To b e or not to b e a drug trafficke
r: Mo deling criminal o cc upational
choice s
Viridiana Rios
Octob er 11, 2009
Abstract Violent de aths , kidnapping and extortion
have spiked in Mexico’s b order towns s inc e
2004. Using a forma l mo de l and c ase studies from Mexico, I argue that such phe nom
ena are partially e xplaine d by changes in the comp osition of ille gal lab or marke ts .
Government p e rm issive ne ss fos tered territorial wars b etwee n Me xic an drug c arte ls.
To sustain such inte r-cartel fights, drug leaders promoted the rec ruitment of outs ide rs into
their forc es; as a re sult, an illegal lab or m arke t –s o far close d to non-blo o d-related
individuals– op e ne d and interacte d with legal lab or market inc entives . The outcome
was the e me rge nc e of a new ge ne ration of drug de alers that (a) dis dain old m afia
laws, (b) are more violent and (c) are also more prone to take part of othe r form s of
“entrepre ne urial” illegal o c cupations such as kidnapping and extortion. Re cent change s
in the sc op e, leve ls and forms of violence in Me xic o c an b e unde rs to o d by analyz ing
who is b e coming a drug trafficker and why.
1
1“Let’s
meet in the Mexican si de. If Harvard has given us the honor to come to hel l,
the city wil l remain calmed”
1 Intro duction
Drug traffic violenc e has recently spike d in Mexico. With over 5,880 homic ides in 2009, M
exico is arguably the mos t dangerous and violent c ountry in Latin America (Fernande z Me
nendez and Salazar 2008), making countries s uch as Nicaragua and Colombia lo ok p eaceful,
a laughable assertion only a f ew years ago (CIDAC 2009). Indeed, no one then would have
predicted that the numb er of drug-relate d casualties in M exic o would double the numb e r
oamong c oalition tro op causalities in I raq (El Universal, 2009) and es calate to a p oint where
US b order towns and state s would b e calling for f ederal tro ops to protec t their citizens.
As Figure 1 s hows (CNDH 2008), drug- re lated deaths through 2002 we re pretty c onstant at
around 1,200 cas ualties p er year. In only one year, from 2004 to 2005, violent de aths
increased 36% from 1,304 to 1,776. Grow th rate s remained steep until 2007 w hen anothe r
increase in viole nce to ok plac e. This time violent de aths almos t doubled. Rep orted numb e
r of deaths may b e downward biased given that most of the assassinations are not rep orted to
the authorities. Journalistic accounts (Guerrero 2009a), based on a scan of all the events that
had b een covered by media and lo cal new spap ers , indeed show significantly higher numb
er of deaths . Reforma, one of the most re sp ected newspap ers in Mexico, argues that
violence doubled again from 2007 to 2008. Some states, like Chihuahua, rep orted up to ten
times more violent crimes in 2008 than 2007. The homicide rate in 2009 is exp ected to b e
larger than ever.
(Figure 1 ab out here)
Although the M exican government pro claims that most de aths are b orne by traffickers, we
know that government authorities are also increasingly targeted (Freeman 2006, CNDH 2009).
In 2008, 12% of the victims of drug-related violence were p olic eman and 2% came from the M
exican military. In s tates like T ijuana, at least 100 p olicemen die on duty e very year (G uerre
ro 2009a). To put this in p ersp e ctive, in the entire United States 133 p olice officers were
killed in the line of duty in 2008. Police chief s in b order cities are killed systematically. I n
some plac es such as Novalato, Sinaloa, nob o dy wants to b e p olice chief anymore –actually,
the p osition is vacant. In other plac es, s uch as Ase nci´on, p olic e chiefs ran away as p
olitical refuges (Cabre ra
1Unexp
ec ted te xt me ss age rece ived in Mc Allen, Texas. Author was b eing invite d, along with Alfredo
Corchado journalist of the Dallas Morning Ne ws, to have a p ersonal intervie w with a s ecre t inform ant of the
Golf cartel in Reynos a, Tamaulipas.
2
2009, Cano 2008, Fern´ande z Men´endez and Salazar Slack 2009). High-profile p olitic ians mayors , p olic e executives, attorney generals - are also prime targets. Even the head of the s
tate have received serious murder threats, an action that s ome decades ago would have b e
en thought imp ossible.
The brutality of the violence has also increased, mainly in the f orm of execution- style murders.
Among all of the homicides related to drug traffic, more than one in te n had signs of torture,
their b o dies of te n riddled with mes sages to other cartels or p otential vic tims and lef t in the
streets. Furthermore , old mafia rules have b egan to b e violate d. Until recently, carte ls were
known for their re sp ect towards the family memb e rs of their leaders (Navarro, 2009).
Daughters, sons and wive s were normally left out of the battle s unless the y we re dire ctly
involved in the organization. Now, c omplete families have b een killed, rap ed and tortured with
unprecedented levels of cruelty and violence.
Othe r forms of c rime , such as kidnapping and extortion have also s piked (Zep e da Leucona
2008, Ortega 2008). Busine sses lo cate d at b order towns have b ecome easy prey for
extortioners who ask for monthly fees of up to 5,000 USD in e xchange f or “protection” to avoid
b eing kidnapp ed or assassinated (Garza 2009). As a re sult a large numb er of M exican
business es, particularly res taurants, have moved into Ame ric a and tourism has plummeted.
Newspap er editors , j ournalis ts and managers have also migrate d into the US lo oking f or
the protec tion and sec urity that only the US can offer (Sierra 2009, Ram´irez 2009).
The causes b ehind this change in level, sc op e and forms of violence remain debatable.
Several e xplanations have b een prop ose d to e xplain this increas e in violence (Rios and
Sab et 2009, Guerrero 2009a) but no convinc ing theory has b een se t forward to understand b
oth changes in levels and the scop e/forms of viole nce.
This pap er contributes to the lite rature by e lucidating a phenomenon that has caus ed not
only increas es in levels but also in the sc op e and typ e of violence: the emergence of a new
typ e of drug trafficker. I argue that inter-c artel territorial wars c reated a necess ity to recruit
outs iders into drug c artel force s. As a result, the illegal-drugs lab or market, which is normally
closed to non- family-related individuals, op ened and interacted with the incentive s ge nerated
by le gal lab or markets. The outcome was the emergence of a new generation of drug dealers
that (a) neglect old mafia laws, (b) are more violent and (c) are more prone to diversify their
criminal p ortfolios by taking part in other illegal o ccupations such as kidnapping and extortion.
In s hort, inc re ase s in the levels/scop e/form of violence can b e partially explained by
changes in the typ e of individual who dec ides to b ecome a drug trafficker. This pap er is the
first attempt to formally comprehend criminal versus legal o ccupational choices in Me xic o.
I rely on formal mo deling as my main to ol. By making us e of two main streams of lab or
economics literature: (a) the classic approach of B ecke r (1968) where individuals face single
3
criminal vs . legitimate market wages and (b) the Roy (1951) mo del p ersp e ctive of diffe rent
returns to skills in the c riminal vs. legitimate lab or market sec tors, I mo del career decisions
made by M exic an criminals. The mo de l she ds light on the imp ortant and s eve rely
understudied relationship b etween law enforcement p olicies, formal lab or markets and c rime
rates. In particular, it shows that (a) wage structure , (b) income inequality, (c ) state capacity
and (d) individual’s levels of risk aversion have played a decisive role in sorting individuals into
criminal activities . Those with high e ntrepreneur s kills and high tastes for viole nce are the
ones who have rec ently j oined the cartel force s. The result has b een an change in the profile
of organized crime. New drug traffickers have inc re ase d general le vels of violenc e, and by p
erforming other forms of c riminal activitie s, have also inc re ase d rates of kidnappings and e
xtortion.
The pap er is organiz ed as follows. In the firs t s ection, I pres ent an account of re cent
increas es in levels/scop e/forms of violence in Me xic o and an account on how changes in (a)
co caine de mand, (b) law enf orcement, and (c) lab or markets inc entives have interacted to
generate the most violent p erio d in Me xic o’s rece nt history. In this sec tion, I pres ent the
reasons why a new generation of drug traffickers have emerged and the short te rm
consequences of this phenomena. A s econd section develops a theoretical mo del to
understand why this new gene ration of drug traffickers is diffe re nt from the old one. The mo
del shows how changes in illegal/le gal lab or market ince ntives have caused change s in o
ccupational sorting, promoting e ndogenous sele ction of more viole nt p eople into the drug
industry. Each of my results is linked to the e mpirical evidence presented in the first se ction.
Finally, I conclude by summarizing my main results and linking them with p olicy re comme
ndations . In an app endix, I pres ent particular p oints where I would like to get f eedback and
summarize some mathematical concerns.
2 A new and increased drug violence
Mexico has long b ee n a player in international drug trafficking. I ts two main drug c artels –
known as Juarez and G olf– are fairly we ll established and have b een running very profitable
busines ses f or decades. I ts pro duc ts –mainly co caine , marihuana and opium– supply ab
out 80% of the demand of illicit drugs in the US, and the US is by far the largest ille gal drug de
mander of the world.
Ye t in recent years M exico has exp erienced puzzling changes in its levels, f orms and typ es
of drug related violence . Not only have levels of violenc e jump e d (i.e. numb e r of fatalities)
but even more puzz ling, violenc e has b e come more cruel and savage than eve r. Furthe r,
forms of organized crime such as kidnappings and extortion have s piked.
Change s in le vels of violence can b e understo o d by analyzing change s drug demand, law e
nforcement and s ecurity p olicies . First, as demand for co caine in the US has shrunk, Me
xican drug carte ls have fac ed stronge r ince ntives to control the ir territories and invade othe
rs ’. Cartels
4
have thus engaged in blo o dy inter- cartel fights to c ontrol what is le ft f rom an increasingly f
eeble market. Sec ond, with demo cratization and the consequential de centralization of the Me
xican state , M exico’s fe deral government has b ecome less able to enforce control over drug
cartels. As a result, inter-cartel territorial fights have emerged. Finally, violence has also
increased due to changes in Mexico’s se curity p olicies. Rece ntly, M exico has pursued a
more active p olicy to reduce drug traffic. T he s o called ”drug war” has resulted in increas ed
rates of seiz ure s and in the capture of several high-profile drug trafficke rs w hich in turn, has
increased intra- cartel instability.
Understanding increases in the forms and scop e of violence requires a different
explanation. Such changes can only b e understo o d by as sess ing who is b ecoming a drug
trafficker and why the profile of thes e individuals is different from the previous generation.
An argume nt to understand changes in drug-relate d of violence is develop ed in this se
ction.
2Change
s in co caine demand are ce rtainly one of the main susp ects to e xplain changes in
violence levels. There has b een a general de cline in co caine us e in the US over the last
twenty years. Almost 3 p ercent of Americans were co caine users in 1985; that numb e r is ab
out 0.5% currently (SAMHSA, annual), a highly s ignificant reduction. Among high scho olers,
co caine has halved sinc e the 1980s and 1990s. The general tendenc y of co caine
consumption is presented in Figure 2.
(Figure 2 ab out here)
The co caine b o om happ ene d during the 80’s. Back then, c o c aine was so cially acce pted
in high s tatus circles. Yet, at the b e ginning of the nineties c o caine consumption starte d to
drop. Asso ciation of co caine with HI V and the eme rgence of a new more health-orie nted c
ulture among high-income/high-s tatus individuals explains a big part of this de cline. The
market has s ince reduced, returning in just a decade to pre-b o om levels . According to
consumer surve ys , de mand for co caine has remained pretty much stable s ince 2002
(SAMSHA annual).
As demand fell, comp etition and violence among cartels have grown. Inter-carte ls wars have
emerged to c ontrol the fe w routes that remain largely profitable . T wo examples are C iudad
Ju´are z (E l Paso, Texas ) –the main p ort of entrance of co caine into Chicago– and Tijuana –
California’s drug provider. Both have b ecome incre asingly violent. B lo o dy wars have b een
fought b etween T ijuana/Ju´arez c artel and its common enemy the Sinaloa Carte l (G uerre ro
2009b).
Furthermore, the decrease in the de mand for co caine in the US has le d to a re alignment of
2Marijuana
us e has also fallen sinc e its p eak in the late 1970s, e sp ecially among high s cho ol youth, where the
re has b ee n a 25% dec rease in re gular use over the las t 8 ye ars (Johnston and O’Malle y, annual)
5
the co caine marke t in two more ways: (a) more co caine is directed toward E urop ean cons
umption, in particular Spain (Fern´andez Me n´endez and Salazar Slack 2009); and (b) a lo cal
Me xican market has e me rged (SSA 2002). The link b etwee n diminished demand and
violence is, again, profits. Fewer us ers in the US le ads to an e ven more comp etitive, tighter
market to kill over.
3With
a smaller US market, Mexican carte ls have lo oked to other p otentially profitable
markets. Though Europ e is not a market that Mexican cartels are particularly comfortable with
(due to geographic distance), Mexican c artels have b e gun business. Countries like Brazil and
Arge ntina have b e come substantial players in E urop e, to o, adding to violence since gangs
from Mexico are engaging in c onfrontations with carte ls from these countries. Pressure from
comp e tition has increas ed the leve l of viole nce within Mexico. As the s upply of co caine
from Mexico has increased in Europ e, co caine us e has surged, particularly in the United K
ingdom and Spain (Europ ean Monitoring Center on Drugs and Drug Addiction, 2007).
Change s in state c apacity and law enforce ment have also played a role in explain the spike
in viole nce. In particular, de mo cratization has re duced the centraliz ation of the M exican s
tate and its ability to enforc e informal pacts that we re kept b etween drug traffickers and gove
rnment officials during the nineties.
4Follow
ing the Mexican revolution, Mexico was ruled by a single hegemonic party -the I
nstitutional Revolution Party (P RI ) - for more than seventy years . During the PRI regime,
authorities agre ed to allow drug cartels to p erform the ir illegal activities as long as a strict co
de of conduct was resp e cted (Re sa Nestares 2001b). As Ricardo Monreal, the f ormer G ove
rnor of the state of Zacate cas and ex-PRI official describ ed, authoritie s used “extra- offic ial
mechanisms” to enforce a set of informal rules that every carte l had to follow (Guerrero, 2009).
Among the most imp ortant one was an stric t requirement of order and resp ec t for each cartel
territories. The size and b orders of territories we re delimited and granted by the PRI
The enforc ement of the se rules was p ossible b ecaus e of the s trict c ontrol that the
PRI-regime had over s tate and municipal governments, as we ll as other branche s of
government such as the judicial authorities and lo cal p olices . Corruption was well
institutionaliz ed and as such the pact
3Dem
and patterns p e rtaining to typ e of drug have als o affe cted the cartels. Extra-offic ial acc ounts show that
2005 was the first year that Mexico’s organiz ed c rime carte ls re ce ive d large r profits from marijuana than from
co c aine (Fern´ande z Me n´e ndez and Salaz ar Slack 2008, p. 25). This is a symptom of a reduc tion in ge ne ral
profits. Marijuana us ed to b e a se condary market for Mexicans b e cause it generates lower ave rage profits as it
is re quire d to com p ete (in pric e and quality) with lo cally-grown Ame ric an m arijuana (Rios and Sab et 2008).
4The othe r nine rules included (1) No dead p eople in the stree ts, (2) No drugs in the scho ols, (3) No me dia sc
andals, (4) Pe rio dic s eiz ure of illegal drugs and im prisonment of lower le vel trafficke rs , (5) Generation of e
conom ic re venue s for s mall, p o or communitie s, (6) No gangs, (7) No de als with other le vels/branche s of
gove rnme nt and/or bure auc rac y., (8) Mistake s are to b e punished with imprisonme nt, not death, (9) Re
venue s mus t re turn to Mexico in the form of inve stme nts .
6
remained a relatively s tabilizing force in the country (Resa Nes tares 2001b).
Demo crac y changed the picture. In 2000, Vice nte Fox a charismatic leader of right opp os
ition party (National Action Party, PAN), was elec te d pres ide nt in what many analysts b
elieve to b e the first truly demo cratic election in Mexican history. The arrival of Fox in p ower
brought several changes , among them a dramatic redefinition of the relationship b etwe en the
gove rnment and drug cartels . Mexico’s demo cratiz ation reduc ed government centralization,
weakening Fox’s ability to enforce the old pact (Patin 2007, Valle 2009). I ns tability was f
urther enhanced by a particularity of the M exican cartels : unlike Colombia, Mexican carte ls
we re and had always b ee n comp etitive and in opp os ition to each othe r. A lack of state
capacity to enforc e the old pact reduced the costs of engaging in territorial inter-c artel fights
(Freeman 2006).
In orde r to invade other te rritorie s, c artels neede d to increas e their f orces . B oth Sinaloa
and Golfo cartels recruited new, young memb ers to expand the ir p ower. In previous years,
drug traffickers were normally re cruite d from family/f rie ndship networks via recommendation.
The drug lab or market was relatively closed to outsiders as getting in re quired connec tions
and loyalty asses sments. As the environment changed, most of the ne w memb ers were
outsiders, “hire d” from w ithin the Me xican military force s.
Thes e new drug trafficke rs , known as “Ne gros” if affiliated with the Sinaloa cartel, and “Z
etas” if affiliated with the Golfo c artel, had imp ortant characteristics ; the y were more violent
than traditional traffickers, more prone towards diversif ying their criminal p ortf olios (p
erforming dif ferent illegal o ccupations s uch as kidnapping and e xtortion), and generally
neglected old-mafia law s and honor co des (Valle 2009, Jorge 2009). In general, they were
“more sophisticated and more savage (WOFA 2007).”
Their cruelty was much higher. Unlike traditional drug traffickers who conc entrate d the ir eff
orts only in transp orting illicit drugs, Zetas are real c riminal entre pre neurs. They kidnap,
extortion and run all kinds of ille gal busines s such as prostitution, human traffic , and even
illegal immigration. T hey als o us e strong intimidation te chnique s such as burning the dead b
o dies of their enemie s in fueled barrels . An FB I ass essme nt rep ort shows that new me mb
ers “are alle gedly more violent than their leaders and may b e b ehind much of the drug- re
lated turmoil o ccurring along the b order (WOFA 2007). The Negros have a p enchant for
assassinating p olice men with high-p owe re d as sault we ap ons, a practice that back in the
PRI-regime days was uncommon. They even invented the term “p olic e-killer” to ref er to a
high- as sault weap on that can pierce p olicemen bullet-pro of ’s ves ts .
The so cial characteristics of Zetas and Ne gros are also different from those of the traditional
traffickers. They tend to b e more urban, have higher levels of formal education and share the
tas te s of the Mexican middle classes . Even their music preferenc es are diff erent; they listen
to American rapp ers, not to the traditional Mexican “c orridos .”
7
(Figure 3 ab out here)
In Decemb e r of 2003 b oth c artels finally fought each other and the result was the blo o diest
inter-cartel war Mexico has eve r witnesse d. The epice nter was Nuevo Laredo. When the G
olfo carte l was weakene d by the arrest of its leader –Osiel Cardenas–, the Sinaloa cartel b e
gan a war to take control of the b order c ity of Nuevo Laredo. Furthermore, Golf o started a
fight against “chachos” and “texas“ two small lo cal gangs (C orchado 2009a). Nuevo Laredo is
a crucial p ort of entrance into the US: 40 p ercent of all M exican e xp orts cross into the US
via this small town. With just 350,000 inhabitants , Nuevo Laredo is the fas te st way to Dallas
coming from Mexico City. From there, drugs are distributed to New Orleands, Houston and
Chicago (Corchado 2009a). Just during 2005, there were more than 180 killings in Nuevo
Laredo, a city of 350,000 inhabitants, and national figures were much higher. Sho otouts on city
s treets b ecame common, some lasting as long as 30 minutes, prostitution, kidnappings and
extortion b ecame out of control (WOFA 2007). I n the words of Raul Cas so (2009), Attorney
Gene ral of Laredo, “it was Al C ap one typ e stuff.”
Violence was furthe r e nhanced by the arrival of Felip e Calder´on into office. The new pres
ident of Mexico, also f rom the PAN, to ok office in Dec emb er of 2006. By then, the problem
of drug trafficking was e xtremely severe. Violence b etween the two main Mexican cartels was
p eaking. The conflict was already generating a death toll of ab out 2,200 individuals p e r ye ar
in 2006, and Calder´on was committe d to eliminating the c artels. Drug trafficke rs controlled
several b order cities ; Zetas had control over most of the lo cal media in Laredo and in some
regions of Mexico –s uch as the mountains of Chihuahua, Michoac´an and Guerrero– the s tate
was de facto exp elled (Artz 2009). N et ec onomic loss es (mainly in the form of inversion
losses ) attributed to drug traffic had quadrupled from 2003 to 2007. It was e stimated that Me
xico lost ab out 11 billion dollars in inversions only in 2007 (Rios and Sab et 2009) (Figure 4).
(Figure 4 ab out here)
It did not take long until Felip e Calder´on realized that to increase the governability of his
country, he would have to reduce the influence of cartels. His justification was straightforward:
no other p olicy could b e efficie ntly implemente d w ithout first recovering official control ove r
the are as w here drug trafficking was op e nly taking place (Fe rnandez M enendez and
Salazar 2009, Corchado 2009).
Calder´on targeted his efforts into three main areas: (a) de creas ing the amount of drugs that
cross the b order, (b) capturing high- profile cartel leade rs , and (c) destroying illegal crop
cultivation. As Figure 5 s hows, there has b een a large increase in mone y and we ap ons
confiscation since 2006. The amount of dollars confiscated increased 14 times, and large weap
ons, fuel, and gre nade seizures rose seven- fold from 2006 to 2007.
8
The short-term outcome of such p olicie s was a further increase in violenc e. In particular, the
capture of drug lords sho ok up the internal structure of the cartels, resulting in more violence
within the cartels the mselves. Cartels dis integrated into several cells , generating larger
internal fights ove r the s uccess ion of the territories. Violence is evidence of the weakening of
the cartels, not - as several media accounts have p ortrayed- of the ir p ower (Guerrero 2009a,
Freeman 2008). Furthermore, the seizure of illegal drugs, the confiscation of money, weap ons,
go o ds and the eradication of illegal c rops, has led to a shrinking in the profitability of drug
traffic and an asso ciate d inc re ase in violence. Large confiscations lead to punishment in the
internal s tructure of the c artels. People in charge of the cargo are killed as well as all those
who were sus p ected to b e unfaithful to the organization (Gonz alez 2007).
(Figure 5 ab out here)
To summarize, levels of violence have increased as a result of inter-cartel fights promoted by
(a) a reduction in the demand of co caine inside the US, (b) a reduction in the c apacity of the
state to enf orce territorial b orders b etween carte ls, and more re cently (c) a fall in cartels ’
profits caused by larger seiz ures and confiscations. Furthe r, levels of violence have also
increased as a result on internal cartel destabilization caused by the capture of drug lords. But,
neither of the two theories ab ove can explain w hy violence also changed in scope and form.
Such changes are the result of the e mergence of a ne w gene ration of drug dealers. Se veral
ques tions emerge. Why are these drug traffickers different from the old ones ? Why are they
more viole nt? Who is b ec oming a drug trafficker and why? T he f ollowing se ction presents a
formal mo del to addre ss these questions. I show that answers are to b e found in wage
structure, inc ome inequality, s tate capac ity and individual’s levels of risk aversion
3 Who b e comes a drug trafficker?
In this s ection I pre sent a theoretical mo del to understand puzz ling change s that have trans
formed organiz ed crime violence in Mexico during the last years. By showing the incentives
that p eople follow to b ec ome a drug trafficker, and how those incentive s interact w ith the
legal lab or market, I argue that the recruitment of a new generation of drug traffickers brought
highly viole nt and entrepreneurial individuals into the criminal lab or markets. The combination
of changes in drug traffickers profiles and diminishe d s tate capacity is the c ause b ehind
changes in levels/scop e/form of violenc e in M exico.
3.1 Theore tical mo de l
Individuals allo c ate their time t in e ither i illegal activities (drug trafficking) or l legal activities.
Time used in illegal activities is denoted as ti; tldenotes time used at le gal activities .
Individuals
9
are endowe d with one unit of time such that
tl + t i = 1
There are two p erio ds: the PRI- regime Ppr
i–when a pac t was enforc ed b etween drug
carte ls and gove rnment– and the PAN
-regime Ppan–when b e cause of state weaknes
s and decentraliz ation, the pac t c ould no
longer b e e nforce d. Assume that during
Pthere were no entry costs for legal ac tivities
but illegal ac tivities remained closed to the
gene ral p opulation. Only those who b elonge
d to traditional carte l familie s could have t* ipr
i> 0. During P, cartels b egan to expand the ir
re cruitme nt mechanisms as pre paration for
territorial wars. Assume that during Ppanthere
are no entry costs f or either legal or illegal ac
itivities.pan
Returns to illegality I and legality L are given
by
*
wl*
wi
L = tl
I = ti
where
wl (1) el2 l~ N (0, s) el= f (ξ , ν , t )
wi (2) ei~ N (0, si2 i) ei= f (ξ , ν , t )
> 0, ∂ el < 0, ∂ el > 0, ∂ ei > 0, ∂ ei > 0, ∂∂ et i
+ el = m l
+ e= mi
∂ el
∂ν
∂t
∂ξ
∂ν
∂ξ
an > 0. Equations (1) and (2) can b e understo o d as describing earnings distributions
d comp osed by
l and mi) and a payment to non- obse rvable abilitie s (
e
i
i
i
i
and wcan take negative values . A very unable drug dealers may lo ose
a the mercha
baseline salary ( mduring transp ortation and would have to pay for it; a ve ry incomp etent e ntreprene
legal lab or market may end up with liabilities. If eor eare p ositive, individual has hi
ability than average and thus, receives a higher salary. Non-observable abilities are
function of tastes f or viole nce ν , entrepreneurial ability ξ and others t . Note that e
b oth increas ing in ξ and t , but only eis increas ing in ν .i
10
i
ib e
s2 i
the variance in individuals’ non- obse rvable abilitie s. A
> 0, p (1) = 1, and F
l
Let s2
i
. Studies of c riminal lab or markets and my own fie ld work (Levitt and Venkates h 1998,
C orchado 2009c) have shown that income differentials tend to b e higher in illegal
marke ts . Salaries at b oth the b ottom/top of the illegal inc ome distribution are much
lower/higher than legal income s.
l > 0 b e the corre lation b e
or e . Let ρξ
and e
Define ρ as the correlation b etwee n e ν
t
Net returns of ti
i
>
11
0
,
Assume that p
p
an
d ewith res p ect to entrepreneurial ability, ρ< 0 b e the correlation b e twee n e< 1 b e the
correlation b etween eland ewith resp e ct to tastes f or violenc e, and -1 < ρwith resp ec t
to other abilities.
It has b een empirically show n that entrepreneurial ability is highly rewarded in b oth legal
and illegal lab or markets (Fairlie 2002, Rios 2009, Fairlie and Wo o druff 2004). Succ
essful drug dealers p osses s unobse rved characteristics, such as low leve ls of risk
aversion and a preference f or autonomy, that are highly corre lated w ith e ntrepreneur
ability. Actually, among c riminals who b ec ome legal workers, the probability of b e
coming a succe ssful entreprene urs is much higher f or thos e that did their criminal
careers in the illegal drugs industry (Fairlie 2002). Furthermore, succ ess or failure among
the upp er-le vel drug deale rs and smugglers is partly de te rmine d by their business s
kills , i.e. marihuana dealers have proven to have highly s ophisticated strategies to
maximiz e his cliente le while minimizing his exp osure to arrest and comp etition (Adler
1985 and Sullivan 1989 as cited by Fairlie 2002). The existence of high returns to entre
pre neurial ability in contested in lab or economics , yet studies w ith credible instruments
for entre pre neurial ability have proven large effects of such ability in income (M cKenzie
and Wo o druff 2006)
Tastes for violence are rewarde d in illegal lab or marke ts but punished in legal lab or
markets. Violence is highly re warded in the drug industry. Ethnographic studies have s
howed that dealers that thrive in the drug industry are brave and savage (Corchado 2009c,
Sierra 2009, Rios 2009a). They are not afraid of dying or killing. Other very desirable p
ersonality traits such as dep e ndability and re sp onsibility are rewarded in le gal lab or
markets (He ckman 2003). Violence in the legal indus try is asso ciate d with impatience
and other non-p ositive characteristics.
are uncertain and conditional to whether an individual is (or not) c aptured
by the p olice. W ith probability p (t) the individual is captured and is force d to pay a fine F
(t) > 0. Note that time is assume d to b e proxy for the s ize of the crimes (i.e. each hour
that criminals sp end in c riminal activitie s yields a fixed numb er of s ame sized crimes)
> 0. The probability of b eing c aptured and the fine inc re ase as time devoted to illegal
activities inc re ase s. The probability of b eing capture d is a conve x function (Reuter
1993). B ecaus e of law enforcement diffic ultie s, if an individual is a full time criminal,
the probability of b eing captured can b e less than one .
Individuals’ utility func tion is given by U (w ) where w is total income and has two p otential
realizations. With probability p (ti) w = wu, where wui)) w = ws, where wsis total inc ome when
individual was capture d (criminal was unsuc cessf ul). With probability (1 - p (tis total income
whe n individual was not captured (criminal was s uccess ful).
Both p otential realizations of w can b e decomp osed as:
i)wl = (1 - t=
+ tiwi
i
w
ws
s - F (t )
wu
dws < 0. Thus, U (ws) > U (wu), U (ws) < U (wu
Follow ing convention, U(w ) > 0, U (w )
dwu
dti
dti
) and U(ws) < U (wu). Note also that give n that F> 0,>
Individuals maximiz ation problem will b e give n by:
maxti,tl p (ti)U
+ tiwi - F (ti)] + (1 - p (ti))U [ tlwl + tiwi
[tlwl
i
= 1 +ti
p i
i
i
l
(
t
l
i
maxti
s
] s. t. t= 0; t= 0; t
)(wl) + (t
i
i
i
i
l
i
i
3.2 Main r esults
In Ppr i
pan
p (ti)[U (wu
Which c an also b e state d
] (3) s. t. t= 0
as:
, equation (3) b ecome s trivial since general p opulation individuals can on
0. In P, individuals solve equation (3) yielding the follow ing FOC:
)
U [(1 - t
) - U (w )] - p (t ) (wu)F + (wi - wl)[E U (w )] = 0 (4)
U
E U (w ) = [(1 - p (ti))U (ws ) + p
(ti)(
U
(wu
)] c an b e conceptually understo o d as the exp ected change in utility whe n salary changes.
Recall that b ec ause utility is conc ave, salaries change at a diff erent rate if individual is
convicted than if not. Utility changes faster when the individual pays a fine.
a new lab or market is op en and new incentives are generate d. Now, inNote that in Ppan 12
* idividuals
i: if FOC >
c an cho os e a 0 = t= 1. I n particular, we can identify thre e p otential solutions for t*
0 t* i* i= 1, if FOC= 0 0 = t* i= 1 and if FOC < 0 t* i= 0. The key to solve the mo del is
the n identify the c onditions under w hich 0 = t= 1.
Prop osition 1: Indep endently of p enalties and conviction rates, a neces sary –but not
sufficient– condition f or an individual to b ecome criminal is that his exp e cte d salary as a
criminal is larger than his exp ec te d s alary in the legal lab or marke t. The first term of
equation (4) is always going to b e ne gative b ecause p (ti) > 0 and U (wu) - U (w) < 0. The se
cond term is also going to b e negative b ecause p (ti) > 0, U (wu) > 0 and F s> 0. We can also
know that E U (W ) > 0 b ec ause U (W ) > 0 and p (t) > 0. I n order to offset the negative values
of the first and second terms, we need wi> wl.i
This result is s imple but show s c onsis te ncy with re ality. Given that illegal markets yield
more uncertain res ults (including life-time prison or worse , extradition), individuals will only
consider illegality if e xp e cted salaries are much higher in such marke ts . Zetas’ and Negros’
wage s are much highe r than formal lab or markets (Rios 2009a). Their annual salaries are
approximately $28,000 which is cons ide rable higher than what they would b e paid in legal
markets given their normally low level of formal educ ation. A college-educ ated Mexican has
an average salary of $7,200; the top dec ile of c ollege-e ducated have s alaries of around
$43,000. Salaries are certainly considered when deciding to enroll as Z eta. In the words of one
of them: ”I rather living like a king for three years that as a b eggar my whole life (Corchado
2009)”
Ye t, higher illegal salaries do e s not nec essarily imply that some one will b ecome a drug traf
ficker. Further required conditions will b e des crib ed b e low.
Prop osition 2: The fraction of time sp ent in criminal activities 1. Is negative f unc tion of
income at the legal industry 2. Is p ositive function of income in the illegal industry 3.
Decreases as lab or markets b e come more unequal
and wl
> wl, then (ei - el) > (ml - mi
i
Reca
ll that
wi
are dete rmine d partially by sto chastic pro cesse s. Thus, from e quations (1) and (2) we c
an show that if w). The upp er- b ound fraction of time s p ent in c riminal activitie s will b e
given by:
) > (ml - mi
- e i)
l
13
P = P r [(e ) (5) = 1 - F(m- m
li
where
(ei
-8
- el
2 l)
s
~ N (0, + s2 i),
and
2
+ si
F(ml - mi) = 1v 2p
( ml - mi )
dP d( l - mi) > 0,
m
d( ml- | >
Furthermore, dP
mi )
Note that
exp[ -x2(s2
l2
d( ml- m)
dmii
| dP
|>
ds2
< 0,
|
) ] d x . (6)
d( ml- m)
dmli
> 0 and
dP d( s2
l + s2 i )
< 0.
dP
d
s2 l
|.
i
|
The exp ec te d inc re ase in time devoted to criminal
activitie s will b e larger w hen base line wages
change than whe n the disp ersion of wages
changes . As equation (6) show s, b oth miand ml
affect P quadratically, w hile ( + s2
i
s2 l
Even if wi > wl , to have a solution in the range 0 < t* < 1 we ne
i
ed
) affec ts it linearly.
We also e xp ect inequality in le gal lab or markets to
affect P less than inequality in ille gal markets b
ecause we know that s. In othe r words, p e ople w ill b
e more prone towards legality if illegal wages are gene
rally diminished than if illegal wages ’ distribution is
truncated.
The p olicy implications of this result are
straightforward. As I discuss ed in the last se ction, Fe
lip e Calder´on has fo cus his e fforts in capturing
high-profile c artel leaders. Capturing drug lords is p
ortrayed as more efficient b ec ause (a) it ge nerates
instability inside the c artel s tructure and (b) it sets an
e xample f or those w ho want to b ecome part of the
drug industry. My mo del predicts that (b) is mistaken.
Capturing drug leaders is e quivale nt to reducing the
variance of salaries inside the illegal markets by trunc
ating the upp er b ound of drug traffickers’ wage dis
tribution. This is a les s efficie nt deterrent than it
would b e to c apture individuals f rom all wage levels
inside the drug lab or marke t. M exico would do b ette
r in reducing the numb er of drug traffickers if they f o
cus in capturing a random selec tion of all p eople
involved in the busine ss, instead of jus t the heads of
the organization.
Prop osition 3: Even if the exp ected salary of the
individual in the illegal lab or market is higher than his
2
l
< s2 i 5
legal wages , he may not b ecome a c riminal if:
1. U(w) is sufficie ntly concave. 2. The probability of
conviction is sufficiently high. 3. The fine, given
conviction, is sufficie ntly high.
(wi - wl)[E U (W )] = p (ti)[U (wu) - U (ws)] - p (ti)U
14
5
Along this m o del we as sume than lab or markets c lear and
are p erfec tly comp etitive . If this were not the cas e, we would
have W determined not only by the dis tribution of individual’s
ability but by other fac tors such as se arch cos ts , barriers to
entry/e xit, and s o on.
(wu)F
E (W ) can also b e express ed (ws) + p (ti)(U (wu) - U (ws)). We know E U
U as U
(W ) will increase as the concavity of U (w ) increas es. A very concave U (w ) means
that as wealth increases, an e xtra unit of money gives marginally much less utility to
the individual. Intuitively, individuals would b ecome satiated f aster w ith the money
that they make. On the contrary, if U (w ) is le ss conc ave, individuals c an thought
to b e more “gree dy” –they satiate their utility at a slower pace.
= U (wu
i
(W ) dF
1 p(
ti )
6
1
5
dislike violence.
6Normally,
U (wu
u)
>0
U ( w) U (
wuu)
) > 0 dE U= -p (t)U “(w
t
c
a
n
b
e
s
h
o
w
n
t
h
a
t
:
d
E
U
Intuitively, when the probability of conviction or the fine inc re a
I
ec omes bigger (or les s negative). Note that if> -is true, inc re
capture is a more efficient deterrent for crime than increasing t
This re sult is simple but p owerful. I ncreas ing the c apacity o
riminals may b e more efficient than inc re asing the fines b ec
individuals b ecoming a criminal is le ss attractive when captur
threshold at which capture is a deterre nt de p ends on how mu
Greedy individuals will have much more tolerance to risk.
Empirically, this seems to b e the case. As Z etas normally sta
years as kings than always as b eggars. (Corchado 2009c )” T
the average life exp ectanc y of a drug trafficke r. Ac tually, s o
with their very first paycheck (Rios 2009a).
Prop osition 4: The distribution of ability into e ach o cc upation
endoge nous selection of o cc upations . In particular:
1. Higher ability e ntrepreneurs pre fer to work as drug traffi
higher tastes for violence prefer to work as drug trafficke rs
gal lab or market (a) are lower ability entrepreneurs or (b)
) would b e interprete d as a meas ure of ris k avers ion. Yet, I have som e
this inte rpretation unde r my s etting. See App endix for a more de tailed d
and wl
i* and wl
In a world where 0 > ti* > 1, and
given that b oth wi
mi
l
- mi
issl.
si
sl
Define
Qi
ar
e
d
et
er
m
in
e
d
p
ar
ti
al
ly
b
y
a
n
st
o
c
h
a
s
tic
di
s
tri
b
ut
io
n
of
i|wi
l
i
> wl) - E (w ).
a
bi
lit
y
(s
e
e
e
q
u
at
io
n
s
(1
)
y
(2
)),
in
e
q
ui
li
br
iu
m
,
w
*
wi
ll
b
e
e
n
d
o
g
e
n
o
u
sl
y
d
e
te
r
m
in
e
d.
U
si
n
g
e
q
u
at
io
n
(5
)
a
n
d
(6
),
it
w
e
c
a
n
s
h
o
w
n
th
at
:
E (wi|wi > wl) = mi
+ ss2 llsi + s 2i ( - ρ )λ (7)
sis
l
E (wl|wi
> wl) = ml
+ ss2 llsi + s 2i s(ρ sli )λ (8)
where
) 1 - F(m) The s econd terms in (7) and (8) define the kinds of selec tion bias es
λ generated by individuals’
= F(ml income-maximizing b ehavior. Equation (7) shows that the average wage of new criminals
may b e b etter or worse than the average criminal wage b ef ore o ccupational change
according to whether ρ >or not. Similarly, e quation (8) s hows that the average wage of a
legal employee, once criminals have le ft the legal lab or marke t, may b e higher or lower
than the average legal wage b efore o ccupational change s dep ending on ρ >
l
= E (w
> wl) - E (wi) and Ql = E (w |
w
> 0 and Ql
l
si
From equation (7) and (8) know that, when only considering ξ , < 0 b ec ause s< ρ < sisl
Qi
i
When only considering ν ,
Qi
T
his
is p
erh
aps
the
mo
st
imp
orta
nt
res
ult
of
the
mo
del.
Hig
h
abili
ty,
low
risk
ave
rse
entr
epr
ene
urs
pref
er
to
wor
k
as
cri
min
als
. In
si < 0 and Ql> 0 b ecause
sl> ρ > ssl
suc
ha
mar
ket
the
y
will
hav
e
acc
es
s to
a
fart
her
righ
t
tale
wa
ge.
Furt
her
mor
e,
tho
se
wh
o
sel
ect
cri
min
al j
obs
w ill
out
p
erfo
rm
orig
inal
cri
min
als.
E
mpi
rica
lly,
we
wo
uld
e
xp
ect
that
cri
min
als
that
got
into
illeg
al
mar
ket
s in
Par
e
mor
e
viol
ent
and
mor
e
entr
epr
ene
uria
l
tha
n
tho
se
that
wer
e
cri
min
als
in
Ppr
ipan.
As
my
disc
us
sio
n in
sec
tion
1
sho
we
d,
this
is
ce
rtai
nly
the
cas
e.
Ne
gro
s
and
Zet
as
are
kno
wn
for
thei
r
unp
rec
ede
nte
d
viol
e
nce
and
thei
r
abili
ty
to
tak
e
part
of s
eve
ral
mor
e
entr
epr
ene
uria
lc
rimi
nal
bus
ine
sse
s.
The
y
hav
e
cre
ate
d
org
ani
zati
ons
of e
xtor
tion
and
kid
nap
pin
g in
se
ver
al
tow
ns
aro
und
the
b
ord
er.
Nu
evo
Lar
edo
and
Ciu
dad
Ju´
are
z
hav
eb
ee
n
part
icul
arly
targ
ete
d.
The
mo
del
als
o
pre
dict
s
that
indi
vid
ual
s
wh
o
disli
ke
viol
enc
e
will
re
mai
n in
the
leg
al
ind
us 1
6
ml
+ s2 sl
d
u
try b e caus e the ir abilities cannot b e sold into the criminal industry. This is certainly the
case. As a Zeta state d: “I like to kill, that is why I have this job (Rios 2009b).”
i
= ss2 llsi
Prop osition 5: Patterns of talent drain can also b e predicted: 1. Entrepreneurial talent drain
from the legal to the illegal lab or markets de creas es as salaries
in the legal lab or market increases . Consider what happ ens to Qiwhen mchanges : Qil
Qi < 0. A larger Qi
We know that dλ d( ml- mi) > 0, Thus, the sign of Qi
ml
l
ml
w
il
l
b
e
d
e
t
e
r
m
i
n
e
d
b
y
t
h
e
s
i
g
n
o
f
ρ
.
W
h
e
n
ρ
>
0
( si - ρ ) d
λ
a
n
d
s
u
ffi
c
i
e
n
tl
y
l
a
r
g
e
–
a
s
i
s
t
h
e
c
a
s
e
f
o
r
ξ
–
c
a
n
b
e
i
n
t
e
r
p
r
e
t
e
d
a
s
l
a
r
g
e
r
e
n
t
r
e
p
r
e
n
e
u
ri
a
l
d
r
a
i
n
f
r
o
m
t
h
e
l
e
g
a
l
t
o
t
h
e
il
l
e
g
a
l
l
a
b
o
r
m
a
r
k
e
t.
T
h
u
s
,
a
s
m
i
n
c
r
e
a
s
e
s
,
t
h
e
r
a
t
e
o
f
i
n
d
i
v
i
d
u
a
l
s
t
h
a
t
b
e
c
o
m
e
c
ri
m
i
n
a
l
s
i
s
g
o
i
n
g
t
o
b
e
r
e
d
u
c
e
d
.
T
h
i
s
r
e
s
u
lt
i
s
p
r
e
tt
y
i
n
t
u
it
i
v
e
.
I
n
d
i
v
i
d
u
a
l
s
c
a
n
s
e
ll
t
h
e
ir
n
o
n
o
b
s
e
r
v
a
b
l
e
a
b
il
it
i
e
s
e
it
h
e
r
i
n
t
h
e
l
e
g
a
l
o
r
i
n
t
h
e
il
l
e
g
a
l
i
n
d
u
s
t
r
y
.
A
s
s
a
l
a
ri
e
s
i
n
c
r
e
a
s
e
i
n
t
h
e
l
e
g
a
l
m
a
r
k
e
t,
i
n
d
i
v
i
d
u
a
l
s
w
il
l
r
e
m
a
2.
E
nt
re
pr
e
n
e
ur
ia
l
i
n
l
e
s
s
a
tt
r
a
c
t
e
d
t
o
b
e
c
o
m
i
n
g
d
r
u
g
t
r
a
ffi
c
k
e
r
s
.
ta
le
nt
dr
ai
n
fr
o
m
th
e
le
g
al
to
th
e
ill
e
g
al
la
b
or
m
ar
k
e
ts
d
e
c
re
a
s
e
s
a
s
le
g
al
la
b
or
m
ar
k
e
ts
b
e
c
o
m
e
m
or
e
u
n
e
q
u
al
.
when sl
i
i
dλ
) (si - ρ )(1 ssl ρ)
i
sl
2l3
)
- m i)
(ml
2
i
sl
(s2 l
Q
l
*
i
si
sl
Be caus e |ρ | = 1, the first te rm is always going to b e non- p ositive. T he will b e determined by the signs of (- ρ )(
s ign of
implicity, let’s ass ume that t) > 0. Then,
l
i
<
0.
m
ρ
)
<
0,
(1 - ξ
ρξ) < 0,
l
Qi
sl
7L
a
b
or
m
ar
k
e
t
in
e
q
u
al
ity
m
a
y
h
a
v
e
s
o
m
e
p
o
sit
iv
e
e
xt
er
n
al
iti
e
s.
A
s
le
g
al
w
a
g
e
in
e
q
u
al
ity
in
cr
e
a
s
e
s,
hi
g
h
er
a
bi
lit
y
e
nt
re
pr
e
n
e
ur
s
g
e
t
a
c
c
e
ss
to
m
or
e
ri
g
ht
-t
al
e
w
a
g
e
s
w
hi
c
h
re
d
u
c
e
s
th
e
re
la
tiv
e
at
tr
a
cti
v
e
n
e
ss
of
dr
u
g
tr
a
ffi
c
.
T
al
e
nt
dr
ai
n
fr
o
m
th
e
le
g
al
to
th
e
ill
e
g
al
in
d
u
st
ry
is
re
d
u
c
e
d.
Consider what happ
ens to Q
7
changes
: Q= s(s2 lls2 i+ s2 i3)(ρ2- 1)λ ss+ s
i
i
i
Note that, in a market w he re (m) < 0 s uch that sls2 i- m
d(ml
l
i
(s2 l
+ s2 i)3 (ρ2 (s- 1)λ < s2 lis2 l+ s2 ( sis-l ρ )(1 sisl ρ ) d λd (ml- mi) - mi)
i)3
17
(ml
Drug traffic offers relatively larger s alarie s to high ability individuals. Individuals w ho know
their high ability would prefer to work as drug trafficke rs b ecause such j obs offer b etter
top-e nd salarie s. As salaries at the top b ecome eve n more dis tant f rom salaries at the
top of the legal income distribution, individuals b ec ome more prone towards drug traffic. It
is not only le vels of salarie s what matte r. For p eople at the right tail of the ability
distribution, what matters the most is the dis p ersion. They know they will b e at the tail of
the income distribution. Thus , they only care ab out how far they c an make it into the salary
distribution. Kee ping average s alaries c onstant and equal, high ability individuals will
always pre fer to work in the marke t with higher variance. I n this case, that is the ille gal
market.
Note however that this is not the case for tastes for violence . Those individuals w ho like
violence are going to b e well paid as drug traffickers but badly paid as le gal e mployees .
The re will b e a c lear s ort by taste. All those with high viole nce taste will go to the illegal
industry and the opp os ite will b e true for those who dislike violence. Unlike in the entre pre
neurial ability case, in this case the legal and the illegal markets are not comp eting for
individuals with the s ame characteristics.
3. Entrepreneurial talent drain from the legal to the illegal lab or markets increas es as the
legal and illegal se ctors b ecome more similar (i.e. demand the same abilities in their
employees ).
when ρl
) (1 sil 2 iρ )λ + s(s 2 l 3 ( s - ρ ) d
l
iρ =
2i
λd u u
i
Consider what happ ens to schanges : Qis3 l
s
Qi
2 + s )
(s2 + s2 3
s
s
l
l
18
i
Qi
ρ
or the case of entre pre neurs ( ρ > 0) with u
> 0,
< 0. F
In words , as the abilities required by the d
with the abilitie s required in the legal industry,
ec ome criminals.
This result is partic ularly interesting b e caus e
Calde r´on’s drug war. B y increasing the diffic
governme nt is fostering that drug traffickers in
ations that are not valuable in the legal market
drug busine ss b ec omes less similar to the le
nt sorts more
inc re ase s in wage ine quality will generate large r (not smalle
the ille gal indus try.
adequately, leading those whose talents are valuable for the legal industrie s to re main
there.
4 Conclusion
The re sults of my the oretical mo del, summariz ed in Figure 6, shows the reas ons b ehind the
changes in levels/scop e/forms of violence that Mexico has exp erimented in recent years. As
explained in section 2, even though Mexico has always b een a ma jor player in the illicit drug
industry, rece ntly drug-related violence has reached unprec edent levels. The typ e and scop e
of viole nc e have also changed. Since 2003, violence is not only more common (measured as
numb er of violent deaths ) but also more inte nse. Criminals have b ecome particularly blo o dy
and c rue l. Furthermore, other forms of organize d c rime , such as kidnappings and extortion,
have also s piked.
Over the c ourse of this pap er I argued that the reasons b ehind these change s are to b e
found in the interaction b etween legal and ille gal lab or markets. A new generation of drug
dealers has emerged in Me xic o. They are more viole nt and more keen on criminal
diversification. When the ille gal lab or market op ened to outsiders in 2003 –and b ecause of
the large r variance in salaries in the illegal vers us the legal industry– highly talented
entrepreneurs and individuals with higher tastes of violence sorte d into illegal o ccupations .
These new drug traffickers have levels of entrepreneurial ability and viole nce that are much
higher that those of the traditional drug trafficke rs . Furthermore, entreprene urial talent is
draining into the illegal lab or markets.
Self- selec tion and talent run-off have b e en contained by recent efforts of the Mexican
government. Felip e Calder´on’s war against drug traffic has increased the probability of
capture and fines for drug dealers. He has also reduced the profits of the drug industry which
has in turn diminishe d salarie s within illegality. Lower criminal s alaries are indeed one of the
ma j or disince ntives for p eople to devote time to illegality.
Ye t, this strategy has not b e en efficie nt to deter very greedy individuals, or those who are
less risk averse. Individuals that have very high tastes f or violence may also not b e deterred.
Their abilities are much valuable in the drug industry than in any le gal job. My mo del predicts
that changing Mexico’s sec urity p olicy towards capturing all typ es of drug traffickers (not just
drug lords as has b een the cas e) would created further disincentives for p eople to b e come
drug traffickers. This is inferred from the fac t that drug traffickers are more de te rred by ge ne
ral changes in s alarie s than by truncating their wage distribution.
Finally, my mo del predicts that wage inequality may in fact have some p ositive exte rnalities.
Increasing the variance of wage s in legal markets w ill reduce the attractive ness of illegal
markets for highly able individuals. Talent drain is a negative function of inequality. Indee d, this
result should b e take n c arefully. Inequality may b e generate d in several different forms and
not all
19
of the m w ill have as a re sult a decrease in the numb e r of drug traffickers. Only increases in
upp er- tail ine quality as payoffs to entrepreneur ability (or other abilities highly rewarded in b
oth legal and illegal lab or markets) will have as a res ult a reduction in criminal rates.
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21
Ram´irez, Ram´on. Ow ner of Diario E l Manana. Intervie wed by Viridiana Rios. August 4rd,
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22
App endix
i),
jus t have one e N (0,
here
Fur the r ideas to explore and main concer ns
• Gene ral se t up and order of the pap er. A b etter organization of it may make the
puzzle more attractive. I want the mo del to contribute to the understanding of a puzzle
that othe rw ise would b e intuitively difficult to grasp. Is this the case? How to do it b
etter?
• Equations 1 and 2 may need to b e formulated in a diff ere nt way. I was thinking on ins te
ad of having two parameters for ability (eland e
S=
ξsi
X X sl
=
sP R P sνR
R R st
si = sξ
N
R
sl
8.
N
sν
R
R
R
st
8
0 > X > 1, 0 > R > 1, P > 0, N < 0. W hat I want is to express that (a) wage s are
determined by an sto chastic dis tribution of abilities (normally distribute d), (b) there
are three abilitie s (e ntrepreneurial ability ξ , tastes for violence ν and others t , (c) ξ
contributes p ositive ly to wages in the illegal/legal lab or markets, (d) ν contributes p
ositively(ne gatively) to wages in the ille gal(le gal) lab or markets, and (e ) t may
contribute p ositively or ne gatively to legal/illegal lab or markets. In addition, I do not
know how to think ab out X intuitively.
• This mo del is ab out individuals but yields re sults that can b e interpreted as
aggregate. For example, my mo del predic ts the share of the time that and individual
would use to p erform criminal activities . In the aggregate, this could b e interpreted as
the share of the p opulation that is full time criminal. This would b e more interesting. Yet,
I do not know is this is a go o d idea or can b e done with the mo de l as it is now .
• Anothe r interes ting res ult, relate d to discussion in prop osition 2, would b e to think in
terms of likeliho o d ratios. As in the c lass ical re sults of a moral hazard proble m, the
likeliho o d ratio would tell us how imp ortant are abilities in determining final wages
ab out
I the action
n23
a
mo
ral
ha
zar
d
pr
obl
e
m,
the
lik
eli
ho
od
rati
o
de
te
rmi
ne
s
ho
w
s
tro
ng
is
the
inc
ent
ive
sc
he
me
goi
ng
to
be
ac
c
or
din
g
to
ho
w
mu
ch
inf
or
ma
tio
n
the
out
put
giv
es
l
ml
s2 l
- el
2
l
- mmii
i
2 i)
i
l
(wu
l
or s2 i)) is higher.
Am I getting this
right? • In prop
os ition 3,
normally, U
tial2wu
2) + U (wu)( /par
/par tial t2 i ), not by U
u
s
(wu
i
(wu)(/par tial w/par
tial tui
2
i
dt2 i
)
i
s
i
(b) U (wu
U ( w) U (
wuu)
– Second, if U (w
i
f
(
x
)
f
(
x
)
Like liho o d would b e defined as :
L = F (ml
A low
L
w
o
u
l
d
m
e
a
n
t
h
a
t
a
b
i
l
i
t
i
e
s
) F(m) =- m+ s
) give us few
wage ( m- mi) is going to lo ok like . Some c omparati
example, abilitie s are more inf ormative w hen mis lo
quality (s
) would b e inte rpre
Three ideas /problems c ome to my mind:
– First, in my setting, individuals are maximiz ing their
not with res p ect to w . Risk aversion thus –I think– w
T he c onfus ion come s f rom the fact that that wis a
following convention I as sumed that U(w ) > 0 and U
individuals cannot b e risk lovers with resp e ct to wea
come to joint all re sults/inte rpretations is that (a) ind
resp e ct to we alth,
(
e
) is not a measure of risk ave rs ion,
(c)
i
d U ( wu
u
= w - F (t
u
(w
and F (t
2dU
( w) dt2 iu
24
is a me asure of ris k aversion, (c)
individuals can b e risk love rs /averse/neutral with resp ec t to t. Am I getting it right?
) would b e interpreted as a measure for risk avers ion, what would b e the interpre tation
of U) given that we know that w)? – Third, p erhaps the b est way to interpretis as “first
order” likeliho o d ratio. A likeliho o d ratio (hazard rate) is de fined as. The exac t meaning
of this idea, as well as the role of t) would have to b e determined.
• If risk aversion is de fine d , the sign of the second order condition is partially determined by it.
as
Differentiating utility with resp ec t to tyields the following results:
dU (w) dtis= dU (w) dwss∂ w∂ tsii
= U (ws)(wi i - wl
u
u) dwu
)
i
= U (wu)((w
dtiu
wl) - F
2U (w)
2= dU
D t2 is
(w) dw2
ss
) dU (w= dU (w∂ w∂ t
∂ w) ds∂ ws
∂ ∂
ti ti
)
+ dU (wupar ti al wu
= U (ws)(wi - wl 2) u
p
i
d2U (w)
dt2 iu
= d2U (w)
dw2 uu
= U (wu
i
i
par tial w
2U
(w
l
u
(
)
par
tial
t
w
d
w
dt
par tial t
-
)((w
2i
i
u
l
par tial2w
U
-w )-F s
(ws)(wi ) - U
- w )] + [p d ) dt
l
2
)] γ = p(wu)((wis- wU (w ) dt] = p
[U (wu)((wi- wl
+ (1
d
i
-U
l
)((w w
Second order condition is given by:
[U (wu) - U (ws)] + 2p [ U (wu
)F
2
u)
u
)
2
2i
(
F
i
l
U (w )
dt2 i]
) - F ) - U (w )(w - w
(w )(w - w
)] + (1 - p )[U
2]
[ U (wu) - U (w
) - F 2)
d
2i
(w u)(F
l
= a + 2γ + E [ d2
)] E [
s
i
where
a=p
[U
We can think on E 2dU ( w] as the exp ec ted risk aversion of the individual once the probability of e
[
alization of w has b een taken into account. If) dt2 iu2dU ( w> 0 individuals are risk p
if) dt2 iu< 0 individuals are risk averse, and if2dU ( w) dt2 iu2dU ( w= 0 individuals are risk
neutral. T he same can logic c an b e applied to) dt2 is.
- wl) - F 2dU ( wu
We know that a < 0. The sign of γ dep e nds on ((wi
2
2d
i - wl
i
2i
2dU
( w) dt2 is
). γ will always b e non p os itive unles s (w) > F . The most imp
ortant variation comes f rom) dtand
U(w)
. The second term of E [ dt ] is always negative. This means individual is
always
25
92
2dU
dt2 i
(w)
F
|>|U
individual is risk ave rs e (with res p ect to
wu).
∂ ti* ∂
p
i
i-
a
n
d
∂ ti* ∂
F
i
i
u*)
wl) > F
= U (ws
i
ti* = c , tl
2
6
• Finally, I would also like to calculate
risk averse with re sp ect to income when crime is s uc
cess ful
. The s ign of the firs term of E [] de p
9
(wu)((wUi<
SOC would b e negative (which means
or t* = 0 only if individual is suffic iently
(w. The se are pretty restrictive conditio
in the criminal industry have to b e large
salary whe n crime is unsuc cessf ul ha
should b e marginally increas ing in t. •
condition in which after a certain thres h
of their time in b oth legal and illegal act
ecomes larger than c , the y have to giv
would b e helpful.
.In
order to do this I need to use implicit diffe re ntiation. I
do not know how to pro c eed mathematically on this e
ndeavor but I thought on a way to cheat. I f in
equilibrium, U (w*), mathe matics are simplified
significantly. Yet, I do not know how far interpretations
would go with this cheat.
I am not sure on w he ther this re sult is right. Should this b e interprete
d as risk prop ensity? In pre vious bullet I addre ss ed this iss ue