variables, then, assumes that a city on the other side of the state from the actual conflict zone experiences the same risk of violence as a similar city located in territory under military contestation. Clearly, this is not the case, and therefore the inclusion of accessibility is necessary to explain why the risk of violence changes over time. Modeling diffusion using only geographic measures of accessibility leads to faulty inferences. Ability variables can explain variation in risk over time, but do not differentiate base levels of risk between units. Violence is not a disease that is equally likely to infect any location in a certain proximity it is the outcome of a strategic decision-making process by rational actors with limited resources. This means that modeling the spread of violence as a blind, geographically deterministic process will not accurately reflect the patterns seen in reality. Insurgents do not pick new targets based solely on proximity; instead, they pick targets within reach where violence will be most effective. Employing both strategic and ability variables captures not only how attractive a target may be to insurgents, but how able insurgents are to project force and attack that target. This makes intuitive sense while an insurgent group may view the state capital as a highly 8

9 attractive target for the duration of a civil war, the fact that insurgent groups generally spring up in remote areas (Weidmann 2009) makes it unlikely that they will be within striking distance of the capital in the beginning of a conflict. Geographic and demographic features affect how likely a given location is to experience violence (Raleigh & Hegre 2009); however, the effects of these variables are contingent on the ability of insurgents to project a sufficient level of force to a given location even though the expected benefit of attacking a given target may remain constant, the ability of insurgent forces to attack that target may change over time. My research improves on previous work in two ways. First, I explicitly model the diffusion of civil war violence as a function of rational insurgent decision-making that is highly dependent on geographic factors. While previous work has found that local factors like population, strategic location, and distance from the state capital affect overall patterns of violence dispersion (Raleigh & Hegre 2009, Chojnacki & Metternich 2008), they do little to take into account the way in which the insurgent decision-making process is affected by their ability to export violence to that location. These models focus primarily on utility variables, essentially assuming that an insurgent group has the same military and logistical capability to strike at any location within the state. Intuitively, this seems problematic when attempting to predict patterns of violence diffusion during a civil war. Instead, I model how the ability of insurgents to strike at a given target changes as the front of the conflict changes. Second, my model adds a higher level of specificity and more accurate operationalizations that better capture spatial and temporal diffusion effects. I do so by using use a more finegrained level of analysis the population center than most previous work, protecting my inferences from falling into an ecological fallacy. Additionally, this study goes beyond the geographic scope of previous work in that it addresses civil war diffusion using a large cross-national data set. This allows me to separate individual country-level effects from the core dynamics of insurgent violence. In this way, I can increase the external validity of my 9

10 results by showing that they hold or do not hold across multiple countries, regions, and continents. 4 Assumptions My theory rests on two sets of assumptions. The first set is about the general nature of civil war and violence, while the second refers to the behavior and motivations of insurgent groups in particular. 4.1 Assumptions about Civil War First, I assume that civil war is essentially a contest of power between two parties: an incumbent (the state) and an insurgent (a group seeking to change the balance of power at the national or sub-national level). Specifically, I use Lohman & Flint s (2010) definition of civil war as a violent political process through which peoples or groups, who are excluded from power, contest the ruling authority to alter or replace existing power relationships (1154). This definition covers most types of substate violence, including secessionist and nationalistic wars with ethnic or non-ethnic components as defined by Sambanis (2004). Second, I assume that the way both sides contest political power is by shifting control of the civilian population. Kalyvas (2006) points out that control of civilian populations is necessary for both sides in civil war; both incumbents and insurgents draw resources and recruits from the civilian populace, and therefore their strength to contest the other s power is drawn directly from their control of civilians. Clearly, this definition is extremely limited; it leaves out strategic location (Chojnacki & Metternich 2008), natural resources (Buhaug & Rod 2006), and other factors that influence where violence occurs during civil war. In the future, I plan to relax this assumption to create a broader model of civil war diffusion, but in the interests of simplicity I limit my study solely to contestation of civilian control. Third, I assume that these contests take place through territorial conflicts. Clearly, it 10

11 is impossible to control the civilian population without controlling the space in which they exist. This means that control of territory, adjusted for population density, can serve as a proxy of control over the civilian population. This is similar to previous geographicallymotivated analyses of civil war (e.g. McCall 1969) but treats territory as a means rather than an end in this case, territory is only as important as the civilian population occupying it, from which either side can draw resources and recruits. Therefore, I conceptualize civil war as a series of localized contests to redefine and redistribute the control of territory. Fourth, I assume that these contests are purely military in nature. Once armed conflict has broken out, both incumbents and insurgents swiftly converge on violence as the primary method of vying for control of civilians popular appeal, political maneuvering, and other rhetorical devices quickly fall by the wayside (Kalyvas 2006). Violence serves two purposes in this case: first, to increase one s own level of control over the civilian population, and second, to decrease the enemy s control over the same group. Therefore, I assume that violence is the only tool used by insurgents and incumbents in their struggle for control. In this way, I conceptualize violence as a way to capture transfer of control the winning side in a military contest gains some measure of control, and the defeated side loses some measure of control, which is mirrored in many game-theoretic models of conflict as contest (Skaperdas 2002, Smith 1998). Fifth, I assume that the ability to project force and engaged in localized military contests is predicated in part on geographic distance. Boulding s (1962) conception of the loss-ofstrength gradient has been used repeatedly in conflict literature to discuss the ability of the state to project power to different locations within its borders (e.g. Buhaug 2010). The farther a location is from the seat of a combatant s power, the more costly and difficult it is to project the same level of force to that location. This is most obvious for the incumbent, given that it has a clear seat of power in the state capital, but is intuitively also true for insurgents who lack a clear, fixed base of operations weapons and personnel still need to get to the site of conflict. To conceptualize of some measure of insurgent LSG, I assume that 11

12 geographic distance and power projection plays a major role in insurgent decision-making, and that insurgent violence serves as a proxy for insurgent presence at a given location. 4.2 Assumptions about Insurgents Within this simplified framework of civil war, it is also necessary to make a number of assumptions about the nature, number, and goals of insurgent actors. First, I assume that a single insurgent group is the sole perpetrator of violence during civil war, leaving out both the presence of other insurgent groups and the actions of the incumbent itself. Obviously, this is not the case attempting to model civil war diffusion examining only insurgent activity is like analyzing a game of chess from only observing one set of pieces. However, attempting to model diffusion as the product of two related, dynamic processes incumbent and insurgent increases the difficulty of the modeling process dramatically. Complicating matters further is the fact that there are often multiple insurgent groups acting in a single country for example, Nigeria has seen violence from upwards of 80 separate insurgent groups in the last ten years. As such, I sacrifice real-world accuracy for modeling simplicity in this case, and leave the inclusion of incumbent activity and other insurgent groups for future research. Second, I assume that insurgents enjoy an advantage of private information. This assumption reflects the common setting of civil wars, in which insurgent forces are initially numerically and materially inferior to incumbent forces. These weaker insurgent groups resort to guerilla tactics in order to combat stronger incumbent forces, blending into friendly populations and using rough terrain to their advantage (Wickham-Crowley 1990). This adoption of guerilla tactics often gives insurgents first-mover status they can pick and choose targets to attack, forcing the incumbent to take a defensive role while it attempts to pin down elusive insurgent forces in conventional battle. My core assumption is that in a given time period, insurgents choose the locations of all violent acts. Third, I assume that insurgents are rational, unified, utility-maximizing actors. Given that my previous assumptions model violent engagements between insurgents and incum- 12

13 bents to redefine control over the civilian population at a given location, and given that the assumption of superior private information affords first-mover status to insurgents, this assumption means that insurgents will choose targets that provide the highest expected utility. This metric of expected utility takes both costs (risks and difficulty of attacking) and benefits (increased control over the civilian population from a successful attack) into account. I assume that insurgents will choose targets where the balance of expected costs to expected returns is most desirable. These assumptions lay the groundwork for a bare-bones model of conflict diffusion based on the strategic choices insurgents are faced with. In a given time window, utilitymaximizing insurgents will use violence in locations that provide the greatest possible chance for victory and the greatest possible shift in control from incumbent to insurgent. However, their ability to project force to these locations is predicated on geographic factors, primarily travel distance through hostile areas controlled by the incumbent. 5 Variables and Hypotheses My outcome of interest is the occurrence of insurgent violence at a given place and time during a civil war. I define insurgent violence as any violent clash involving an insurgent group and either incumbent forces or civilians. This measure is necessarily crude there is no differentiation in the scale of violence (insurgents blowing up a bus in a small rural village versus tanks rolling into the capital city, for example) and there is no differentiation between types of violence (military clashes versus massacring prisoners or razing a town). Since the goal of this study is to measure the spread of all insurgent activity, I leave the dependent variable broad enough to capture the maximum number of observations. Future work will narrow down this measure, attempting to calculate different processes leading to different scale and types of violence. I analyze diffusion at the population center level of analysis. In this case, the popu- 13

14 lation center refers to any unique, named human settlement within 10km of a major road network. This allows me to analyze the risk of attack at each location using spatiallyreferenced variables. This level of analysis is fitting in two ways. First, because the core of my theory treats civil war as a violent contest over population centers, rather than solely over territory, it is logical to use the population center as the location of interest. While this does mean that I will lose a certain amount of data not every violent incident during a civil war occurs in or near a population center preliminary exploration of the data has shown that the vast majority of events are associated with settled areas, so this should not be a major obstacle. Second, analyzing diffusion at the population-center level provides stronger spatial inferences than previously-used measures, which often take the approach of carving up a state into arbitrarily-sized squares and using these squares as the unit of analysis (see for example Buhaug & Rod 2006). This approach does a poor job of measuring spatially dependent processes, as it necessitates extremely crude measures of distance and neighborhood, and furthermore, because the data in these grid-squares are still aggregated, leaves open the possibility of committing an ecological fallacy (Anselin & Cho 2002). Using the population center as the level of analysis deals with both of these problems. Distance between nodes can be measured more accurately, allowing for more precise measures of spatial dependence, and there is little danger of over-aggregating data. Finally, because I am interested in measuring diffusion rather than dispersion, my unit of analysis must necessarily have a temporal component to differentiate between events occurring at different times. I therefore divide the total observation time for each population center into months. This is a fine-grained enough measurement that I feel comfortable treating time as a continuous variable, while being aggregated enough to minimize noise due to measurement error. Therefore, my data are well-suited to duration analysis, measuring the probability that a given population center will experience insurgent violence in any given month as a function 14

15 of population characteristics and previous patterns of insurgent activity. It is impossible to create a meaningful model of diffusion without including both of these sets of variables. Attempting to predict violence over time by only examining the structural characteristics of each unit removes spatial and temporal dependence from the model. Removing this dimension means that we assume geography and spatial features play no part in how violence spreads during civil war, which is clearly incorrect. Likewise, treating all units as identical and focusing solely on the spatial and temporal patterns of violence diffusion removes the crucial component of insurgent decision-making from the model. Given that violence is a conscious, strategically-informed phenomenon, modeling the spread of violence as a blind process will severely weaken a theory s predictive power. 5.1 Strategic Value: Population Density I expect that population density will be strongly related to the risk of insurgent violence. This represents a test of the classic Maoist prescription for revolution should it be the case that insurgents target rural or isolated areas in a bid for territorial control, there should be a negative relationship between population density and the risk of violence. However, I argue that since violence is used as a tool to contest control of the civilian population, rational insurgents should disproportionally target costly violence in densely populated areas (Kliot & Charney 2006). As I am treating civil war as a series of localized contests over civilians, areas with highly concentrated civilian populations are prime targets for violence, as the rate of return for violence is much higher. Therefore, I expect that cities with higher population density are at higher risk of insurgent violence at any given time. 5.2 Strategic Value: Political Salience Violence shifts control of civilians to insurgents in two ways: first, it can show the dominant strength of insurgent forces in a given area, providing higher incentives for civilians to directly support insurgents; and second, it can show the inability of the incumbent to protect the civilians under its charge, effectively raising the perceived costs for civilians to support the incumbent 15

16 (Mason 1996, Wolf 1965). Striking at targets of political importance, such as regional or national seats of government, accomplishes this second goal - successful attacks in the seats of incumbent power send a strong signal to civilians that the incumbent is weak and ineffectual, and therefore they might be best served to support the insurgent or flee from the area. Therefore, I expect that local and national capital cities are at higher risk of insurgent violence at any given time. 5.3 Strategic Value: Political Protest Civil wars generally do not arise in states where the population is happy with the state of government. Insurgents recruit heavily from the civilian population, either by promising justice under a new status quo or by promising more immediate material rewards for participation, or through simple old-fashioned coercion (Weinstein 2005, Humphreys & Weinstein 2006). All else being equal, however, it is easier to recruit from a willing than an unwilling population. It may be that riots and political protests during a time of civil war send a signal to insurgents as to the local population s level of discontent with the incumbent, and therefore the ease with which they can be recruited by insurgents or dissuaded from supporting the incumbent. This may be especially the case in repressive regimes, which tend to see fewer incidents of political protests but higher levels of overall violence (Regan & Norton 2005). Therefore, I expect that cities experiencing riots and political protests in the previous month are at higher risk of insurgent violence in the current month. 5.4 Accessibility: Distance from previous violence The work on civil war diffusion commonly uses the distance from a given location to the most recent incident of violence as a predictor of future violence (Raleigh & Hegre 2009, Zhukov 2010). Previous insurgent activity serves as a useful proxy for measuring insurgent presence clusters of violent incidents or trends in the geographic distribution of violence over time can help predict the ability of insurgents to export violence to new locations. Therefore, I expect that locations closer to recent incidents of insurgent violence are at higher risk of violence in the current month. 16

17 6 Local-Level Variables and Data 6.1 Unit of Analysis This study deals with all insurgent activity covered in the Armed Conflict Locations Event Dataset (ACLED), currently including 22 African and South Asian countries between 1997 and 2010 (Raleigh et al 2010). The table below shows the list of countries, as well as the years during which they experienced insurgent activity on any major scale. I code each country as being in conflict if they were coded as such either the UCDP-PRIO 2010 conflict data set or the Political Instability Task Force s data sets on ethnic and revolutionary wars during each year within the data set: Insert table 1 about here. The level of analysis in this study is the city-month. Within each country, I created a data set of population settlements by merging the US Geological Survey s World Gazetteer 1994 with the Environmental Systems Research Institute (ESRI) s Major Cities 2000 data set. This gave me a data set of world population centers that was as complete as possible while maintaining a high level of accuracy and coding quality. Within each country, I coded a city as being any unique, named populated place located on or near a major road network as measured by the National Imagery and Mapping Agency s Digital Chart of the World data set. One important note: this decision to only keep connected cities had the effect of dropping potentially valuable data from the analysis, as not all villages are connected by major roads. I am currently working to obtain more detailed road data, which will allow me to expand the number of observations within each country. This coding process led to the creation of a dataset including 7, 331 cities over the 22 countries being measured. Out of these cities, a total of 1, 134 incidents of insurgent violence were observed a large enough ratio of events to non-events to easily draw significant inferences from. For the purposes of this analysis, I coded the data set for single-event hazard analysis, meaning that cities were removed from the risk pool upon experiencing their first event of insurgent violence. This means that each failure in this dataset represents the onset of violence, and does not account for repeated events. This has both substantive and statistical impact, which I discuss in more depth 17

18 in the next section of the paper. My outcome of interest, then, is the onset of insurgent violence. These are extremely finegrained data, and have only recently become available on a cross-national scale with the release of the Armed Conflict Location Events Dataset (Raleigh et al 2010). This dataset is unique not only in its scope and level of detail, but also in that each observation is time- and location-referenced. This means it is possible to analyze these data over both time and space, making this dataset perfectly suited for the scope of this project. I coded insurgent violence as any ACLED entry that: 1. Involved an armed non-state actor on at least one side; 2. Involved the direct use of physical violence resulting in fatalities; and 3. Occurred within ten kilometers of a population center. It is important to make note of this last coding rule. This may appear to be selecting on the dependent variable, as only measuring incidents near population centers may bias the study toward supporting my hypotheses, but in this case it was a necessary decision. Because I measure the diffusion of violence as a process that spreads from population center to population center, I have no way of including or accounting for violence that occurs away from road networks and populated places. Therefore, this protocol is essentially building an entire theoretically appropriate population for analysis, rather than selecting cases out of a larger population that I believe will support my theory. Furthermore, the actual impact of this coding choice is not particularly large the vast majority of recorded incidents occur in or very near population centers, so the resulting biases in results will be minimal. One more important note: This dichotomous outcome is crude in that it cannot differentiate between one incident and one hundred incidents in the same city-month (which would have very different substantive interpretation) but was chosen for ease of analysis at this preliminary stage. 6.2 Population Density To capture the population density of a given city, I use the Center for International Earth Science Information Network (CIESIN) s Gridded Population of the World 3 data set, containing 18

19 population density estimates of the entire globe at a 2.5 arc-minute resolution, or about 21 square kilometers. I created the variable used in this analysis by extracting the population-density value of the square on which each population center was located, interpolating with surrounding squares to account for some level of inaccuracy between the different formats of the population density and population center data sets. Resulting values were then logged to account for large outliers. 6.3 Capital Cities To code whether or not a given population center was a state, regional or provincial capital, I referenced ESRI s Major Cities 2000 data set and coded each city as 1 if they were entered as an administrative capital and 0 if not, where administrative capital is defined as any city that is the official national, provincial, or other local-level seat of governmental power. 6.4 Previous Riots To code whether or not a given city had experienced civil unrest in the previous month, I referenced the ACLED data set and used identical coding procedures to calculate the occurrence of civil unrest, riots or protests in each city-month. Observations were coded as 1 if any civil unrest was recorded, and 0 if not. Overall, riots were very rare in most countries which is unsurprising, given that autocratic regimes in the middle of dealing with insurgency likely have little tolerance for civil unrest but they are still prevalent enough in the ACLED data to be theoretically interesting and methodologically tractable. 6.5 Distance to Previous Violence To compute the distance to the closest previous incident of violence in each city-month, I calculated the logged distance by road between all cities in a given country, then used the minimum distance between each city and all other cities experiencing violence in the most recent month in which violence occurred. If the most recent incident of violence occurred within that particular city, I coded this distance as zero. Mathematically, this variable is calculated as Closest ij = Min(D (i v),j ), where i I represents months, j J represents cities, and D is a Jx J matrix of 19

20 distances between cities. 7 Analysis and Results Because these data consist of repeated observations of one population over time, it is naturally well-suited to duration analysis. In this case, I chose a semi-parametric Cox regression model to analyze the relationships between my independent and dependent variables. The choice of the Cox model over parametric models like the Weibull or inverse-gamma was motivated by two factors. First, the Cox model is the most widely-used in most social science applications, is highly flexible, and lends itself well to many diagnostic tests (Box-Steffensmeier & Zorn 2002). Second, the Cox model frees the modeler from making prior assumptions about the functional form of time, which often has a major impact on the interpretation of hazard rates in parametric models (Jones & Box-Steffensmeier 2004). One important similarity between the Cox and Weibull models, however, is the assumption of proportional hazards that the effect of a given covariate on the hazard rate is time-invariant and thus remains the same over the entire duration of observation. Within this analytical framework, I am faced with the pressing challenge of dealing with unobserved subgroup heterogeneity. Because my data includes a large number of countries that vary widely across many factors population size, regime type, economic prosperity, geographic location, and so on only analyzing local-level variables will include a huge amount of noise brought on by unobserved heterogeneity at the state level. In an effort to account for this kind of heterogeneity, I calculate an additional state-level frailty term within the Cox model. In so doing, I can capture (to some degree) the effects of unobserved variables that impact the hazard rate differently between states. This serves to increase the strength of my inferences and the overall fit of the model, but also creates new challenges in interpreting coefficients, which I describe in more depth in my discussion of model results. In the future, I plan to move toward a more theoretically informed hierarchical model that accounts for both local-level and state-level variables more explicitly. Running the Cox model with sub-group level frailty produces the following estimates: Include table 2 about here. 20

21 For all four variables, the coefficients are highly significant and in the expected directions. In this case, all four of my hypotheses are confirmed. Exponentiating the raw coefficients gives the hazard ratio estimates shown in the right-hand column these can be interpreted as the magnitude of shift in the hazard rate resulting from a one-unit increase in one covariate, all others being held constant. For example, these results show that cities that are state, local or regional capitals are nearly six times more likely to experience insurgent violence, all other factors being equal. Likewise, a one-unit increase in the distance from the most recent incident of violence decreases the odds of experincing violence by approximately 5%. While these results may seem fairly straightforward, one central assumption has to be examined further. As mentioned previously, the Cox model is a proportional-hazards (PH) model. This means that interpretation of any resulting coefficients is only accurate if these effects are indeed static over time. Fortunately, graphical and statistical tests of this assumption exist. In many cases, visual examination of residuals can be useful in assessing whether there is evidence to reject the null hypothesis of proportionality, but these assessments are necessarily non-specific and can in fact be visually misleading in the presence of outliers (Jones & Box-Steffensmeier 2004). Given this, I rely on two statistical tests of proportionality based on the Schoenfeld residuals from this model: Harrell s ρ statistic (1986) for individual covariates, which calculates the correlation of residuals with ranked time; and Grambsch and Therneau s (1994) global test for nonproportionality on the model as a whole. Results of the tests are shown below: Insert table 3 about here. These results show two issues that require further examination. First, there is overwhelming evidence to reject the null hypothesis of non-proportionality for the effects of distance on the hazard rate of insurgent violence over time. This appears to be the key factor driving the rejection of non-proportionality for the overall model as well. Second, there is some cause to doubt the proportionality rule for population density, as well despite the fact that the p-value for this test approaches 0.1, and that the Harrell s ρ test is fairly non-conservative, I still believe that it is worth looking into. Since at least one of my key covariates displays strong evidence of non-proportionality, it is 21

22 necessary to address this issue. Currently, there are two common approaches taken when addressing non-proportionality: stratification and interaction with time. Stratification on the covariate of interest has the effect of estimating different baseline hazards for each grouping of covariate values, which makes interpretation easier but has the downside of rendering the impact of that variable s actual impact on the hazard rate impossible (Box-Steffensmeier & Zorn 2002). Since I am interested in the impact of these variables, I chose to go the route of interactions with time. This method explicitly introduces non-proportionality into the model by interacting the offending variable(s) with the metric of time or some transformation thereof. There are many transformations that can be performed on time in this case squaring, logging, and taking square roots are common but overall, taking the natural log of time has proven to be a reasonable standard when creating non-proportional hazard interactions, performing at least as well as most other transformations in the majority of settings (Hosmer & Lemeshow 1999). Therefore, I introduce two interaction terms log(pop Density) * log(t ime) and log(closest Distance) * log(t ime) to account for potential non-proportionality in the effects of these two variables. The model with time-interactions is shown below: Insert table 4 about here. The effects of whether or not a city is a state, local or regional capital are large, significant, and in the expected direction, as are the effects of whether or not a city experienced major riots or political unrest in the previous month. Both of these variables increase the hazard rate for a given city, increasing the likelihood of experiencing insurgent violence in a given month. The two non-proportional variables population density and proximity to previous violence are still significant, but the sign for violence proximity has changed. Both of the interaction terms are statistically significant, meaning that at least at first glance there is a significant change in how these two covariates impact the chance of violence over time. However, given that both of these interaction terms include two continous covariates, only looking at regression output tables can be misleading. One useful way to visualize the actual impact of these interactions is to plot marginal hazard ratios over time. Doing so produces some very interesting results as to the nature of the relationship between these variables.both population density and the 22

23 distance from most recent attack display surprising changes over time in their effect on insurgent violence, which I will discuss in turn. First, the effect of population density is initially significant and quite large at time t = 1, a one-unit increase in the log of population density leads to a roughly 17-fold increase in the likelihood of a given city experiencing insurgent violence in that month. However, this impact changes rapidly as time increases, as shown below: Insert plot 1 about here. By time t = 12 (one year into an insurgency) the effects of an additional one-unit increase in the log of population density have dropped significantly, only increasing the hazard ratio by roughly 400%. This decrease continues as time goes on, until by time t = 84 (seven years into an insurgency) the effect becomes insignificant. Contrast this to the effect measured by the proportional-hazards model, denoted by the dashed horizontal line on the plot above. The two lines tell dramatically different stories, with the time-interacted variable capturing a significant change in the relationship between population density and violence as time goes on. Substantively, this has interesting implications. Given this model, I can conclude that population density is a strong predictor of how and to where violence will spread in the early stages of insurgency. It appears that, especially in the first six months to a year of violence, insurgent activity spreads primarily among urban, densely-populated cities. As time goes on, there appears to be a trickle-down effect as violence spreads more into rural, lightly populated areas. Examining the interaction of time and the distance from the most recent incident tells an interesting story as well. I hypothesize that the effects of proximity will be negative the farther away violence is from a given city, the worse job it does of predicting future violence in that city. However, the interacted variable shows that this is not always the case. Insert plot 2 about here. In fact, the early stages of insurgency, the effect is actually positive and significant a one-unit increase in a city s distance from the most recent incident of violence actually raises the hazard ratio by roughly twofold. This means that violence appears to be highly dispersed, at least in the first months of conflict. However, as time goes on, the effects of proximity change sign, becoming 23