Does Civil Protests Affect the Decision to Demobilize from Illegal
Armed Groups? Evidence from Colombia
∗Ana Mar´ıa Ib´a˜nez † David Zarruk Valencia‡
June 26, 2013
Abstract
This paper is a first approach to the determinants of individual demobilization in the context of an ongoing civil war. We test for the existence of a causal effect of the civil protests against illegal armed groups on demobilization rates from them. We develop a theoretical model that explains the decision of the combatants inside illegal groups to demobilize, or not, depending on the civilian support towards the group. Using municipal quarterly data from Colombia during 2000-2008, we estimate the impact of civil protests on the insurgents’ demobilization rate. To solve possible endogeneity issues in our estimations, because of double causality and ommited variables, we instrument the number of civil protests with the number of internet connections on each municipality. We find a positive impact of civil protests on demobilization rates of guerrilla groups. Moreover, we find that the impact of civil protests is heterogeneous among combatants of illegal armed groups depending on their rank, time in the group, gender and marital status.
JEL Classification: C70, D01, D74, N46
Keywords: Civil protests, Demobilization, Combatants, Illegal armed groups, Conflict, Civil war.
∗
We are very grateful to Adriana Camacho, Juan Pablo Cote, Camilo Garc´ıa-Jimeno, Nicol´as Idrobo, Paula Jaramillo, Daniel Mej´ıa, Andr´es Zambrano, Rom´an Andr´es Z´arate and Rom´an David Z´arate for their valuable comments and sug-gestions. All remaining errors are ours.
†
Department of Economics, Universidad de los Andes. [email protected] ‡
1 INTRODUCTION
1
Introduction
“(A guerrilla) can always sink back into the peaceful
population which is the sea in which the guerrilla
swims like a fish.”
— Mao Tse-tung (1937) Although the existing economic literature has studied the emergence and outcomes of conflicts and rev-olutions, not much research has been done on the individual determinants of participation in conflicts. Political scientists, in contrast, have largely tried to understand the individual determinants of participa-tion in civil wars. Most of their research has focused on the decision of individuals to joinrebel groups, but little research has explored the causes of demobilization during civil wars. Despite the apparent symmetry of both decisions, the determinants behind the decision to demobilize are different from the determinants to join, mainly because combatants receive indoctrination inside the illegal group, which may change their preferences. Rebel groups strive on building up ideology among their combatants against the status quo, making them keener to cooperate with the group. There is large evidence that this has been the case in many of the left-winged guerrillas of the twentieth century (Grossman,1999;
Tullock,1974). Furthermore, people that join insurgent groups accumulate human capital that has little value outside war, such as military skills, criminal networks and abilities for illegal drug production and trafficking. Thus, even though many of the determinants that lead people to join rebel groups will also determine the decision to leave, there are subtle differences that must be examined carefully.
The few studies that have dealt with demobilization decisions, have focused on the consequences and success of disarmament, demobilization and reintegration (DDR) processes, but not their individual causes. These analyses are based on collective demobilization processes after civil wars have ended, where the decision to give up war has been made collectively by the whole insurgent group, and not by individual motivations. The literature has not examined the determinants of individual demobilization from rebel groups in the context ofongoing wars.
The lack of research in this area may be a consequence of the difficulty to access reliable data sources during civil wars. Not only the nature of conflict makes it difficult for researchers to find trustworthy data, but governments and official institutions have little incentives to publish related statistics. Survey based data may be quite mistrustful since individuals might have incentives to underreport their actual living conditions and overstate living standards at war. Besides, there is a selection bias in survey
1 INTRODUCTION
data, since those who answer the surveys are usually the ones that have had positive results in the reintegration process and still make part of it. The demobilized combatants that do not succeed in the process either go back to criminal activities, or simply disappear from the government supervision. This difficulty has made it impossible for the literature to identify the processes underlying demobilization.
This paper studies the determinants of individual demobilization in an ongoing civil war. Specifically, we study the impact that civil protests towards illegal armed groups have had on individual demobiliza-tion patterns, since there exists anecdotal evidence that points towards the existence of such causality. We take advantage of a rich municipal panel with detailed information on demobilization, civil protests, and economic municipal variables.
This paper has two main contributions to the existing literature on conflict. First, to our knowledge, this is the first paper that studies the determinants of demobilization based on a trustworthy, non-survey dataset. We use administrative data of the Government’s office for demobilization and a rich dataset on conflict variables. The main advantage of this data is that it has a smaller selection bias than survey data, since the government offers strong incentives to the combatants to report their demobilization, through protection1, monetary rewards, legal benefits and education and job search programs. Thus, we will be able to estimate the global impact of civil protests on individual demobilization, since our estimations are based on almost the whole set of demobilized combatants, and not just on a subsample.
Second, the existing literature on participation in civil wars has commonly ignored the existence of en-dogeneity among conflict variables (Blattman and Miguel,2009). Particularly, in our estimations there exist several potential endogeneity sources. On the one hand, there exists a double causality between civil protests and demobilization rates: more civil protests lead to higher demobilization rates, since lower support of the civil population reduces the probability that illegal groups win the war. Also, higher demobilization rates may lead to more civil protests, since the capacity of punishment of the ille-gal groups falls (Kalyvas,2001). Moreover,Kuran(1991b,a) argues that the emergence of civil protests depends on the capacity of repression of the government which, in turn, depends on its relative military size. When the governments are more repressive, it is more difficult for the citizens to organize civil protests. On the other hand, there are ommited variables that determine demobilization rates, such
1
There is anecdotal evidence for the Colombian case that shows that demobilization is seen by the illegal groups as a betrayal and is commonly punished with death penalty. Thus, the majority of the demobilized combatants report their demobilization to the government and remain under its protection to prevent being punished.
2 THE DETERMINANTS OF PARTICIPATION
as motivation and ideology of the combatants, severity of punishments and harshness of the leaders in each guerrilla front, credibility on the demobilization process in different regions, socio-demographic composition of the guerrilla fronts, and health conditions and access to medicine, among others. To solve the endogeneity, we use the number of internet connections per 100,000 inhabitants as instruments for civil protests. Internet connections have been a very popular way of promotion and spread of civil protests and, as we discuss in the empirical section, these are not correlated with demobilization. Thus, we are able to identify an exogenous source of variation of civil protests to estimate its causal effect on demobilization decisions.
The remainder of this paper is organized as follows. Section 2 reviews the literature on the determi-nants of participation in civil wars that we consider relevant to demobilization. No review is done on demobilization, since there has been no research on this topic. Section 3 discusses the importance of the Colombian case to the present research. Section 4 presents a model of the interaction between the combatants of illegal groups, who decide to demobilize, or not, and a representative agent of the civil society, who decides the level of support towards the illegal group. Section 5 describes the dataset we use in our empirical analysis, presented in section 6. Section 7 presents the main results of our empirical analysis, and section 8 shows robustness tests that support our findings. Section 9 concludes.
2
The Determinants of Participation
Civil wars often rise as a defiance to thestatus quo by a rebel group pursuing the establishment of new property rights and institutions, or seeking to enthrone a new ruling class (Grossman,1999)2. In this sense, insurgent groups are not productive enterprises since their output is no other than war. In order to sustain large, illegal, clandestine armies and to feed and pay its combatants, rebel groups require huge funding sources. This has usually led rebel groups to get involved in illegal activities such as extraction of natural resources and illegal drug production; as a result, many insurgent groups have been classified as criminal bands and drug trafficking organizations, no different from ’bandits or pirates’ (Grossman,
1999). Thus, when a person decides to join an insurgent group, many dimensions should be considered, ranging from ideology coincidences with the rebel group and grievance, to private benefits from illegal economic activities.
2
Although the economic and political science literature has proposed several definitions of civil wars, most of them agree that a civil war is a violent conflict between two or more groups that fight against each other to take the power of a region and establish new government policies. Some claim that one of the conflicting groups should be the current government of the region where the war is taking place (Fearon,2007;Gleditsch et al.,2002;Harbom and Wallensteen,2007)
2 THE DETERMINANTS OF PARTICIPATION
Some authors argue that the discontents of individuals due to inequalities and social exclusion in so-ciety, and resource or political deprivation determine the decision of individuals to participate in civil conflicts (Gurr, 1970, 2000). These do not depend on the rationalism foundations of individuals, but instead on their discontent with some aspects of society or their willingness to act in favor of a group’s interests. The theorists of revolutions have widely studied the pillars of these inequalities and economic and political deprivation, concentrating on land and income inequality, social class differences, ethnic and political differences, absence of non-violent means to express concerns in society and vengeance (Humphreys and Weinstein,2008;Walter,2004).
Inequality theories date back to Karl Marx(1968), who argued that grievances generated by inequality between social classes inside the capitalist societies would trigger revolution, leaded by the industrial proletariat. Further research found, instead, that revolutions were in fact being held by the rural peas-ants who were suffering from extreme poverty or worked for landlords that were not willing to assent their demands (Paige,1975;Scott,1976). Others have stressed the importance that land inequality has had on the decision to participate in an insurgent group. Individuals in regions with high inequality in the distribution of land are more prone to participate in conflict, as has been the case in many Latin American conflicts (Jaramillo,2001;Wickham-Crowley,1992;Muller and Seligson,1987).
Political deprivation and absence of non-violent means to express concerns in society may be a moti-vation to participate in civil conflicts when individuals are not able to satisfy their economic, political and social expectations. Dissatisfaction often arises when there exists a gap between the individuals’ expectations and achievements. As this gap widens, people’s willingness to engage in conflict increases (Gurr, 1970; Davies, 1962). Individuals resort to violence and non-legitimate ways of reaching their goals. Thus, political deprivation has been a common explanation of participation in civil wars (Walter,
2004). In Colombia, at the end of the 1950s, the two leading political parties colluded to alternate power during 16 years, through a pact known as theFrente Nacional. It has often been argued that the political deprivation caused by the exclusion of political minorities led in the following decades to the creation of rebel groups.
Grievance has proven to be a necessary ingredient inside insurgent groups, since it is an effective way to generate cohesion and motivation inside the group. Leninist theories of rebel organization argue that most of the population where combatants are recruited from is not aware of being oppressed, so rebel
2 THE DETERMINANTS OF PARTICIPATION
groups often inculcate grievance among their soldiers to consolidate the armies. Much literature on history and sociology has studied armed group cohesion and highlights the importance of social identity in generating solidarity and commitment (Gabriel and Savage,1979;Shils and Janowitz,1948).
In addition, there are behavioral and experimental explanations that suggest that individuals are often willing to incur in the costs of being at war, in order to punish unfairness and violations of social norms. As Blattman and Miguel (2009) argue, “this willingness to punish unfair behavior appears to have neural-psychological underpinnings and is consistent with preferences for equity” (de Quervain et al.,
2004;Charness and Rabin,2002;Fehr and Schmidt,1999).
Recent research claims that if participation in conflict does not bring private benefits to the individuals, the collective action problem will generate free riding. Since the triumph of revolution would imply the creation of public, non-excludable goods, if there are no benefits contingent on participation, rational individuals would not bear the costs of war (Olson,1965;Lichbach,1990;Goodwin and Skocpol,1989;
Arjona and Kalyvas,2011). Hence, there must be private incentives that lead individuals to join insur-gent groups. Only if there exist private benefits will people participate in conflict. In fact, Grossman
(1999) and Tullock(1974) suggest that Lenin, Mao, Ho and Castro’s armies gave excludable incentives to their combatants in order to overcome the free riding problem.
There are two types of private incentives that may foster participation in rebel groups: positive in-centives to participation offered by the insurgent groups, and negative inin-centives to nonparticipation, through costs of not joining. The positive incentives to individuals are represented by direct benefits given to the combatants in terms of money, loot, land, positions of authority or natural resources. Lich-bach (1995) argues that successful social movements offer positive incentives to individuals that make part of them. There is evidence of the existence of selective incentives by insurgent groups to their combatants in Vietnam, Mozambique, Sierra Leone and Peru (Popkin,1979,1988;Weinstein,2007).
There may also exist negative incentives that make the individuals better off in the insurgent groups. For example, when violence by armed groups against civilians is recurrent or when there exists threats of forced recruitment, the individuals are better off inside the armed group, since it gives them protection that they would not have otherwise (Goodwin,2006;Lichbach,1995;Mason and Krane,1989). Arjona and Kalyvas(2011) find that combatants that decide to join illegal armed groups in Colombia come from areas where victimization rates are, on average, higher that in the rest of the country. Furthermore,
3 COLOMBIAN REBEL GROUPS AND THE MAIN PATTERNS OF DEMOBILIZATION
conflict may have a negative impact on wages of rural markets, increasing relative returns of illegal markets and making some individuals better off at war (Azam,2006).
Finally, there exist social sanctions that may determine individual participation in conflicts (Humphreys and Weinstein,2008). Individuals in communities with strong links will have higher incentives to join when their community supports the rebel group. Taylor (1988) argues that social ties were the incen-tives that raised revolutions in France and Russia, but not in China. While in France and Russia the rural communities had very strong links and were relatively autonomous from outside control, in China the rural peasants were much more independent from each other, so their community was not able to monitor the behaviour of individuals. This led to the emergence of revolutions in the first two, but not in the latter.
We argue that the decisions to join or demobilize from an illegal group, although similar, are different because the dynamics of war change individuals’ preferences. However, the determinants of demobiliza-tion are quite similar to the determinants that lead individuals to join civil wars. The theoretical model in Section 3 explains the decision to demobilize.
3
Colombian rebel groups and the main patterns of demobilization
Colombia’s current conflict is a consequence of historical social discontents towards land and income inequality, power concentration on elites and lack of political participation for minorities that have ex-isted long before independence. Rebel groups surged as a response to thestatus quo that has benefited landlords and has excluded the bulk of the population for political and economic participation. This section summarizes the main events that led to the emergence of rebel groups, their role in the current conflict and the demobilization patterns of the last years.
Back from before Colombia’s independence, land has been concentrated in the hands of powerful land-lords. In the decades of 1920 and 1930, strong agrarian movements emerged and violence between the dispossessed, rural population and the landlords rapidly rose (LeGrand,1986). In 1948, when the chief of the Liberal Party and candidate for the elections of 1950, Jorge Eli´ecer Gait´an, was assassinated, the Liberal and Communist parties’ followers left the cities and created small guerrilla groups and Colombia was immersed into a situation of extreme violence thereafter. In 1958, seeking to reduce the violence of the last decades, the Liberal and Conservative parties signed a treaty called theFrente Nacional, in
3 COLOMBIAN REBEL GROUPS AND THE MAIN PATTERNS OF DEMOBILIZATION
which they agreed to alternate power during four consecutive presidential periods, excluding all political actors that were not part of the two dominant political parties (S´anchez et al.,2003).
Political exclusion, the increasing demands for land reform and the military attacks from the State armed forces led these groups to create the Revolutionary Armed Forces of Colombia (FARC) and the National Liberation Army (ELN), presumably supported by the Communist Party and the left wing part of the Liberal Party, known as the Liberal Revolutionary Movement. These groups demanded the establishment of a different economic model and a profound land reform. From their very beginning, these guerrillas had strong presence in areas where the agrarian movements that emerged in the 1930s were stronger (Jaramillo,2001). During the 60s and 70s, both groups experienced a moderate growth in the number of men and a modest expansion along the national territory, but continued to be small armies. However, during the 80s guerrilla groups started producing and trafficking drugs, which boosted their economic growth and the number of men in their rows. This led them to significantly increase their military power and to control sizable parts of the National territory after 1990 (Alape,1985; Pizarro,
1991). Figure 1shows the growth of the number of men and military fronts of both groups.
[FIGURE 1 GOES ABOUT HERE]
During the decade of 1980, as a response to the increasing power and presence of guerrilla groups over the national territory and the incapacity of the government to control their rapid growth, illegal paramilitary groups surged, financed by the large land owners. Although during their first years they were small, independent, private armies that protected landlords in the regions where guerrillas were present, in the decade of 1990 all these small armies unified to create the Colombian United Autodefense Group (AUC). Soon after its emergence, this group was present in places where the State military forces were absent. Their main objective was to attack guerrilla groups and those that declared to support them. However, their actions went far beyond this line and the AUC engaged in recurrent massacres, kidnappings and illegal recruitment, among other atrocities. During the 1990s, also financed by drug trafficking, these groups grew exponentially (Cubides, 1999; S´anchez et al.,2003). During the decade of 1990, Colombia was immersed into one of its bloodiest decades.
During the first years of the twenty-first century, both guerrillas and paramilitaries were present in a sizable portion of the national territory and had large and powerful armies. FARC and ELN engaged in coercive practices to gain support among the civil population, through terror and intimidation, and
3 COLOMBIAN REBEL GROUPS AND THE MAIN PATTERNS OF DEMOBILIZATION
In addition, seeking to increase the number of men in their lines, guerrillas started recruiting children, who were unable to oppose resistance and whose ideologies could be easily trained and brainwashed towards the revolutionary cause. According to the government and some demobilized combatants from guerrilla groups, a bulk of the current members of rebel groups were forcefully recruited. In 2002, when violence had reached a historical peak, Colombians massively voted for ´Alvaro Uribe’s radical anti-guerrilla discourse, taking him to power in 2002. Immediately after Uribe took office, and taking advantage of the increasing foreign financial aid and military support of the last decade, his military strategy significantly harmed the guerrilla structures, which led the State to take control of areas that had been historically controlled by rebel groups3. Furthermore, a peace negotiation between the govern-ment and the AUC led to their demobilization between 2003 and 2006. Parallel to the military strategy to attack guerrilla groups, the State engaged in a massive campaign to encourage demobilization, offering monetary rewards, judicial amnesties, protection and benefits through reinsertion programs. Between January, 2000, and December, 2008, 12,800 guerrilla combatants demobilized from FARC and 2,700 from ELN. On December, 2012, the Minister of Defense publicly announced that FARC had less than 8,000 men and ELN less than 1,500 . Figure 2 (left) shows the total quarterly demobilization from 2000 to 2008. Figure 2 (right)shows the demobilization patterns, classified by the motivations that led combatants to leave war. We classify the motivations into three categories: a. personal motivations, b. bad conditions in the group and, c. government pressure4. There has been an increasing trend of combatants that demobilize motivated by government pressure, both in absolute and relative terms. This evidence suggests that, indeed, the military strategies after 2002, as well as the demobilization programs and campaigns, have effectively increased demobilization rates.
[FIGURE 2 GOES ABOUT HERE]
Arjona and Kalyvas (2011) conducted a survey among former combatants of guerrilla groups, to find evidence on the determinants that led them to join the conflict. Although their sample has a selection bias, their results are interesting. When asked for the reasons that led combatants to join the illegal group, the most frequent answers were, in descending order,“Attracted by promise of money or goods” 3During the decade of 2000, four members of the FARC secretariat (command group, usually formed by seven members) were killed. Also, most of the politicians and members of the armed forces that were kidnapped were either rescued by the army or released by the rebel groups as a consequence of national and international pressure.
4a. personal motivationsincludes combatants that declared being bored at war, unmotivated, having lost their ideology, wanted to change their lives, have a better future, were disappointed with the group or had been advised to leave; b. bad conditions in the group, includes combatants that declared having been forcefully recruited, were mistreated, threatened, humiliated, had health problems or not enough to eat, or felt there were injustices inside the group; c. government pressure, refers to combatants that declared being captured by the armed forces, incentivized by advertising campaigns, tired of the government’s military pressure or attracted by demobilization programs.
4 THEORETICAL FRAMEWORK
(23%),“Ideology” (12%) and“Power”(12%). Furthermore, they find evidence that people that decided to join were, on average, more victimized and threatened, and lived in areas where the illegal group had a strong presence. On the same line, Fundaci´on Ideas para la Paz5 (FIP) made a qualitative research on the determinants of demobilization of middle-ranked guerrilla combatants. Although they did not carry out a survey among all the demobilized combatants, their study presents qualitative evidence of interviews carried out to 28 former combatants. Their research finds that, among the determinants that led the middle-ranked combatants to demobilize are the loss of connection of the insurgent group with the civil society and the loss of legitimacy of the group among civilians.
Finally, there exists wide anecdotal evidence that points towards the fact that civil protests have had an impact on the attitude of combatants towards war. The following declaration made by Luis Eladio P´erez6 supports our hypothesis: “Gerardo Aguilar, also known as C´esar, laughed at us and said that if more than one million people attended the protest, FARC would leave up war, in an ironic tone... I saw
combatants about to cry, because they realized that the civil population did not support FARC...”7.
The Colombian case is important for the present research because, after more than fifty years of war, an important fraction of the guerrilla groups has individually decided to demobilize throughout the country, at different moments in time. This will allow us to estimate the determinants of individual demobilization taking advantage of a municipal panel with information on conflict and economic conditions, with spatial and temporal variation. The Colombian case is particularly interesting because civil protests against conflict have been a commonplace during the last decade. There have been hundreds of civil protests against illegal groups, which may have boosted the rapid growth of demobilization rates from them. We have information of every protest against conflict in Colombia, with variation across municipalities and time for a period of nine years. Last, but not least, research on demobilization in Colombia is scarce, so this paper contributes significantly towards a better understanding of the current conflict.
4
Theoretical Framework
This section aims to formalize the decision of the combatants of a guerrilla group, composed by a continuum of heterogeneous individuals who decide whether to demobilize, or not. The combatant’s utility depends on an individual ideological parameter. We assume that the government’s military
5
A Colombian think tank that does research on security issues.
6Luis Eladio P´erez was kidnapped in 2001 by FARC and released in 2008. 7
4 THEORETICAL FRAMEWORK
expenditure is an exogenous parameter that will affect the decisions of the combatants.
4.1 The agents’ decisions
Each individual inside the illegal group has an ideology towards revolution, either because insurgent groups invest resources on indoctrination among their combatants, or because they have an initial ide-ology towards revolution. Also, combatants accumulate different military skills and have different ranks inside the group. The insurgent group is made up of a continuous of individuals distributed uniformly along the interval [0,1], each of which differs from the rest on a parameter Ii that captures differences
in ideology, skills and rank inside the group. We will refer to Ii as an ideology parameter.
The combatant’s decision to stay inside the illegal group or demobilize depends on the costs and benefits of both alternatives. If the indirect utility of staying inside the illegal group offsets the indirect utility of demobilizing, the individual will choose to stay, and vice versa. The utility of the individuals inside the insurgent group depends positively on the ideology parameter, so more revolutionary or higher-ranked individuals are more prone to stay inside the group. We normalize the utility of staying inside the group, so the utility of demobilization does not depend on the ideology parameter of the combatants.
The indirect utility of individual iinside the illegal group (VWi) is the sum of the present value of the indirect utility of life inside the illegal group (UW) and the expected utility of individualiif he decides
to stay inside the group and the group wins the war (Up). Thus, the indirect utility for individual i
during the war is given by:
VW(Ii) =UW +Up(Ii)
The parameter UW depends positively on the illegal markets’ wages and negatively on the intensity
of conflict, since both affect the indirect utility of staying at war. Higher illegal markets’ wages will increase the living standards inside the group, while higher conflict intensity will worsen life quality at war. On the other hand, the indirect utility of the individual that demobilizes (Vd) is given by the
indirect utility of life in the legal markets (Ud), minus the costs that demobilization implies (T):
Vd=Ud−T
The parameter Ud depends positively on the wages of the labor market outside of the conflict, on the
social investment by the government and on the demobilization programs, among others. The parame-terT, among other costs, includes transportation costs and discrimination that ex-combatants must face.
4 THEORETICAL FRAMEWORK
Individuals for which VW(Ii)< Vd will choose to demobilize and those for which VW(Ii)> Vd will stay
inside the insurgent group. The individual for which VW(Ii) =Vd is indifferent between demobilizing
and staying inside the group. We assume that the indifferent individual chooses to demobilize. We will refer to the proportion of combatants that demobilize as the demobilization rate.
Given the parameters UW, Ud and T, there exist three possible demobilization outcomes. The first
outcome is an interior demobilization rate, and occurs when some individuals experience higher utility inside the illegal group and some others experience higher utility if demobilized. The demobilization rate takes a value inside the interval (0,1). The second and third outcomes are corner demobilization rates and occur when, either every individual has a higher utility inside the group and, thus, no one would demobilize (the demobilization rate is zero), or every individual is better off outside of the conflict, in which case the whole insurgent group chooses to demobilize (the demobilization rate is one).
The expected utility if the group takes power for individual i that chooses to stay (Up(Ii)), is the
product of the probability that the insurgent group wins the war (p) times the benefit that i receives if so. Without loss of generality, we assume that the benefits the individual would receive in case that the illegal group takes power are equal to Ii, since these benefits must be strictly monotonically
increasing on the ideology parameter. The ideology parameter Ii is normalized, so that it includes both
the benefits that individual i would receive depending on his ideology, and the benefits that are given to all combatants independent of their ideology.
Up(Ii) =p·Ii
We assume that the probability (p) that the illegal group wins the war depends on the demobilization rate of the insurgent group (A), on the military expenditure (E) and on the support the insurgent group has among the civil society (θ). We assume thatpis a continuous, decreasing function ofAandE, since a higher demobilization rate or a bigger military expenditure by the government makes the illegal group relatively weaker. Also, p is a continuous and strictly increasing function of θ, since higher support among the civil society means more collaboration with the illegal group through information of the enemy or protection (Kalyvas, 2000; Mao, 1937). Then, p(A, E, θ) satisfies Properties 1-3. Properties 4-5 are the usual concavity conditions8:
8
4 THEORETICAL FRAMEWORK
1. ∂E∂p <0
2. ∂A∂p <0
3. ∂∂θ2p2 <0
4. ∂θ∂A∂2p >0
5. ∂p∂θ >0
Hence, given the values ofUW,Ud,T,E and θ, there exists a demobilization rate,A, that indicates the
proportion of individuals that choose to demobilize. Since individuals know the distribution of Ii and
can estimate which portion of the insurgent group will leave war, the demobilization rate is of common knowledge ex-ante and, therefore, p is a fixed parameter. The following proposition states that if the interior demobilization rate described above occurs, then the demobilization rate equals the ideology parameter of the individual that is indifferent between demobilizing and staying inside the group.
Proposition 1. If there exists i∈[0,1]such that UW +p·Ii=Ud−T, then A=Ii.
6. Proof. See Appendix I.
Therefore, since individuals know that the demobilization rate should be given by the ideological param-eter of the marginal individual, then the whole insurgent group knows ex ante that the demobilization rate should be given by the value of I that satisfies:
UW +p(I)·I =Ud−T.
The demobilization rate is thus:
A=
0 if UW +p(Ii)·Ii > Ud−T, ∀i∈[0,1]
1 if UW +p(Ii)·Ii < Ud−T, ∀i∈[0,1]
Ii if UW +p(Ii)·Ii =Ud−T, for some i∈[0,1]
We now need to rule out the cases in which UW +p(Ii)·Ii =Ud−T has more than one solution, since
the demobilization rate must be unique. The following proposition states the conditions under which the solutions to this equality are unique, and therefore it makes sense to refer to the solution as the demobilization rate.
Proposition 2. Given pas defined above, if p is such thatp+I·∂I∂p >0,∀I ∈[0,1], and if there exists an individual i∈[0,1] such thatUW +p(Ii)·Ii =Ud−T, then:
1. i is the only marginal individual,
2. The demobilization rate is unique,A=Ii
5 DATA
Onwards, we assume that the functionpsatisfies the condition required for the demobilization rate to be unique. Also, we will denote the demobilization rate asI and the reaction function of the demobilization rate as I∗, since it is determined by the ideology parameter of the indifferent individual. The following proposition states that the demobilization rate is lower when the rebel group has higher support among the population, since the expected utility of staying at war is higher.
Proposition 3. I∗ satisfies the following property:
∂I∗ ∂θ <0
Proof. See Appendix I.
Figure 3(left) shows the demobilization rate I∗ for different values ofθ. It is clear that higher popular support must lead to lower demobilization rates, since the expected utility of staying at war increases. Furthermore, to study heterogeneity among the decision of demobilization between different types of combatants, if we divide the illegal group between those combatants with a “high” ideology parameter (with more revolutionary ideology, higher rank, more time inside the group, etc.) and those with a “low” parameter, the demobilization rates should be higher for the latter, asFigure 3illustrates. In the empirical analysis, we study the impact of civil protests against illegal groups on demobilization, which can be understood as negative civil support. Figure 3 (right) shows the way in which demobilization rates depend on civil protests.
[FIGURE 3 GOES ABOUT HERE]
5
Data
Our first source is the administrative data from theColombian Agency for Reintegration (ACR), which has information of each combatant that demobilized from an illegal group between January, 2000, and August, 2008. For each demobilization event, the database contains: date, municipality and institution where the person arrived, gender, age, name of the illegal group, rank inside the group, reason for demo-bilizing, time inside the group and military front to which the combatant belonged. The database has 21,153 observations, including demobilized combatants from guerrilla and non-guerrilla groups. Since the purpose of this paper is to understand the impact of civil protests on individual demobilization, we will only use the data of demobilized combatants from guerrilla groups, as paramilitary groups demo-bilized collectively, after they signed an agreement with the government in 2004.
6 EMPIRICAL STRATEGY
The second source is a database with information of all the civil protests against conflict in Colombia during 2000-2008, from the Center for Research and Popular Education/Program for Peace (CINEP), which is a foundation that collects data on conflict-related variables in Colombia. We have information of 1,226 civil protests against conflict with the exact date and municipality where each protest was held, the duration of the protest and the group against which the protest took place. From the 1,226 protests, six of them were nationwide protests, and 1,220 were at the municipal level.
The third source of data is the Center for Research on Economic Development (CEDE) from Universi-dad de los Andes, which collects yearly data on a wide range of economic and conflict-related variables for each municipality since 1993. In this paper we use per capita industry and commerce tax collection, per capita investments in education, an index for fiscal performance of the local government, density of population, proportion of rural population with respect to urban population, coca hectares cultivated and eradicated and kidnappings, massacres and landmines per each 100,000 inhabitants.
Finally, the data regarding the number of municipal internet connections comes from the Ministry of Information Technology and Communications which, through the Unified Information System for the Telecommunications’ Sector (SIUST), collects statistics on different communication systems since 2006. The data on the number of national internet connections since 2000 comes from the Commision for Regulation of Communications, also adhered to the Ministry.
6
Empirical strategy
This section describes the empirical strategy used to test whether civil protests against illegal armed groups cause an increase in demobilization rates. To deal with the endogeneity of the OLS specification, we use as instrument the number of internet connections in each municipality, for every quarter. The validity of the instrument is discussed in this section. For our estimations, we use a quarterly municipal panel with the data described in the past section, during January, 2000, and August, 2008.
We should warn that, although in Colombia there currently exist 1,222 municipalities, in our estimations we eliminated those municipalities that did not have all the controls during the whole period, to have a balanced panel. Therefore, our estimations are based on the information of 747 municipialities. Since the municipalities that we eliminated of our sample could be the smallest ones, or those that have different conflict dynamics, it could be argued that our conclusions are not global for the Colombian
6 EMPIRICAL STRATEGY
case. Nonetheless, we did all the empirical estimations9 that we present in this paper with the whole sample of municipalities and with the reduced sample, excluding all the controls. We find no difference, neither on the first stage, nor on the second stage results.
6.1 OLS specification
As the theoretical model suggests, civil protests against illegal groups should have a positive impact on demobilization rates. That is, more pressure against the conflicting groups should lead to higher demobilization rates. A na¨ıve approach would estimate this causal effect using an OLS approach such as the following model:
Demobi,t =βP rotesti,t−1+γXi,t+µi+πt+i,t (1)
where Demobi,t is the number of demobilizations per 100,000 inhabitants in municipality iat quarter
t,P rotesti,t−1 is the number of civil protests against conflict in municipalityi lagged one quarter, and Xi,t is a vector of economic, institutional and conflict-related controls. We include municipality fixed
effects (µi) and quarter-year fixed effects (πt) that capture many non observable characteristics of each
municipality and each period of time that may be related to conflict. We include the following economic controls: industry and commerce tax collection per capita, as a measure of economic performance of the municipality, investment in education per capita, as a measure of social investment by the government, the number of coca hectares cultivated, as a measure of the illegal groups’ economic activity, and number of coca hectares eradicated, as a measure of economic shocks to the illegal groups’ economy. We include an index of fiscal performance of the municipality to control for institutional performance of the local governments. We include the following sociodemographic controls: population density and an index that shows the proportion of rural population with respect to urban population. Finally, as is discussed below, we estimate the models with and without the following crime-related controls: number of kidnappings, massacres and landmines per each 100,000 inhabitants. The parameter i,t is
a normally distributed stochastic error. The coefficient of interest is β, which is the average municipal demobilization rate, the quarter immediately after a civil protest against conflict is held. We expect it to have a positive sign.
6.2 IV specification
Specification (1)is not an appropriate approach to estimate the impact of civil protests on demobilization rates, since there exist several potential sources of endogeneity through double causality and ommitted
6 EMPIRICAL STRATEGY
variables. Estimating only equation (1)would imply finding a biased estimator of ˆβ. On the one hand, there exists a double causality between civil protests and demobilization, since a higher demobilization rate would imply a relatively weaker illegal group and this would lead to more civil protests towards it (Kalyvas,2001;Kuran,1991b,a). It is worth to mention that the sign of the bias caused by the double causality is ambiguous, and depends on the values of α and β10. Namely, the sign of the bias is the same as the sign of11:
α
(1−αβ) (2)
Given that α >0, the bias should be non-negative whenαβ <1 and negative whenαβ >1. Theoreti-cally, the bias depends on the elasticity of the demobilization with respect to the civil protests and the elasticity of the civil protests with respect to the demobilization rate in the equilibrium point. When either the impact of demobilization on civil protests or the impact of civil protests on demobilization are low enough, such that αβ < 1, the OLS estimation will tend to overestimate the effect of civil protests on demobilization. However, if both impacts are sufficiently high, such that αβ >1, the OLS underestimates the real effect of civil protests on demobilization.
On the other hand, there may be ommitted variables that explain demobilization rates, such as mo-tivation of combatants, harshness of the punishments imposed by the leaders of each guerrilla front, intensity of the conflict in different areas, and socio-demographic composition of each front, among others. The sign of the bias caused by the ommitted variables is again ambiguous, since it depends on the way in which each of the variables correlate with the demobilization rates. Therefore, we are not able to identify neither the sign, nor the magnitude of the bias ex ante. To correctly assess the impact that civil protests has had on demobilization, we will use an instrumental variables approach. We will instrument the protests in the following way:
P rotesti,t=φInstrumentsi,t+γXi,t+µi+πt+i,t (3)
where Xi,t, µi, πt and i,t are the same as in equation (1). As instrument, we use the number of
internet connections. The variable of internet connections was constructed as follows: the government of Colombia has statistics on the number of internet connections for each municipality since 2006. Given that our period of analysis goes from 2000 to 2008, we do not have statistics for each period. Yet, we have information of the total number of internet connections in Colombia for each year. The variable we use as instrument is the municipal mean of internet connections per 100,000 inhabitants between
10
The parameterαis the coefficient of estimating the impact of demobilizations on civil protests. Namely,αis given by estimating: P rotesti,t=αDemobi,t+γXi,t+µi+πt+i,t
11
6 EMPIRICAL STRATEGY
2006 and 2008, interacted with the yearly growth of national connections to capture the trend over time. We expect the coefficient of our instrument to be positive, since internet connections, being a way of communication and difussion, facilitate the creation and promotion of new protests. Equation (3) results to be the first stage of a 2SLS in which the second stage is:
Demobi,t=βP rotestsˆ i,t−1+γXi,t+µi+πt+i,t (4)
whereP rotestˆ i,t−1are the predicted values of the first stage. The resulting ˆβis the number of combatants
that decide to give up war and demobilize, the quarter immediately after a civil protest against war is held.
6.3 Validity of the instruments
Internet connections in a municipality are a relevant instrument to explain civil protests because, at least for the case of Colombia, internet is the easiest way to communicate and to spread ideas and events. There is anecdotal evidence that some civil protests against conflict have been organized, dif-fused and promoted through social networks and online newspapers12. There is a higher probability that a civil protest is organized and held in a municipality where more people have access to the internet.
Also, we argue that this instrument is not correlated with demobilization rates. First, guerrilla combat-ants hide from the government in the jungle, and their access to the internet during the first years of the past decade was scarce. Thus, internet connections do not directly determine demobilization rates. Second, although it could be argued that there are less internet connections in less developed or smaller municipalities, which, in turn, are related to higher conflict intensities, we are including economic and socio-demographic controls that capture this effect. It could also be argued that in municipalities with higher intensity of conflict, the internet providers are less likely to supply the market because the in-vestments in infrastructure are subject to attacks by the illegal armed groups. However, the “dial-up 56k internet access”13, requires a small investment by the supplier in indoors’ infrastructure (namely, in servers), that is not subject to attacks by illegal groups. It could also be argued that the presence of an internet supplier in a municipality depends on the conflict intensity. Nonetheless, the 56k internet is supplied by local telephone providers, which have been present in all the municipalities in Colombia thoughout the decade14.
12As an example, the biggest civil protest of the last decade against guerrilla groups, held on February 4th, 2008, was organized through Facebook. For information about this protest, visitRevista Semana’s website.
7 RESULTS
7
Results
Table 1presents descriptive statistics for variables used in the estimations. Quarterly, there is an average of 0.4 demobilized combatants in each municipality. The maximum number of demobilized combatants is 190. Finally, the quarterly municipal average for civil protests is 0.2, both for total protests, as for protests against guerrillas. Table 1 also presents the statistics of the instruments, and economic and conflict-related controls used in the regressions. Figure 4 shows the demobilization patterns by categories of combatants. Quarterly, there is a higher total demobilization of low-ranked combatants compared to those that have higher rank. Also, there is higher demobilization of combatants that have been inside the group for less than five years, single combatants and men. The results of the estimations presented below show that, indeed, the effect of the civil protests is higher on these groups.
[TABLE 1 AND FIGURE 4 GO ABOUT HERE]
This section describes the main results of the OLS and IV estimations. All results are presented in
Tables 2 and 3. Panel A shows the OLS estimations, while Panel B shows the IV estimations in the first line, and the estimators in terms of standard deviations in the second line. We estimatedequations (3) and (4) including conflict-related variables to eliminate potential sources of endogeneity of our instrument, and without conflict variables, since the inclusion of possibly endogenous variables could bias our estimates. Our coefficients of interest do not change with the inclusion of conflict controls.
[TABLES 2 AND 3 GO ABOUT HERE]
We find a positive impact of civil protests on demobilization. On average, an additional civil protest against conflict causes the demobilization of 11.5 combatants in the quarter following the date of the protest. In terms of standard deviations, an increase in the number of civil protests of one standard deviation causes an increase of 1.3 standard deviations in the number of demobilized combatants. The OLS estimations show that, indeed, there was a negative bias on the estimators, since the IV coefficients are bigger than the OLS coefficients.
To study heterogeneous effects on different types of combatants, we divided the sample into the following categories: a. combatants that were on the illegal group for more and less than 5 years, b. low-ranked and high-ranked, c. single and married, d. men and women. The results are presented in Tables 2 and in Colombia, only two of them, Piamonte in Cauca and Cumaribo in Vichada, lacked local telephone services by 1998. The rest of the municipalities have had access, supplied either by the National Telecomunications Enterprise (TELECOM), or by its associate municipal enterprises. Consulted inhttp://banners.noticiasdot.com/termometro/boletines/docs/ paises/america/colombia/gob_col/1999/gob_col-telefonia-colombia98.pdf, in April, 2013.
8 ROBUSTNESS CHECKS
3. While, on average, and additional civil protests causes the demobilization of 9.6 combatants that have been inside the group for more than 5 years, the impact is not statistically significant for those with less than 5 years. While an additional civil protest causes the demobilization of 9.6 low-ranked combatants, the impact falls to 1.8 for high-ranked combatants. This last result supports the predictions of our model (seeFigure 3), since combatants with more revolutionary ideologies or higher ranks inside the group are less responsive to civil protests when deciding to demobilize. Also, we find heterogeneity by the marital status and gender. The impact of protests is higher for married than for single com-batants (8.8 demobilizations per protest for the former and 6.8 for the latter). This may be because many combatants may have their spouses outside of the illegal group, so they have higher incentives to demobilize. Finally, the impact of protests is almost two times as high for men (7.9), as it is for women (4.3).
The Cragg-Donald F statistic of the first stage is sufficiently high (732) to conclude that our set of instruments explains satisfactorily the endogenous variable. The results of the first stage are shown in
Table 4. The instrument is statistically significant and the coefficient has a positive sign, which is what we expected.
[TABLE 4 GOES ABOUT HERE]
8
Robustness checks
As a falsification test, we randomly permutated theDemobi,tvariable, assigning each value to a different
moment in time and/or municipality. The permutated variable had, thus, exactly the same mean and standard deviation as the original variable. We then estimated the IV model exactly in the same way as we did in the past section. We did this excercise 100 times, to exclude the possibility that the results were a consequence of a particular random assignment. We expect the second stage of the IV estimation to be non statistically significant.
Table 5shows the statistics for the coefficient of the variableP rotestsi,t in the second stage, for the 100
estimations. The first two columns present the statistics for the estimations including economic controls, and the last two columns present the statistics for the estimations with economic and conflict controls. The mean of the p-value of the variable P rotestsi,t is high above 0.1, so the permutated variable does
not explain demobilization, on average. Just on 7 of the 100 estimations, was the p-value under 0.1, and just on 3 was it below 0.05. This test shows that the variation of the civil protests does explain the
8 ROBUSTNESS CHECKS
variation in the dependent variable.
[TABLES 5 AND 6 GO ABOUT HERE]
It could be argued that a possible channel through which civil protests may have increased demobiliza-tion rates is through a reducdemobiliza-tion in overall crime rates. If this were the case, the estimademobiliza-tions presented in the last section would be spurious, since the increase in demobilization rates would have been a consequence of the reduction in crime and not of the civil protests. In this case, our conclusions would be misleading because there would not exist a direct effect of civil protests on demobilization. To test that the civil protests had an impact on demobilization, as we argue, and not on overall crime rates, we estimated the IV model using as dependent variables the number of thefts to commerce, thefts to residence and homicides per 100,000 inhabitants. Table 6shows the results of the estimations. As we expected, the civil protests have had an impact just on demobilization and not in overall crime rates.
To show that the magnitudes of the coefficients obtained are robust to different specifications, we use another set of instruments and repeat the exercises described in the last section: total rainfall and rainfall squared, and the interaction between the number of newpapers “El Tiempo” sold per 100,000 inhabitants in 2004, with the number of times that the following words appeared on the online edition of this newspaper: “homicide” and “deputies”15. We use the number of newspapers sold in 2004, because this is the only year for which “El Tiempo” has trustworthy data16.
The instrument is relevant, since the appearance of certain conflict words on the media may generate nonconformity among civilians, that may lead them to protest against conflict. As the number of newspapers sold per 100,000 inhabitants increases, the probability of a protest being organized and held does so. Our instrument is exogenous, because the fact that we use the number of times that each word appears on the nationwide edition of the newspaper makes it difficult to argue that the instrument is correlated with municipal conflict dynamics. Also, since we are including controls for municipal conflict dynamics, there is no reason to think that the appearance of the word “kidnapping”, for example, may be related to the conflict dynamics through other channel different from the kidnapping itself. The results, presented in Tables 7 and 8, are consistent with the ones presented in the last section. Every civil protest causes, on average, the demobilization of 6-12 combatants.
15
In 2002, twelve members of the Departmental Assembly of Valle del Cauca were kidnapped and eleven of them were killed in 2007.
16
The data on the number of newspapers sold comes from the administrative databases of “El Tiempo”. The number of times each of these words appeared on the online edition of the newspaper comes from the software in https://ngrams. cavorite.com/, designed and implemented by Alejandro Gav´ıria and Juan Manuel Caicedo, from Universidad de los Andes.
9 CONCLUDING REMARKS
[TABLES 7 AND 8 GO ABOUT HERE]
Finally, in order to show the relevance of the “word” used in the instrument, we estimated the model using the number of newspapers interacted with the number of times that the words “beauty pageant” and “chocolate” appeared, as placebos. As expected, the instrument is not statistically significant in the first stage17.
9
Concluding remarks
The existing economic literature on the determinants of demobilization from illegal armed groups is scarce. Most research has been done on the determinants of collective demobilization, and the few studies that deal with individual demobilization are based on survey data with a large selection bias. Moreover, most of the literature has not dealt with the possible endogeneity existing among the deci-sion to demobilize and other conflict variables (Blattman and Miguel,2009). This article estimates the impact of civil protests on demobilization rates, dealing with both problems. First, for our estimations we use a dataset with a smaller selection bias than survey data, since we use the administrative data from the government’s office for demobilization, which gives strong incentives to the combatants to report their demobilization. Therefore, our conclusions are much more accurate regarding individual demobilization, than those of past studies. Second, we solve the potential endogeneity problems using an instrumental variable approach. We use the total number of internet connections, as instrument for civil protests against conflict.
We find evidence that civil protests have had a positive effect on the demobilization rates of illegal armed groups. Indeed, we find that each additional protest causes the demobilization of 11 combatants per 100,000 inhabitants in the municipality where the protest took place, on the quarter following the date of the protest. Our results show that the impact of civil protests is heterogeneous on different types of combatants. There is a stronger effect of protests on lower-ranked individuals, combatants that remained inside the group for more than 5 years, married combatants and men. All of our results are robust to the use of different instruments, which gives us confidence that our estimates are trustworthy.
These findings allow us to conclude that civil opinion towards or against a combatting group turns out to be an important factor during a civil war, since its impact on the probability that the group wins the war is twofold. On the one hand, higher civil protests against one of the combatting groups
17
9 CONCLUDING REMARKS
reduces the collaboration that the society may give to it, which directly reduces its military control and power (Kalyvas, 2001; Tse-tung, 1937). On the other, what our results show is that higher civil protests increase the demobilization rate inside the illegal group, reducing even more its military ca-pacity with respect to the other conflicting groups and, thus, reducing its probability of winning the war.
Two other questions, not studied in the present research but of equal relevance, are crucial to under-stand the role of civil opinion during a civil war. The first one is whether the effect of civil support is symmetric to that of civil protests, meaning that higher civil support in favor of one of the conflicting groups has a positive impact in the number of men that join the group. The second question is whether more civil protests towards one of the conflicting groups is correlated with higher civil support towards the opponent groups during the conflict. According to the theoretical model presented and to Kalyvas
(2001), the answer to the second question should be affirmative, since during conflicts civilians support the strongest group to prevent being punished. The fear of being punished should lead individuals in the civil society to show resistance against the opponent groups. If the answers to both questions were positive, the importance of the civil society in civil wars would be much stronger that the pointed out in this research. Not only would more civil protests towards a group increase its demobilization rates, but also the resulting increase in civil support towards the oponent groups would led more people to join them, reducing even more the probability that the group with civil opposition wins the war.
During the last decade, Colombia has seen a rapid decrease in the probability that guerrilla groups win the war against the government. As our results show, the civil protests of the last decade against illegal groups have played a role in this fact, through its impact on demobilization rates. Moreover, the government has done several publicitary campaigns to increase the civil support towards the State’s military forces. Two examples are the Facebook campaign known as “Mi polic´ıa y yo, con un mismo coraz´on”18 in favor of the police forces, and the media campaign“Los h´eroes en Colombia s´ı existen”19
in favor of the army. It would be interesting to study whether these campaigns led to an increase in the number of men that joined the armed forces during the last decade, and if they increased the number of civil protests against guerrilla groups as a result of the higher civil support towards the government.
The main caveat of this research is that we do not have information on those combatants that decided not to demobilize, nor on the size of the guerrilla groups in each municipality. Then, although we are
18
SeePolic´ıa Nacional de los Colombianos. 19
9 CONCLUDING REMARKS
able to identify the absolute impact of civil protests on demobilization rates, we are not able to study the relative impact. If the number of men in the guerrilla groups had grown faster than demobilization during the last decade, our results would be meaningless, since the relative impact of civil protests would have been negative. However, the size of guerrilla groups fell drastically during the last decade. The last estimate of the Ministry of Defense, made public by the minister on December, 2012, is that FARC had, by that year, less than 8,000 men and ELN less than 1,500. This means that by the end of the decade FARC and ELN had almost half and one third of the number of men they had at the beginning of the decade, respectively. Therefore, even though we are not able to estimate the exact relative impact of civil protests on demobilization, we are confident to assert that this impact has been positive, and increasing, during the last decade.
We have to warn that the information of the number of men in the guerrilla groups in each munici-pality does not exist for the Colombian case. The government has yearly estimates of the overall size of the guerilla groups, but not of their size in each municipality. Although there may be spontaneous information for some guerrilla fronts in some moments in time, due to information given by demobilized combatants, the Ministry of Defense does not have a systematized dataset with this information. Thus, for the Colombian case it is not possible to estimate the relative impact of civil protests on demobiliza-tion taking advantage of the municipal variademobiliza-tion in these variables.
REFERENCES
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Appendix I: proves of propositions
Proof of Proposition 1:
Individuals inside the illegal group know ex-ante the demobilization rate, A, sop is a fixed parameter. Leti0 ∈[0,1] such thatUW+p·Ii0 =Ud−T. SinceVW(Ii) =UW+Up(Ii) is a monotonically increasing
function ofIi,Ii0 must be the only value that satisfiesVW(Ii) =Vd. Furthermore,∀i∈[0, Ii0) it must be
that VW(Ii)< Vd, and ∀i∈(Ii0,1] it must be thatVW(Ii)> Vd. Since we assumed that the indifferent
individual chooses to demobilize, all i∈[0, Ii0] choose to demobilize. Therefore, A=Ii0.
Proof of Proposition 2:
1. For the function VW to be strictly increasing in I, it must be that ∂V∂IW =p+I ·∂p∂I >0. Given
this condition, since there exists an individual i∈[0,1] such thatUW +p(Ii)·Ii=Ud−T, theni
is the only individual that satisfies this equality.
2. This is a consequence of item 1 and Proposition1.
Proof of Proposition 3:
A is such that satisfies:
UW +p(I∗)I∗=Ud−T. (5)
Thus, to prove item 1, it suffices to take the total derivative of (5) with respect toθ:
0 = dp dθI
∗
+pdI ∗
dθ
dp dθ =
∂p ∂I∗
∂I∗ ∂θ +
∂p ∂θ
0 =
∂p ∂I∗
∂I∗ ∂θ +
∂p ∂θ
·I∗+p∂I
∗
∂θ
0 =I∗ ∂p ∂I∗
∂I∗ ∂θ +I
∗∂p
∂θ +p ∂I∗
∂θ = ∂I∗
∂θ
I∗ ∂p ∂I∗ +p
+I∗∂p ∂θ
REFERENCES
∂I∗ ∂θ
I∗ ∂p
∂I∗ +p
| {z }
>0
=−I∗∂p ∂θ
| {z }
<0
Therefore, ∂I∂θ∗ < 0. Items 2-5 are analogous to item 1, so the proves are ommited. Finally, to prove that I∗ is a strictly convex function ofθ, we take the second derivative of (5) with respect toθ:
0 = ∂
2I∗
∂θ2
I∗ ∂p ∂I∗ +p
| {z }
>0 +∂I ∗ ∂θ |{z} <0 ∂I∗ ∂θ |{z} <0 ∂p ∂I∗ |{z} <0
+I∗ ∂
2p
∂I∗∂θ
| {z }
>0 + ∂p ∂θ |{z} >0 +∂I ∗ ∂θ |{z} <0 ∂p ∂θ |{z} >0
+I∗ ∂
2p ∂θ2 |{z} <0 + ∂p ∂θ |{z} >0
+I∗ ∂
2p
∂θ∂I∗
| {z }
>0 ∂I∗ ∂θ |{z} <0
REFERENCES
Appendix II: figures and tables
Figure 1: Number of men and fronts in each guerrilla group: 1978-2000
0 20 40 60 80
Number of guerrilla fronts
0 5,000 10,000 15,000 20,000
Number of men
1980 1985 1990 1995 2000 Year
Men Fronts FARC
0 10 20 30 40
Number of guerrilla fronts
0 1,000 2,000 3,000 4,000 5,000
Number of men
1980 1985 1990 1995 2000 Year
Men Fronts ELN
Source: Ministry of National Defense
Figure 2: Demobilized combatants from guerrilla groups - quarterly from 2000 to 2008
0 200 400 600 800 1000
Demobilized
2000q3 2002q3 2004q3 2006q3 2008q3 Quarter
All FARC ELN
Total demobilizations
0 1,000 2,000 3,000
Demobilized
2002 2003 2004 2005 2006 2007 2008 Demobilizations by reason
Personal motivations Bad conditions in group Government pressure