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International Journal of Drug Policy 25 (2014) 226–234

Contents lists available at ScienceDirect

International Journal of Drug Policy

j ourna l h omepa ge: www.elsev ier .com/ locate /drugpo

esearch methods

system dynamics approach to the study of Colombian cocaultivation and the counter-intuitive consequence of law enforcement

ebastian Jaéna,∗, Isaac Dynerb

Departamento de Ingeniería Industrial, Universidad de Antioquia, Colombia, Calle 67 # 53-108, Office 21-407, Medellin, ColombiaUniversidad Jorge Tadeo Lozano and Universidad Nacional de Colombia, AA 1027 Medellin, Colombia

r t i c l e i n f o

rticle history:eceived 24 August 2012eceived in revised form3 December 2013ccepted 15 January 2014

eywords:ystem dynamics

a b s t r a c t

A large-scale expansion of the Colombian coca cultivation is one of the most revealing signs of a structuralchange in the illegal cocaine market in the Andean region. From being a modest and domestic production,in the space of five years Colombian coca cultivation supplied a competitive market, capable of substitut-ing almost completely the foreign sources of supply. The purpose of this work is to explore the role andpotential of system dynamics (SD) as a modeling methodology to better understand the consequencesof drug policy. As a case study, this work tests the hypothesis that the outbreak of Colombian coca culti-vations is a consequence of the take down of large cartels, leading to the surge of small drug-trafficking

oca cropolombia

llegal monopoliesounter-intuitive behavior in illegalarkets

aw enforcement

firms called “cartelitos.” Using an SD model, and elements from the economic theory of the criminalfirm, our work shows how the formation of these small firms might significantly contribute to the con-figuring of a more competitive domestic coca industry (and hence to a more efficient crime industry).We conclude that SD seems an appropriate dynamic modeling-based approach to address policy issuesregarding drug markets. The methodology takes into account the dynamic nature of drug markets andtheir multi-dimensional responses to policy interventions.

ntroduction

Illegal drug markets appear to be different than legal marketsn a number of dimensions related to their complexity, dynamics,nd response to policy interventions (Reuter, 2001). This suggestshe need for methodologies that take into account these markets’haracteristics and provide new opportunities for policy analysisnd design. This work explores the role and potential of systemynamics (SD) (Forrester, 1994) as an approach for addressingnd understanding the behavior of illegal markets. As an exam-le, the work introduces a case study that analyses the outbreak

f Colombian coca cultivations. The paper tests the suitability ofhe approach for addressing the causes of the problem, and sug-ests its future use when considering the consequences of lawnforcement.

∗ Corresponding author. Present address: Calle 67 # 53 108, Office 21 407,edellin, Colombia. Tel.: +57 4 219 55 79; fax: +57 4 219 55 79.

E-mail address: jjaen@udea.edu.co (S. Jaén).

955-3959/$ – see front matter © 2014 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.drugpo.2014.01.010

© 2014 Elsevier B.V. All rights reserved.

The case study

By the mid-1980s, cocaine was prevalent in most cities inthe United States (US), where the Colombian drug dealers werethe main suppliers (Chepesiuk, 2005). Although Colombian car-tels were the main producers of cocaine, they were not themain farmers of coca (Thoumi, 2009). They also had to smug-gle coca paste, obtained from Peruvian and Bolivian middlemen,conducting logistical operations that included clandestine run-ways and overnight flights (Chepesiuk, 2005; Krauthausen, 1998).In fact, by the middle of the 1980s Colombian coca crops wasonly 9% of the Andean cultivation, while the Peruvian and Boliv-ian cultivations amounted to 61% and 30% respectively (US StateDepartment, 2011, 2010). A different scenario was seen fifteenyears later, when the Colombian coca production peaked at76% of total Andean cultivation (Fig. 1), while Peru and Boliviawere by then supplying only the remainder (UNODC, 2010,2011).

This work tests the SD methodology for exploring thehypothesis that the expansion of coca cultivations in Colombia,in 1995, is related more to the take-down of the mainColombian drug cartels (Medellín and Cali), than to the tra-

ditional explanations for such expansions. Although this paperdoes not discard traditional explanations, it does challengethe effectiveness of the Peruvian Air Bridge Denial Program(ABDP).

S. Jaén, I. Dyner / International Journal of Drug Policy 25 (2014) 226–234 227

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Fig. 1. Evolution of coca cuource: United Nations (UNODC, 2010) and Rocha (1997).

ackground

The history of law enforcement operations against the mainolombian cartels begins after their expansion during the 1980snd 1990s (Levitt & Rubio, 2000). The Government reacted by get-ing support from the US, focusing its efforts mainly on the Medellínartel (Thoumi, 2001). This American cooperation was a preambleo “Plan Colombia” (1999–2005), which consisted of a compre-ensive strategy whose main component was to strengthen theolombian armed forces and national police (DNP, 2006). After allhe coordinated efforts against the Medellín cartel, the Cali cartelecame the largest single player in the cocaine industry, attractinghe attention of Colombian law enforcement (Chepesiuk, 2005). Itsefeat left a hole in the Colombian drug scene, where a multitudef trafficking organizations were in the contest to become primaryuppliers (Mallory, 2007). This led to the formation of an estimated60–360 of the so-called “cartelitos” or baby cartels (Garzon, 2008;rossman, 2006; ICG, 2005; Mallory, 2007). These small firms werearder to penetrate, became more elusive, and collectively were

ust as successful in exporting cocaine as the large cartels had beenCorcoran, 2007; ICG, 2005).

he Peruvian eradication policies

Parallel to events in Colombia, Peruvian coca cultivationecreased by 27% between 1996 and 1997. Like Peru, Bolivialso registered substantial declines in coca cultivation during theate 1990s (Bagley, 2011). Peruvian Government documents sug-est that much of the success of the US-backed coca eradicationnd alternative-development programs in Peru and Bolivia in theate 1990s is attributable to the disruption of the “air bridge,”

hich allowed the transport of coca paste from these two Andean

ountries into Colombia (Bagley, 2011; Thoumi, 2003). The reducedvailability of Peruvian and Bolivian coca paste explains a rapidxpansion of coca cultivation into Colombia (Bagley, 2011). Thisheory has become one of the most accepted explanations for

ions in the Andean region.

the migration of coca production. Several authors (Fukumi, 2008;Huskisson, 2005) had repeated what the early reports by Crane,Rivolo, and Comfort (1997) and Crane (1999) had found.

However, as Navarrete-Frias and Thoumi (2005) point out, thisexplanation has its problems because even though the ABDP thatstarted during 1990 was intensified over four years, showing resultsin terms of the number of neutralized airplanes, coca prices inthe Upper Huallaga (Peru) remained high and relatively stableand did not fall until late 1995. Although the decline in Peruvianand Bolivian cultivations during 1996–2000 coincided with a fewairplane neutralizations, which provides some evidence for us toassume that these captures represented a mere fraction of the cocapaste trade between Peru and Colombia that was transported byplane. The estimated number of clandestine flights between thosecountries had been 20 per month. The effectiveness in terms ofplane captures thus represents little more than 10% effectivenessduring the best year (Thoumi, 2003).

Ronken, Ledebur, and Kruse (1999) came close to estimatesby Thoumi (2003), indicating that the ABDP had only 12%success—capturing one in eight of suspicious airplanes. Success ofthe program was claimed on the basis that there was a 47% reduc-tion in the number of clandestine flights, assumed to be the resultof a deterrence effect (Soberón, 1997). The authors also remarkthat there is no consensus about the number of intercepted air-planes. In 1995, the DEA (2003) confirmed the interception of20 airplanes, while the National Narcotics Intelligence ConsumersCommittee (NNICC) declared a total of 39 (NNICC, 1996), but Peru-vian authorities reported captures of as many as 70 airplanes in1992, 67 in 1993, 36 in 1994, and, up to August of 1995, 21planes (Soberón, 1997). Likewise, Rumrrill (1998) remarks thateven though the ABDP affected a percentage of the transit ofcoca paste from Peru to Colombia, fluvial and terrestrial routes

should not be underestimated. They suggest that the market rapidlyadapted by incorporating new fluvial and terrestrial corridors thatproved to be useful during the 1980–1983 period. The shift towardfluvial routes had begun in 1993, the most successful year in terms

228 S. Jaén, I. Dyner / International Journal o

Table 1Period comparison of law enforcement rates, 1990–1995, and 1996–2000.

Colombian growth rates per year

1990–1995 1996–2000

Law enforcement budget 9% 6%Soldiers and policemen 6% 1%Eradicated coca hectares 166% 29%

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Destroyed laboratories 4% 19%Captured drug dealers 6% 50%

f airplane captures, and by 1995–1996 they were fully operational.y 1998, the Peruvian and American authorities acknowledged thathe terrestrial and fluvial routes had become the preferred smug-ling routes (Ronken et al., 1999). In 2005, a report to congressionalequesters acknowledged that the ABDP in Colombia had imple-ented new safeguards, but their effect on drug trafficking was

ot clear (GAO, 2005).The UNODC (2011) shows the number of coca bush hectares

radicated during 1995 were 25,402 in Colombia, 5493 in Bolivia,nd 7512 in Peru. Those efforts did indeed achieve an increase inradications with respect to previous years. However, those valueset us conclude that even when the increases in eradication wereigh, there was only a 10% decrease in total production in Bolivia,nd a 6% decrease in Peru (UNODC, 2011)—just enough to fuel aesistance against those policies by coca farmers from indigenousommunities in Peru and Bolivia (Navarrete-Frias & Thoumi, 2005;CG, 2005). Meanwhile in Colombia, eradications destroyed 33% ofts production. What made the Peruvian increase in eradications soisible was the fact that from 240 hectares eradicated in 1994, theyeached 7512 hectares in 1995 (UNODC, 2011). The area of erad-cated cultivations in Peru was not more than eighteen thousandectares in any one year during the whole 1994–2004 decade. Theeruvian authorities could explain the drop in cultivations if theestroyed hectares per year were, on average, larger than 10,000,ut the efforts per year did not seem to surpass an average of 6700ectares (UNODC, 2011). This revision suggests the most impor-ant factor in the decrease in Peruvian coca cultivation after 1995as that Colombian traffickers no longer sought coca paste from

eru. The reason for this was the destruction of the big cartels andhe emergence of a large number of small groups of traffickers forhom it was not attractive to buy large quantities of drugs in Peru

Navarrete-Frias & Thoumi, 2005).

he Colombian law enforcement role

In Colombia, in almost every variable related to the ‘war’, theres evidence of constant increases during the last two decades. Theaw enforcement budget grew on average 7.6% per year during990–2000 (Villamizar & Espejo, 2004), while the armed forces andanpower grew 5% per year during 1990–2003 (BICC, 2010). The

radicated coca bush hectares increased on average 104% per yearrom 1990 until 2000, while the cumulative number of destroyedlandestine laboratories increased by 23% over the whole period. As

result of all combined efforts, the number of drug dealers capturednd shot down increased by 41% per year (DNE, 2004) (Table 1).ven though the eradication policy was aggressive, its efforts couldot counterbalance the expansion of coca farming. In fact, the ini-ial efforts of law enforcement just led to a greater increase in theumber and sizes of coca-bush crops spread across the Colombian

andscape, until eventually the cumulative experience and effortsf eradication started to pay off. Table 1 shows a comparison of

he law enforcement performance and budget during the periodoncerned. The ABDP seems to have accelerated an already exist-ng migration phenomenon but does not entirely account for the

igration of coca crops to Colombia (Ronken et al., 1999).

f Drug Policy 25 (2014) 226–234

Method

This paper uses a system dynamics model in order to verify thefeasibility of the hypothesis described above. Both the modelingtechnique and the causal relationships that support the theoreticalframework of this research came from a careful review of the litera-ture to be discussed below. The model simulates the scenario whereColombian law enforcement focuses its action on cocaine produc-tion and the trade of large firms (big cartels), within a concentratedcriminal industry. In this context, the model is capable of explaininghow the market reacted by decreasing both firm size and demandfor foreign coca, as well as increasing competition among illegalfirms. Simulation reproduces the observed data, suggesting that theproposed dynamic hypothesis might be an alternative explanationof the coca outbreak in Colombia, and further research is necessaryto verify such possibility. Moreover, these findings provide a basisfor questioning the role of law enforcement efforts when interven-ing in an illegal system, and what the appropriate kinds of tools arefor supporting such decisions.

SD is a computer-aided approach to policy analysis and designthat might be applied to problems arising in complex social, man-agerial, economic, or ecological systems, at the strategic level. Theapproach is appropriate for a dynamic system that is characterizedby interdependence, mutual interaction, information feedback, andcircular causality (Randers, 1980). In this way, the input of param-eters and data is directed in a different way than econometrics,as relatively few variables are represented exogenously (Randers,1980). The method enables concentration on the required levelof interest without being overwhelmed by lower-level details(Sterman, 2000). It focuses on the essential determinants of thesystem’s behavior; transparency and structural validity are morevalued than the precise and quantitative representation of empir-ical observations. As a methodology for system modeling, systemdynamics also faces some drawbacks that should be considered.Given the context of interdisciplinary societal problems, it is notalways possible to determine exactly when a conceptual or empir-ical model contains enough aspects captured in such a way that themodel can be used as an adequate representation of reality. Evenwhen the construction of a model of a societal problem is carriedout with as much knowledge, methodological support, and humaneffort as is available, such models will still contain a large amountof uncertainty (Randers, 1980). However, system dynamics is alsodescribed as a tool for overcoming the limitations of mental models,and for structuring relationships among variables. It is a methodol-ogy for problem analysis and alternative solutions in a systematicmanner (Sterman, 2000).

Literature about dynamic modeling

As a response to the heroin epidemic in the US, several quantita-tive models have appeared since the 1970s, and they became morecommon after the spread of cocaine during the 1980s (Caulkins,2002). Those models were mainly focussed on the perspective ofa consumer country, and from an economic approach (Behrens,Caulkins, Tragler, Haunschmied, & Feichtinger, 1999; Gardiner &Shreckengost, 1987; Homer, 1993; Liccardo Pacula et al., 2009;Rydell, Caulkins, & Everingham, 1996; Yalc ın, 2004). They acknowl-edge the need for dynamic modeling to understand better the illegaldrug market behavior (Boyum & Reuter, 2005; Reuter, 2001), andperhaps most importantly, the likely occurrence of unintended con-sequences of drug policies (Reuter, 2009; Caulkins & Reuter, 2006;Caulkins & Tragler, 2004; Kleiman, 1993; Kleiman & Reuter, 1986).

Indeed, the manifest complexity of illegal drug markets, their unex-pected changes, and the unintended evolution, have encouragedsome scholars to migrate from static assumptions to dealing withnonlinearities, feedbacks, and the concept of systems (Caulkins,

S. Jaén, I. Dyner / International Journal o

2eo1cau(

c

Fig. 2. Basic dynamics of illegal firms.

001; Grass, Caulkins, Feichtinger, Tragler, & Behrens, 2008). How-ver, as a methodology, the system dynamics literature had alreadyffered its contributions (Gardiner & Shreckengost, 1987; Homer,993; Levin, Roberts, & Hirsch, 1975); though not focusing on aost-effectiveness analysis (Behrens & Tragler, 2001), all of themcted under the assumption that the conceived policies might be

seful as a result of their understanding of the systems involvedSchlenger, 1973).

The contribution of dynamic modeling and of the system con-ept was made even more visible by its value in explaining

Fig. 3. Illegal firms’ dynamics and

f Drug Policy 25 (2014) 226–234 229

counter-intuitive effects of some law enforcement policies withinillegal drug markets. For instance, Lee (1993) provides a theoreticalmodel that shows how the decriminalization of marihuana con-sumption might be followed by an unexpected decrease in demand.Scott and Jensen (2001) show how, under certain conditions, alaw enforcement policy can enhance the criminals’ “marketing”,increasing the number of addicts and consumption. Also, the USPresident’s Commission on Organized Crime (1986) describes therise of Mexican and Burmese heroin trafficking as a consequenceof a disruption of the French connection. There are more exam-ples that emerge from the theoretical analyses and dig into thisparticular issue of unintended consequences of law enforcementinterventions, using a cost-effectiveness perspective (Garoupa,2007; Poret, 2002; Poret & Téjédo, 2006). What they have in com-mon is the description of how system structure is misunderstood,triggering unintended causalities whose negative impact on thesystem only can become apparent when the policy has already beenimplemented. The review of this literature helped us to understandwhy the Colombian case might be analyzed from a systems per-spective, given the fact that illegal drug markets are systems thatrespond in either an intuitive or counter-intuitive way to the effectof policies. In other words, with the support of the literature review,this paper identifies SD as a methodology well suited to testing thehypothesis that the expansion of the Colombian coca crops might bean unintended consequence of an intervention in the illegal system.

System dynamics model

The model relies on two basic assumptions: in the illegal drugindustry there are large, medium, and small firms who attend to

law enforcement response.

230 S. Jaén, I. Dyner / International Journal of Drug Policy 25 (2014) 226–234

ltivati

dcoisscwsthin

Fig. 4. Simulation of the coca cu

emand, and the Andean coca hectares’ production is considered alosed system, which means no coca cultivation is imported fromther countries. The size of a firm depends on its production capac-ty for attending to its demand, and its competition for a markethare with other producers (Rubin, 1973). In the long run, one pos-ible scenario could be that in a given market, large and small firmso-exist (Papadonogas & Droucopoulos, 2004). Our model beginsith the description of the illegal-firm dynamics in a broad per-

pective. Illegal firms are constrained to three basic interactionshat determine their success, or failure. Cycle I (industry) represents

ow, as in any industry, competition among firms in illegal markets

s ruled by the scheme of supply and demand (Fig. 2). Cycle C (crimi-al competition) shows their second interaction, with violent rival

Fig. 5. Scenario 1: simulation without the law en

on trends in the Andean region.

competition, causing firms to exit from the industry (Gambetta,1993; De León-Beltrán & Salcedo-Albarán, 2007). Finally, the effectof their size is indicated by how much larger their market shareis, making them visible to law enforcement (cycle LE), increasingtheir probability of being captured and constituting a third causefor exiting from the industry. This basic representation argues thatan increase in the probability of being captured will decrease thenumber of firms in the industry. However, this assessment would betrue if all the firms were homogeneous in terms of size. Experiencetells that they vary greatly in size, which is why law enforcement

drives its offensive in the way it considers efficient, by dismantlinglarge firms rather than the small ones (Fiorentini, 1999). For thisreason, we need to present a more detailed cause-effect diagram

forcement intervention on the large firms.

S. Jaén, I. Dyner / International Journal of Drug Policy 25 (2014) 226–234 231

enfor

ft

biosaBrsvlot2tot

spfcbbtPmsic

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Fig. 6. Scenario 2: simulation of the law

or taking into account all of the differences among firm sizes andhe discretionary law-enforcement strategy toward large firms.

Cycle R1 in Fig. 3 depicts how the market is composed of a num-er of small firms that are competing for market share. The increase

n revenues and the low barriers to entry allow for the emergencef many small firms into the market (Fiorentini, 1999). Therefore,ome small firms make progress by becoming large because of theirccumulated drug processing and trafficking experience (De León-eltrán & Salcedo-Albarán, 2007). This diagram can also explain theelationship between firm sizes and coca paste demand. Initially,mall firms were importing the coca paste from Peru and Bolivia inery meager quantities (Thoumi, 2001), but with the emergence ofarge firms, the Colombian traffickers could afford massive importsf coca paste from those countries as their capacity for buying andransporting was expanding (López-Restrepo & Camacho-Guizado,003). The initially precarious smuggling process became an indus-rialized and almost safe procedure that resulted in the possibilityf scaling the cocaine deliveries from grams to kilos, and eventuallyons (Chepesiuk, 2005).

The small firms’ market share is squeezed during the expan-ion of the large firms’ market share. It causes them to become lessrofitable and then having to address the highly risky—and there-ore unaddressed—gaps in the market (Krauthausen, 1998). Thisontinued until the small firms could find a way to survive, eithery subsuming themselves within the large firms as outsourcers,y becoming highly specialized suppliers, or by paying ‘rent’ forhe right to operate under the cartel’s ‘protection’ (Fiorentini &eltzman, 1995). The role of law enforcement is related to the firm’sarket share (Poret, 2002; Poret & Téjédo, 2006). Large market

hare leads to large numbers of illegal transactions. Their growthncreases the firm’s visibility, increasing their probability of beingaptured (Poret, 2002; Poret & Téjédo, 2006).

Although the reasoning is valid for large and small firms alike,rms with a large market share (Cycle B2) are the primary objective

f law enforcement (Fiorentini, 1999; Fiorentini & Peltzman, 1995).y focusing on organizations involved in large-scale trading of ille-al goods, law enforcement expects to eliminate organizations thatre rather difficult to replace in the short run (Fiorentini, 1999;

cement intervention on the small firms.

Fiorentini & Peltzman, 1995). However, by following the strategyof focusing on large organizations, law enforcement provided relieffor those affected by the large firms’ concentration process and cre-ated positive externalities for the small market-participants andnewcomers. Finally, by tackling larger organizations, law enforce-ment was promoting a process of replacement that is natural tothe criminal career (Blumstein & Cohen, 1987; Venkatesh & Levitt,2000). At least in Colombia, there is evidence that because of theCali cartel’s demise, there was a sort of criminal career path orheritage of positions among the former members (Vice-Presidencyof Colombia, 2006). Buchanan (1973) asserts the “convenience” ofcriminal monopolies, precisely because of their output restriction,lack of competition, and high prices. Conscious of the critics andendorsements to Buchanan’s statement (Backhaus, 1979; Martens,1986; Sisks, 1982), the use of the methodology explores the con-sequences of taking down a concentrated market. It is importantto clarify that large firms were also supplied by local providers,and possibly even some of the small firms imported coca paste,as well. However, as is agreed in the literature, most of the largecartels were supplied by Peruvian traffickers (Duncan, 2006; López-Restrepo & Camacho-Guizado, 2003; Thoumi, 2003; Vargas, 2004).And small firms, given their nature, were mainly supplying thedomestic market. Therefore, the model treats as insignificant thedomestic demand for coca and the import of coca paste by smallfirms.

Model equations

The model is a stylized representation of the market dynamicsand is not intended to describe it in detail. Variables that describethe market (e.g. number of firms in each stage, production capac-ity, supply, and captures) are estimations of the actual data and inmost of the cases convey the average values in the industry. The

model of the described system has three main components. Thefirst component establishes the distinction between small and largefirms operating in the industry. Given the UN estimations of thedemand for cocaine (UNODC, 2011), and the description by Uribe

2 rnal of Drug Policy 25 (2014) 226–234

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a

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Table 2Measures of goodness of fit.

Colombia Peru and BoliviaActual vs. simulated Actual vs. simulated

Coeffecient ofdetermination, R2

0.94 0.95

Median absolutedeviation (MAD)

11,230 11,750

Mean absolutepercentage error(MAPE)

27 13

Mean absolutepercentage deviation

0.17 0.10

Mean square error(MSE)

216,450,165 206,344,962

this policy would decrease the large firm’s output and then its

32 S. Jaén, I. Dyner / International Jou

2000) of the cost and quantities required for processing cocaine,e made an assumption about the firms’ production capacities,hich allowed us to distinguish between them. Large firms have

he advantage of addressing the whole market, while small firmsompete for the demand that is unmet by the large firms, con-tituting their own niche. The arrival of small firms depends onhether the market is profitable or the probability of being cap-

ured is low. Large firms surge in the market as a consequence of themall firms’ criminal careers. However, to do so, they have to over-ome the internal competition and incarceration risk. We modelompetition among firms as a function of the number of firms thatan address the demand. If the firms’ supply surpasses demand,owering prices, some firms are forced to leave the industry as a

ay of regulating profits (Fiorentini, 1999; Fiorentini & Peltzman,995). Law enforcement action depends on the market share andhe length of time required for taking them down, which is longeror large firms (Fiorentini, 1999; Fiorentini & Peltzman, 1995). Theecond component explains the market share co-optation processnd the demand for coca paste, given the type of firm. The Peru-ian and Bolivian coca cultivations increase as a consequence of thearge firms’ cocaine demand; meanwhile, the small firms increaseomestic coca paste processing. Eradication rates in both coca mar-ets are exogenous parameters provided by UN reports (UNODC,010, 2011). Here we specify some of the basic equations, for aetter understanding of the model. Cocaine Demand in tons (D)

s modeled as a sigmoid, according to Homer (1993), where twoarameters are considered: maximum demand (D*) and a constant,

dD

dt= (D∗ − D)kD∗ (1)

Firms’ production capacity in tons (PC) is modeled as follows,ccording to the SD modeling.

dPC

dt= (D − PC)

T(2)

Average firms’ supply in tons (FS), considering seizures (s):

S = F · PC(1 − s) (3)

Probability of being captured, p, depends linearly on their mar-et share (MS) and a parameter l (Poret & Téjédo, 2006):

= MS

Fl (4)

The model assumes that competition (C), which results in thexit of firms, is the result of a saturated market. That is, whenhe actual number of firms (F) supplying the market surpasses theelation D/PC, the market has at least two firms competing, andventually one of the firms would defeat the other after an averageeriod of time T.

=

⎧⎪⎨⎪⎩

0 → F ≤ D

PC

(F − (D/PC))T

→ F >D

PC

(5)

ata, parameters, and initial conditions

For research on criminal markets the data may not be abun-ant. As Andreas (2004) and Reuter and Greenfield (2001) pointut, the estimations are often ‘guesstimates,’ at best, and are par-icularly susceptible to distortion and manipulation. This requires

heavy dose of skepticism of official data and a high sensitivity to,

nd tolerance for, the limitations of quantification (Andreas, 2004).n our model, demand triggers the firms’ production, so demand is

odeled as an epidemic process following the approach describedy Yalc ın (2004) and Homer (1993), with the data provided by

Theil index 0.085 0.059

United Nations report (UNODC, 2011). We are concious of the dif-ferent estimates for the amount of coca crop in Colombia reportedby the US Secretary of State as compared with the UN, however bothof their trends are similar, and do not disturb our main findings.Data from Maya’s (2000) study was used in the model, to establishthe amount of coca paste required for producing cocaine. Pricesin Colombia and the US are provided by United Nations report(UNODC, 2011) and by Reuter and Greenfield (2001). The num-ber of small firms in the industry depends on current estimations(Bagley, 2011; Gootenberg, 2011; Mallory, 2007; Vice-Presidencyof Colombia, 2006), and the number of formerly existing large firmsis provided by Krauthausen (1998).

Findings

The model was simulated over the period 1979–2010, witha set of parameter values giving the closest possible overall fitto the historical indicator data. The baseline simulation is vali-dated according to tests suggested by Forrester and Senge (1980)and Barlas (1989) (Fig. 4). These findings allow us to pondermore carefully the role of the law enforcement interventionas an alternative hypothesis for explaining the coca outbreak.The proposed structure of the system shows how the surge ofthe small firms increased competition, boosting the domesticcoca-base demand. Table 2 depicts several forecast error measure-ments.

The model fits the data relatively well. Our analysis suggeststhat the model captures the main structure of the market, eventhough there are some elements of coca hectare productivity anddemand that have changed over recent years. Thus, the modelis appropriate for simulating alternative scenarios, where ourdynamic hypothesis can be tested more carefuly. A first scenarioexplores a situation where law enforcemnet is not focused onlarge firms. Fig. 5 shows the results of a counterfactual simula-tion to test this alternative industry structure (e.g., keeping themarket concentrated in one or two cartels). The simulation indi-cates that under this scenario, coca cultivation would have stayedin Boliva and Peru as a consequence of their large productioncapacity.

A second scenario considers a counter-intuitive interventionwhere law enforcement focuses its initial intervention on smallfirms (before tackling large cartels) with the purpose of concen-trating even further this criminal industry. Fig. 6 depicts how

demand for domestic and foreign coca paste. Nevertheless, the largefirms’ high level of concentration would increase their visibility andprobability of being captured, prompting their demise in the longrun.

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S. Jaén, I. Dyner / International Jou

onclusions

This work shows how it is possible to explain the Colombianxpansion in coca cultivation, given the structure of competi-ion among firms and the role of law enforcement. Use of theD approach facilitates the combination of elements dispersedcross the literature, in order to simulate some of the main marketlements. As a result, the findings show how the role of law enforce-ent might impede the formerly high degree of concentration

n the illegal industry, thereby boosting competition among rivalrms, and explaining unintended consequences of law enforce-ent. The paper also explores the potential of the SD approach for

ddressing complex systems. In providing models capable of repro-ucing the observed data, the methodology indicates its potentialor deeper analysis of the studied problem. It also serves as a com-utationally based aid for guiding thinking and policy design.

The Colombian case, modeled here, illustrates an example thats insightful for the design of contemporary drug policy together

ith the support of the SD approach. It shows how law enforcementould determine the level of competition in the industry with allts varied consequences. It calls for greater care in analyzing whathe rationale of the discretionary power of law enforcement shoulde. Regarding the war on drugs in Latin America, these remarks arespecially relevant when further direct confrontations with largeriminal organizations seem likely in the coming decade (US Stateepartment, 2012). Maybe Buchanan’s theory is a useful point of

eference for examining the phenomenon from a different perspec-ive. The consequences of dismantling large organizations mightot have the same magnitude and intensity as in Colombia, buthey would certainly be undesired by any other country.

cknowledgments

This work was supported by Colciencias and the Universidadacional de Colombia doctoral fellowships. The authors would also

ike to thank Dr. Nuno Garoupa, Dr. Robert Evan Ellis, Dr. Bethanyarman and Dr. Paul Ellis for their insightful feedback in editing

his manuscript. The authors would also like to thank Guillermoestrepo-Gonzalez for his support.

onflict of interest

The authors declare no conflict of interest.

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