Scarcity Without Leviathan: the Violent Effects of Cocaine Supply Shortages in the Mexican Drug War∗

Scarcity without Leviathan: The Violent Effects of Cocaine Supply Shortages in the Mexican Drug War∗

Juan Camilo Castillo† Daniel Mejía‡ Pascual Restrepo§

This version: April 2015

Abstract

In this paper we show how scarcity increases violence in markets without third party enforcement. We construct a model in which supply shortages increase contested revenues and induce more violence. We test our model using the cocaine trade in Mexico. Scarcity created by cocaine seizures in Colombia – Mexico’s main supplier – increase violence in Mexico, especially in municipalities near the U.S. border, in municipalities with multiple cartels, and where crackdowns on the cocaine trade are more frequent. Our results indicate that the sharp decline in the cocaine supply from Colombian observed between 2006 and 2009 may account for 10%-14% of the increase in violence in Mexico in this period, and 25% of the differential increase in the North.

Keywords: Rule of Law, War on Drugs, Violence, Illegal Markets, Mexico. JEL Classiﬁcation Numbers: D74, K42.

∗We are grateful to Daron Acemoglu, Michael Clemens, Dora Costa, Leopoldo Fergusson, Bruno Ferman, Claudio Ferraz, Dorothy Kronick, and Otis Reid, as well as seminar participants at Universidad de los Andes, Stanford, UCLA, ITAM and the AL CAPONE and LACEA meetings for their very helpful comments and suggestions. Melissa Dell, Horacio Larreguy, and Viridiana Ríos kindly provided most of the data used in this paper. We gratefully acknowledge funding from the Open Society Foundation and from the Center for Global Development. †Economics Department, Universidad de los Andes, e-mail: [email protected] ‡Corresponding author. Economics Department, Universidad de los Andes, e-mail: [email protected] §Economics Department, MIT, e-mail: [email protected] 1 Introduction

According to Thomas Hobbes, in a world without the rule of law, where the state does not have a monopoly on violence and where no reliable third party can enforce laws and contracts, the life of man becomes “nasty, brutish and short”(Hobbes, 1651). The rule of law and a central authority’s monopoly on violence—the Leviathan—are essential requirements for the absence of conflict and violence. Contemporary writers like Steven Pinker also argue that the rise of the Leviathan was one of the main driving forces behind the decline in violence during the last millennium (see Pinker, 2011). The logic is simple: Outside the rule of law, there is no reliable source of third party enforcement and property rights are poorly defined; wealth and assets can be appropriated by others through the use of force, and violence becomes a rational choice. Not only does the exercise of violence allow people to prey on others, it also protects them from potential predators. Despite the great expansion of the state and its monopoly on violence since Hobbes’ times, several regions, markets, and periods still lie outside the scope of the Leviathan. In these contexts, violent appropriation and private protection are the rule rather than the exception. In many developing countries, local strongmen contest areas with no monopoly on violence by the state (see Acemoglu et al., 2013; Fearon and Laitin, 2003; Sánchez de la Sierra, 2014), and warlords fight over the extraction and control of valuable resources without well defined property rights (see Skaperdas, 2002). Markets for illegal goods are another example, as the state cannot provide a legal framework for third-party enforcement. Illegal drug markets in Colombia, Mexico, and Afghanistan are all ruled by illegal armed groups that resort to violence in order to solve disputes and protect de facto property rights. The scale and salience of violence may vary, but other markets with poorly defined property rights are constantly subject to violence as well, regardless of the type of goods being transacted.1 In this paper, we study the role of scarcity in environments lacking reliable third party enforcement. By third party enforcement we refer to a situation wherein market participants are subject to the state’s monopoly of violence, and property rights and contracts are enforced in an impartial and reliable way. The intensity and salience of violence in these environments varies, making it important to understand its determinants. We study the role of scarcity—supply shortages—as one important factor that exacerbates the use of violence in these environments. Our basic intuition is that scarcity increases violence if the demand for the goods produced and transacted is inelastic: A decrease in supply causes a greater increase in prices, thereby increasing total revenues. This leads to more predation and violence as participants contest the larger rents. Thus, in the absence of reliable third party enforcement, markets with highly desirable goods and commodities in short supply exhibit more vio-

1For instance, The New York Times recently described the use of violence by ﬁshermen in the banned sea cucumber trade in Mexico. Sea cucumbers are extracted from the bottom of the ocean and thus lack well deﬁned property rights. Full story here .

1 lence. We study the role of scarcity in the context of Mexico and the cocaine trade. This market suits our purposes for several reasons. First, cocaine production is illegal, meaning that the state cannot act as a source of reliable third party enforcement and market participants must enforce property rights and contracts on their own. Second, cocaine is a highly desirable commodity with an inelastic demand (see Becker et al., 2006). Third, changes in enforcement in cocaine producer countries – in our case Colombia – create scarcity in transit countries and downstream markets, increasing revenue and violence. The combination of these factors has nurtured extreme violence wherever the cocaine market has ﬂourished. Mexico is the most recent example: As the cocaine trade expanded, there was a dramatic increase in violence. The homicide rate in 2010 was almost three times that of 2005 (see Figure 1). Most of this surge in violence can be attributed to confrontations between different drug trafﬁcking organizations (DTOs) or cartels, and between DTOs and Mexican authorities. In 2007, there were 8,686 homicides in Mexico, out of which 2,760 were estimated to be drug-related; in 2010, there were 25,329 homicides, out of which 15,258 were drug-related. Since 2006, there have been more than 60,000 drug-related killings in Mexico, a greater death toll than that observed in Afghanistan since 2001 (estimated to be between 30,000 to 45,000 since 2001) (see Crawford, 2011). 25 20 15 10 5 Yearly homicides per 100.000 pop. 0 2003m1 2004m7 2006m1 2007m7 2009m1 2010m7 Month

INEGI homicide rate Drug related homicide rate

Figure 1: Homicide rate in Mexico. The total homicide rate reﬂects the data provided by INEGI. The drug-related homicide rate was published by the President’s Ofﬁce. These data are only available beginning in December 2006.

Mexico has been the main point of entry of drugs into the U.S. since at least the turn of this century. Illicit drugs produced in the Andean countries, most importantly cocaine, used to be shipped to North American markets through the Caribbean. However, following intensiﬁed enforcement in the Caribbean by U.S. authorities, Colombian and Mexican drug trafﬁckers began to use the Mexican

2 route more intensively to smuggle drugs. Since then, struggles between DTOs striving to control drug trafficking routes has become a major source of violence in Mexico. Since Mexico does not produce cocaine, the industry behaves like a vertical market. Mexican cartels purchase cocaine from producers in Colombia and, to a lesser extent, in Peru and Bolivia, and then smuggle it across the U.S. border using a variety of imaginative techniques. For instance, the Sinaloa Cartel use underground tunnels and catapults to throw drug packages across the U.S. border, where his men could pick them up on the other side of the border, and (Valdés, 2013). In this paper, we ask whether the surge in drug-related violence in Mexico since 2006 is related to cocaine supply shortages caused by larger and more frequent cocaine seizures in Colombia.2 Cocaine seizures in Colombia curb supply in downstream markets and increase revenue due to an inelastic demand. This triggers a violent competition between cartels to control the additional rents. In 2006, the Colombian government redefined its anti-drug strategy, emphasizing the interdiction of drug ship- ments and the detection and destruction of cocaine processing labs over the eradication of coca crops. This caused a large increase in cocaine seizures that went from 127 metric tons (mt) in 2006 to 203 mt in 2009. As a result, the supply of Colombian cocaine fell from 522 to 200 metric tons in this period (see Figure 2), and varied significantly from month to month depending on the success of interdiction operations.3 This large negative supply shock (the Colombian cocaine drought) was noticeable throughout the region, and even in cocaine street prices in U.S. retail markets. More precisely, the price per pure gram of cocaine went up from about $135 in 2006 to about $185 in 2009 for purchases of two grams or less, and from $40 to $68 for wholesale purchases between 10 and 50 grams. We test the hypothesis that the scarcity created by larger and more frequent interdiction events in Colombia exacerbated violence in Mexico since 2006, during the so-called Mexican Drug War. To guide our empirical analysis we present a model of illegal drug markets, but with general insights for other markets without third party enforcement. In our model, exogenous supply reductions in upstream markets increase revenue, assuming demand is inelastic. As a consequence, drug cartels invest more in the fight over the control for the higher rents, increasing the level of violence. Violence may take several facets: Cartels may fight for turf when its control command higher rents, they may expropriate other cartels’ assets and cash, or they may extort other cartels receiving higher revenue. Our model also shows that the effect of cocaine shortages on violence is greater in places with at least two cartels; in places where more frequent arrests and crackdowns against cartel leaders increase turnover, and hence informal cooperation arrangements cannot sustain less violence; and in places

2Although Mexico also produces drugs such as cannabis, heroin and ATS (Amphetamine-type stimulants), a large share of the profits (between 50% and 60%) obtained by Mexican DTOs is generated via drug-trafficking activities, especially those related to cocaine, and not via drug production (see Kilmer et al., 2010). 3The change followed intense criticism of the Colombian government’s focus on early stages of the cocaine production chain, such as eradication of coca crops, which account for a low share of the value added. The new focus on later stages greatly increased the efficiency of interdiction efforts (see Mejía and Restrepo, 2013b).

3 where drug trafficking is more intense (e.g., in northern of Mexico). We test these predictions using monthly data for Mexico, from December 2006 to December 2010. We exploit the fact that cocaine is produced in the Andes—mostly in Colombia—and, as a consequence, cocaine seizures in Colombia provide an external source of scarcity in the Mexican markets. These seizures only affect the Mexican cocaine market through scarcity, unlike seizures in Mexico, which affect cartels through many other channels. Figure 2 shows that the rise of violence in Mexico since 2006 coincides with the sharp decline of cocaine supply in 2006. However, it would be naive to interpret this as evidence of a causal effect of scarcity on violence, as this long-term correlation could simply reflect a change in policies in both countries after 2006 (Calderón’s war on drugs in Mexico, and the emphasis on interdiction policies in Colombia). In order to overcome this difficulty, we exploit monthly variation in cocaine seizures in Colombia as a source of shocks to scarcity in Mexican cocaine markets. The key identifying assumptions are, first, that the potential coincidence in timing between policies in Mexico and Colombia breaks down at higher frequencies once we flexibly control for long-term time trends; and second, that other determinants of violence in Mexico are not correlated with interdiction efforts in Colombia at high frequencies. Our interpretation also hinges on the assumption that seizures in Colombia only affect Mexican drug markets by creating scarcity. We will argue that all these assumptions hold (see section 4.6). 25 500 20 400 15 Metric tons 300 10 Yearly homicides per 100.000 pop. 5 200 2002 2004 2006 2008 2010 Month

Net cocaine production INEGI homicide rate

Figure 2: Net cocaine production in Colombia (in metric tons, left axis) and overall homicide rate in Mexico since 2000 (per 100.000 inhabitants, right axis). Net production is defined as potential production minus seizures and computed from UNODC cultivation and productivity figures, and official seizures statistics.

We ﬁnd that violence increases in Mexico during months with supply shortages caused by temporal increases in cocaine seizures in Colombia. We also ﬁnd that violence increases especially in places near the U.S. border. Violence increases more in municipalities with cartel presence, but only in those with two or more cartels or with two or more non-allied cartels operating at the time of the supply shock. Finally, the effects are larger in municipalities that have historically supported PAN, President Felipe Calderón’s party (whose term lasted from December 2006 until November 2012).

4 Because these municipalities were more likely to support federal government efforts against cartels in their area (see Dell, 2012), the turnover of cartel leaders was more frequent, precluding informal cooperation arrangements and amplifying the effect of scarcity on violence. The fact that the effect of cocaine seizures in Colombia on violence in Mexico is mediated by these variables suggest that the effect occurs through scarcity and the fight among cartels contesting the higher rents it creates. Our evidence shows that Colombian cocaine supply shocks created scarcity and contributed to the increase in violence in Mexico. Our preferred estimates suggest that a 1% increase in monthly cocaine seizures in Colombia increases the homicide rate in all of Mexico by about 0.059%-0.091%; by about 0.082%-0.106% in municipalities in the first and second quintiles of distance from the U.S. border; and by about 0.119%-0.161% in municipalities in the first quintile of distance from the U.S. border. Under additional assumptions mentioned in the text, our estimates imply that the sharp decline in the net cocaine supply from Colombia between 2006 and 2009 (from 520 mt to 200 mt per year) accounts for about 10%-14% of the increase in the homicide rate in Mexico during the same period and for 25% of the differential increase in violence observed in the north of the country relative to the mean. Beyond our interest in the Mexican case in and of itself, documenting the role of scarcity in markets lacking reliable third party enforcement is important for two main reasons. First, it sheds light on the nature of the associated violence. The fact that cartels respond to economic incentives in the manner predicted by economic theory means that violence is a rational choice made by agents moti- vated by profit or greed. Once the nature of violence is recognized, better policies can be designed. Furthermore, since scarcity increases violence by raising revenues, policies that reduce revenue and limit the incentives to prey are the best alternative to actually enforcing property rights adequately. A second reason is that many well intended policies that increase scarcity in markets with poorly defined property rights may end up increasing violence. For instance, limits on formal mineral extraction—of gold or diamonds, for example—create scarcity and increase prices. Supply reduction policies implemented under the war on drugs also create scarcity. Likewise, commercial restrictions to trade in certain resource-abundant countries with poor institutions could increase rents and violence. The rest of the paper is organized as follows. Section 2 outlines the related literature and frames our contribution. Section 3 presents a simple model for understanding the effects of scarcity on violence, and proposes some testable predictions. Section 4 describes our data and empirical results. Finally, section 5 concludes.

2 Related literature and contribution

Our paper is related to at least three branches of literature. The ﬁst one is the broad literature on property rights and violence. The fact that interpersonal violence emerges when the state lacks the monopoly on violence is a classic theme in the social sciences, at least since Hobbes (1651), and

5 has been treated more recently by Elias (2000) and Pinker (2011). The possibility of using force or the threat of force to appropriate resources, as opposed to via ordinary market transactions, has been addressed in the economic literature since Grossman (1991) and Hirshleifer (1991, 1994, 2001). More specifically, our paper is related to the literature concerned with the effect of resources and rents on violence, in contexts with weak institutions and property rights. Increases in rents, or revenue from resources, have two effects. On the one hand, conflict over the control of valuable resources may increase violence through rapacity—the temptation to prey on others and the necessity to defend against potential predators (see Gambetta, 1996; Skaperdas, 2002; Collier and Hoeffler, 2004; Grossman, 1999); on the other hand, resource booms may also increase wages, and hence the opportunity cost for people of engaging in violent activities (see Becker, 1968; Grossman, 1991). Consistent with theory, the empirical findings are mixed. For instance, Collier and Hoeffler (2004) find that exports of commodities have a strong positive effect on the risk of conflict. Fearon (2005) shows that this result is driven by oil. On the other hand, Miguel et al. (1994) show that higher national income, instrumented by rainfall, reduces the likelihood of conflict in Africa, probably because of an increased opportunity cost. Brückner and Ciccone (2010) reach a similar conclusion using variation in commodity prices. Dube and Vargas (2013) find that coffee booms—which are likely to increase wages—reduce violence in Colombia, while oil booms– which are not likely to increase wages– increase violence. Buonanno et al. (2012) find that mafia-type organizations were more likely to appear in Sicilian municipalities with sulfur extraction, a valuable commodity with poorly defined property rights. In a similar vein, Couttenier et al. (2013) show that, during the U.S. gold rush, interpersonal violence increased in the vicinity of mineral discoveries, but only when there was no strong state presence. The apparent consensus is that rents associated with resources tend to increase violence when property rights are poorly defined, but tend to decrease it when they cause an increase in wages. We contribute to this literature by showing that in illegal drug markets, a strong rapacity channel operates and is amplified by scarcity. In drug markets, rapacity appears to dominate the opportunity cost channel, presumably because illegality precludes formal property rights over resources and the labor share in the cocaine trade is small (see Dal Bó and Dal Bó, 2011).4 Second, our paper is related to the literature on violence in illegal markets. Goldstein (1985) la- beled violence among suppliers in illegal markets—as the one documented in this paper—as systemic violence. Several papers have studied the correlation between violence and the supply side of drug markets, with some mixed findings. Angrist and Kugler (2008) and Mejía and Restrepo (2013a) find that the rise of the cocaine trade in Colombia and increases in external demand have spurred violence in Colombia. On the other hand, Lind et al. (2013) argue that the causation goes from violence to

4Levitt and Venkatesh (2000) offer evidence suggesting a small labor share in the drug dealing business. They ﬁnd that the wages of gang members are barely above the minimum wage.

6 opium cultivation in Afghanistan. Some other works focus on other illegal goods. García-Jimeno (2012) shows that alcohol prohibition, especially the intensity of enforcement, caused an increase in crime in U.S. cities during this period. Owens (2011) shows that the Temperance movement increased violence among young people. The relation between illegal markets and violence is not limited to vice goods. Chimeli and Soares (2010) explore how illegality generates violence in a completely different market: The exploitation of mahogany in the Brazilian Amazon. Our paper contributes to this branch of literature by identifying systemic violence and documenting the role of scarcity as one of its determinants in the context of the Mexican drug war. We show that the level of violence in Mexico is largely driven by profit incentives and rapacity over the large revenue associated with this trade. Our paper adds to the increasing body of evidence by suggesting that participants in illegal drug markets rely on violence because of the absence of reliable third party enforcement. We also show that supply reduction policies have collateral effects in the form of more violence if they significantly increase total revenue. The systemic violence that emerges with scarcity due to supply reduction policies is, in our opinion, the largest cost of the war on drugs. Third, our paper is related to an ongoing debate regarding the causes of the large upsurge in violence observed in Mexico since 2006.5 Many observers blame President Calderón’s strategy of targeting cartel leaders for the surge in homicides since 2007, since it creates voids of power that incite fights between former lieutenants and splits cartels into smaller factions that fight over control of the business ran by the former organization (Guerrero, 2010, 2011a; Merino, 2011). Other studies (Poiré and Martínez, 2011; Villalobos, 2012) support Calderón’s strategy by arguing that it will decrease violence in the long term. More recent papers have taken endogeneity issues seriously when determining whether Calderón’s policies are the cause behind the wave of violence. Dell (2012) uses a regression discontinuity design, comparing municipalities where PAN, Calderón’s party, won local elections by a small margin with those municipalities where PAN lost by a small margin. She argues that it was easier for the Federal Government to intervene in municipalities with a PAN mayor, thus intensifying Calderón’s war on drugs. She finds that these interventions caused significant increases in violence after the election and generated spillovers in neighboring municipalities. Calderón et al. (2012) combine a difference in differences methodology with synthetic control groups and show that, while Calderón’s interven- tion increased violence, it was only a temporal effect. Two recent papers shift the focus away from Calderón’s policies. Dube et al. (2013) show that negative agricultural shocks facilitated the rise of the Mexican drug sector, and increased violence as a consequence. Finally, Dube et al. (2012) find that the level of violence in Mexico increased as a consequence of the 2004 expiration of the U.S. Federal Assault Weapons Ban, which generated a positive shock on gun availability in northern Mexico.

5Grillo (2011) and Valdés (2013) provide thorough reviews of the history of drug trafﬁcking in Mexico and its nexus with crime and violence.

7 Our paper contributes to the debate by showing that Colombian anti-drug policies have also played a role in increasing violence in Mexico. Cocaine seizures in Colombia have increased dramatically since 2006, creating large and frequent shortages in Mexican wholesale cocaine markets. This translates into more frequent and larger surges of violence in Mexico since 2006. We do not see this as an alternative explanation for the increase in violence in Mexico, but rather a complementary one. As we show in the empirical section, the effect of cocaine shortages is ampliﬁed in municipalities that have historically voted for PAN, and which, following the logic outlined in Dell (2012), tend to ﬁght cartels more aggressively. Calderón’s policies interacted with cocaine shortages to create the conditions for rapacity to spur violence, as opposed to providing an environment conducive to tacit and peaceful agreements among cartels.

3 A model of scarcity and violence

In this section we present the model that guides and motivates our empirical analysis. We start with a static model and then introduce a dynamic extension. We denote a municipality with subscript i, with i ∈ {1,2,...,I}. Let si be its relative importance in cocaine trafﬁcking, measured as the share of total revenue from the cocaine trade that is disputed in municipality i. Intuitively, municipalities close to

U.S. entry points have a large si since most of the trafficking activities take place there, and control of these locations translates into a greater share of total cocaine trade revenue. Let Qs be the supply of Colombian cocaine.6 We assume that there is an iceberg cost, 1 − h, of trafficking, so that the final supply of cocaine reaching the U.S. is hQs. This iceberg cost is shaped, among other things, by interdiction policies in Mexico. Drugs are sold at a final price, Pd(hQs), with Pd being the inverse demand function, which is assumed to be inelastic. We assume that a fraction η of the revenue is protected; while the remaining 1 − η is at risk of expropriation by other cartels. Thus, η is a measure of the exogenous extent of third party enforcement. The illegal nature of drug markets implies a low value of η. The total drug trade revenue in municipality i that is vulnerable to appropriation by others is thus s (1 − η)sihPQ .

There are N cartels, indexed by c ∈ {1,2,...,N}. Let Ni be the set of cartels operating in municipality i. The location of cartels is exogenous, which we think is a good assumption when looking at high frequency variation. Let Ic be the set of municipalities in which a cartel operates. Finally, we assume that cartels are price takers.7 Even if there is some level of collusion, all we require is that

6We simplify the analysis and assume that Colombia is the only supplier of cocaine to Mexican cartels. This assumption does not change our results so long as Peru and Bolivia (the other two cocaine producing countries) do not have a perfectly elastic supply. 7The term cartel is therefore misleading. The powerful Colombian DTOs of the 1980s and 1990s called themselves carteles to emphasize that a few organizations controlled the whole trade, even though they did not collude to increase

8 the degree of competition be high enough that residual demands are elastic while market demand is inelastic. In order to appropriate or defend revenue, cartels engage in a conflict against one another in the municipalities where they operate. Each cartel invests gc,i in weapons, personnel, recruitment and training in municipality i. By doing so, cartel c is able to obtain a fraction qc,i of the total revenue being contested in municipality i, where qc,i is determined endogenously according to the following contest success function:8 gc,i qc,i = , ∑ ′ c ∈Ni gc,i ∑ and the aggregate level of drug-related violence in municipality i is given by vi = c∈Ni gc,i. The conflict function, qc,i, is a reduced form representation of all strategies available to cartels for appropriating drug rents. For instance, they can act as toll collectors and extort payments from other cartels operating in municipality i. They could also fight for turf in order to use routes and labor for their trafficking activities, prey on one another by violently stealing cash, weapons, assets or other resources, or seek to eliminate competition in key municipalities to increase their market share. The timing of events is as follows:

1. Nature draws Qs randomly from some distribution, F, with support [0,∞). In our empirical application, the random nature of Qs is due month-to-month ﬂuctuations in cocaine seizures.

s s s 2. Participants observe Q . Each cartel buys Qc units of cocaine at price P , trafﬁcs it, and sells it at d s s price P = P (hQ ). The variable convex cost C(Qc) of running the cartel operations satisﬁes the s s usual Inada conditions. At this point, the cartel has already paid P Qc to Colombian producers s and C(Qc) in operating costs.

3. Cartels choose their conﬂict strategies, gc,i, to defend their revenue and expropriate others’ in all municipalities where they operate.

4. Payoffs are realized. More speciﬁcally, cartel c obtains proﬁts

s s s η s η s −P Qc −C(Qc)+ hPQc + ∑ qc,i(1 − )sihP∑Qc′ − gc,i i∈Ic c′ !

Given the random and exogenous supply of drugs from Colombia, Qs, the equilibrium achieved consists of market clearing prices and quantities in the U.S., P(Qs) and Q(Qs), a market clearing price prices. The name stuck, and present-day Mexican organizations use the same term (see Gonzalbo, 2012). 8The contest success function is standard in the conﬂict literature, and its precise form is not essential for our results (see Skaperdas (2002) for more on contest success functions). All we need for our results is that the function be concave in gc,i, satisfy the Inada conditions, and exhibit either increasing differences in the vector of gc,i, or small cross-derivatives if they are negative. This implies that larger stakes increase violence, which is what one would intuitively expect.

9 s s s for the cocaine supplied by Colombia P (Q ), and conflict strategies gc,i(Q ). We now characterize the equilibrium and some important properties. s The objective of cartels is to choose the amount of Colombian cocaine they intend to traffic, Qc, s and their conflict strategies gc,i in order to maximize profits. Since supply in the U.S. is hQ , the final price of cocaine is given by P(Qs)= Pd(hQs). Let R(Qs) be the total cocaine trade revenue generated by Mexican cartels, which is equal to hQsPd(hQs). It increases when Qs falls, since demand is inelastic.9 In equilibrium, the revenue s s disputed in municipality i only depends on Q , and is given by (1 − η)siR(Q ), which is fully determined by Qs. Thus, when choosing conflict strategies, a cartel faces an independent problem in each municipality where it operates. Cartel c’s maximization problem in municipality i is:

s maxqc,i(1 − η)siR(Q ) − gc,i. gc,i

s Choices over Qc do not have to be taken into account when determining conﬂict efforts, since market clearing conditions imply a unique level of equilibrium revenues, and payments to Colombian cartels are bygones (i.e., they are not contested).10 We show in detail the full solution to the model in the appendix. The unique Nash equilibrium among cartels operating in municipality i is symmetric and the resulting level of violence is

s |Ni|− 1 s vi(Q )= (1 − η)siR(Q ). (1) |Ni| This expression leads to our main proposition.

Proposition 1. Suppose that demand is inelastic, such that revenue R(Qs) is decreasing in Qs. A decrease in the Colombian supply of cocaine, Qs, increases revenue and leads to more violence (on average) across Mexico. The increase in violence is larger under the following conditions:

• When third party enforcement is absent or weak (η is small).

• In municipalities that are more important for cocaine trafﬁcking (si is larger).

• When there are more cartels, |Ni|. In particular, violence only increases if there are at least two rival cartels operating in the same municipality.

Proof. The proof follows by differentiating equation 1 to obtain comparative statics on the level of violence. The key observation is that expenditures on conﬂict increase with total revenue in a municipality—and total revenue increases when supply falls—because demand is inelastic.

∂ 9Mathematically, logR = 1 − 1 , which is positive if and only if |εd| > 1, i.e., whenever demand is inelastic. ∂ logQs |εd | 10The convex cost guarantees that it is possible to have more than one cartel demanding cocaine from Colombia. Other s cartels will choose Qc = 0 and become toll collectors.

10 This proposition provides some assertions that we test in our empirical application. The first part suggests that months with low supply of cocaine from Colombia due to more seizures should be months with higher levels of violence in Mexico. There should also be a differential effect on the north of Mexico, where si is larger. Finally, the model suggests that it “takes two to tango” –that is, violence should increase as a consequence of scarcity only where there are at least two cartels operating. Two key assumptions drive our results. First, cartels fight over the share of revenue vulnerable to appropriation. They fight over revenue and not profits because payments to Colombian cartels are treated as bygones. Thus, cartels are the full residual claimants of the rents they appropriate and protect from others. The assumption behind this feature is that there is no perfect risk sharing between Mexican cartels and suppliers in Colombia. We believe that the absence of third party enforcement precludes the possibility of these vertical relationships.11 Second, demand is inelastic so revenue increases as supply tightens. This is widely believed to be the case for drugs, especially for cocaine. Becker et al. (2006) summarize the evidence of an elasticity of less than 1 for most drugs, with a central tendency towards 1/2, especially over the short run.12 We now move on to a dynamic setup. In our empirical application we focus on high frequency shocks, so we construct a dynamic version of the model to illustrate the effect of temporal shocks. A dynamic setup allows us to focus on Subgame Perfect Equilibria (SPE), which capture the possibility of some degree of cooperation. This is relevant since, in a world without third party enforcement, participants rely not only on violence, but also on informal arrangements sustained under the threat of retaliation. It also allows us to model a key dimension of Calderón’s strategy. This is, the emphasis on beheading cartels by arresting or killing their leaders. This policy affects the discount rate of cartel leaders, reduces the extent of informal cooperation and interacts with supply shocks producing even more violence. Our dynamic model is based on Rothemberg and Saloner (1986), Abreu et al. (1990), and Castillo s (2013). The game described above is played out repeatedly, with an independent draw of Qt in each period. At the end of each period, nature reveals which cartel leaders were arrested. A cartel leader in municipality i is arrested with probability ai, and is then replaced by a new one. We assume that decisions made by leaders maximize cartel profits at their own discount rate (1 − ai)β, and not at

11If cartels and suppliers were able to establish complex contracts, cartel payments to suppliers would depend on the conflict success, and cartels could end up fighting over profits rather than revenue. Even if this is the case, violence would increase as shown in alternative models (see Mejía and Restrepo, 2013b; Castillo, 2013). 12The relevant value in our model is the short-run elasticity of demand, which is considerably smaller than that over the long run (see Becker and Murphy (1988)). Early papers found inelastic demands mainly for marijuana and heroin (Nisbet and Vakil, 1972; Roumasset and Hadreas, 1977; Silverman and Spruill, 1977). Wasserman et al. (1991) and Becker et al. (1994) find demand elasticities between -0.4 and -0.75 for cigarette consumption over the short run. Concerning cocaine, results in more recent studies are consistent with an inelastic demand as well. See, for instance, Bachman et al. (1990), DiNardo (1993) and Saffer and Chaloupka (1999).

11 what would be the “market” discount rate β if the incentives of leaders and cartel “shareholders” were aligned. Arrests thus make cartel leaders behave more impatiently than they would otherwise.13 We focus on equilibria in which quantities are chosen as in the static model, and cartels play an independent game when choosing conﬂict efforts in each municipality. Just as in the static problem, s s s the amount paid for drugs, Pt Qc,t, the cost of running the cartel operation, C(Qc,t), and the revenues η s not subject to appropriation, hPtQc,t, are bygones, and revenue is only determined by the realizations s of Qt . Thus, in each period, cartel c operating in municipality i chooses gc,i,t in order to maximize expected payoffs β t−t0 t−t0 η s Et0 ∑ (1 − ai) qc,i,t(1 − )siR(Qt ) − gc,i,t. (2) t≥t0 Let gN(Qs) be the symmetric static Nash equilibrium when supply is Qs, which coincides with the solution to the static model. We focus on a recursive equilibrium, with all cartels spending C s N s N s g (ai,Q ) ∈ [0,g (Q )), and reverting to g (Q ) as punishment if anyone deviates. This is not the most cooperative SPE, but it is the simplest one and it helps us illustrate our point. The equilibrium is characterized in the following proposition:

Proposition 2. Suppose demand is inelastic, such that R(Qs) is decreasing for Qs. The equilibrium that sustains the most cooperation through reversion to the static Nash MPE is recursive and involves C s N s C gc,i = g (ai,Q ) ∈ [0,g (Q )). The function g satisﬁes the following properties:

s N s • If revenue is unbounded from below, then, for Q ≥ Q(ai), g (ai,Q )= 0. Thus, for any arrest

probability, there is no violence if revenue is sufﬁciently low. Moreover, Q(ai) is increasing for

ai.

N s s • If revenue is unbounded from above, then g (ai,Q ) > 0 for Q if it is sufﬁciently small, even s if β(1 − ai) → 1. If revenue is bounded as Q → 0, then a fully cooperative equilibrium where N s s g (ai,Q )= 0 ∀Q can be sustained if β(1 − ai) > β, for some β.

N s • g is increasing in ai, decreasing in Q and the cross partial derivative is negative. Thus, supply shortages have a greater impact on violence in municipalities with a higher arrest rate, especially in those that are important for drug trafﬁcking.

Proof. The proof follows Rothemberg and Saloner (1986), and is presented in Appendix B.

The key idea is that in the absence of third party enforcement there is room for some de facto protection of property rights, sustained by the threat of future retaliation. When ai is low and β high,

13The assumption behind this feature is that, once a cartel leader is arrested or killed, the next leader cannot credibly compensate him for long-term investments. This stems from the lack of enforceable contracts in environments without reliable third party enforcement.

12 an equilibrium with no violence can be sustained (a variant of the Folk theorem). As the effective discount rate decreases, participants value the future less and some level of violence must be allowed in the SPE, especially with high revenues. Short term shocks are especially likely to bring violent upsurges and have two effects. On the one hand, they increase current revenues, and hence the incentives to prey. Additionally, expected revenue in the future is lower due to less seizures. As a consequence, future retaliation is less severe and more violence takes place in the present.14 A higher arrest rate makes retaliation less severe, which interacts with the second effect of a temporal increase in seizures C s and explains why the function g (ai,Q ) has a negative cross partial derivative. As shown by Dell (2013), Calderón’s actions against cartels required the cooperation of local mayors, and were more recurrent in municipalities with PAN mayors. This suggests that arrest rates and turnover of leaders are higher in municipalities that, due to large popular support for the PAN, are more likely to elect PAN mayors or favor Calderón policies. Thus, another testable implication of this proposition is that supply shocks have a greater effect in these municipalities.

4 Empirical evidence and data

4.1 Data

Throughout, we focus on the period from December 2006 to December 2010, for several reasons. First, this coincides with the period of violence and intense cartel activity in Mexico known as the Mexican Drug War. Second, Colombia shifted its drug policy from eradication to interdiction at the end of 2006, after which operations resulting in large seizures became more frequent. This means that there is an exogenous source of supply shocks during this period that allows us to identify the effect of scarcity on violence. Third, it coincides with Calderón’s term, allowing us to study the interaction between his policies—especially his policy of beheading drug cartels—and scarcity created by seizures in Colombia. We use a monthly panel of 2,438 Mexican municipalities from December 2006 to December 2010. Our dependent variables are different measures of the monthly homicide rates in each municipality. Our main source is the monthly homicide rate produced by INEGI (Mexico’s Instituto Nacional de Es- tadistica y Geograﬁa). This data is available for our whole period of analysis and includes all reported homicides. We also use data on drug-related homicides published by the Mexican Presidency.15 This

14We have ignored the possibility of storage in our model for simplicity. The same logic still applies, but a good storage technology dampens the effect of a supply shortage because cartels hedge against it by accumulating drugs. However, cocaine storage does not remove the inﬂuence of large and unanticipated supply shocks (as the ones we study in the empirical section). Storage creates forces for long term shocks having more severe effects than short term ones, just as in permanent income models. 15Unfortunately, the new Mexican government under Enrique Pena Nieto, who took ofﬁce in December 2012, stopped publishing the data on drug-related homicides, which were previously available online.

13 dataset only counts homicides related to the illegal drug trade. Given the ongoing debate regarding the reliability of this classification, we only use this data as a secondary source in some of our estimations.16 We explore the effect of scarcity on violence and how it is mediated by the relative importance of trafficking, the number of cartels and the political power of the PAN party. We use the proximity to the nearest U.S. entry point as our proxy for trafficking importance. This is computed as the negative distance from the centroid of each municipality to the closest U.S. entry point. To explore heterogeneity in terms of the number of cartels, we construct yearly dummies for the presence of cartels in each municipality, for the presence of non-allied cartels (we use the alliances described by Guerrero (2011b)), and for the presence of at least two cartels (independently of alliances). We obtain the raw cartel data from Coscia and Ríos (2012), who built a yearly panel of cartel presence based on web content and covering the main cartels during our period of analysis.17 Finally, in order to explore heterogeneity with respect to PAN political power, we use the average voting share for PAN candidates in municipal elections from 1980 to 2000, a period preceding the Mexican drug war. Table 1 summarizes our main data. The table presents statistics separately for all of Mexico (average distance from the U.S. is 763km), for municipalities in the two first distance quintiles to U.S. entry points (where average distance is 507km), and for municipalities in the first quintile of distance from U.S. entry points (where average distance is 333km). The Mexican population is concentrated in the north: The first quintile of distance includes 25% of the national population, while quintiles 1 and 2 include 60%. Many of our results focus on these two quintiles. As the table shows, the north of Mexico (quintiles 1 and 2) is more violent than other parts of the country as measured by the INEGI homicide rate and by drug-related homicides. While violence was homogeneous across the Mexican territory in 2006, it increased disproportionally in the north in the following years. A similar pattern emerges for drug-related crimes. Consistent with the intuition that northern Mexico is more important for cocaine trafficking, the data shows that the vast majority of homicides in the north are drug related, whereas homicides in other areas of the country are less so. There is also more cartel activity in quintiles 1 and 2 than in the country as a whole. In 2010 cartels were active in 40% of the municipalities in the first two distance quintiles, and in 29% of all Mexican municipalities. Furthermore, most homicides in our data took place in these two quintiles: 55% of all homicides in 2006, and 75% of all homicides in 2010. Finally, northern municipalities are slightly more supportive of the PAN party historically, but these differences are not significant. On average, PAN’s vote share from 1980 to 2010 was 0.22 (s.d=0.62).

16For some articles about the data, see Lizárraga (2012) and Proceso (2012). The data have been criticized on the grounds that the criteria for classifying homicides as drug related, or as aggressions, confrontations, and executions is subjective and inconsistent between different times and places. 17Cartel de los Hermanos Beltrán Leyva, Familia Michoacana, Cartel del Golfo, Cartel de Juárez, Cartel de Sinaloa, Cartel de Tijuana and Los Zetas

14 iern ttemnhyfeunyfo eebr20 ( 2006 December from frequency monthly the at runs Time akt rae ycciesiue yClminauthoritie Colombian by seizures cocaine by created markets eueti lentv esr sa nes rx fscarci of proxy inverse an A as measure trend. alternative time this flexible i use a exercise we with this production in in exploiting changes up frequency end However, we Mexico. variation reaching The drugs of figures. supply the of measure a as eismodel series re ots u oe,w s ezrsi oobaa nexoge an as Colombia in seizures use highe we to model, our due test scarce to becomes order cocaine when predictio Mexico main in the of increases favor in evidence providing by start We evidence series Time 4.2 Mex in Th violence on Colombia polynomial. in time seizures of cubic effect a the identify and dummies th year exploit out only 20 partialling We and variation. 2008 monthly in considerable seri seizures is in monthly there increase the strong presents a 3 is There Figure th average. study. at reported our is of data period This whole Defense. of Ministry Colombian the oiiert nMxc sdntdby denoted is Mexico in rate homicide iue3 otl oan ezrsi oobafrte2000- the for Colombia in seizures cocaine Monthly 3: Figure 18 u aito nsact oe rmhg rqec changes frequency high from comes scarcity in variation Our esuytetm eisefc fspl hcso ilneb violence on shocks supply of effect series time the study We eas osrc otl upyfiue e fsiue o C for seizures of net figures supply monthly construct also We

Metric tons

2003m1 0 10 20 30 40 2004m7 ln h t h = t n oan ezrsi oobaby Colombia in seizures cocaine and , β 0 2006m1 + β 1 15 ln ty. eysmlr ic nalo u ersin ermv low remove we regressions our of all in since similar, very s Month S lterslsrpre eehl fisedo sn seizure using of instead if hold here reported results the ll hsmtoooyrqie nepltn nulproductio annual interpolating requires methodology this t 2007m7 00pro.Tedse iepeet eryaverages. yearly presents line dashed The period. 2010 + lmi ntsoni h als,aduete directly them use and tables), the in shown (not olombia F t ( γ ihfeunyvrainotie after obtained variation frequency high e t + ) npooiin1 aeyta violence that namely 1, proposition in n s. = c speetdi iue4. Figure in presented is ico 9 u otipratfrorresults, our for important most but 09, 2009m1 18 sfrsiue,a ela t yearly its as well as seizures, for es ε vn ee n saalbefrthe for available is and level event e )t eebr 00( 2010 December, to 0) ossoko supply, of shock nous ntespl fcciei upstream in cocaine of supply the in t oan ezrsi ooba In Colombia. in seizures cocaine r ihfeunyvrainue to used variation frequency high e . oan ezrsdt oe from comes data seizures Cocaine siaigtefloigtime following the estimating y 2010m7 S t h term The . Q t s = . 8.The 48). F t ( γ = ) (3) n s nnrhr Mexico). northern correlat in raw (the series both between correlation positive ataldot fe hc osdrbemnht ot var month to month Colombi considerable in which after seizures out, and partialled rates homicide in abso variation completely is residual variation frequency low up since of Mexico, effect in the identify to Colombia in seizures in variation rsnigorresults. pote our discuss We presenting Mexico. in violence on Colombia in reductions h term The ∑ Mexi in rate homicide INEGI the s of cocaine deviations of monthly deviations monthly log log and shows ﬁgure The 4: Figure nucsfli eetn n nedcigaccieshipm cocaine a mili interdicting a and whether detecting (i.e., in markets luck unsuccessful drug by in mostly changes determined secular is other variation to othe or to Mexico, exogenous in arguably olence is seizures in at variation down breaks monthly correlation spurious this to that Calderón is president assumption since Mexico upwa in the crackdowns to related in not increase is measure secul we or effect the relations instance, frequency For low First, reasons. of number a ic ezrsi oobardc supply, reduce Colombia in seizures since n 3 = ipeOSrgesosaeeog ooti ossetest consistent a obtain to enough are regressions OLS Simple h nlso fteterm the of inclusion The 0 γ n t n + ε t η sa ro emta salwdt ehtrseatc u mo Our heteroskedastic. be to allowed is that term error an is y nldsbt ui oyoiladya ume ocontrol to dummies year and polynomial cubic a both includes

Log of monthly rate (deviations from trend) −40 −20 0 20 40 2007m1 F t ( γ Variation exploitedforallMexico = ) 2008m1 ∑ n 3 = 0 Q γ s n n raescarcity. create and , t Months 2009m1 n 16 + δ iue nClmi rmisted(ih xs otdline) dotted axis, (right trend its from Colombia in eizures ofo t rn lf xs oi line). solid axis, (left trend its from co y mle htw nyepothg frequency high exploit only we that implies o agsfo . nalo eiot 0.35 to Mexico of all in 0.2 from ranges ion temcciespl hcso violence on shocks supply cocaine stream 2010m1 ihrfeunis eod h resulting the Second, frequencies. higher n) rb atr xgnu oMexico to exogenous factors by or ent), rted ontcnon u estimates. our confound not do trends ar ainremains. iation ayo oieoeaini ucsflor successful is operation police or tary bdb hstr.Fgr rsnsthe presents 4 Figure term. this by rbed dtedi ezrsi oobaadthe and Colombia in seizures in trend rd hnmn fetn h eeso vi- of levels the affecting phenomena r netelwfeunyvrainis variation frequency low the once a kofiea h n f20.Tekey The 2006. of end the at office ok ta het oti nepeainafter interpretation this to threats ntial ebleeta h ihfrequency high the that believe We . mt of imate β 2011m1 1 stu h feto supply of effect the thus is β 1 e ugssthat suggests del n t tnaderrfor error standard its and β −150 −100 −50 0 50 100 eil o ietrends. time for flexibly 1 log of seizures in Colombia (deviations from trend) sietfidfo the from identified is β 1 > 0 , , (i.e., politics or funding in Colombia). Third, our model suggests that short term shocks with little persistence are actually more likely to have an effect on violence. Besides the reasons outlined in the model, the short term demand is more inelastic and there is less room for substitution towards cocaine from other source countries, implying that these supply shocks have a significant impact in downstream markets. Finally, both resulting series are independent over time (no serial correlation), as modeled. This implies we can safely ignore more complicated dynamics. Appendix C presents an analysis of the time series properties of these series. We now present several estimates of equation 3 in Table 2. The table has five panels, each one with a different dependent variable. In columns 1 and 2, we use the monthly homicide rates for all Mexican municipalities as the dependent variable. In columns 3 and 4, we focus only on municipalities in quintiles 1 and 2 of distance to the U.S. border. In columns 5 and 6 we zoom into the municipalities in the first distance quintile, and use the homicide rate in these municipalities as the dependent variable. Even columns add time series controls varying at the monthly level, including the unemployment rate and a measure of economic activity (IGAE). Although we regard these controls as endogenous and prefer our estimates without them, it is reassuring to see that our main results hold with their inclusion. As expected from our model, all estimates are uniformly positive except for drug-related aggressions. Our preferred estimates, in columns 1, 3 and 5, suggest that a 1% increase in seizures in Colombia increases violence as measured by the INEGI homicide rate by 0.119% in municipalities in the first quintile (s.e=0.033); 0.082% in municipalities in quintiles 1 and 2 (s.e=0.033); and 0.059% in all of Mexico (s.e=0.027). We also find an increase in drug-related homicides that is driven by executions and confrontations (although the effect on confrontations is not significant at the 10% level). This is consistent with our model, since these categories are more closely related to inter-cartel violence. On the other hand, aggressions are targeted homicides resulting from DTOs attacking government forces, which are less related to the mechanisms in our model. We now explore in more detail the time series properties of our estimates using the INEGI homicide rate and estimate several variants of equation 3. Our results are presented in Table 3, which again contains three panels: One for municipalities in all of Mexico, another for quintiles 1 and 2 and the last one for the first distance quintile. Column 1 reproduces our main time series estimate for all of Mexico. In the last row, we present a test that revals no significant serial correlation up to of order 4. Thus, once we remove trends, violence shocks are independent over time, and the usual OLS robust standard errors are consistent. In column 2, we add three lags of the homicide rate as explanatory variables. The lags are not significant and they do not affect the estimate of our coefficient of interest. This further suggests that we can safely ignore more complicated dynamic issues in the homicide rate. Columns 3 to 6 explore the timing of the effects by adding lags and leads of seizures in Colombia. We find that contemporary seizures have the stronger effect on violence and, if anything, their effect lasts

17 y781. o onsi unie n fdsac oMexi to distance of 2 and 1 period, quintiles this in in points experienced log increase 7.8-10.1 points the by log of 5.6-8.7 10%-15% by about rate to tri homicide was the reduction productio increased the cocaine reduction of potential by Most and fell cultivation Colombia tons). coca from although metric supply 200 cocaine to tons 2009, metric and 2006 Between 1%. iue5 h gr hw h aho h NG oiiert a rate homicide pane INEGI left The the lines. of dashed in path plotted the is interval shows confidence figure The 5: Figure hcshv h aeefc.Scn,w sueta seizures that e that drugs—an imply of assume supply Colombian we net the Second, on effect their assume through effect. we same one, the persistent have more a shocks Fir least t at and assumptions. 2, or two Table shock, requires of calculation permanent panel Our top the 3. Table in of 5 15 and 3 2009 1, to columns 2006 in from cocaine estimates of supply Colombian the in reduction espeieyetmtdhere. estimated T precisely in less outlined properties qualitative pre-shock the its with to consistent back is declines then and shortage overal INEGI cocaine the fir the by the measured for as panel violence, that right see the we and results border; U.S. the Me to in distance rate of homicide 2 the on effects the presents panel left The ed fln of leads 6 patterns. same the reveal and Mexico c of remaining north The the hig assumes. this model at s our Mexico unanticipated—as leads, in mostly conditions of market effect lagged significant to any react find not not do do We period. one for the 2; and 1 quintiles in municipalities for panel middle the oilsrt h uniaieipiain forestimat our of implications quantitative the illustrate To eas rsn h uldnmcefc fspl hcsi ev in shocks supply of effect dynamic full the present also We

Homicide rate change in log points −.2 −.1 0 .1 .2 .3 −5 β S 1 t atrsteefc fapritn euto ntespl o supply the in reduction persistent a of effect the captures oeuto n ltec fteotie ofcet.Figu coefﬁcients. obtained the of each plot and 3 equation to Months relativetoevent All Mexico 0 5

Homicide rate change in log points −.2 −.1 0 .1 .2 .3 −5 Months relativetoevent Quintiles 1and2 rsnsteetmtdpt o uiiaiisi l fMe of all in municipalities for path estimated the presents l 18 ih ae o uiiaiisi h rtquintile. first the in municipalities for panel right 0 be3 huhteidvda ofcet are coefficients individual the though 3, able on %ices nsiue ttm .Te95% The 0. time at seizures in increase 1% a round lofl.Oretmtsipyta this that imply estimates Our fell. also n io h idepnlfrqitls1and 1 quintiles for panel middle the xico; oiiert,icesseatyduring exactly increases rate, homicide l s ecmueteefc ftesharp the of effect the compute we es, ee ihsm ml essec.This persistence. small some with level tqitl.Cnitn ihteprevious the with Consistent quintile. st rqec n htspl hcsare shocks supply that and frequency h 5 t ic h euto nspl a a was supply in reduction the since st, cuinrsrcin ohassumptions Both restriction. xclusion nalo eio hc corresponds which Mexico, of all in lmspeetsmlretmtsfor estimates similar present olumns getn htsiue nColombia in seizures that uggesting htsotrnsok n persistent and shocks short-run that n-td grs ead6lg and lags 6 add We figures. ent-study oadb 13-54lgpit in points log 11.37-15.4 by and co n ticesdtehmcd rate homicide the increased it and grdb nices nseizures, in increase an by ggered nvoec nMxc.W s the use We Mexico. in violence on eetmtsi oun ,1 and 10 5, columns in estimates he nClmi nyafc violence affect only Colombia in Homicide rate change in log points −.2 −.1 0 .1 .2 .3 −5 56lgpit fo 520 (from points log 95.6 e5cnan he panels. three contains 5 re ooba oan by cocaine Colombian f Months relativetoevent First quintile 0 5 xico; the first distance quintile. This also accounts for 10% to 15% of the increase in violence in this period in both regions.19. However, in 2010 violence kept increasing in Mexico while the supply of Colombian cocaine stabilized, suggesting less explanatory power in this period. Besides the long- run implications of our estimates, they show that more frequent and larger supply shocks created by seizures in Colombia since 2006 have contributed to the rise of drug-related violence in Mexico, at least in the short run. (In fact, our model predicts that larger volatility in the seizures process increases violence on average, since supply shocks have asymmetric effects in the SPE of the dynamic model.)

4.3 Heterogeneity by importance for trafﬁcking

In this section we investigate the prediction in proposition 1 regarding the importance of a municipality for the cocaine trade. We use the distance from U.S. entry points as our proxy for the importance for trafficking. We focus on this proxy for three reasons. First, unlike heroin or cannabis, cocaine is not produced in Mexico, so the strategic position of a municipality in terms of trafficking deter- mines its importance. Second, internal consumption is unimportant when compared to revenue from exports to the U.S. (see Kilmer et al., 2010). Third, as shown in the summary statistics, violence and cartel presence are concentrated in northern Mexico, suggesting that these are the places with more incidence of the drug trade.20 To begin, we estimate the time series equation (equation 3) separately for groups of municipalities located at 901 moving windows of distance from the U.S., each one covering 10 percent of the municipalities. Figure 6 plots the estimated effects and their confidence intervals as a function of the average distance from the U.S. in each window. Most of the effect of seizures is driven by increases of violence in the north, especially among municipalities within 400 km of the U.S. This was already anticipated by our previous results and figure 5. A 1% increase in cocaine seizures creates about a 0.16% increase in violence in the north of Mexico (first window), which implies that the decline in cocaine supply from Colombia from 2006 to 2009 explains roughly 12% of the increase of violence in this area. On the other hand, there does not seem to be any significant effect on municipalities in the southern areas of the country. This suggests we are capturing an effect that is specific to the drug trade in the north. 19This is only a suggestive calculation, since in practice there are reasons why short-run and permanent shocks may have different effects. On the one hand, the possibility of storage implies larger effects from persistent shocks. On the other hand, the possibility to substitute for cocaine from other source countries implies smaller effects from persistent shocks. Likewise, our theoretical discussion highlights the fact that temporary shocks have a larger effect than permanent ones. The reason is that a temporal shortage that is soon reversed implies large revenues today and low revenues tomorrow. Therefore, the potentiality of future punishment appears less severe, meaning that higher violence must be allowed for today. In contrast, permanent shocks also raise the deterrence power of the possibility of future punishment, and so raises violence less. 20Cocaine seizures are also concentrated in northern Mexico. The only exceptions are Michoacan and Guerrero, two important entry points for cocaine from the Andes in southwestern Mexico.

19 in.Tid tde o ufrfo h nietlparamet incidental Finally, the directly. from effects suffer fixed not municipality does it Third, efficient—u necessarily tions. not consistent—although also is it lar with variables dependent non-negative with plications 2010 Wooldridge, (see advantages several has model Poisson maue nhnrd fk) eaeitrse nexplainin in interested pality are We km). of hundreds in (measured 18)adWodig 19) h oe t h olwn co following the fits model The (1999). Wooldridge and (1984) eaiedsac rmmunicipality from distance negative odr oi santrlaao otemdlepoe ntet the in explored model m the by to analog caused natural Colombia a is in it shocks so border, supply to reacts violence which hori The month. one kilometers. during in a cocaine measured left on of The Colombia supply points. Colombian in entry the production U.S. in to cocaine distance net of of groups different effect The 6: Figure aieeecs,isedo otoln o xdefcs w effects, fixed for controlling of instead exercise, native Here, p i 21 × epeettotpso siae.Frt eetmt Poiss a estimate we First, estimates. of types two present We enx xmn h vdnemr ytmtclyi regres a in systematically more evidence the examine next We eas xeietdwt am oes hspoue simil produced This models. gamma with experimented also We ln i δ S uigmonth during i t . and α t ul oto o grgt aito n uiiaiyinv municipality and variation aggregate for control fully t , Increase in violence in log points h

i −.2 −.1 0 .1 .2 .3 , t safnto fmncplt xdefcs ieefcsan effects time effects, fixed municipality of function a as , 200 E h i , t = δ 400 i i oteUS ers nr on,wihw ilcl proximity call will we which point, entry nearest U.S. the to α Distance toentrypointsinkilometers t exp β ( a eitrrtda h nraei h lsiiywith elasticity the in increase the as interpreted be can β 600 s ierneo uiiaiycaatrsisa contro as characteristics municipality of range wide a use e p i hw h ecn nraei ilnecue ya1 fall 1% a by caused violence in increase percent the shows xis 20 i × ln otlai lt h itnefo h ers nr point entry nearest the from distance the plots axis zontal vrl oiiertsi eiofrmncplte in municipalities for Mexico in rates homicide overall S t edseso—iehmcd ae.Second, rates. homicide dispersion—like ge 800 + rrslsntpeetdt aesae nti alter- this In space. save to presented not results ar drvr eea itiuinlassump- distributional general very nder p hpe 8:Frt ti eindfrap- for designed is it First, 18): chapter , m eissection. series ime r rbe,alwn st oto for control to us allowing problem, ers i h xetdhmcd aei munici- in rate homicide expected the g × nfie fet oe si asa tal. et Hausman in as model effects fixed on dtoa xetto otedata: the to expectation nditional F t ( 1000 γ vn 0 mtwrsteU.S. the towards km 100 oving )) infaeok Let framework. sion . ratcaatrsis The characteristics. ariant 1200 21 h interaction the d p i ethe be ls. (4) Second, we also estimate the following simpler linear model

Eln(hi,t + r)= δi + αt + β pi × lnSt + pi × Ft(γ). (5)

The left hand side is a monotone transformation of the homicide rate that deals with the large dispersion in homicide rates and is well defined at zero. The constant r > 0 is the 90th percentile of the homicide rate in our sample. We choose this particular value for r because the estimated residuals are normally distributed, suggesting that the transformation adequately removes the skewness present in the raw data, and a linear conditional expectation is a good approximation.22 The transformed value is hi,t +r approximately equal to lnh , , so the estimates can be interpreted as elasticities after multiplying hi,t i t them by the sample average of hi,t +r (still, this is a coarse approximation). hi,t Contrary to the models in the previous section, we identify β from within municipality variation. The effect we measure arises from the difference in the short-term reaction of violence to supply shocks between municipalities near the U.S. and municipalities far from it. Both models include the term pi ×Ft(γ), which flexibly controls for differential trends and year-to-year variation in homicides γ ∑3 γ n η in the north. Just as in equation (3), the term Ft( )= n=0 nt + y guarantees our estimate does not capture secular trends in violence near the U.S. borders. The inclusion of time effects implies that we exploit a source of variation that is orthogonal to the time series dimension used in the previous section. We compute standard errors that are robust to heteroskedasticity and arbitrary serial correlation within municipalities. The inclusion of time effects means that we do not need to cluster observations at the time level. Table 4 presents our results using both estimation strategies. Columns 1 to 4 focus on municipalities in all of Mexico, while columns 5 to 8 restrict the sample to municipalities in distance quintiles 1 and 2. The top panel uses the INEGI homicide rate as the dependent variable. Column 1 presents our main Poisson fixed effect estimates, and indicates that every 100 km of proximity to the U.S. imply an additional 0.03% (s.e=0.011) increase in homicide rates following a 1% increase in seizures in Colombia. (This estimator drops observations with no homicides during our period of analysis.) In column 2, we control flexibly for enforcement policies that were implemented during our period of analysis. In 2006 the Calderón administration initiated an aggressive campaign of cracking down on cartels. As shown by Dell (2012), this was especially the case in municipalities run by PAN mayors. We control for differential cubic trends by historical PAN support, an exogenous predictor of current PAN electoral success.23 Our estimates do not change much, suggesting they are not confounding

22We also experiment with different values of r and obtained similar results. In particular, we set r equal to different moments of the homicide rates distribution, including its minimum value, 10th, and 50th percentile. These results are not presented to save space. 23We obtain very similar results (not shown here) using the presence of a PAN mayor as a control. Although this control is endogenous, it shows that our estimates are not driven by the election of PAN mayors during Calderón’s administration.

21 the deployment of Calderón’s anti-drug strategies. In columns 3 and 4 we estimate analogous models using the transformation in equation 5. These estimates suggest that every 100 km of proximity to the U.S. imply an additional 0.014% (s.e=0.004) increase in homicide rates following a 1% increase in seizures in Colombia (the estimates are already adjusted so they can be interpreted roughly as elasticities). In columns 5 to 8 we reproduce the estimates in columns 1 to 4 restricting the sample to municipalities in quintiles 1 and 2 of distance from the U.S. border. We still find a positive and significant interaction that is consistent with the results in previous columns. The second panel presents results using the drug-related homicide rate as the dependent variable with the same structure as in the top panel. The qualitative pattern resembles that in the first panel, namely that seizures in Colombia have a stronger effect on violence as one moves closer to U.S. entry points. The bottom panels explore the categories into which drug-related homicides are separated. Our findings agree, in general, with the time series results in Table 2, showing that the effect on drug-related homicides is again driven by executions and confrontations, whereas the coefficients for aggressions are small and not significant. Our results show that the scarcity created by larger and more frequent negative supply shocks in Colombia since 2006 has contributed to an increase in violence in northern Mexico relative to the rest of the country. To illustrate these effects, we use the estimate in column 5 of the top panel and assume that the effect of a permanent supply fall is the same as for a short-term shock. During our period of analysis, the Colombian monthly supply of cocaine fell by 95.6 log points. Thus, scarcity created by Colombian policies could explain up to 31 log points, which account for 25% of the 128 log point differential increase of violence in northern Mexico in this period.

4.4 Role of cartels: It takes two to tango

As suggested by our model, the presence of cartels in a municipality is an important determinant of the effect of supply shocks on violence. More precisely, our model predicts that in the absence of cartels negative supply shocks should not affect violence. Moreover, whenever a single cartel fully controls a municipality, its property rights over the revenue stream generated in that municipality are well established, so scarcity shocks have no effect on violence. In contrast, when there are two or more cartels present in a municipality there is violent competition over revenue. In order to secure rents, they must ﬁght each other; in principle, however, they would like to divide the pie without resorting to violence, but every cartel is tempted to deviate and use violence to appropriate a bigger share. This is the classic Olson paradox in the context of inter-cartel conﬂict (see Grossman (2001) and Kalyvas (2006) for a similar argument).24

24This argument has also been used by many critics of the Calderón administration, who have pointed out that his policy fragmented cohesive cartels, leading to more violence (see Guerrero (2010, 2011a) and Merino (2011)).

22 We use the data on cartel presence in order to test these hypotheses, and use the INEGI homicide rate in this exercise—which is our preferred proxy of violence. We begin by estimating equation 3 for the subsample of municipalities with no cartels, one cartel, two non-allied cartels and at least two cartels at the time of the shock, using the INEGI homicide rate as our dependent variable. Notice that the composition of each group changes every year, since the cartel presence variables vary at this level. However, the set of year effects included in the equation controls for any compositional changes. Figure 7 presents event study figures depicting the change in the homicide rate in log points following a 1% increase in cocaine seizures in Colombia at month zero (as in figure 5). As suggested by these figures, seizures in Colombia do not affect violence in municipalities with one or no cartels. In contrast, there is a large spike in homicides coinciding with the time of the cocaine shortage in municipalities with two or more cartels during the year when the shock occurred, or with various cartels (at least two).

No cartels One cartel .3 .3 .2 .2 .1 .1 0 0 −.1 −.1 Homicide rate change in log points Homicide rate change in log points −.2 −.2 −5 0 5 −5 0 5 Months relative to event Months relative to event

Non−allied cartels Various cartels .3 .3 .2 .2 .1 .1 0 0 −.1 −.1 Homicide rate change in log points Homicide rate change in log points −.2 −.2 −5 0 5 −5 0 5 Months relative to event Months relative to event

Figure 7: The ﬁgure shows the path of the INEGI homicide rate around a 1% increase in seizures at time 0. The 95% conﬁdence interval is plotted in dashed lines. The top-left panel presents the estimated path for municipalities with no cartels; the top-right panel for municipalities with one single cartel; the bottom-left panel for municipalities with at least two non-allied cartels; and the bottom-right panel for municipalities with at least two cartels.

Table 5 explores the heterogeneity by estimating equation 3 for different groups of municipalities, using the INEGI homicide rate as the dependent variable. The top panel present time series estimates of equation 3 for municipalities with no cartels (columns 1 and 2), one cartel (columns 3 and 4), at least two non allied cartels (columns 5 and 6), and at least two cartels (columns 7 and 8). The cartel

23 indicators vary every year so the group composition changes, but year effects fully control for these changes. Even columns include three lags of the homicide rate to control for dynamics. Our results suggest scarcity has no effect in Mexican municipalities with one or no cartels. In contrast, we ﬁnd a positive and signiﬁcant effect on violence in municipalities contested by non-allied cartels and in municipalities with at least two cartels.

We explore these patterns in more detail in a regression framework. Let DTOiy be a vector of variables related to cartel presence in municipality i during year y. This vector includes a dummy for the presence of at least one cartel, a dummy for two or more cartels, and a dummy for the presence of two non-allied cartels. To investigate how the number of cartels mediates the effect of cocaine scarcity and supply shocks, we estimate equations 4 and 5 by adding interactions of lnSt and pi × lnSt with

DTOiy. We include a full set of interactions of the form DTOi,y × Ft(γ1) and pi × DTOi,y × Ft(γ2), to control for the expansion of cartels and its yearly variation (recall that Ft include year dummies) and their effect on violence, as well as for any long term trends in municipalities with different numbers of cartels. The model thus compares the differential short term response to supply shocks between municipalities with different values of DTOi,y at the time of the shock. The results of this exercise are shown in Table 6. The table is divided into two panels. The left-hand side of each panel (columns 1 to 3) presents the results from the Poisson fixed effects estimator, while the right-hand side (columns 4 to 6) presents the results from the linear model with the transformed homicide rate as dependent variable. The top panel presents estimates for all of Mexico, while the bottom panel restricts the sample to municipalities in the first two distance quintiles from the U.S. border. All effects are evaluated at the Mexican-U.S. border, and the interaction between supply shocks and proximity to the U.S. is evaluated in municipalities with no cartel presence. A clear pattern emerges. Column 1 and 4 show no significant differential effect of supply shocks in northern Mexico when no cartels are present. In municipalities with cartels, there is some additional effect of seizures on violence which increases with proximity to the U.S., but it is not precisely estimated. However, when we separate municipalities with cartels depending on whether there are non-allied cartels (columns 2 and 5) or more than one cartel (columns 3 and 6), we find positive, and mostly significant, interactions between seizures in Colombia and the presence of multiple or non- allied cartels. On the other hand, the interaction between seizures in Colombia and cartel presence becomes smaller or negative and far from significant. These results suggest scarcity does not cause measurable violence in municipalities with a single or allied cartels; it only has a large effect when there are various or non-allied cartels. A similar pattern holds for the triple interaction between cartel presence, proximity to the U.S. and seizures in Colombia. Northern municipalities react with more violence to supply shocks only if there are multiple or non-allied cartels in the municipality. This is clear evidence that the presence of cartels is necessary for violence to respond to scarcity shocks, but one cartel is not enough: It “takes two to tango,” as suggested by our model.

24 The results in this sub-section suggest that most of the effect of cocaine seizures in Colombia on violence in Mexico is explained by its effect on municipalities with multiple cartels. From 2006 to 2010, the percentage of municipalities with multiple cartels increased from 5% to 17%. As a consequence, the effects of seizures on violence has been ampliﬁed by the territorial expansion and overlap of cartels in the Mexican territory.

4.5 The role of enforcement in Mexico

During our period of analysis, the war on drugs was spearheaded by Calderón and the PAN party. The key ingredient of Calderón’s strategy during our period of analysis was to behead cartels by killing or arresting their leaders (see Guerrero, 2011a; Merino, 2011; Guerrero, 2010). Although this was a federal strategy, its implementation relied strongly on the cooperation of local authorities, and municipalities with PAN mayors were more likely to crack down on cartels during Calderón’s term (see Dell, 2012). In a similar line, we argue that places where the PAN has had more historical support, as measured by its vote share in municipal elections during the period 1980-2000, saw an intensification of crackdowns on cartels during the Caldeon era. There are two potential mechanisms at play. First, these places are more likely to elect PAN mayors (a simple cross sectional regression shows that a 10% increase in the historical PAN vote share increases the likelihood of electing a PAN mayor during our period of analysis by 7.4% (s.e=0.5%)); and second, incumbents in these places may be under more pressure from their electorate to cooperate with PAN’s national policies. Thus, cartel leaders face higher turnover rates, because of arrests and killings, in municipalities where the PAN has had more support historically. Our model predicts stronger effects of cocaine seizures in Colombia on violence in these municipalities. We begin by estimating equation 3 using the INEGI homicide rate for municipalities with low PAN support—defined as an average historical PAN vote share below 28%, and municipalities with high PAN support—defined as as an average historical PAN vote share above 28%. The 28% threshold matches the average vote share of the PAN party in local elections between 1980 and 2000. Alterna- tively, we use a 20% threshold, which coincides with the 75th percentile of historical voting shares. Figure 8 presents event study figures depicting the change in the homicide rate in log points following a 1% increase in cocaine seizures in Colombia at month zero (as in figure 5). As suggested by the figures, scarcity does not affect violence in the sample of municipalities with low PAN support (measured using either of the thresholds). In contrast, in municipalities with high PAN support, seizures in Colombia cause a large contemporary spike in homicides. This conclusion is also supported by the time-series results in the bottom panel of Table 5. In columns 1 and 2, we find a small and not significant effect of cocaine seizures in Colombia on violence in municipalities with low PAN support, defined as municipalities with an average historical PAN vote share below 28%. In contrast, we find

25 a positive and signiﬁcant effect in columns 3 and 4 when we focus on municipalities with average historical PAN support above 28%. Columns 5 to 8 present similar results using the 20% threshold.

Low PAN support (<.28) High PAN support (>.28) .3 .3 .2 .2 .1 .1 0 0 −.1 −.1 Homicide rate change in log points Homicide rate change in log points −.2 −.2 −5 0 5 −5 0 5 Months relative to event Months relative to event

Low PAN support (<.2) High PAN support (>.2) .3 .3 .2 .2 .1 .1 0 0 −.1 −.1 Homicide rate change in log points Homicide rate change in log points −.2 −.2 −5 0 5 −5 0 5 Months relative to event Months relative to event

Figure 8: The ﬁgure shows the path of the INEGI homicide rate around a 1% increase in seizures at time 0. The 95% conﬁdence interval is plotted in dashed lines. The top-left panel presents the estimated path for municipalities with low PAN support; the top-right panel for municipalities with high PAN support, coding high support as an average historical vote share above 28%. The bottom-left panel presents the estimated path for municipalities with low PAN support; the bottom-right panel for municipalities with high PAN support, coding high support as an average historical vote share above 20%.

As in the previous section, we further investigate the role of enforcement in a panel regression.

Let PANi be a dummy for high PAN support, defined using the 28% or 20% threshold. We estimate equations 4 and 5 by adding interactions of lnSt and pi ×lnSt with PANi. Additionally, we control for differential trends by PAN support, and by PAN support interacted with proximity to the U.S., so that our interactions do not capture a secular increase in violence in the municipalities where Calderón’s strategy was deployed with more resolve. Thus, our estimator only exploits the different short-term reactions of violence to cocaine shortages in municipalities with different historical support for the PAN party. Table 7 presents our results. We use the INEGI homicide rate and focus on all of Mexico in the top panel and in quintiles 1 and 2 in the bottom one. Columns 1 and 2 in each panel show Poisson fixed effect estimates, while columns 3 and 4 present results using the transformation of the homicide rate in equation 5. All effects are evaluated at the Mexican-U.S. border and at municipalities with low PAN support. In columns 1 and 3 we use the 28% threshold to define municipalities with high

26 PAN support, and in columns 2 and 4 we use the 20% threshold. As predicted by Proposition 2, our estimates suggest that cocaine seizures have a larger effect on violence in municipalities with higher PAN support, independently of how me measure it (or the sample used), though the estimates for the first two quintiles are less precise when using the 20% threshold. Moreover, this effect is stronger for municipalities in the north of Mexico, where drug trafficking is more important, as suggested by the triple interaction. To get an idea of the quantitative implications of our results, take two municipalities near U.S. entry points with different historical PAN support. For instance, the historical voting for PAN in Ciudad Juarez, Chihuahua, was about 44%, whereas it was 14% in Nueva Laredo, Tamaulipas. A reduction in the supply of cocaine of 95.6 log points (as was observed between 2006-2009), would cause an increase of 43 log points in homicides in Ciudad Juarez relative to Nueva Laredo (using the estimates in column 1, bottom panel). During this period, homicides fell in Nueva Laredo by 23.4 log points and increased by 236.9 log points in Ciudad Juarez. The interaction between the sharp decline in the net supply of cocaine from Colombia and the greater PAN support in the later municipality may explain up to 15% of this differential increase in homicides among these northern municipalities following stark trajectories. To further understand the interaction of the policies implemented during the Calderón administration against drug cartels and supply shocks in Colombia in creating violence, we re-estimate versions of equations (3) for all the period 2003-2010. These results are not presented to save space, but we find that negative supply shocks only had a significant and robust effect on violence during Calderón’s term.25 The findings in this section mean that Calderón’s policies interacted with supply reductions in Colombia to create violence in Mexico. This is evident at the cross-sectional level, where supply shocks had a larger effect on violence in municipalities aligned with Calderón’s party, and at the time series level, where we find no effect of cocaine seizures in Colombia on violence in Mexico before Calderón’s term. Based on our model, we believe this is related to the special focus of Calderón’s administration on killing or arresting kingpins, which had the undesirable consequence of increasing discount rates and reducing the scope for informal arrangements to reduce violence. The evidence is consistent with a regime shift during Calderón’s administration: Before 2006, there were few cartels localized geographically, and informal arrangements kept violence low. In this environment, scarcity only had negligible or no effects. After 2006, cocaine shortages in Colombia found a very different environment in Mexico, one in which cartels were fragmented and their locations overlapped more. The aggressive policy of killing and arresting leaders destroyed informal arrangements that had kept rapacity low or prevented it altogether. Our estimates suggest that Calderón’s policies interacted with

25Another interpretation is statistical: Seizures were less volatile and a less important determinant of supply before Colombia changed its anti-drug strategy in 2006. Thus, the coefﬁcients for this period are attenuated.

27 cocaine shortages in Colombia, at least over the short run, by creating the conditions for rapacity to be resolved via high levels of violence, instead of through tacit cooperation.

4.6 Is scarcity (and the price effect it brings) the right channel?

We have documented that cocaine seizures in Colombia are associated with large spikes of violence in Mexico at high frequencies. We argued in our theoretical model that this occurs through an increase in cocaine revenues, which is the case so long as demand is inelastic. In this section we defend our interpretation. Unfortunately, we cannot measure the amount of drug-related rents that are being contested in a municipality, or the amount of drug revenue in Mexico on a monthly basis, which precludes any econometric exercise.26 Instead, we provide some reality checks suggesting that cocaine shortages in Colombia seem to increase revenues focusing on longer term variation. Figure 9 shows that wholesale cocaine prices increased dramatically from 2007 until 2010, as Colombian supply declined. While net cocaine production in Colombia went down from about 520 MT per year in 2006 to about 200 MT in 2009, the price per pure gram of cocaine on U.S. streets went up from about $135 in 2006 to about $185 in 2009 for purchases of two grams or less, and from $40 to $68 for purchases between 10 and 50 grams during the same period. Taking into account net production from Peru and Bolivia—which increased and reduced the upward pressure on prices—, the total gross drug trade revenue measured using wholesale prices in the U.S. increased by about 7% between 2006 and 2009. This suggests that cartels face an inelastic market demand as assumed in our model, even at low frequencies. The possibility remains that other factors drive the documented relationship. For instance, demand shocks increase prices and production, and hence seizures in upstream markets such as Colombia. This would create a spurious correlation between seizures in Colombia and violence in Mexico. A similar concern is that changes in enforcement in Mexico and market conditions create violence and at the same time increase the demand for Colombian cocaine. An alternative story is that there are complementarities in enforcement, and when Mexico cracks down on the cocaine trade, the Colom- bian government seizes more cocaine. We do not think any of these alternatives explains our results for several reasons. First, we ﬁnd a negative (but not precisely estimated) effect of seizures in Colom- bia on seizures in Mexico.27 If anything, there is less cocaine in downstream markets when seizures

26There is no reliable data on cocaine prices, especially at high frequencies. UNODC reports yearly prices, while quarterly prices can be constructed using STRIDE undercover purchases in the U.S. However, there are sizable doubts regarding the quality of quarterly series based on these data (see Horowitz (2001), and Arkes et al. (2008)). Furthermore, there are only 12 quarters of data. 27One would expect that seizures in Colombia have a significant negative effect on seizures in Mexico. We do find a negative relationship, which supports our interpretation, but it is not significant at traditional levels. We believe that other strategic reactions could mask this relation. For instance, cartels could use drugs they had stored to take advantage of temporal profit opportunities due to the higher prices. These creates counteracting forces against the reduction of seizures in Mexico.

28 u sas nomtv fteseiccanldiigtere the driving channel speciﬁc the of uncover informative we also effects is the but of at heterogeneity are the predictions Thus, Both paper. the Colombia. in car seizures more single induce a also with municipalities for enforcemen correlation in spurious complementarities a were there If support. viol PAN and Colombia in seizures between seizur correlation affected spurious a Mexico in munici conditions market to If speciﬁc are support. PAN uncovered we effects the shown, have we ohcutista r o rsn ntedt.Telc fsu reducti of supply lack between The complementarities on data. based the nations in present not are that observe countries also both would vio one both losses), the up for driving compensate were drive (to Mexico caine not in are seizures Colombia if in Third, seizures Mexico. rea that not view do our Colombia supports in This seizures that suggest s effects our of of years timing the demand during with slowly consistent decreased not has is demand that cocaine fact a Colombia, in high are quarter. per tons TIE(ih xs.Pie r ndlasprpr rmi wh in gram pure per dollars in are Prices axis). (right STRIDE iue9 urel oan rdcini oobanto se of net Colombia in production cocaine Quarterly 9: Figure oefcs hs eut ntsoni h ae)sgetth suggest paper) the in shown (not results These effects. no ewudas bev fet ee huhteei oecoop some is there frequencies. Though high here. at effects observe also would we 28 ieie hnw siaeteefcso eono marihuan or heroin of effects the estimate we when Likewise,

Metric tons

2007m1 0 50 100 150 2008m1 urel rdcinCocaineprice Quarterly production 2009m1 Month 29 tmltr rplc oprto r o rvn u result our driving not are cooperation police or military at zrs(etai)adqatrycciepie sreported as prices cocaine quarterly and axis) (left izures lsl rnatos hl rdcini nhnrdmetri hundred in is production while transactions, olesale rto ntann,adavsn,ti osnttk place take not does this advising, and training, in eration ezrsi oobao ilnei eio eﬁnd we Mexico, in violence on Colombia in seizures a e,a prtosaantti atlwould cartel this against operations as tel, nplce nbt countries. both in policies on 2010m1 sults. oiiecreainbtensiue in seizures between correlation positive a di o nycnitn ihtemodel, the with consistent only not is ed hcreainas ue u te expla- other out rules also correlation ch nei eia uiiaiiswt low with municipalities Mexican in ence si ooba n ol loobserve also would one Colombia, in es uy(e ND,21) eod the Second, 2012). UNODC, (see tudy coscutis n ol observe would one countries, across t tt atvoetusre nMexico. in upsurges violent past to ct ec n eadfrClminco- Colombian for demand and lence hcsdiigoretmts nfact, In estimates. our driving shocks aiiswt aiu atl n high and cartels various with palities ycagn aktcniin in conditions market changing by n dswt h vdnepeetdin presented evidence the with odds 2011m1

100 120 140 160 180 200 Retail price per gram 28 ial,as Finally, ,or s, by c 5 Concluding remarks

This paper investigated the role of scarcity as a determinant of violence in commodity markets lacking third party enforcement. A simple model emphasizing predation and rapacity over revenue, in the absence of well-defined property rights, suggests that scarcity increases violence if the demand for an illegal commodity transacted in international markets is inelastic. Moreover, the increase is sharper when there are several groups contesting unprotected revenue, in locations more important for the trade of the commodity, and in places where policies lead to arrest and killing of cartel leaders, thus making agents more shortsighted and limiting informal cooperative arrangements. We test our model using monthly data from Mexican municipalities from December 2006 to De- cember 2010, a period coinciding with what has been called the Mexican Drug War. Exploiting high frequency monthly variation, we find that the scarcity created by temporal increases in cocaine seizures in Colombia increases violence in Mexico. Moreover, violence increased especially in the north, and within the north, specifically at locations close to U.S. entry points. We find that most of the effect is driven by municipalities with at least two cartels (or non-allied cartels), while there are no effects in municipalities with one or no cartels. Thus, scarcity causes violence only when cartels dispute the larger revenues at stake. President Calderón’s strategy of beheading cartels amplified the effect of scarcity during our period of analysis. This can be seen cross-sectionally, since the effect of seizures in Colombia on violence was large in Mexican municipalities more supportive of PAN (Calderón’s party), and in the time series, since the association between seizures in Colombia and violence in Mexico only arises during Calderón’s presidency. The effect of scarcity is thus mediated by many variables exactly as it was predicted by our model, providing compelling evidence that the mechanism we propose for scarcity breeding more violence operates in this context. Our results indicate that cocaine seizures in Colombia—which became larger and more frequent after 2006—created scarcity in wholesale cocaine markets, raised prices and contributed to the increase in Mexican violence. In particular, the sharp decline in the net supply of Colombian cocaine from 2006 to 2009 of 95.6 log points may account for 10%-14% of the increase in violence in this period. The interaction of scarcity with the expansion and fragmentation of cartels, PAN policies and proximity to the U.S., also helps explain the current cross-sectional distribution of violence in Mex- ico, and its divergence in the north after 2006. For instance, our estimates imply that the sharp decline in the net supply of Colombian cocaine from 2006 to 2009 may explain up to 25% of the differential increase of violence in the north of Mexico. Although these calculations require additional assumptions mentioned in the text, our paper demonstrates that, at least over the short run, the frequent and larger supply shocks created by Colombian supply reduction efforts have had negative spillovers in the form of more violence in Mexico during its so-called War on Drugs. Our framework also suggests that the illegal character of cocaine precludes third party enforce-

30 ment in this market, and creates social costs in the form of systemic violence, as the one documented in this paper. On top of that, supply reduction policies spearheaded by the U.S. in source, transit and consumer countries, artiﬁcially increase scarcity and contribute to the already high levels of violence in this market. Our evidence refers to a particular context, but the economic forces modeled and documented in our empirical exercise are relevant for many commodity markets lacking reliable third party enforcement. Cocaine markets may be special in that it is illegal and the role of the state as a provider of third party enforcement is precluded from the start. Thus, the magnitude of the effects we analyze might be smaller in other contexts with poorly deﬁned property rights. Nevertheless, our analysis is still useful in highlighting the relevant economic forces and informs the design of policies to mitigate and reduce violence in such environments.

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34 Table 1: Summary statistics.

Year: 2006 2007 2008 2009 2010 All Mexico (2,457 municipalities) INEGI homicide rate 9.74 8.15 12.68 17.59 22.53 [ 22.55] [ 19.40] [ 28.92] [ 38.17] [ 50.52] Drug-related homicide rate 0.69 2.59 6.30 8.69 13.57 [ 8.63] [ 18.42] [ 26.26] [ 34.99] [ 57.78] Cartel presence 0.12 0.16 0.24 0.27 0.29 [ 0.33] [ 0.37] [ 0.43] [ 0.44] [ 0.45] Quintiles 1 and 2 (983 municipalities) INEGI homicide rate 8.76 7.79 13.98 19.76 27.81 [ 16.83] [ 14.55] [ 29.49] [ 40.99] [ 59.12] Drug-related homicide rate 0.41 2.76 8.42 10.86 17.32 [ 5.07] [ 21.26] [ 30.89] [ 40.53] [ 70.11] Cartel presence 0.17 0.24 0.35 0.37 0.40 [ 0.38] [ 0.43] [ 0.48] [ 0.48] [ 0.49] First quintile (492 municipalities) INEGI homicide rate 9.37 8.62 19.97 28.67 44.46 [ 21.14] [ 18.14] [ 41.17] [ 56.50] [ 83.54] Drug-related homicide rate 0.77 3.64 14.03 18.90 31.40 [ 7.79] [ 31.64] [ 42.64] [ 57.47] [ 103.90] Cartel presence 0.24 0.34 0.42 0.43 0.49 [ 0.43] [ 0.47] [ 0.49] [ 0.50] [ 0.50] Note.- The table presents summary statistics for the main variables used in our empirical exercises. The data is presented separately for municipalities in all Mexico, in the ﬁrst two distance quintiles to entry points in the U.S., and in the ﬁrst distance quintile to entry points in the U.S.. Standard deviations for each variable are reported below the corresponding mean in square brackets.

35 Table 2: Time series effects of cocaine seizures in Colombia on violence in Mexico.

All of Mexico Quintiles 1 and 2 First quintile (1) (2) (3) (4) (5) (6) Dependent variable: INEGI homicide rate. log of seizures in Colombia 0.059∗∗ 0.056∗∗ 0.082∗∗ 0.079∗∗ 0.119∗∗∗ 0.120∗∗∗ (0.027) (0.025) (0.033) (0.032) (0.033) (0.034) Observations 49 49 49 49 49 49 R-squared 0.950 0.957 0.947 0.953 0.950 0.952 Dependent variable: drug-related homicides rate. log of seizures in Colombia 0.120∗∗ 0.123∗∗ 0.126∗∗ 0.126∗∗ 0.134∗∗ 0.137∗∗ (0.055) (0.055) (0.057) (0.057) (0.060) (0.061) Observations 49 49 49 49 49 49 R-squared 0.952 0.955 0.961 0.964 0.959 0.961 Dependent variable: drug-related executions rate. log of seizures in Colombia 0.123∗∗ 0.131∗∗ 0.124∗∗ 0.128∗∗ 0.122∗ 0.130∗ (0.057) (0.056) (0.060) (0.059) (0.065) (0.066) Observations 49 49 49 49 49 49 R-squared 0.951 0.955 0.957 0.961 0.956 0.958 Dependent variable: drug-related confrontations rate. log of seizures in Colombia 0.140 0.096 0.095 0.048 0.266 0.222 (0.221) (0.223) (0.191) (0.196) (0.184) (0.187) Observations 48 48 47 47 46 46 R-squared 0.720 0.731 0.733 0.747 0.720 0.739 Dependent variable: drug-related aggressions rate. log of seizures in Colombia -0.047 -0.043 -0.061 -0.070 0.035 -0.018 (0.168) (0.175) (0.151) (0.166) (0.280) (0.256) Observations 43 43 41 41 34 34 R-squared 0.588 0.595 0.426 0.434 0.348 0.393 Time series controls: Unemployment rate IGAE Note.- The table presents estimates of the effect of cocaine seizures in Colombia on aggregate violence for different groups of municipalities in Mexico. The dependent variable is the log of the homicide

rate indicated in each panel, aggregated at the monthly level. The explanatory variable is the log of the monthly cocaine seizures in Colombia. We estimate the model for all 49 months from December,

2006 to December, 2010. All models include a cubic polynomial in time (months) and year dummies, so that only high frequency variation is exploited. Even columns add the monthly unemployment

rate and a measure of economic activity as controls. Columns 1 and 2 present estimates for Mexico as a whole; columns 3 and 4 for quintiles 1 and 2; and columns 5 and 6 for the ﬁrst quintile. Standard

errors robust against heteroskedasticity are reported in parenthesis. Coefficients with ∗∗∗ are significant at the 1% level, with ∗∗ at only the 5% level and with ∗ at only the 10% level, using the first set of

standard errors.

36 Table 3: Additional time series estimates of the effect of cocaine seizures in Colombia on the INEGI homicide rate in Mexico.

All Mexico Quintiles 1 and 2 First quintile (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) log homicide rate t − 1 0.036 0.077 0.151 (0.162) (0.182) (0.152) log homicide rate t − 2 -0.012 -0.021 0.064 (0.168) (0.203) (0.189) log homicide rate t − 3 -0.176 -0.090 0.028 (0.227) (0.240) (0.184) log of seizures in Colombia t + 3 0.024 0.025 0.040 0.042 0.072 0.074 (0.026) (0.028) (0.037) (0.038) (0.046) (0.047) log of seizures in Colombia t + 2 -0.011 -0.006 -0.019 -0.013 0.012 0.018 (0.043) (0.033) (0.052) (0.041) (0.060) (0.048) log of seizures in Colombia t + 1 0.029 0.047 0.025 0.040 0.040 0.061 (0.032) (0.039) (0.044) (0.052) (0.051) (0.059) log of seizures in Colombia t 0.059∗∗ 0.056∗∗ 0.073∗∗ 0.062∗ 0.091∗∗ 0.082∗∗ 0.080∗∗ 0.092∗∗ 0.082∗ 0.106∗∗ 0.119∗∗∗ 0.112∗∗∗ 0.137∗∗∗ 0.125∗∗∗ 0.161∗∗∗ (0.027) (0.025) (0.028) (0.032) (0.040) (0.033) (0.037) (0.036) (0.041) (0.051) (0.033) (0.039) (0.036) (0.043) (0.054) log of seizures in Colombia t − 1 0.065∗ 0.072∗ 0.067 0.070 0.083 0.090 37 (0.038) (0.043) (0.049) (0.054) (0.057) (0.062) log of seizures in Colombia t − 2 0.019 0.033 0.005 0.019 0.026 0.043 (0.026) (0.029) (0.035) (0.040) (0.043) (0.048) log of seizures in Colombia t − 3 -0.023 -0.023 -0.037 -0.040 -0.037 -0.041 (0.028) (0.025) (0.036) (0.033) (0.048) (0.045) Observations 49 49 49 46 46 49 49 49 46 46 49 49 49 46 46 R-squared 0.950 0.953 0.958 0.953 0.962 0.947 0.948 0.954 0.950 0.957 0.950 0.953 0.956 0.953 0.960 Test for serial correlation: estimated residual on lagged ones (separate regressions for each). Lagged residual -0.012 -0.056 -0.120 0.121 0.025 -0.002 -0.068 -0.067 0.133 0.090 0.080 -0.090 0.014 0.188 0.127 (0.147) (0.147) (0.147) (0.153) (0.155) (0.148) (0.147) (0.148) (0.153) (0.154) (0.147) (0.147) (0.148) (0.151) (0.153) Residual t − 2 0.086 0.138 0.057 -0.073 -0.125 -0.026 0.014 -0.007 -0.144 -0.131 0.001 -0.110 -0.011 -0.014 -0.044 (0.152) (0.150) (0.152) (0.155) (0.155) (0.152) (0.152) (0.152) (0.153) (0.154) (0.148) (0.146) (0.148) (0.151) (0.151) Residual t − 3 -0.172 -0.015 -0.233 -0.032 -0.143 -0.173 -0.085 -0.204 -0.047 -0.141 -0.031 -0.075 -0.089 0.042 -0.075 (0.145) (0.149) (0.143) (0.147) (0.147) (0.145) (0.149) (0.145) (0.149) (0.149) (0.150) (0.149) (0.150) (0.152) (0.153) Residual t − 4 -0.099 -0.046 -0.071 -0.149 -0.152 -0.056 -0.034 -0.114 -0.103 -0.160 -0.089 -0.096 -0.157 -0.164 -0.243 (0.145) (0.145) (0.142) (0.146) (0.144) (0.145) (0.145) (0.142) (0.148) (0.147) (0.149) (0.146) (0.145) (0.151) (0.149) Note.- The table presents estimates of the effect of cocaine seizures in Colombia on aggregate violence for different groups of municipalities in Mexico. The dependent variable is the log of the INEGI homicide rate, aggregated at the monthly level. The explanatory variable is the

log of the INEGI homicide rate. We estimate the model for all 49 months from December, 2006 to December, 2010. All models include a cubic polynomial in time (months) and year dummies, so that only high frequency variation is exploited. Columns 1 to 5 present estimates for

Mexico as a whole; columns 6 and 10 for quintiles 1 and 2; and columns 11 to 15 for the ﬁrst quintile. Standard errors robust against heteroskedasticity are reported in parenthesis. The bottom panel presents estimates of a regression of the estimated residual on its ﬁrst four lags

(separately for each lag). Coefficients with ∗∗∗ are significant at the 1% level, with ∗∗ at only the 5% level and with ∗ at only the 10% level, using the first set of standard errors. Table 4: The differential effects of cocaine shortages on violence in Mexico by distance from the nearest U.S. entry point.

All of Mexico Quintiles 1 and 2 Estimation method: Poisson model Dep. var. ln(p + x) Poisson model Dep. var. ln(p + x) (1) (2) (3) (4) (5) (6) (7) (8) Dependent variable: INEGI homicide rate.

Seizures in Colombia × Proximity to the U.S. 0.031∗∗∗ 0.023∗∗ 0.014∗∗∗ 0.013∗∗∗ 0.043∗∗ 0.045∗∗ 0.022∗∗∗ 0.023∗∗∗ (0.011) (0.011) (0.004) (0.004) (0.019) (0.019) (0.008) (0.008) Observations 98245 85309 120296 97902 42973 42189 48167 47089 Dependent variable: Drug-related homicides rate.

Seizures in Colombia × Proximity to the U.S. 0.067∗∗∗ 0.062∗∗ 0.026∗∗∗ 0.026∗∗∗ 0.128∗∗∗ 0.127∗∗∗ 0.053∗∗∗ 0.054∗∗∗ (0.024) (0.025) (0.008) (0.008) (0.044) (0.044) (0.017) (0.017) Observations 56203 53214 120296 97902 27342 27097 48167 47089 Dependent variable: Drug-related executions rate.

Seizures in Colombia × Proximity to the U.S. 0.037∗ 0.029 0.016∗∗∗ 0.016∗∗ 0.073∗ 0.073∗ 0.031∗∗ 0.032∗∗ (0.021) (0.021) (0.006) (0.007) (0.039) (0.039) (0.014) (0.014) Observations 53900 50911 120296 97902 25970 25725 48167 47089 Dependent variable: Drug-related confrontations rate.

Seizures in Colombia × Proximity to the U.S. 0.124∗ 0.124∗ 0.023∗∗∗ 0.026∗∗∗ 0.198∗ 0.197∗ 0.053∗∗ 0.054∗∗ (0.070) (0.070) (0.009) (0.010) (0.108) (0.107) (0.021) (0.021) Observations 20090 19943 120296 97902 12348 12299 48167 47089 Dependent variable: Drug-related aggressions rate.

Seizures in Colombia × Proximity to the U.S. 0.041 0.042 0.001 0.001 -0.017 -0.017 0.002 0.002 (0.124) (0.124) (0.002) (0.002) (0.221) (0.220) (0.004) (0.004) Observations 7448 7448 120296 97902 4655 4655 48167 47089 Covariates: Differential trend by distance to U.S. Differential trend by PAN support Note.- The table presents estimates of the interaction between cocaine seizures in Colombia (measured at the monthly level in logs) and proximity to U.S. entry points (measured in 100km) on violence in Mexico. The dependent variable is the homicide rate indicated in each panel. All estimates include a full set of municipality and time ﬁxed effects, as well as a differential cubic trend by distance from

U.S. entry points. Additional covariates are indicated at the bottom of the table. Columns 1 to 4 present estimates for all of Mexico, while columns 5 to 8 present those for quintiles 1 and 2. Columns

1,2,5 and 6 use a Poisson fixed effects model; while columns 3,4,7 and 8, use a monotone transformation of the dependent variable, ln(p + x), with p the 90th percentile of x. Standard errors robust to heteroskedasticity and serial correlation within municipalities are reported below each estimate in parenthesis. Coefficients with ∗∗∗ are significant at the 1% level, ∗∗ only at the 5% level, and ∗ only at the 10% level.

38 Table 5: Additional time series estimates of the effect of cocaine seizures in Colombia on the INEGI homicide rate in Mexico for different subsamples of municipalities.

Panel A: Heterogeneity by Cartel presence No cartels One cartel Non-allied cartels Various cartels (1) (2) (3) (4) (5) (6) (7) (8) log homicide rate t − 1 -0.209 -0.013 0.049 0.044 (0.134) (0.127) (0.151) (0.150) log homicide rate t − 2 -0.187∗ -0.242∗ -0.024 -0.016 (0.104) (0.125) (0.173) (0.161) log homicide rate t − 3 -0.287∗ -0.351 0.030 0.008 (0.144) (0.221) (0.208) (0.208) log of seizures in Colombia t 0.021 -0.001 0.053 0.038 0.083∗∗ 0.079∗∗ 0.084∗∗ 0.082∗∗ (0.023) (0.025) (0.039) (0.037) (0.033) (0.034) (0.032) (0.033) Observations 49 49 49 49 49 49 49 49 R-squared 0.809 0.847 0.913 0.935 0.936 0.936 0.943 0.943 Test for serial correlation: estimated residual on lagged one. Lagged residual -0.179 -0.275∗ 0.147 -0.012 0.026 -0.018 0.007 -0.034 (0.148) (0.146) (0.146) (0.147) (0.147) (0.147) (0.147) (0.147) Panel B: Heterogeneity by PAN support 28% threshold 20% threshold Low PAN support High PAN support Low PAN support High PAN support (1) (2) (3) (4) (5) (6) (7) (8) log homicide rate t − 1 -0.135 0.181 -0.242∗∗ 0.136 (0.128) (0.156) (0.112) (0.175) log homicide rate t − 2 -0.187 0.065 -0.148 -0.020 (0.143) (0.199) (0.127) (0.205) log homicide rate t − 3 -0.351∗∗ -0.046 -0.294∗∗ -0.086 (0.142) (0.222) (0.143) (0.244) log of seizures in Colombia t 0.028 0.009 0.102∗∗∗ 0.103∗∗ 0.030 0.016 0.084∗∗ 0.082∗∗ (0.028) (0.023) (0.034) (0.038) (0.027) (0.027) (0.033) (0.036) Observations 49 49 49 49 49 49 49 49 R-squared 0.926 0.943 0.943 0.946 0.914 0.930 0.943 0.945 Test for serial correlation: estimated residual on lagged one. Lagged residual -0.138 -0.204 0.072 -0.115 -0.247∗ -0.167 0.061 -0.062 (0.146) (0.144) (0.147) (0.147) (0.143) (0.145) (0.147) (0.147) Note.- The table presents estimates of the effect of cocaine seizures in Colombia on the homicide rate for different groups of municipalities in Mexico. The dependent variable is the log of the INEGI homicide rate. The explanatory variable is the log of the monthly cocaine seizures in Colombia. We estimate the model for all 49 months from December, 2006 to December, 2010. All models include a cubic polynomial in time (months) and year dummies, so that only high frequency variation is exploited. Each model is estimated for the subsample of municipalities in the group indicated on top of the estimate. Standard errors robust against heteroskedasticity are reported in parenthesis. The bottom row below each estimate presents estimates of a regression of the estimated residual on its ﬁrst lag.

Coefficients with ∗∗∗ are significant at the 1% level, with ∗∗ at only the 5% level and with ∗ at only the 10% level, using the first set of standard errors.

39 Table 6: Differential effects of cocaine shortages on the INEGI homicide rate based on distance from U.S. entry points and cartel presence.

Poisson model Dep. var. ln(p + x) (1) (2) (3) (4) (5) (6) Panel A: All Mexico.

Seizures in Colombia × Proximity to the U.S. 0.017 0.017 0.016 0.009 0.009 0.008 (0.015) (0.015) (0.015) (0.005) (0.006) (0.006) Seizures in Colombia × Cartel presence 0.237 0.108 -0.056 0.114∗ 0.022 -0.025 (0.150) (0.166) (0.165) (0.061) (0.069) (0.079) Seizures in Colombia × Proximity to the U.S. × Cartel presence 0.031 0.010 -0.010 0.015∗∗ 0.002 -0.003 (0.019) (0.021) (0.021) (0.008) (0.009) (0.010) Seizures in Colombia × Non-allied cartels 0.250 0.236∗∗ (0.185) (0.104) Seizures in Colombia × Proximity to the U.S. × Non-allied cartels 0.043∗ 0.036∗∗ (0.025) (0.014) Seizures in Colombia × Various cartels 0.433∗∗ 0.239∗∗∗ (0.173) (0.091) Seizures in Colombia × Proximity to the U.S. × Various cartels 0.062∗∗∗ 0.032∗∗∗ (0.023) (0.012) Observations 98245 98245 98245 120296 120296 120296 Panel B: Quintiles 1 and 2.

Seizures in Colombia × Proximity to the U.S. 0.012 0.012 0.009 0.013 0.013 0.012 (0.031) (0.031) (0.031) (0.012) (0.012) (0.012) Seizures in Colombia × Cartel presence 0.289 0.104 -0.089 0.103 -0.008 -0.060 (0.203) (0.225) (0.214) (0.085) (0.094) (0.103) Seizures in Colombia × Proximity to the U.S. × Cartel presence 0.048 0.006 -0.023 0.013 -0.007 -0.014 (0.037) (0.042) (0.039) (0.014) (0.016) (0.017) Seizures in Colombia × Non-allied cartels 0.328 0.262∗∗ (0.224) (0.119) Seizures in Colombia × Proximity to the U.S. × Non-allied cartels 0.077∗ 0.046∗∗ (0.043) (0.020) Seizures in Colombia × Various cartels 0.541∗∗ 0.271∗∗ (0.212) (0.108) Seizures in Colombia × Proximity to the U.S. × Various cartels 0.101∗∗ 0.044∗∗ (0.040) (0.019) Observations 42973 42973 42973 48167 48167 48167 Note.- The table presents estimates of the interaction between cocaine seizures in Colombia (measured at the monthly level in logs), proximity to U.S. entry points (measured in 100km), and cartel presence on violence in Mexico. The dependent variable is the INEGI homicide rate. All estimates include a full set of municipality and time fixed effects, as well as a differential cubic trend by distance from U.S. entry points. The top panel present estimates for all of Mexico, while the bottom panel for quintiles 1 and 2. Columns 1 to 3 use a Poisson fixed effects model; while columns 4 to 6, use a monotone transformation of the dependent variable, ln(p + x), with p the 90th percentile of x. Standard errors robust to heteroskedasticity and serial correlation within municipalities are reported below each estimate in parenthesis. Coefficients with ∗∗∗ are significant at the 1% level, ∗∗ only at the 5% level, and ∗ only at the 10% level.

40 Table 7: The differential effects of cocaine shortages on the INEGI homicide rate based on distance from U.S. entry points and historical PAN support.

Poisson model Dep. var. ln(p + x) PAN support threshold: 28% 20% 28% 20% (1) (2) (3) (4) Panel A: All Mexico. Seizures in Colombia × Proximity to the U.S. 0.009 0.012 0.010∗∗ 0.011∗∗ (0.011) (0.011) (0.004) (0.004) Seizures in Colombia × High PAN support 0.425∗∗∗ 0.374∗∗ 0.178∗∗ 0.134∗ (0.162) (0.166) (0.076) (0.072) Seizures in Colombia × Proximity to the U.S. × High PAN support 0.049∗∗ 0.041∗ 0.021∗∗ 0.015∗ (0.025) (0.023) (0.010) (0.009) Observations 85309 85309 97902 97902 Panel B: Quintiles 1 and 2. Seizures in Colombia × Proximity to the U.S. 0.020 0.030∗ 0.018∗ 0.021∗∗ (0.018) (0.018) (0.009) (0.010) Seizures in Colombia × High PAN support 0.458∗∗ 0.395∗ 0.234∗∗ 0.167 (0.192) (0.203) (0.114) (0.125) Seizures in Colombia × Proximity to the U.S. × High PAN support 0.071∗∗ 0.059 0.038∗∗ 0.026 (0.036) (0.037) (0.018) (0.020) Observations 42189 42189 47089 47089 Note.- The table presents estimates of the interaction between cocaine seizures in Colombia (measured at the monthly level in logs), proximity to U.S. entry points (measured in 100km), and historical

PAN support (a dummy defined using the threshold specified in each column) on violence in Mexico. The dependent variable is the INEGI homicide rate. All estimates include a full set of municipality and time fixed effects, as well as a differential cubic trend by distance from U.S. entry points. The top panel present estimates for all of Mexico, while the bottom panel for quintiles 1 and 2. Columns 1 to

2 use a Poisson fixed effects model; while columns 3 to 4, use a monotone transformation of the dependent variable, ln(p + x), with p the 90th percentile of x. Standard errors robust to heteroskedasticity and serial correlation within municipalities are reported below each estimate in parenthesis. Coefficients with ∗∗∗ are significant at the 1% level, ∗∗ only at the 5% level, and ∗ only at the 10% level.

41 Appendix (not for publication)

Appendix A: Details on the solution of the model

The rest of the model can still be fully solved as follows. Plugging the optimal choice of gc,i into the cartel’s objective function yields 1 − PsQs −C(Qs)+ ηhPQs + ∑ (1 − η)s hP ∑ Qs. (A1) c c c |N |2 i c i∈Ic i c∈N

s Therefore, the optimal choice of Qc ≥ 0 solves as follows: 1 Ps +C′(Qs) ≥ ηhP + ∑ (1 − η)s hP, (A2) c |N |2 i i∈Ic i

s achieving equality if Qc > 0. The convex cost, C, which satisfies the Inada conditions, was introduced so that it is possible for this equation to have a solution for more than one cartel. Otherwise, one cartel– the one present at the best locations– would buy all of the drugs and the others would simply prey on it. We do not think that this alternative situation is unrealistic, as many cartels are toll collectors and simply prey on others, while not involved in cocaine trafficking directly. In fact, even with the convex cost, it is possible for some cartels to specialize in preying on others while not trafficking at all. Here, Ps and P are taken as given by the cartel. The equilibrium prices, P(Qs),Ps(Qs), are the only prices that guarantee market clearing.

Appendix B: Proof of proposition 2

C s Let g (ai,Q ) be the maximum level of cooperation that can be sustained with a threat of reversion to s s static Nash. Here, we focus only on symmetric equilibria. Let A(Q )=(1 − η)siR(Q ) be a random variable describing vulnerable revenue in municipality i. The incentive compatibility constraint at this level is given by

∞ 1 s C s t t N s C s x s A(Q ) − g (ai,Q )+ E ∑ β (1 − ai) (g (Q ) − g (ai,Q )) ≥ max A(Q ) − x. (A3) x C s Ni "t=1 # x +(Ni − 1)g (ai,Q ) Θ E ∑∞ β t t N s C s Let (ai)= t=1 (1 − ai) (g (Q ) − g (ai,Q )) ≥ 0. At this point, it is not clear that this s amount is uniquely determined for each value of Q . Nonetheless, we demonstrate it below. The incentive compatibility constraint simply states that the gains from deviating to any other level of C s violence x are dominated by playing the cooperative strategy g (ai,Q ) and obtaining the differential continuation value Θ(ai) > 0. Solving for x, we obtain

C s s C s x = (Ni − 1)g (ai,Q )A(Q ) − (Ni − 1)g (ai,Q ) ≥ 0. (A4) q

42 Plugging in this value yields the incentive compatibility condition

1 s C s C s s − 1 A(Q )+ Θ(ai) ≥ Nig (ai,Q ) − 2 (Ni − 1)g (ai,Q )A(Q ). (A5) Ni q C s N s N s The right-hand side is decreasing for g (ai,Q ) ∈ [0,g (Q )], and has a minimum at g (Q ). This C s means that the above condition implies a lower bound for g (ai,Q ), or the smallest possible level of conﬂict that can be sustained with a reversion to static Nash upon deviation. C s The most cooperative equilibrium is thus given by the unique solution, g (ai,Q ) ≥ 0, to the functional equation

1 s C s C s s − 1 A(Q )+ Θ(ai) ≥ Nig (ai,Q ) − 2 (Ni − 1)g (ai,Q )A(Q ), (A6) Ni q C s which achieves equality if g (ai,Q ) > 0. Let Q(ai) be such that

(Ni − 1)A(Q(ai)) = NiΘ(ai). (A7)

s C s For Q ≥ Q(ai), the above condition holds as an inequality, so g (ai,Q )= 0 for large values of supply Qs as stated in the proposition. If A(Qs) is bounded, the above condition also holds as an C s inequality where g (ai,Q )= 0 when β(1 − ai) → 1. Thus, for sufficiently low discounting, there is always an equilibrium that exhibits no violence along the equilibrium path if revenue is bounded. If, on the other hand, revenue is unbounded, there is a sufficiently low Qs such that the above condition C s C s s does not hold for g (ai,Q )= 0, meaning that g (ai,Q ) > 0 for sufficiently low values of Q . These observations establish the first two parts of the proposition.

Before continuing, we claim that Θ(ai) is decreasing in ai. We start from β (1 − ai) Ni − 1 s C s Θ(ai)= E[A(Q )] − E[g (ai,Q )] . (A8) 1 − β(1 − a ) N2 i i s For Q < Q(ai), 2 s (Ni − 1)A(Q ) − NiΘ(ai) gC(a ,Qs)= . (A9) i N p i p ! Plugging this into the above expression yields

1 − β(1 − a ) i N2 + N Θ(a )= 2 (N − 1)N E A(Qs) . (A10) β(1 − a ) i i i i i i p p hp i This expression implies that Θ(ai) is unique (hence, the uniqueness of the solution) and also that it is decreasing in ai as desired. The above claim, together with equation A7, also implies that Q(ai) c s is increasing in ai, as mentioned in the ﬁrst item of the proposition. Using the formula for g (ai,Q ) c derived above, this also implies that g is increasing in ai as mentioned in the proposition.

43 Now, we focus on the role of Qs:

C s s ∂g (a ,Q ) (Ni − 1)A(Q ) − NiΘ(ai) N − 1 i = i A′s) < 0. (A11) ∂Qs N A Qs p i p !s ( )

s s The inequality follows from the observation that for Q < Q(ai) we have (Ni − 1)A(Q ) > NiΘ(ai). Θ s In the above derivation, it is key to notice that (ai) does not depend onp the current realizationp of Q , because of the independence assumption on the draws. This shows that violence increases when supply is tighter in this equilibrium as well. Thus, informal arrangements are not enough to eliminate the impact of supply shortages on violence when there is sufﬁcient discounting and supply is tight enough. Moreover, we get 2 C s ∂ g (ai,Q ) s < 0, (A12) ∂Q ∂ai because Θ(ai) is decreasing in ai. This proves the item in the proposition regarding the cross partial derivative.

Appendix C: Time series properties of the high frequency variation exploited in the paper.

In this appendix we document the key time series properties of the INEGI homicides rate and seizures in Colombia. We focus on the detrended series obtained after removing a cubic polynomial on time and year dummies. First, we focus on the seizures series. The detrended series is presented in Figure 4 in the main text. Figure A1 presents a correlogram of the series. We plot the OLS estimate of the j-th lag on the contemporary level for j = 1,2,...,15 and its 95% confidence interval. As can be seen, there is no evidence of any type of serial correlation or autocorrelation patterns in the series. Thus, we can treat the high frequency variation in seizures as independently distributed over time, as in the model. We also conducted several unit root tests (Dickey-Fuller, Phillips-Perron and a GLS version of Dickey- Fuller) and were able to reject the non-stationarity of the series in all of them at the 1% confidence level. Finally, we focus on the high frequency variation in homicides. We do this exercise for the INEGI homicide rate, which is our preferred measure. The detrended series is presented in Figure 4 in the main text. Figure A2 presents a correlogram of the structural error in equation 3. We plot the OLS estimate of the j-th lag on the contemporary level for j = 1,2,...,15 and its 95% confidence interval. As can be seen, there is no evidence of any type of serial correlation or autocorrelation patterns in the series. Thus, we can treat the high frequency variation in homicides as independently distributed over time, as in all of our estimates. Moreover, we also conducted several unit root tests (Dickey-Fuller, Phillips-Perron and a GLS version of Dickey-Fuller) and were able to reject the non-stationarity of

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