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ORIGINAL PAPER
Are Repeatedly Extorted Businesses Dierent? AMultilevel
Hurdle Model ofExtortion Victimization
PatricioR.Estévez‑Soto1 · ShaneD.Johnson1· NickTilley1
© The Author(s) 2020
Abstract
Objectives Research consistently shows that crime concentrates on a few repeatedly vic-
timized places and targets. In this paper we examine whether the same is true for extortion
against businesses. We then test whether the factors that explain the likelihood of becom-
ing a victim of extortion also explain the number of incidents suffered by victimized busi-
nesses. The alternative is that extortion concentration is a function of event dependence.
Methods Drawing on Mexico’s commercial victimization survey, we determine whether
repeat victimization occurs by chance by comparing the observed distribution to that
expected under a Poisson process. Next, we utilize a multilevel negative binomial-logit
hurdle model to examine whether area- and business-level predictors of victimization are
also associated with the number of repeat extortions suffered by businesses.
Results Findings suggest that extortion is highly concentrated, and that the predictors of
repeated extortion differ from those that predict the likelihood of becoming a victim of
extortion. While area-level variables showed a modest association with the likelihood of
extortion victimization, they were not significant predictors of repeat incidents. Similarly,
most business-level variables significantly associated with victimization risk showed insig-
nificant (and sometimes contrary) associations with victimization concentration. Overall,
unexplained differences in extortion concentration at the business-level were unaffected by
predictors of extortion prevalence.
Conclusions The inconsistent associations of predictors across the hurdle components sug-
gest that extortion prevalence and concentration are fueled by two distinct processes, an
interpretation congruent with theoretical expectations regarding extortion that considers
that repeats are likely fueled by a process of event dependence.
Keywords Repeat victimization· Hurdle model· Extortion· Organized crime· Crimes
against businesses
* Patricio R. Estévez-Soto
patricio.estevez@ucl.ac.uk
1 Department ofSecurity andCrime Science, University College London, 35 Tavistock Square,
LondonWC1H9EZ, UK
Published online: 9 October 2020
Journal of Quantitative Criminology (2021) 37:1115–1157
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1 3
Introduction
Decades of research suggest that crime is concentrated on a small proportion of places (Lee
etal. 2017) and victims (SooHyun etal. 2017). In fact, the patterns observed have been so
consistent that Weisburd (2015) has recently coined the term “the law of crime concentra-
tion at place.” However, it is unclear how universal this empirical pattern might be across
countries, as well as crime and target types, as most research has focused on the US and
Canada, a handful of European cities, and Australia1 ( e.g. Andresen etal. 2016, 2017;
Curman etal. 2015; Farrell etal. 2005; Sagovsky and Johnson 2007; Tseloni etal. 2004;
Perreault etal. 2010; Lynch etal. 1998; Johnson and Bowers 2010), and on “traditional”
crimes against individuals and households2 (e.g. Daigle etal. 2008; Osborn and Tseloni
1998; Tseloni etal. 2002; Tseloni and Pease 2004, 2003; Johnson etal. 1997; Tseloni etal.
2004; Kleemans 2001; Young and Furman 2007).
In particular, there is a notable scarcity of research that has systematically studied the
concentration of organized crimes,3 an area of study that could benefit considerably from
more rigorous quantitative assessments (Sansó-RubertPascual 2017,p.29–30). Thus, this
study is concerned with understanding the concentration patterns of extortion—an arche-
typal organized crime (Tilley and Hopkins 2008,p.449). Specifically, it examines patterns
of extortion among Mexican businesses to determine if concentration occurs, and if it does,
to determine the factors that may explain it.
Current research suggests that crime concentration on specific targets (henceforth
“repeat victimization”) is driven by two mechanisms: Risk heterogeneity (Pease 1998;
Johnson 2008) proposes that enduring differences in target characteristics make some tar-
gets more attractive than others; while event dependence (Pease 1998; Johnson 2008) sug-
gests that the risk of victimization is dynamic, with the risk to victimized targets increas-
ing—at least temporarily—following an initial offense. Though studies have found that
both mechanisms have a part to play (e.g. Johnson 2008; Lauritsen and DavisQuinet 1995;
Pitcher and Johnson 2011; Lynch etal. 1998; Tseloni and Pease 2004, 2003), it is gener-
ally assumed that the risk factors associated with victimization prevalence—the likelihood
of becoming a victim—also explain its concentration—the number of incidents per vic-
timized target (Pease and Tseloni 2014,p.31). Thus, analytic studies generally focus on
explaining incidence—the number of incidents per potential target—using a single set of
predictors to examine the entire distribution of crime, rather than examining whether the
predictors that differentiate victims from non-victims also explain the amount of crime suf-
fered by victimized targets (Pease and Tseloni 2014,p.31).
However, this assumption is largely based on previous findings concerning household
property crimes (Osborn etal. 1996), and it is unlikely to apply in the case of extortion. To
explain, like crimes such as personal fraud (see Titus and Gover 2001,p.135), extortion
requires the victim’s cooperation for the offender to succeed (Best 1982,p.109), thus rep-
etition may be influenced by a victim’s level of cooperation (which can only be observed
1 Only a small number of recent studies have examined patterns in radically different contexts such as Bra-
zil (Melo etal. 2015), Malawi(Sidebottom 2012), Taiwan(Kuo etal. 2012) and South Korea(Park 2015).
2 For exceptions see Andresen etal. (2017), Bowers etal. (1998), van Dijk and Terlouw (1996), Salmi etal.
(2013), Burrows and Hopkins (2005), Gill (1998), Hopkins and Tilley (2001), Matthews etal. (2001), and
Yu and Maxfield (2014).
3 Welcome exceptions are the studies on kidnapping for ransom in Colombia by Pires etal. (2014) and
Stubbert etal. (2015), and Dugato’s (2014) study on bank robberies in Italy.
Journal of Quantitative Criminology (2021) 37:1115–1157
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1 3
through interaction), rather than by a stable set of characteristics. Furthermore, extortion is
often characterized as a long-term relationship between victims and offenders (Elsenbroich
and Badham 2016; Kelly etal. 2000,p.64); thus, repetition may be unaffected by stable
risk factors once an extortive relationship has been established.
To examine this, this study uses data from Mexico’s national commercial victimization
survey to trial a novel modeling strategy—the multilevel negative binomial-logit hurdle
model—to assess whether the predictors associated with the likelihood of extortion vic-
timization are also associated with the number of repeat extortions suffered by businesses.
If predictors are inconsistent across the two measures, this would suggest that extortion
concentration is fueled by a process distinct from that which might explain extortion prev-
alence. Thus, this study contributes towards expanding our understanding of micro-level
patterns of crime concentration in two ways. First, to our knowledge, this study represents
the first application of a multilevel negative binomial-logit hurdle model to study crime
concentration,4 highlighting its potential usefulness to study other crime types where rep-
etitions are thought to be driven by distinct processes—such as domestic violence5 (Bider-
man 1980; Rand and Saltzman 2003). Second, the study contributes to the literature on
crime concentration by examining whether or not the patterns consistently observed else-
where also apply to: a) a crime type that has received little research attention, and b) a
country that has so far been neglected in the literature.
The article proceeds as follows. In the next section we briefly introduce the background
of extortion in Mexico. Next, we review the literature on modeling repeat victimization,
and on the predictors of extortion victimization. The next section covers the data and ana-
lytical strategy employed, followed by the research findings and a discussion of their impli-
cations and limitations.
Background: Extortion inMexico
Extortion is the third most common crime against Mexican businesses, after petty theft
and robbery (INEGI 2014a). However, extortion is very prominent in the public agenda, as
it has been linked to notorious episodes of violence. During the first two months of 2011
there were 119 arson attacks linked to extortion in the infamous Ciudad Juárez6 (Guerrero-
Gutiérrez 2011). Later that year, an arson attack against a casino that refused to comply
with extortion demands in Monterrey (a city in northeast Mexico) killed 52 people, mak-
ing it one of the deadliest criminal incidents in Mexico’s recent history (Corcoran 2012;
Wilkinson 2011). Lastly, widespread extortion of farmers in 2012 and 2013 led to a politi-
cally destabilizing uprising of autodefensas—self-defense paramilitary groups—in many
rural areas of the country (Shirk etal. 2014,p.10).
4 However, the approach has been used in crime research to study sentencing (Hester and Hartman 2017;
Rydberg etal. 2017), intimate partner violence (Hellemans etal. 2015), specific types of homicides (Guer-
rero-Gutiérrez 2011; Baller etal. 2009), and the influence of incarceration on health care availability (Wal-
lace etal. 2015).
5 Though Hellemans etal. (2015) used hurdle models in a study of intimate partner violence (IPV), their
study is focused on the relationship between lifetime experience with IPV and victims’ relational and sexual
well-being, and does not address the factors associated with IPV repeat victimization.
6 A city on the Mexico-U.S. border, across from El Paso, Texas. In 2010, Ciudad Juárez was the most
violent city in the world(Redacción 2010), with a murder rate of 216 per 100,000 inhabitants (Rios 2012).
Journal of Quantitative Criminology (2021) 37:1115–1157 1117
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1 3
Over the past two decades, Mexican organized crime has been transformed from a few
powerful groups focused mainly on drug trafficking, to a plethora of small—though far
more violent—organizations involved in drugs, extortion, kidnapping, murder and other
crimes (for reviews, see Bunker 2013; Shirk and Wallman 2015). Three broad hypothe-
ses have been proposed to explain this transformation. The first focuses on how Mexico’s
transition to democracy7—after 71 years of one-party-rule—dissolved informal political
control mechanisms that kept organized crime in check, leading to violent power strug-
gles for control of lucrative criminal markets (Rios 2015; Duran-Martinez 2015; Dell 2014;
Astorga 2012; Aguirre and Herrera 2013). The second links changes in international drug
markets to conflicts over strategic territories (Corcoran 2013; Rios 2012; Paul etal. 2011;
Brophy 2008). Finally, the third focuses on the instability created by the Mexican gov-
ernment’s crackdown on organized crime from 2006 onwards (Rios 2012; Calderon etal.
2015; Correa-Cabrera etal. 2015; Jones 2013; Dickenson 2014; Osorio 2015).
These approaches, concerned as they are with broad manifestations of organized crime,
may explain trends in organized crime violence in Mexico—and by extension in extor-
tion—at the national, sub-national, or even city level. However, they are inadequate to pro-
vide insight into patterns at the micro-level of places (in this case, businesses), which is the
focus of this study.
Repeat Victimization
Repeat victimization (RV) occurs when a target (however defined) suffers the same offense
two or more times during a given time period (Grove and Farrell 2010; Pease 1998). In a
seminal study, Farrell and Pease (1993) noted that according to the 1982, 1988, and 1992
sweeps of the British Crime Survey, repeat victims suffered between 71% and 81% of all
incidents, yet they amounted to only 14–20% of respondents. International evidence is con-
sistent with these findings. Based on results from 17 countries originally reported by Far-
rell and Bouloukos (2001), Farrell and Pease (2011) estimate that around “40 per cent of
crimes against individual people and against households are repeats ... with variation by
crime type and place” (p.123).
Patterns of RV were first identified during the 1970s with the advent of victimization
surveys. These were instituted to measure the extent of crime while overcoming the fact
that many crimes were not reported to (or recorded by) the police (Gottfredson 1986;
Sparks 1981b; Wetzels etal. 1994). Surveys provide two measures of crime: the number
of victims (prevalence), and the number of crime incidents (incidence)—both usually
expressed as per capita rates. The ratio of incidence to prevalence (concentration) provides
a crude summary of repeat victimization. However, these summary measures are insuf-
ficient to grasp the extent of concentration, as they ignore the wide disparity in crime
risks experienced across the population. Thus, the extent of crime concentration is better
represented by the frequency distribution. Early studies that analyzed such distributions
demonstrated that concentration was unlikely to be the product of chance (Hindelang etal.
1978,p.125–149; Sparks et al. 1977,p.88–106). This was demonstrated by comparing
the observed frequencies to those generated by a Poisson8 process, which indicated that
8 Events generated by a Poisson process are random and independent insofar as they occur at a constant
rate (
𝜇
) not affected by past events (Sparks 1981a).
7 For discussions on the transformation of Mexican democracy, see Camp (2012) and Smith (2012).
Journal of Quantitative Criminology (2021) 37:1115–1157
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1 3
there were far more repeat victims than those expected (Sparks etal. 1977; Hindelang etal.
1978). These non-random patterns, in turn, suggested that either events were not independ-
ent—and concentration was due to a contagion-like process—or that the population could
not be characterized by a constant rate—meaning that the some individuals faced differ-
ent risks of victimization (Sparks 1981a, p. 766–767). More recent research which has
explicitly examined risk heterogeneity and event dependency, however, suggests that both
mechanisms contribute to repeat victimization, and that the processes act in concert (see
Johnson 2008; Pease 1998; Pitcher and Johnson 2011).
Empirical backing for the first mechanism—known as “boosts” (Pease 1998), “state
dependence” (Lauritsen and DavisQuinet 1995; Osborn and Tseloni 1998), and “event
dependence” (Johnson 2008, the term we use hereafter)—comes from longitudinal studies
that have found that victimizations suffered in previous periods increase the risk of suffer-
ing crimes in the future, even after controlling for stable risk factors (e.g. Lauritsen and
DavisQuinet 1995; Lynch etal. 1998; Tseloni and Pease 2004, 2003). Further evidence
for event dependence is found in the temporal and spatial patterns of repeat and near-repeat
victimization (see Morgan 2001), which show temporary increases in risk to victimized
targets and those in their vicinity shortly after an offense has taken place (Polvi etal. 1991;
Johnson etal. 1997; Johnson and Bowers 2004; Johnson etal. 2009). On the other hand,
evidence for the second mechanism—known as “flags” (Pease 1998), “population hetero-
geneity” (Osborn and Tseloni 1998; Nelson 1980; Lauritsen and DavisQuinet 1995; Wit-
tebrood and Nieuwbeerta 2000), and “risk heterogeneity” (Johnson 2008, the term we use
hereafter)—is found in studies that have analyzed how individual and contextual character-
istics are associated with differing risks of victimization (Miethe and Meier 1990; Miethe
and McDowall 1993; Lauritsen 2010; Lauritsen and Rezey 2018).
In terms of theory, both mechanisms are underpinned by environmental criminology
(Bouloukos and Farrell 1997; Farrell and Pease 2014; Wartell and Gallagher 2012). The
rational choice perspective (Cornish and Clarke 1985; Clarke and Cornish 2017) explains
why a) certain characteristics make some targets appear more attractive or vulnerable to a
wide range of offenders, as they speak to the effort, risks, and rewards that offenders con-
sider when engaging in a crime (Cornish and Clarke 1987; Clarke and Cornish 2017), and
also b) how knowledge gleaned from past crimes influences future target selection (Cor-
nish and Clarke 1985). On the other hand, the routine activity approach (Cohen and Fel-
son 1979; Felson 2017) and crime pattern theory (Brantingham etal. 2005; Brantingham
and Brantingham 1993) explain how human ecology and urban topology shape the con-
vergence of suitable targets and likely offenders in the absence of capable guardians, and
thus provide explanations for a) the heterogeneous distribution of risk (Grove and Farrell
2010; Maxfield 1987b), as well as b) the constraints imposed by the underlying ecological
and urban structure to temporary increases in crime risk following an initial event (Johnson
etal. 1997; Sagovsky and Johnson 2007; Rosser etal. 2016).
Modeling Repeat Victimization
In addition to measuring crime, victimization surveys capture a wealth of information
regarding respondents and their environments, such as demographic and socioeconomic
characteristics, the presence of protective and security equipment, lifestyle details, percep-
tions and fear of crime, and measures of neighborhood disorder (UNODC/UNECE 2010;
Cantor and Lynch 2000; Pease and Tseloni 2014). Such information has provided oppor-
tunities to investigate the potential associations between victimization risks and target (as
Journal of Quantitative Criminology (2021) 37:1115–1157 1119
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1 3
well as contextual) characteristics (e.g. Hindelang etal. 1978; Sparks etal. 1977; Miethe
etal. 1987; Tseloni etal. 2004).
However, most early approaches to modeling victimization focused on the prevalence
of victimization. These studies applied logistic regression to identify the factors associ-
ated with the risk of being victimized (e.g. Maxfield 1987a; Miethe et al. 1987). Such
approaches, however, disregard the differential risks associated with repeat victimization
(Pease and Tseloni 2014,p.35). Pease and Tseloni (2014) ascribe this to the fact that the
significance of repeat victimization had been somewhat neglected, and to a lack of acces-
sible statistical tools and techniques suitable for the analysis of count data (p.35).
Crime incidents are recorded as discrete counts with a lower bound of zero, requiring
special modeling frameworks such as the Poisson (e.g. Berk and MacDonald 2008; Mac-
Donald and Lattimore 2010). Furthermore, incidence data tend to be heavily right-skewed,
with many observations for zero incidents and a long tail with few observations for targets
that suffered many incidents. This leads to overdispersion, which occurs when the vari-
ance of a distribution exceeds its mean (Cameron and Trivedi 2013,p.4; Hope and Nor-
ris 2012,p.544). The implication of this for modeling is that the standard Poisson model
(which assumes that the mean of a distribution equals its variance) can generate erroneous
standard errors (Rydberg and Carkin 2016,p.63). Thus, the preferred distribution to model
crime incidence is the negative binomial (see Pease and Tseloni 2014; Tseloni 1995). This
allows overdispersion to be incorporated via a dispersion parameter (see the “Analytical
Strategy” section), which captures unexplained differences in crime incidence between two
targets that are otherwise identical in terms of the covariates included in the model (here-
after “unexplained heterogeneity”, Osborn and Tseloni 1998). This modeling approach has
been further strengthened by the use of multilevel9 models (e.g. Goldstein 2011) which can
incorporate hierarchically structured and repeated measures data and can help (in the con-
text of crime and place) distinguish how much unexplained heterogeneity can be attributed
to area and individual-level sources (for a seminal study, see Tseloni 2006).
With this modeling framework, studies test the risk heterogeneity hypothesis by incor-
porating covariates thought to affect a target’s expected victimization incidence. For exam-
ple, in a study on burglary victimization across Europe, Tseloni and Farrell (2002) used
a multilevel negative binomial model to investigate the effects of household and country-
level characteristics on burglary incidence in eight European countries. Controlling for the
effect of previous victimizations, the study found significant sources of risk heterogene-
ity consistent with the routine activities theory: absence of guardianship (e.g.being sin-
gle or divorced), being close to likely offenders (as measured by household poverty), and
increases in target attractiveness (e.g.car ownership as a sign of household affluence) were
associated with increases in burglary incidence, to cite a few examples (Tseloni and Farrell
2002,p.156–157). Furthermore, the study also found there was essentially no unexplained
heterogeneity due to between-country differences, meaning that unexplained differences in
burglary risk were likely due to target and subnational (e.g.city or region) level differences
(Tseloni and Farrell 2002,p.155–156).
Event dependence, on the other hand, can be tested by incorporating the temporal
dimension using longitudinal data (Lynch etal. 1998, p. 15). While Tseloni and Farrell
(2002) included measures of previous victimization experiences, the cross-sectional nature
of the data they used (the International Crime Victims Survey, see Mayhew and van Dijk
9 Terminology varies according to specific disciplines, but multilevel models are also known as mixed
effects models and hierarchical linear models (Bell etal. 2008,p.1112).
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1 3
2014) impeded their ability to explicitly model the effects of event dependence on crime
incidence (see Lynch etal. 1998). Studies that have employed longitudinal victimization
data (e.g.repeated interviews with the same target), have found that victimization experi-
ences in earlier observations are significant predictors of victimizations in posterior obser-
vations, even after controlling for risk heterogeneity (e.g. Lauritsen and DavisQuinet 1995;
Lynch etal. 1998; Tseloni and Pease 2004, 2003).
Most victimization surveys employ cross-sectional designs (Lynch 2006,p.249; May-
hew and van Dijk 2014,p.2604). In practice, this means that models based on cross-sec-
tional data—the type of data used in this study—cannot distinguish between event depend-
ence and risk heterogeneity, lumping the effects of the former with those of unexplained
heterogeneity (Osborn et al. 1996; Osborn and Tseloni 1998; Pease and Tseloni 2014;
Heckman 1981).
A potential workaround initially considered to explore the effect of event dependence
in the absence of longitudinal data was to assess whether the factors that explain one-time
victimizations differ from those that explain repeated incidents. In a seminal paper, Osborn
etal. (1996) employed a “double hurdle” bivariate probit model to compare the transi-
tion probabilities from non-victim to victim and from one-time victim to repeat victim for
household property crimes, but found that the predictors of first and repeated victimiza-
tions were generally the same (Osborn etal. 1996,p.243). This finding has been influential
in subsequent studies and is widely cited as a justification to use a single set of predictors
to explain the entire distribution of crime incidents (e.g. Tseloni etal. 2002,p.113; Pease
and Tseloni 2014,p.31; Tseloni and Pease 2014,p.5).
This consensus fails to consider that the effect and relative contributions of risk het-
erogeneity and event dependence to repeat victimization may vary considerably across
different crime types (Johnson 2008,p.236). One of the most parsimonious explanations
for event dependence draws from the fact that offenders often return to victimize past tar-
gets (Bernasco 2008; Everson and Pease 2001), suggesting that the choice of future tar-
gets is influenced by previous experience (Johnson 2014; Bernasco 2008; Johnson et al.
2009). It follows that the contribution of event dependence will likely be higher for crimes
where “the effort and/or risk of a second offence is clarified by victim response to a first
offence” (Farrell etal. 1995, p.396). For example, in a study of bank robbery, Matthews
et al. (2001) found that success in past robberies was positively associated with future
incidents—the amount stolen in past incidents adequately predicting future risk. Thus, as
extortion is a crime where success depends on a victim’s willingness (reluctance) to coop-
erate (Best 1982,p.109), the manner in which the victim responds may have a strong bear-
ing on an offender’s decision to repeat the offense against the same target. For example,
compliance in one incident could beget further victimizations as the victim is known to be
lucrative and responsive.
Furthermore, the importance of event dependence is likely to be decisive in crimes
where repeated victimizations are the product of an ongoing relationship between victims
and offenders, such as recurrent violent episodes framed within an abusive relationship
(Biderman 1980,p.29; Rand and Saltzman 2003). It is likely that extortion falls within
this category of offenses, as repeated extortions are often characterized as an ongoing con-
dition (Biderman 1980, p.29; Elsenbroich and Badham 2016; Kelly etal. 2000,p. 64).
Thus, concentration on repeatedly extorted targets may be unaffected by risk heterogeneity
and instead indicate that such an institutionalized relationship exists. Therefore, it is con-
ceivable that the risk factors affecting extortion prevalence may be distinct from those that
affect extortion concentration, which warrants a modeling strategy that is able to differenti-
ate such mechanisms.
Journal of Quantitative Criminology (2021) 37:1115–1157 1121
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1 3
A Hurdle Model ofExtortion Victimization
The hurdle model (Mullahy 1986; Cameron and Trivedi 2013) is a suitable alterna-
tive for distinguishing the factors that influence prevalence from those that influence
concentration. These models (unrelated to the “double hurdle” bivariate probit used by
Osborn et al. 1996) combine two processes: one that generates positive counts (
≥1
)
versus zero counts (
=0
); and another that generates only positive counts (
≥1
) (Hilbe
2011,p.355). The first process corresponds to the prevalence risk and is usually mod-
eled using logistic regression, whereas the second estimates concentration using a trun-
cated count model—usually the truncated-at-zero negative binomial, as the distribution
remains overdispersed (Cameron and Trivedi 2013).
An alternative is the zero-inflated model (Lambert 1992). Zero-inflated models are
similar to the hurdle framework insofar as they consider that counts are produced by
a mixture of two distinct mechanisms. However, these types of model were developed
to handle a specific problem encountered with some data—excess zeroes (e.g. Hilbe
2011,p.355; Park and Fisher 2015,p.1138; Tseloni and Pease 2014,p.22). Rather
than explicitly distinguishing between the processes that lead to prevalence and con-
centration, zero-inflated models consider that there is one process granting “immunity”
to some targets, and a second that determines the incidence of victimizations that non-
immune targets experience (e.g. Park 2015; Park and Fisher 2015). Crucially, the pro-
cess generating counts does not only estimate positive counts, but zero counts as well.
The latter correspond to targets that, although not deemed to be statistically immune to
victimization, did not experience any incidents during the period sampled. Thus, given
that zero-inflated models do not explicitly distinguish prevalence from concentration,
they cannot determine whether predictors are constant across both measures, and as
such are unsuitable for our purposes here. Furthermore, the data used in the current
study showed no signs of zero-inflation when compared to a negative binomial expecta-
tion (see the “Univariate Analysis” section), and hence would also be unsuitable for this
reason.
In contrast, hurdle models first assess the risk of victimization prevalence across all
targets, and then estimate the concentration of incidents experienced by victimized tar-
gets. If victimization patterns are taken as an indirect measurement of offender-deci-
sion making (Hough 1987), then the hurdle model allows us to indirectly test whether
the factors that influence victim-selection decisions are distinct from those that affect
the decision to target past victims. Such an interpretation would be consistent with the
effect of event dependence discussed above, where the decision to commit a repeat
extortion is associated with the outcome of the first extortion attempt. Similarly, the
hurdle model can also be seen as a more appropriate model of an extortive relationship,
with predictors for prevalence explaining the risk of being initially targeted for an extor-
tive relationship, and the predictors for concentration explaining how much exploitation
businesses can expect once the relationship has been established.
In any case, to empirically assess if extortion exhibits a pattern of repeat victimiza-
tion consistent with the hurdle framework, the observed distribution of extortion must
first be shown to exceed chance expectation, as some level of repeat victimization is to
be expected by chance. Thus, our first hypothesis is:
• H1: There are significantly more repeat extortion incidents than would be expected
on the basis of random victimization.
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1 3
If repeat extortion is found to be non-random—and given that the role of event dependence
is expected to be more prominent in the case of extortion, and that extortion often leads
to enduring victim-offender relationships—we expect that once a business is victimized,
extortion concentration will not be consistently associated with the predictors of extortion
prevalence.
• H2: Once a business is extorted, the predictors that explain extortion concentration are
different from those that explain extortion prevalence.
Predictors ofExtortion Victimization
Broadly, extortion is demanding something—such as goods, services, property and espe-
cially money—through intimidation, e.g.by threatening violence or other harms (extortion
2010; Savona and Sarno 2014; Elsenbroich and Badham 2016; extortion 2017). The extor-
tion of businesses is often considered a quintessential activity of organized crime groups
(von Lampe 2005,p.235; Paoli 2014,p.7; Campbell 2013,p.32; Konrad and Skaperdas
1998,p.462; Frazzica etal. 2013,p.99; Schelling 1971,p.646–647; Tilley and Hopkins
2008,p.449). Yet, the literature on extortion has rarely been concerned with understanding
the phenomenon at the incident level, focusing instead on broader manifestations of institu-
tionalized extortion,10 which involves “the continuous, regular and systematic extortion of
several victims” (Elsenbroich and Badham 2016).
Consequently, there has been scant research on the micro-level factors associated
with extortion victimization. Attention has focused instead on macro-level factors that
are thought to be associated with widespread extortion ( e.g. Savona and Zanella 2010;
TRANSCRIME 2009). Therefore, the literature so far makes few suggestions regarding
micro-level variables that may be useful as predictors of extortion risk. In this section we
provide a brief overview of the macro and micro level factors that have been thought to
affect extortion victimization. It is important to note that this review does not aim to list all
possible sources extortion risk, but to identify variables that may be used to test H2.
Macro‑level Inuences
Research on extortion by organized crime emphasizes the importance of macro, area-level
influences. For example, Kleemans (2018) asserts that the level of aggregation relevant
to study extortion is not “a specific point in space where an offender meets a target,” but
broader “territories” controlled by organized crime groups (p.874). Though no study has
examined the effect of area-level characteristics on repeat extortion, it is possible to iden-
tify three potential predictors:
• Rule of law: According to protection theory (see Kleemans 2015, 2018), extortion is an
outcome of “alternative governance” structures imposed by criminal groups absent strong
10 Such phenomena are variously labeled as racketeering (McIntosh 1973), extortion racketeering (Savona
and Sarno 2014; Savona and Zanella 2010), extortion racket systems (Frazzica etal. 2013; LaSpina etal.
2014), private protection (Gambetta 1993; Varese 2001), and violent entrepreneurship (Volkov 2002),
among others.
Journal of Quantitative Criminology (2021) 37:1115–1157 1123
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1 3
legitimate governance (Kleemans 2018), whereby groups “tax” businesses operating in their
territories in exchange for “protection” (Gambetta 1993; Paoli 2002; Kleemans 2014; Var-
ese 2014). Thus, a potential predictor of extortion risk at the macro-level is the “strength” of
legitimate governance structures across Mexican states (Sung 2004; Skaperdas 2001).
• Corruption prevalence: Researchers have also noted that the absence or presence of
legitimate governance is not the only relevant variable, its quality must also be consid-
ered. Thus, studies have found that widespread predatory corruption (a marker of bad
governance) may be an important predictor of increased extortion risks (e.g. Díaz-
Cayeros etal. 2015; Tulyakov 2001; Morris 2013; Frye and Zhuravskaya 2000).
• Nature of local organized crime groups: The term “organized crime” is an umbrella
term used to group a wide variety of criminal structures, activities and extra-legal gov-
ernance arrangements (von Lampe 2016; Paoli and Vander Becken 2014). In particular,
not all organized crime groups engage in the same types of criminal activities. Recent
research classifies Mexican criminal groups into two types: a) those that are mostly
focused on drug trafficking, and b) those that are more reliant on violence and Mafia-
style “protection” markets—i.e. extortion. (Jones 2016; Corcoran 2013; Guerrero-
Gutiérrez 2011). Thus, it would be expected that:
(a) areas where drug trafficking-focused organized crime groups operate may be
associated with lower extortion risks, and
(b) areas where violent, mafia-style organized crime groups operate may be associ-
ated with higher extortion risks.
Micro‑level Inuences
The literature on repeat victimization has consistently found that area crime rates mask
substantial within-area heterogeneity. Indeed, in the case of extortion Savona and Sarno
(2014) and LaSpina etal. (2014) note that victim selection is not random, but is instead
guided by victim vulnerability (see also Savona 2012,p.8). While no research exists that
has systematically analyzed business-level explanations for extortion risk in the Mexican
context, findings from other contexts suggest predictors for use in this study:
• Corruption victimization: While corruption at the macro-level suggests an indirect rela-
tionship between the quality of governance and extortion risk, the often close relation-
ship between organized criminals and government officials in Mexico (Díaz-Cayeros
etal. 2015,p.255–256; Morris 2013) suggests that a direct relationship between extor-
tion and corruption victimization at the micro-level is also plausible. Alternatively, a
relationship at the micro-level could be due to the presence of a variable independently
affecting extortion and corruption risk—e.g.a vulnerability that separately attracts both
extortionists and corrupt officials. This would be consistent with findings on multiple
victimization that suggest not only that a) specific types of crime are concentrated on
a small subset of targets, but also that b) those who repeatedly suffer one type of crime
are more likely to suffer other types (Tseloni etal. 2002).
• Business age: The literature suggests that older businesses may be somewhat protected
from extortion due to long-standing ties developed in their communities (and hence
with organized criminals that operate there)(Varese 2011, 2014), and that new busi-
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1 3
nesses may inadvertently attract organized criminals by drawing attention to themselves
through opening ceremonies or advertising (Chin etal. 1992; Chin 2000).
• Business type: Research on extortion by the Italian Mafia (e.g. Di Gennaro and
LaSpina 2016; LaSpina etal. 2014; Frazzica etal. 2013) and Chinese gangs(e.g. Chin
2000; Kelly etal. 2000; Chin etal. 1992) suggests that some business types—particu-
larly restaurants, hotels and bars—are at especially high risk of extortion. It is assumed
that these business types are particularly at risk due to being inherently vulnerable to
intimidation (Schelling 1971,p.648–649).
• Business size: Several studies have found business size to influence crime risk in gen-
eral and extortion in particular, however the precise mechanism behind this relationship
is unclear. Gill (1998) notes that small businesses in the UK suffer disproportionally
more crime, which may suggest that risk is related to victim vulnerability. Yet, there
is also evidence pointing to elevated extortion risks for larger businesses (Broadhurst
etal. 2011; Kelly etal. 2000), which suggests that extortionists might select victims on
the basis of potential rewards. We speculate that there is a trade-off between vulnerabil-
ity and profitability: while smaller business may be more vulnerable, they offer fewer
potential rewards making them less attractive to extortionists.
In the next section, we discuss the data analyzed and the analytical strategy adopted.
Methodology
Data
The primary data analyzed are from the 2014 sweep of Mexico’s nationally representa-
tive commercial victimization survey, the Encuesta Nacional de Victimización de Empre-
sas (ENVE, INEGI 2014c). This is, to our knowledge, the largest sample survey of busi-
ness crime victimization that has been conducted hitherto and provides a rare opportunity
to subject extortion patterns to systematic quantitative analysis. The survey is conducted
biennially, sampling all business sectors except agriculture and the public sector. The first
part of the survey, the main questionnaire, records the prevalence and incidence of crimes
suffered by respondents during the previous calendar year (in this case, 2013). The victim
form focuses on information concerning each incident of victimization (though capped
at 7 victim forms per crime type per victim, JaimesBello and VielmaOrozco 2013). We
analyzed responses captured in the main questionnaire, as these offer a readily available
uncapped summary of victimization experiences11 (Trickett etal. 1992; Farrell and Pease
1993).
The sample consisted of 33,479 business premises stratified and randomly selected
from INEGI’s National Statistical Directory of Economic Units12 (Directorio Estadís-
tico Nacional de Unidades Económicas, DENUE, with 3.7 million units) (INEGI 2014b).
Responses were collected through face-to-face interviews with the highest-ranking person
11 To mitigate the risk of misclassification, interviewers provide respondents with an index card detailing
the different crime types and their non-legal definitions(INEGI 2014c).
12 The sampling unit for all business types except mining, transport and construction was premises; in the
exceptions, the unit was the business (INEGI 2014b). Stratification was based on business size and the state
in which the premise was established.
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1 3
in micro and small businesses, and with security or finance managers in medium and
large businesses. Computer assisted telephone interviewing (CATI) was used to follow up
incomplete questionnaires(JaimesBello and VielmaOrozco 2013), leading to a response
rate of 84%.
Access to the anonymized individual responses collected by the ENVE is restricted
by INEGI, as the combined characteristics of each respondent could potentially be used
to infer their identity. This means that all analyses presented herein had to be performed
remotely with no interactive access to the data. To overcome this constraint, all analyses
were conducted using automated R scripts13—which provide the additional benefit of
ensuring reproducibility—and remotely processed by INEGI staff in Mexico City on a
Windows platform and R (R Core Development Team 2015). Downsides of this are that
we had very limited control over the computational resources available (including software
availability), and that analyses took longer to complete (as they could not be conducted
interactively).
Dependent Variable
The dependent variable is the number of incidents of extortion14 suffered by surveyed busi-
nesses. The prevalence rate was
80.46
victims per 1000 businesses, whereas the incidence
rate was
132.77
incidents per 1000 businesses. The concentration rate was thus
1.65
extor-
tions per victim. However, the distribution of extortion, shown in Table1, reveals that extor-
tion victimization is far more concentrated than such summary statistics would suggest.
Repeat victims—i.e., businesses that suffered two or more extortion incidents in 2013—
constituted 2% of all respondents (27% of victims) but accounted for 56% of all extortion
incidents. Businesses that experienced three or more incidents amounted to less than 1% of
the sample (12% of victims), yet suffered 38% of all incidents of extortion. Moreover, the
distribution clearly exhibits overdispersion(Cameron and Trivedi 2013,p.4), with its vari-
ance (
0.547
) being more than four times larger than its mean (
0.133
).
It is also relevant to note that the tail of the distribution in Table1 exhibits a clustering
of responses at 10 events, with responses for greater counts occurring only at multiples of 5
or 6. As (Farrell and Pease 2007,p.45) note, such clustering is ubiquitous in victimization
studies and reflects respondents’ tendency to estimate high frequency event counts around
likely reference points (such as multiples of 5 or 10 for the decimal system, or of 6 and 12
for the calendar year). It is generally assumed that some victims are victimized so often
that they must use heuristics to estimate the amount of victimization incidents experienced.
This reflects the well-known just noticeable difference phenomenon (Farrell and Pease
2007), also known as difference threshold (Colman 2015). While this effect does intro-
duce some potential measurement error, it is important to note that such victim estimation
13 Available upon request.
14 The ENVE defines extortion as “any kind of threat or coercion committed against the local unit’s
owner or staff for the purpose of obtaining money, goods or forcing them to do or stop doing some-
thing” (Jaimes Bello and Vielma Orozco 2013, p. 172). This definition is similar to that adopted by
Chin etal. (1992) in a victimization survey of businesses in New York “Chinatowns,” insofar as it treats
“demanding money or the provision of goods and services to avoid violence or harassment” as the working
definition of extortion (p.629). Given that only licit—i.e.officially registered—businesses were sampled,
this study does not consider extortions committed against informal—i.e.unregistered—businesses, or those
against other criminal actors.
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1 3
does not discredit victimization measurements (see Farrell and Pease 2007,p.40–46, for a
discussion).
Alternatively, such clustering may be explained by institutionalized racketeering, as
is expected in the case of organised crime-related extortion. In such contexts, businesses
could be expected to pay extortion demands at regular intervals (e.g. monthly, fortnightly,
weekly), and would thus also cluster at said intervals. As INEGI (2014c,p.29) notes, if
a business is extorted weekly the survey would capture 52 incidents, a figure not much
greater than the maximum event count observed in Table1.
Considering the state-level distribution of extortion (see panels A and B in Fig.1), it is
evident that extortion is not uniformly distributed across the country. Notably, the state dis-
tribution of the prevalence of extortion (panel A) is not the same as that of its concentration
(panel B). This would suggest that states where becoming the victim of extortion is more
likely are not necessarily the same where repeat extortion victimization is more frequent.
To explore this further, we examined the bivariate relationship between state-level preva-
lence and concentration (see Fig.2). The analysis suggested that there was no statistically
significant association between extortion prevalence and concentration at the state level
(
R=−0.086
,
p=0.64
), which supports the view that prevalence and extortion are fueled
by distinct processes (at least at the state level).15
Independent Variables
Given the potential predictors identified in an earlier section, four macro-level variables
measured at the state level (corruption prevalence (log), federal weapon crimes (log), fed-
eral drug crimes (log), and rule of law), and four micro-level variables measured at the
level of individual business units (corruption victimizations, years in business, business
type, and business size) were operationalized as independent variables. We included three
additional macro-level variables (number of surveyed businesses (log), population (log)
and competitiveness16) as controls. Table2 presents descriptive statistics for the independ-
ent variables, while Fig.1 presents a series of thematic maps summarizing how these vari-
ables, as well as key indicators of extortion, vary across Mexico.
Macro-level variables
• Rule of law: To measure the strength of the legitimate governance structure, we used
a rule of law index obtained from the Mexican Institute for Competitiveness (Instituto
Mexicano para la Competitividad, IMCO 2016), a think tank.17
• Corruption prevalence: Measures the number of businesses in a state that reported
being the victim of corruption in the ENVE.
15 In contrast, see (Sidebottom 2013, p.154–155) for a positive and statistically significant relationship
between area-level prevalence and concentration of burglary victimization in Malawi, which suggests that at
least some of the area-level factors affecting burglary victimization in that country also affect the number of
repeat burglaries suffered.
16 We used a modified version of IMCO’s competitiveness index that assesses states on a 100 point scale
(higher is better) according to their 2013 performance in nine subindices measuring business friendliness.
The version we used excluded the rule of law component as this is used as a dependent variable.
17 We used a revised version of the index grading states on a 100 point scale (higher is better) based on
2013 measures of kidnapping incidence, vehicle theft, costs of crime, total personal and household crime
incidence, the dark figure, fear of crime, availability of notaries, and contract enforcement. We excluded
homicide rates from the revised index, as these were collinear with our other independent variables.
Journal of Quantitative Criminology (2021) 37:1115–1157 1127
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1 3
• Federal drug crimes: To estimate the amount of drug trafficking activities in each state,
we used the number of crimes per state related to the General Health Law (used to reg-
ulate prohibited substances) as reported in 2013 by the Attorney General’s Office (Pro-
curaduría General de la República, PGR) to the Executive Secretariat of the National
System for Public Security (Secretariado Ejecutivo del Sistema Nacional de Seguridad
Pública, SESNSP 2015).
• Federal weapon crimes: The number of crimes relating to the Federal Law on Firearms
and Explosives as reported for 2013 by the PGR to the SESNSP (2015). This variable
serves as a proxy measurement of organized crime groups’ capacity to inflict violence,
as such crimes refer to those involving high-powered weapons—as well as seizures of
such weapons and ammunition—traditionally associated with organized crime groups.
Micro-level variables
• Corruption victimizations: Captured as counts in the ENVE by the question: “In total,
how many separate acts of corruption did you suffer during 2013?” (INEGI 2014d). An
act of corruption refers to a situation where a public servant—or a third party acting on
their behalf—directly asked for, suggested, or set the conditions for the payment of a
bribe by the business(JaimesBello and VielmaOrozco 2013; INEGI 2014d).
• Years in business: Calculated by subtracting the year respondents reported that their
business started operations from the survey reference year (i.e.2013). As our inter-
est is modeling the effect of being a new business in comparison to older businesses,
rather than the effect of an additional year in business, nominal categories were con-
sidered more appropriate. Thus, businesses were binned into quintiles from the 20%
youngest to the 20% oldest.
Table 1 The distribution of extortion victimization and the percentage of potential targets affected
Events Prevalence Incidence Target % Victim % Incident % Repeats %
0 25895 – 91.953 – – –
1 1654 1654 5.873 72.992 44.236 –
2 338 676 1.200 14.916 18.080 22.946
3 139 417 0.494 6.134 11.153 18.873
4 55 220 0.195 2.427 5.884 11.202
5 22 110 0.078 0.971 2.942 5.974
6 12 72 0.043 0.530 1.926 4.073
7 3 21 0.011 0.132 0.562 1.222
8 8 64 0.028 0.353 1.712 3.802
10 20 200 0.071 0.883 5.349 12.220
12 3 36 0.011 0.132 0.963 2.240
15 4 60 0.014 0.177 1.605 3.802
20 3 60 0.011 0.132 1.605 3.870
24 1 24 0.004 0.044 0.642 1.561
25 1 25 0.004 0.044 0.669 1.629
30 2 60 0.007 0.088 1.605 3.938
40 1 40 0.004 0.044 1.070 2.648
Totals 28161 3739 100% 100% 100% 100%
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1128
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1 3
Table 2 Descriptive statistics of
independent variables Variable Obs. % Mean S.D. Min. Max.
Business-level variables
Corruption victimizations 28161 0.1 1.3 0 98
Years in business
0–5 (base) 6772 24.0
6–9 5921 21.0
10–14 4984 17.7
15–23 5500 19.5
24–212 4984 17.7
Business type
Retail (base) 10088 35.8
Mining 89 0.3
Construction 820 2.9
Manufacturing 3707 13.2
Wholesale 1952 6.9
Transport 720 2.6
Media 259 0.9
Finance 318 1.1
Real estate 417 1.5
Prof. services 753 2.7
Maintenance 908 3.2
Education 955 3.4
Health 1157 4.1
Leisure 316 1.1
Hotels, Rest. & Bars 2787 9.9
Other 2915 10.3
Size
Large (base) 3052 10.8
Medium 3640 12.9
Small 5840 20.7
Micro 15629 55.5
State-level variables
Corruption prevalence 32 40.1 18.4 14 101
Federal weapon crimes 32 559.6 451.6 31 1632
Federal drug crimes 32 526.9 871.7 37 3738
Rule of law index 32 54.4 13.3 21.4 78.4
Competitiveness index 32 47.7 8.5 25.3 67.8
Population (in millions) 32 3.7 3.15 0.7 16.4
N sampled businesses 32 880.6 236.4 534 1657
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1 3
1000 km500 km
N
G. Population H. Business competitiveness index I. Rule of law index
D. N surveyed businesses E. Federal Drug Crimes F. Federal Weapon Crimes
A. Extortion prevalence B. Extortion concentration C. Corruption prevalence
−2
0
2
4
s.d.
Mexico: State−level summary statistics
Geometries: INEGI, ESRI; Data: ENVE 2014, SESNSP, IMCO
Fig. 1 Thematic maps showing variations in state-level variables, and state-level measures of extortion
Fig. 2 Relationship between
state-level extortion prevalence
and concentration. The results
of a correlation test (shown in
label) suggest that there was no
statistically significant relation-
ship between the variables R = -0.086, p = 0.64
1.5
2.0
2.5
50 100150
Prevalence per 1000 businesses
Concentration
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1 3
• Business type: Captured according to the North American Industrial Classification Sys-
tem’s second level18 (Sistema de Clasificación Industrial de Norte América, SCIAN,
INEGI 2007).
• Business size: Categories (micro, small, medium and large) were provided by INEGI
(2014b) and are based on the number of employees reported by each business.19
Analytical Strategy
Our analysis was conducted in two parts. First, using an implementation of the Kolmogo-
rov–Smirnov test (KS test, Upton and Cook 2014a) for discrete distributions proposed by
Arnold and Emerson (2011), we assessed H1 by comparing the observed distribution of
extortion to that expected under the null hypothesis of random victimization—the latter
estimated by a Monte Carlo simulation of a Poisson process with 500 replicates. Addi-
tionally, to assess if the observed distribution presented more zeroes than expected, we
compared the observed prevalence to that expected under simulated Poisson and negative
binomial distributions using contingency tables.
Next, we used statistical modeling to assess H2. The standard model used to estimate
victimization counts is the multilevel negative binomial20 model (MNB) (Tseloni and Far-
rell 2002). Considering
yij
is the count of extortion victimizations suffered by the
ith
busi-
ness, in the
jth
state, and that
x′
ij
is a vector of covariates thought to determine
yij
, the MNB
model for the mean of event counts,
E
[yij
|
x
�
ij
]=𝜇
ij
, can be represented by:
where
𝛽0
is the intercept, and
𝛽1
is a vector of fixed regression coefficients that quantify the
relationship between
x′
ij
and
ln(𝜇ij)
.
u
0
j
is the random variation in
𝛽0
associated with each
state
j
, and
𝜀ij
is a gamma distributed error term that incorporates overdispersion via the
𝛼
parameter (see Cameron and Trivedi 2013; Tseloni and Farrell 2002; Hilbe 2011). The
probability function of the MNB model (see Cameron and Trivedi 2013; Hilbe 2011, ) is
given by:
(1)
ln(
𝜇ij
)=
𝛽0
+
𝛽1x
�
ij
+
u0j
+
𝜀ij
u
0j∼N(0, 𝜎2
u0
)
exp
(𝜀
ij
) ∼ Γ(1, 𝛼)
(2)
Pr
[yij
|
x�
ij]=
Γ(yij +𝛼−1)
Γ(y
ij
+1)Γ(𝛼−1)
(
1
1+𝛼𝜇
ij )
𝛼
−1(
1−1
1+𝛼𝜇
ij )
y
ij
18 The categories are, in industry: mining, construction, and manufacturing; in commerce: retail and whole-
sale; in services: transport, media, finance and insurance, real estate, professional scientific and technical
services, maintenance providers, education, health, leisure, restaurants, hotels and bars, and other services.
Observations corresponding to 18 businesses classified as utilities and corporate offices were excluded as
there were problems of complete and quasi-complete separation.
19 Micro businesses have 10 employees or fewer; small businesses employ between 11 and 50 people (11–
30 in commerce); medium businesses employ between 51 and 250 in industry, 31–100 in commerce, and 51
to 100 in services; large businesses are those with 101 or more employees (251 or more in industry).
20 We used the standard NB2 formulation of the negative binomial variance function,
𝜎2
ij
=𝜇ij +𝛼𝜇
2
ij
(Cam-
eron and Trivedi 2013).
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1 3
When
𝛼→0
, the probability function collapses to the Poisson (Cameron and Trivedi
2013,p.85), meaning that there is no business-level unexplained heterogeneity. Conversely
as
𝛼
becomes larger, unexplained heterogeneity between businesses increases. Heterogene-
ity at the state level is captured by
𝜎2
u0
, and the formula
𝜌
=𝜎
2
u0
∕(𝜎
2
u0
+𝛼
)
, allows the calcu-
lation of the intra-class correlation (ICC), which represents the correlation of the mean of
extortion incidents between two identical businesses in the same state (see Goldstein 2011;
Tseloni and Farrell 2002). Conversely, the inverse of the ICC,
1−𝜌
, represents the proba-
bility of two identical businesses anywhere in the country experiencing the same number
of extortion victimizations, after controlling for between-state differences.
We hypothesized (H2) that extortion concentration is produced by a process different
from that which generates extortion prevalence, thus the MNB model is unsuitable for our
purposes—as it uses the same probability function (Eq.2) for all values of
y
. The multi-
level negative binomial-logit hurdle model (MNB-LH), in contrast, is a suitable alterna-
tive. The fundamental logic underpinning hurdle models (Mullahy 1986) is that they allow
the specification of distinct probability functions for observations where
y=0
, and
y>0
(Cameron and Trivedi 2013):
where
f1(0)
is the probability of observing a zero count. If the hurdle is crossed (if
y>0
),
the truncated count density is given by
f2(y)∕(1−f2(0))
, which needs to be multiplied by
1−f1(0)
to ensure that probabilities sum to one (Cameron and Trivedi 2013). In practice,
f1(
⋅
)
can be estimated using the logit model, specified in its multilevel form (Goldstein
2011) as such:
where
𝛾0
is the intercept for the binary model,
𝛾1
is a vector of fixed coefficients that quan-
tify the relationship between
x′
ij
and
ln(𝜋ij)
, and
v
0
j
represents the random variation in
𝛾0
associated with each state
j
. The probability of observing zero (
f1(0)
) is given by (Hilbe
2011):
and the probability of crossing the hurdle (
1−f1(0)
) is thus (Hilbe 2011):
Taking the standard negative binomial density in Eq.2 as
f2(
⋅
)
, the truncated density needs
to be rescaled as shown in Eq.3. The
f2(0)
density is
(
1−𝛼𝜇
ij
)
−
1
∕𝛼
(Hilbe 2011), and
1−f1(0)
is shown in Eq.6. Thus, the multilevel truncated negative binomial density for
yij >0
is:
(3)
Pr
[y]=
{
f1(0)if y=
0
(1−f1(0)) f2(y)
1−f
2
(0)if y>
0
(4)
ln(
𝜋ij
)=
𝛾0
+
𝛾1x
�
ij
+
v0
j
v
0j∼N(0, 𝜎2
v
0
)
(5)
Pr
[yij =0
|
x�
ij]=
1
1+𝜋
ij
(6)
𝜋
ij
1
+𝜋
ij
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1 3
where
𝜇ij
is estimated using Eq.1 and restricting
yij >0
. The complete multilevel negative
binomial-logit hurdle model is therefore:
An advantage of the hurdle model is that its components (the prevalence and truncated
count models) can be estimated separately. However, when observations are clustered and
random effects are used, as in the multilevel approach used here, the two stage estimation
procedure assumes that group random effects for prevalence and concentration (
v
0
j
and
u
0
j
,
respectively) are independent, when in fact they may be correlated (Min and Agresti 2005).
This situation would arise when unobserved differences between states affect state-level
prevalence and concentration in the same way, and could bias the results if not addressed.
In response, Min and Agresti (2005) suggest fitting the hurdle model with random effects
following a bivariate normal distribution and estimating the model via approximations (see
also Cantoni etal. 2017).
Unfortunately, the software available at INEGI did not permit the fitting of a hurdle
model with bivariate normal random effects. While this could potentially lead to some
bias in the estimates, (Cantoni etal. 2017,p.2191) note that estimated coefficients and
standard errors are generally robust to this misspecification (see also McCulloch and
Neuhaus 2011). Furthermore, Cantoni etal. (2017) note that when there is no correla-
tion between cluster prevalence and concentration, estimates from independently esti-
mated hurdle models are unbiased. As discussed in the “Dependent Variable” section,
we found no relationship between prevalence and concentration of extortion at the state
level, thus the assumption of correlated random effectcs can be relaxed and the inde-
pendent hurdle approach used can be judged as appropriate.
All models were estimated using the “glmmADMB” package(Fournier etal. 2012;
Bolker et al. 2012). We estimated the standard MNB model as a baseline to com-
pare the estimates of the MNB-LH model. The MNB-LH model was estimated sepa-
rately, with a multilevel logit (ML) estimating the likelihood of observing a victimi-
zation incident, and a multilevel truncated negative binomial (MTNB) estimating the
expected concentration among victimized targets. Model significance of each individ-
ual model (MNB, ML and MTNB) was assessed using likelihood ratio tests (Cameron
and Trivedi 2013,p.49; Hilbe 2011,p.177). Given that MNB and MNB-LH models
are not nested—and hence not suitable for comparison using likelihood ratio tests—
they were compared using the Akaike (AIC) and Bayesian (BIC) information criteria
(Cameron and Trivedi 2013,p.197), with lower values indicating a better model. AIC
and BIC estimates for the hurdle model were calculated by adding the AIC and BIC
estimates of the constituent models (Hilbe 2014, e.g.
AICMNB-LH =AICML +AICMTNB
;
see][p.188).
(7)
Pr
[yij
x�
ij]=𝜋ij
1+𝜋ij
Γ(yij+𝛼−1)
Γ(yij+1)Γ(𝛼−1)
1
1+𝛼𝜇ij
𝛼
−1
1−1
1+𝛼𝜇ij
yij
1−(1−𝛼𝜇ij )−1∕𝛼
(8)
Pr
[yij
x�
ij]
1
1+𝜋ij
if yij =
0
𝜋ij
1+𝜋ij
Γ(yij+𝛼−1)
Γ(yij+1)Γ(𝛼−1)1
1+𝛼𝜇ij 𝛼−11−1
1+𝛼𝜇ij yij
1−(1−𝛼𝜇ij)−1∕𝛼
if yij >
0
Journal of Quantitative Criminology (2021) 37:1115–1157 1133
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1 3
Results
Univariate Analysis
Table1 shows the distribution of crimes across targets. This can also be displayed using
Lorenz curves (Upton and Cook 2014b), which show the cumulative share of crime experi-
enced by the cumulative share of the population that experiences them (Tseloni and Pease
2005). If crime is evenly distributed, the Lorenz curve will approximate the line of equal-
ity shown in the figure. Deviation from this indicates that crime is unequally distributed
(Tseloni and Pease 2005,p.77).
Figure3 shows Lorenz curves for the observed and expected distributions, the latter being
the distribution of the simulated replicates. The panel on the left shows that both observed and
expected frequencies are highly concentrated among all businesses, which is to be expected
given than the vast majority of businesses were not extorted. The right-hand panel, however,
shows the distribution for victimized businesses—thus representing repeat victimization. The
curve of the expected distribution is very close to the line of equality, while the curve of
the observed distribution exhibits far more concentration. Crucially, a KS test (
D=0.044
,
p<0.001
) confirmed that the differences between the distributions are statistically signifi-
cant—there is more repeat victimization than that expected under random victimization.
Lastly, considering the shape of the statistical distribution, Table3 and Fig.4 show that
there are more zeros that would be expected assuming a Poisson distribution (
𝜒2=498.2
,
df = 1,
p<0.001
). However, after taking account of overdispersion by modeling a neg-
ative binomial distribution, there were no significant differences between the number of
observed and expected zeroes (
𝜒2=0.17
, df = 1,
p=0.68
), hence the modeling strategy
does not need to account for zero-inflation.
Statistical Modeling
Table4 presents model statistics for null and fully specified versions of estimated mod-
els. Goodness of fit was assessed using likelihood ratio tests. Fully specified models
were found to be significantly different from null models. Multilevel specifications sig-
nificantly improved fit when compared to single-level models. Similarly, the MNB and
MTNB models proved a significant improvement over Poisson and truncated Poisson
models. AIC and BIC values for the hurdle model were smaller than for the MNB model
(
AICMNB−LH −AICMNB =−219
, and
BICMNB−LH −BICMNB =−38
), which suggests that
the hurdle model of extortion victimization is more appropriate. The table also presents
estimates for state-level variance, the
𝛼
parameter, and the intra-class correlation (ICC),
which are discussed in detail in a later section.
Lastly, multi-collinearity was not deemed to be significant, as generalized variance
inflation factors (Fox and Monette 1992, GVIF,][) were quite small (see Table5). As (Fox
and Monette 1992,p.180) note, to preserve comparability inflation factors must be scaled
by the amount of categories in categorical predictors. Adjusting for this, the largest value
in column
GVIF1∕2df
is
2.08
—well within the thresholds that many practitioners regard as a
sign of severe multi-collinearity21 (O’brien 2007).
21 See also the online discussion on the Cross Validated website: https ://bit.ly/3bt6f 98
Journal of Quantitative Criminology (2021) 37:1115–1157
1134
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1 3
Figure5 shows exponentiated model coefficients22 to facilitate interpretation (
e𝛽
and
e𝛾
).
For count MNB and MTNB models, the exponentiated estimates represent incidence rate
ratios (IRR, Hilbe 2014,p.60), whereas for the binary ML model they represent odds ratios
(OR, Weisburd and Britt 2014,p. 568). Subtracting 1 from the IRR (
IRR −1
) gives the
percentage change on the concentration of extortion victimization for a one unit increase in
the independent variable, while
OR −1
gives the percentage change in the prevalence risk.
For categorical independent variables, the percentage change is relative to the reference
category. IRRs and ORs for log transformed independent variables23 represent change for a
10% increase in the independent variable (given by
1.10𝛽
and
1.10𝛾
).
Macro‑level Eects
Overall, the associations between extortion and state-level variables were quite weak.
Moreover, the associations were inconsistent for the prevalence and concentration com-
ponents, as no state-level variable was significant in the count part (MTNB) of the hurdle
model. Thus, the associations in the MNB model appear to reflect differences in preva-
lence risk captured by the ML model, rather than a state-level effect on repeat extortion
victimization.
All else being equal, the ML model found that a 10% increase in the number of cor-
ruption victims in a state was associated with a 5% increase in the likelihood of a business
becoming a victim of extortion. Similarly, a 10% increase in the number of federal weapon
crimes in a state, was associated with a 4% increase in extortion prevalence risks. In con-
trast, a 10% increase in the number of federal drug crimes in a state was associated with a
2% reduction in the likelihood of a business becoming a victim of extortion. Lastly, differ-
ences in the rule of law index between states showed no association with extortion risks.
22 Raw model estimates can be found in the “Appendix”.
23 Log transformed variables were centered around the log of the mean.
Fig. 3 Lorenz curves with the
observed and expected distribu-
tions of extortion victimization
Journal of Quantitative Criminology (2021) 37:1115–1157 1135
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1 3
Micro‑level Eects
Business-level effects were also inconsistently associated across the components of the
hurdle model, with the exception of corruption victimizations and being a micro-sized
business.
Table 3 Observed and expected
prevalence calculated using a
Monte Carlo simulation with
2000 replicates
Observed Poisson Neg. Bin.
0 25895 24659 25914
≥1
2266 3502 2247
Total 28161 28161 28161
0.0000
0.0025
0.0050
0.0075
24500 25000 25500 26000
Zeroes
density
Distribution
Poisson
Negbin
Fig. 4 Amount of zeroes predicted by 2000 Monte Carlo replicates of a Poisson and a Negative Binomial
distribution based on the observed distribution of extortion. The observed prevalence of zeroes is within the
95% CI of the negative binomial distribution but outside the Poisson expectation
Table 4 Model statistics for null and fully specified multilevel negative binomial (MNB), multilevel nega-
tive binomial-logit hurdle (MNB-LH), multilevel logit (ML) and multilevel truncated negative binomial
(MTNB) models
Degrees of freedom for likelihood ratio tests (LRT), 30.
∗∗∗p
<
0.001
MNB MNB-LH ML MTNB
Null Full Null Full Null Full Null Full
Log. lik. −10111 −9841 −9992 −9700 −7679 −7455 −2313 −2244
AIC 20228 19748 19995 19529 15363 14975 4632 4555
BIC 20253 20020 20029 19982 15379 15239 4649 4744
𝜎2
0.23 0.08 – – 0.25 0.09 0.31 0.21
𝛼
9.12 7.48 – – – – 148.41 148.41
ICC 0.02 0.01 – – – – 0.00 0.00
LRT 540.3*** – 447.9*** 137.7***
n28161 28161 – – 28161 28161 2266 2266
Groups 32 32 – – 32 32 32 32
Journal of Quantitative Criminology (2021) 37:1115–1157
1136
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1 3
The MNB model indicates that a one unit increase in the number of corruption vic-
timizations experienced by a business increases the number of extortion victimizations a
business can expect by 32%. The hurdle components suggest that the effect of corruption
victimizations is consistent for both the prevalence and concentration of extortion. The
ML model suggests that a one unit increase in the number of corruption victimizations
increases the likelihood of becoming a victim of extortion by 12%, whereas the MTNB
model suggests that it increases the number of repeat extortions expected by extorted busi-
nesses by 15%.
Business size categories had contrasting effects for the prevalence and concentration
components. Results from the MNB model suggest that micro-sized businesses suffer
an average of 50% fewer extortion incidents than large businesses (the reference cate-
gory). The insignificant coefficients for small and medium-sized businesses in the MNB
model suggest that they suffer extortion victimization at the same rate as large busi-
nesses. However, the results of the hurdle model paint a more nuanced picture. The
effect of being a micro-sized business is consistent across the hurdle: they are 30% less
likely to become victims of extortion, and experience 66% fewer extortion repeats if
victimized. On the other hand, small businesses face a 42% higher risk of becoming
a victim of extortion, yet they experience 52% fewer extortion repeats once extorted.
Medium businesses also see higher risks of extortion prevalence (23%), yet they experi-
ence repeat extortion at the same rate as large businesses, as the MTNB coefficient was
not significant.
With few exceptions, most business types faced no difference in extortion risks relative to
retailers (the reference category), though some categories presented contrasting effects across
the hurdle components. Hotels, restaurant and bars suffer 48% more extortion incidents than
retailers (MNB), though the hurdle model suggested that this was mainly due to differences
in the prevalence risk, rather than due to repeat victimization. The category faced a 43%
higher risk of becoming a victim of extortion (ML), though it showed no significant effect
in the concentration of repeat victimization (MTNB). Manufacturers, maintenance service
providers, and media businesses experienced fewer extortion incidents overall (from MNB:
−19
%,
−27
%, and
−78
%, respectively), though for manufacturers and media businesses, such
Table 5 Generalized variance inflation factors for independent variables
MNB and ML (
y≥0
) MTNB (y = 0)
GVIF df GVIF
1∕2df
GVIF df GVIF
1∕2df
Corruption victimizations 1.01 1 1.00 1.02 1 1.01
Years in business 1.12 4 1.01 1.14 4 1.02
Business type 1.38 15 1.01 1.43 15 1.01
Size 1.46 3 1.07 1.36 3 1.05
Corruption prevalence (log) 1.81 1 1.35 1.94 1 1.39
Weapon crimes (log) 3.69 1 1.92 4.32 1 2.08
Drug crimes (log) 2.62 1 1.62 2.66 1 1.63
N businesses (log) 1.82 1 1.35 2.12 1 1.46
Population (log) 2.15 1 1.47 2.23 1 1.49
Competitiveness index 1.23 1 1.11 1.23 1 1.11
’Rule of law’ index 1.72 1 1.31 2.27 1 1.51
Journal of Quantitative Criminology (2021) 37:1115–1157 1137
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1 3
●
●
●
●
●
●
●
●
●
●
●
●1.22
●1.2
●1.26
●0.73*
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
1.32***
1.34***
1.5***
1.54***
1.55***
0.72
0.98
0.81*
1.07
0.97
0.22***
0.86
1.15
0.81
1.48***
0.86
1.12
1.02
0.5***
1.03*
1.04***
0.97***
0.96
0.99
0.98**
1
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
1.12***
1.39***
1.43***
1.56***
1.42***
0.87
1.08
0.84*
1.08
1.26
0.3**
1.16
1.3
1.19
0.96
0.87
1.11
0.89
1.43***
0.86
1.23*
1.42***
0.7***
0.99
1.04***
1.05**
0.95
0.98**
0.98*
1
●1.15***
●1.09
●1.15
●1.19
●1.36
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
0.75
0.67
0.87
1.05
0.49**
0.24
0.78
0.97
0.87
0.4**
0.79
1.05
0.96
1.35
1.08
0.78
0.48***
0.34***
1.01
1.01
0.97
1.03
0.97
0.98
1.01
Multilevel Negative Binomial (MNB) Hurdle:MultilevelLogit (ML) Hurdle:Multilevel Truncated NegativeBinomial (MTNB)
0.51.0 1.52.0 0.51.0 1.501234
State: 'Ruleoflaw'index
State: Competitiveness index
State: Population (log)
State: Nbusinesses (log)
State: Drug crimes (log)
State: Weapon crimes (log)
State: Corruption prevalence (log)
Size:Micro
Size: Small
Size: Medium
Type:Other
Type: HotelsRest Bar
Type:Leisure
Type: Health
Type: Education
Type: Maintenance
Type:Prof. services
Type: Realestate
Type:Finance
Type: Media
Type: Tr ansport
Type:Wholesale
Type: Manufa cturing
Type: Constr uction
Type:Mining
Ye ars: 24 to 212
Ye ars: 15 to 23
Ye ars: 10 to 14
Ye ars: 6to9
Corruption victimizations
Exponentiated estimates and 95% C.I.
Fig. 5 Forest plot with exponentiated results from the models. Significance:
∗∗∗p
<
0.001
,
∗∗p
<
0.01
,
∗p
<
0.05
Journal of Quantitative Criminology (2021) 37:1115–1157
1138
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1 3
differences were apparently due to a lower risk of becoming victims (from ML:
−16
% and
−70
% respectively), as they did not suffer differential rates of repeat extortion according to
MTNB estimates. On the other hand, the opposite appears to be true for maintenance service
providers, whose odd ratios were not significantly different from 1, though they experienced
60% less repeat extortion than retailers. Lastly, while overall MNB and ML estimates did not
reveal significant differences between retailers and transport providers, MTNB estimates sug-
gest that once victimized, transport providers experienced 51% fewer repeats.
Business age also showed a contrasting effect across the components of the hurdle
model. Though the MNB model showed a positive and significant effect for all age catego-
ries, the hurdle model suggests that this is due to changes in prevalence risk. According to
estimates from the ML model, businesses aged 6–9, 10–14, 15–23, and 24 years or more
are 39%, 43%, 56%, and 42% respectively more likely to become victims of extortion, when
compared with businesses that had been in operation for 5 years or fewer (the reference
category). However, once victimized, business age categories had no effect on the expected
concentration of repeat extortion, as the coefficients in MTNB were not significant.
Unobserved Heterogeneity
Unobserved heterogeneity refers to differences in extortion victimization that remain unex-
plained by the independent variables in the study. Between-business unobserved hetero-
geneity (
𝛼
in Table4) arises when two identical businesses—in terms of those character-
istics included in the model—suffer unexplained differences in extortion incidence. The
independent variables selected reduced individual unobserved heterogeneity by 18%, from
𝛼null =9.12
in MNB, to
𝛼=7.48
in the fully specified MNB model. The relatively high
value of unexplained heterogeneity that remains suggests that there are factors not included
in the model that clearly influence extortion concentration. Such variables could relate to
risk heterogeneity or event dependence, though it is not possible to tell with this model. On
the other hand, the very substantive amount of unobserved heterogeneity in the count part
of the hurdle model (
𝛼=148.41
in MTNB), which was essentially unaffected by the inclu-
sion of explanatory variables associated with risk heterogeneity, suggests that an alterna-
tive process, such as event dependence, may be responsible.
In contrast, unobserved heterogeneity between states (
𝜎2
in Table4) refers to differences
in extortion risk faced by businesses in different states, after controlling for the variables
specified in the model. In the MNB model, level 2 variance is reduced significantly by the
inclusion of independent variables (
−65
%, from
𝜎2
u
0
null
=
0.23
to
𝜎2
u0
=
0.08
). The hurdle
model, suggests that much of this reduction is due to differences in the risk of extortion
prevalence, rather than in repeat victimization, as the ML models saw reductions of 64%
(from
𝜎2
u0null
=
0.25
to
𝜎2
u
0
=
0.09
) and the MTNB models reduced between-states unob-
served heterogeneity by 32% (
𝜎2
u0null
=
0.31
to
𝜎2
u
0
=
0.21
).
Both the MNB and the MTNB models suggest that the intra-state correlations (ICC in
Table4) are very small, and that between-businesses variations are more relevant. When
comparing all businesses, the ICC for MNB suggests that the probability of two identical
businesses—in terms of the variables included in the model—experiencing the same extor-
tion incidence due to being in the same state was only 1%. Conversely, the probability of
two identical businesses experiencing the same number of extortion victimizations, after
controlling for between-state differences, was 99% (
1−ICC
). For repeat victimization, the
MTNB model suggests that this probability was 99.9%.
Journal of Quantitative Criminology (2021) 37:1115–1157 1139
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1 3
Multilevel Negative Binomial (MNB) Hurdle: Multilevel Logit (ML) Hurdle: Multilevel Truncated Negative Binomial (MTNB)
0.5 1.0 1.52.00.5 1.0 1.5 2.0 01234
State: 'Rule of law' inde
x
State: Competitiv
eness index
State: Population (log)
State: N businesses (log)
State: Drug crimes (log)
State: Weapon crimes (log)
State: Corruption pr
evalence (log)
Size: Micro
Size: Small
Size: Medium
Type: Other
Type: Hotels Rest Bar
Type: Leisure
Type: Health
Type: Education
Type: Maintenance
Type: Prof. services
Type: Real estate
Type: Finance
Type: Media
Type: Transport
Type: Wholesale
Type: Manufacturing
Type: Construction
Type: Mining
Years: 24 to 212
Years: 15 to 23
Years: 10 to 14
Years: 6 to 9
Corruption victimizations
Exponentiated estimates and 95% C.I.
Original Bootstrap Excluding outliers
Fig. 6 Comparison of model estimates with robustness checks
Journal of Quantitative Criminology (2021) 37:1115–1157
1140
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1 3
Robustness Checks
We performed a series of post hoc analyses to check the robustness of our results. First
we calculated bootstrap standard errors for all models. To do this, we randomly sampled
with replacement n business units 99 times, fitted models to each sample, and calculated
the standard error of the bootstrap coefficient estimates. Then, we fitted a further round of
models to a subset of data excluding observations with 30 or more extortions, to rule out
a potential outlier effect. Figure6 presents a graphical comparison of coefficient estimates
and confidence intervals for the original models and post hoc robustness checks. Complete
results tables are available in the “Appendix”.
Post hoc estimates were remarkably consistent with those of the original model. For all
models, bootstrap standard errors for business-level variables were only marginally differ-
ent from the original models, with no changes in inference. Bootstrap standard errors for
state-level variables were consistently smaller, though the changes only affected inference
for control variables, with the exception of drug crimes in the MTNB model. Similarly, the
magnitude and significance of parameters from models excluding outliers were very simi-
lar to those of the original model, with no changes in inference, except for the coefficient
for drug crimes in the MTNB model.
Post hoc checks for unobserved heterogeneity were similarly consistent with original
estimates. In the MNB model, business-level unobserved heterogeneity (
𝛼
) decreased
a marginal amount after excluding outliers, while it remained virtually unchanged in the
MTNB model. Similarly, state-level heterogeneity (
𝜎2
) was largely unaffected after exclud-
ing outliers in all models.
Discussion
This study set out to systematically examine victimization patterns of extortion against
businesses in Mexico to determine if incidents concentrate on repeat victims, and to
explore if the factors that explain the risk of becoming a victim of extortion also explain
the concentration of repeat extortion victimization.
Using data from Mexico’s commercial victimization survey, extortion incidents were
found to concentrate above what would be expected by chance (H1), with repeat extortion
victims suffering a disproportionate amount of total crime incidents—patterns consistent
with findings on repeat victimization for most crime types in many countries (e.g. Farrell
and Pease 2011; Farrell etal. 2005). In all, there were more repeat extortion victims than
one-time victims, and close to 40% of all incidents were repetitions.
The literature on repeat victimization has traditionally considered that the factors that
explain the prevalence of victimization also account for its concentration (e.g Pease and
Tseloni 2014,p.31). However, given that the role of event dependence may be more prom-
inent in determining the risk of repeat victimization in the case of extortion, and that extor-
tion often leads to enduring victim-offender relationships, we hypothesized that the fac-
tors that explain extortion concentration would be distinct from those that explain extortion
prevalence (H2).
Using a multilevel negative binomial-logit hurdle model, we found support for H2.
Overall, only two independent variables (corruption victimization and being a micro-sized
business) showed a consistent effect for both prevalence and concentration. Most variables
Journal of Quantitative Criminology (2021) 37:1115–1157 1141
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1 3
showed inconsistent effects (e.g., a positive effect for prevalence but a not significant effect
for concentration), though some presented contradictory ones (i.e., a positive effect for
prevalence and a negative effect for concentration).24
The literature on protection theory (e.g. Kleemans 2018) suggests that area-level effects
would likely be more relevant for extortion risks as opposed to specific factors associated
with individual businesses. Our findings mostly contradicted this, as state-level variables
were only marginally relevant for predicting extortion prevalence (with the exception of
drug crimes, which post hoc checks suggested were significantly associated with extortion
concentration). Notably, the direction of the effects of the significant variables did fit with
theoretical expectations: Businesses in states with more corruption (and hence with poorer
governance), and with more weapon-related crimes (and hence with more violence-prone
organized crime groups) experienced a higher risk of becoming victims of extortion, while
businesses in states with more drug trafficking activity faced lower risks of becoming vic-
tims of extortion, and less concentration if victimized. Unobserved state-level heteroge-
neity for extortion prevalence was comparatively smaller than for extortion concentration,
though the latter was dwarfed by the residual between-business unexplained heterogeneity.
This suggests that any area-level explanations for repeat extortion are unlikely to be found
at the state level, and instead may be explained by variables measured at sub-state level
(e.g.municipality, city, neighborhood).
Business-level effects proved to be far more important in explaining extortion risks,
though they mostly affected extortion prevalence rather than concentration. We hypoth-
esized that an association at the micro-level between corruption and extortion could be
explained by direct relationships between extortionists and corrupt officials in Mexico—
a link documented in the literature (Díaz-Cayeros etal. 2015; Morris 2013). While our
analysis cannot refute the possibility of a spurious relationship (e.g.that extortionists and
corrupt officials are attracted to the same kind of businesses), the fact that corruption vic-
timization increases the likelihood of becoming a victim of extortion and the amount of
repeat extortion incidents that businesses suffer once they have been extorted suggests that
the relationship is substantive and robust. Nonetheless, having established that an associa-
tion exists, exploring this issue further would seem to be important for future work.
Business size categories showed inconsistent relationships for prevalence and concen-
tration components—with the exception of micro sized businesses which were consist-
ently less likely to be extorted, and suffered fewer repeats once victimized. Small busi-
nesses were more likely to be extorted than large businesses (possibly due to their relative
vulnerability), though they suffered significantly fewer repeat victimizations thereafter (as
potential rewards were possibly clarified following the first offense). Similarly, the higher
24 Such inconsistencies of direction, magnitude and significance in the predictors may appear surpris-
ing, but they are in fact common findings in studies using hurdle models. For example, in a seminal study
using a hurdle model to analyze healthcare utilization in Germany, Pohlmeier and Ulrich (1995) found that
many of the predictors for the prevalence of visiting a physician were inconsistent with the predictors of the
amount of visits by patients with at least one visit, indicating that prevalence and concentration of health-
care utilization were fueled by distinct processes. Similar inconsistencies across hurdle components can be
found in studies of healthcare utilization in Mexico (Brown etal. 2005), workplace training (Arulampalam
and Booth 1997), intimate partner violence (Hellemans et al. 2015), and sentencing decisions (Rydberg
etal. 2017), for example.
Journal of Quantitative Criminology (2021) 37:1115–1157
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1 3
prevalence risk for medium businesses suggests more inherent vulnerability, though the
similar rates of repeat extortion suggest less variability regarding potential rewards.
As expected, hotels, restaurants and bars did experience higher risks of extortion,
though they did not experience more repeat incidents. The lower prevalence risks amongst
manufacturers may point to accessibility as an additional factor influencing vulnerability to
extortion: manufacturers tend to interact mostly with other businesses, while hotels, restau-
rants and bars are generally open to the public, and thus are naturally easier to access for
extortionists. In contrast, the lower prevalence risk for media businesses may be related to
risks perceived by extortionists, as extorting a news outlet such as a newspaper or a televi-
sion station could lead to exposure. Results also showed that after being victimized once,
most business types experienced similar rates of repeat extortion, apart from maintenance
and transport service providers, which experienced less repeat extortion. We believe that
such negative relationship may be related to factors affecting event dependence, such as
victim response to the first offense (Farrell etal. 1995,p.396). For example, transport pro-
viders may decide to avoid certain routes on which they have been previously victimized.
Contrary to our expectations, new businesses (those with 5 or fewer years in opera-
tion) experienced substantially lower risks of becoming victims of extortion, though age
was not associated with extortion concentration. We speculate that the association may
be explained by target visibility, rather than by an inherent attractiveness or vulnerabil-
ity linked to businesses’ age. All else being equal, new businesses may face lower risks
because they are less likely be known by offenders—i.e.they are less likely to feature in
an offender’s awareness space (Brantingham and Brantingham 2011)—and “offenders
can only commit crimes against targets of which they are aware” (Hepenstal and Johnson
2010,p.266). However, once a business is victimized (and thus known to offenders), busi-
nesses appear to be equally vulnerable and attractive to extortionists regardless of how long
they have been in business.
An important advantage of the hurdle model is that it allows clarifying the role of
between-business unobserved heterogeneity for overall extortion risks (captured by the
MNB model) and for the specific risks of extortion concentration (captured by the MTNB
model). Many significant business-level predictors in the MNB model were in fact captur-
ing differences in the prevalence risk, rather than in the risks of repeat extortion. Similarly,
the between-business unobserved heterogeneity in MNB captures unexplained differences
in both prevalence and concentration risks. By restricting observations to extortion victims,
the between-business unobserved heterogeneity reported in the MTNB model refers only
to unexplained differences in (repeat) extortion concentration. The high value of between-
business unobserved heterogeneity, and the fact that it was unaffected by the inclusion of
predictors, strongly support the hypothesis that (repeat) extortion concentration is fueled
by a process distinct from that which explains extortion prevalence. We believe that this
process is likely to be related to event dependence. As mentioned earlier, repeats are often
associated with how victims respond to an initial event. Thus, if an initial extortion event
were successful (in the offender’s view), it may lead to further extortion incidents in the
future, as the victim is known to comply. This would be similar to the case of bank robbery,
where success in past events has been found to be positively associated with suffering a
repeat robbery (Matthews etal. 2001). On the other hand, in the case of extortion the rela-
tionship between past success and future risk could also be negative, as refusal to comply
with an extortion attempt could lead repeated (and escalating) threats, especially if these
occur in the context of an institutionalized extortion relationship—such as those observed
in organized crime-related extortion rackets. However, we were unable to test whether the
outcomes of previous events were associated with repeat extortion, as the data used in this
Journal of Quantitative Criminology (2021) 37:1115–1157 1143
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1 3
study cannot clarify this. However, this certainly appears to be a relevant area for future
research, should the necessary data become available.
As discussed in section “A hurdle model of extortion victimization,” it is important to
remember that model choice was primarily driven by study design: our main hypothesis
required the use of a two-stage model that allowed us to test whether the predictors of the
prevalence of extortion victimization were consistent with the predictors of its concentra-
tion. As Rose etal. (2006) discuss, choosing the “best” modeling approach when dealing
with overdispersed count data should be based on a study’s aim and purpose, as models fit
using zero-inflated and hurdle frameworks can sometimes be indistinguishable (see also
Gray 2005). Thus, while alternative model frameworks (e.g. as zero-inflated models, or
variations of the hurdle components used such as modeling concentration using a mixture
of truncated counts) may also prove suitable to model extortion data, we did not consider
their use to be within the scope of this study. This would certainly appear to be an impor-
tant avenue for future research.
There are, of course, other limitations to the present study. Chief amongst them is the
validity of using victimization surveys to measure extortion against businesses. Di Gennaro
and La Spina (2016; see also LaSpina 2008; LaSpina etal. 2014) suggest that victimiza-
tion surveys are not reliable instruments to measure extortion (p.4), though it is worth not-
ing that their criticism is based on Italian victimization surveys, particularly one by Conf-
commercio-GFK Eurisko (2007), and another by TRANSCRIME (Mugellini 2012). Their
main contention is that the surveys’ low response rates (6.3% and 14%, respectively) lead
to self-selected samples unlikely to produce reliable outcomes (DiGennaro and LaSpina
2016,p.4). Additionally, Asmundo and Lisciandra (2008) note that “victims of extortion
are unlikely to come forward as such” in victimization surveys (p.227). They ascribe this
reticence to the fact that for many Italian—and especially Sicilian—businesses, “extortion
is considered as ‘normal’ and made endogenous by the economic and social system, as
an (ordinary) component of production costs,” and as such it loses its “criminal profile”
(Asmundo and Lisciandra 2008,p.227)—i.e.they do not consider themselves victimized.
We find little evidence of these limitations in Mexico. First, the response rate for the
ENVE’s random sample was much higher at 84% (JaimesBello and VielmaOrozco 2013),
which should assuage fears of self-selection affecting measurement validity. Second, there
is no evidence of a process of extortion “endogenisation” (Asmundo and Lisciandra 2008)
in Mexico; in fact, the opposite appears to be true. Faced with increases in extortion and
other organized crime related violence, the response from the business community in
Mexico has ranged from vociferous protest, to proactive involvement in the improvement
of public security institutions (Shirk etal. 2014). For example, in Monterrey businesses
spearheaded, and funded the creation of a new state police force in association with uni-
versities and civil society (Conger 2014). Thus, we find little reason to believe that busi-
nesses in Mexico would systematically refuse to provide truthful answers regarding their
extortion victimization experiences to the ENVE. As such, we believe that the extortion
estimates captured by the ENVE suffer no more than the well-known measurement limita-
tions shared by all well conducted victimization surveys ( see Lynch 2006,p.245; Skogan
1986; UNODC/UNECE 2010).
Lastly, other important limitations refer to the temporal horizon imposed by the
cross-sectional design based on a 1year period. First, by collapsing the temporal scale
to 1year, the study cannot capture the time-course of repeat victimization (Johnson etal.
Journal of Quantitative Criminology (2021) 37:1115–1157
1144
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1 3
1997)—i.e.it cannot measure how extortion risks change immediately after a victimiza-
tion incident. Second, the reference period artificially imposes a time-window on repeat
victimization—i.e.some extortions early in the period may be repeats of extortions that
took place before the period began and some extortions at the end of the period may have
repeats after it ends—which would lead to an undercounting of repeat victimization (Far-
rell and Pease 1993,p.19). Such limitations are difficult to overcome with the current data,
though perhaps future iterations of the ENVE could incorporate an “embedded panel”
(Hopkins and Tilley 2001) to address some temporal variation.
In conclusion, this study applied a novel modeling strategy—the multilevel negative
binomial-logit hurdle model—to identify whether the processes that lead to extortion prev-
alence are the same as those that lead to extortion concentration, as tends to be consid-
ered in the repeat victimization literature. The findings support the use of the hurdle model
over the negative binomial model. Thus, studies on crimes where repeats are thought to be
strongly influenced by event dependence mechanisms (such as domestic violence), would
do well to test whether the hurdle model is a better fit. Furthermore, the study expands
the crime concentration literature by focusing on a non-traditional crime type (extortion)
in a new context (Mexico). Findings highlight areas that need to be researched further.
These include, for example, analyzing area-level effects at smaller spatial resolutions, and
directly discriminating between risk heterogeneity and event dependence as sources of risk
for repeat extortion using longitudinal data. In addition, a follow up qualitative study of
the most chronically victimized studies would further enhance our understanding of repeat
extortion victimization. Hopefully, subsequent studies will find in this paper a useful start-
ing point to build upon and develop finer insights.
Acknowledgements PRES received funding from Mexico’s National Council of Science and Technol-
ogy (CONACYT) and the State of Nuevo Léon (382181) and Mexico’s Secretary of Education (BC-7698,
BC-6225, BC-4629, BC-2974). The authors thank Mexico’s National Statistics Agency (INEGI) for provid-
ing access to the data used in this study. We also thank the anonymous reviewers for their helpful comments
and suggestions.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License,
which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long
as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Com-
mons licence, and indicate if changes were made. The images or other third party material in this article
are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the
material. If material is not included in the article’s Creative Commons licence and your intended use is not
permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly
from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Appendix
See Tables6, 7 and 8.
Journal of Quantitative Criminology (2021) 37:1115–1157 1145
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1 3
Table 6 Model estimates (log scale) and robustness checks for multilevel negative binomial (MNB) models
∗∗∗p
<
0.001
,
∗∗p
<
0.01
,
∗p
<
0.05
. Bootstrap repetitions: 99
MNB
Original (SE) Bootstrap (SE) Excluding outliers (SE)
Intercept −2.28*** (0.12) −2.28*** (0.14) −2.31*** (0.12)
Business-level variables
Corruption victimizations 0.28*** (0.04) 0.28*** (0.07) 0.28*** (0.04)
Business age (base: 0–5)
6–9 0.29*** (0.08) 0.29* (0.12) 0.30*** (0.08)
10–14 0.40*** (0.08) 0.40*** (0.11) 0.35*** (0.08)
15–23 0.43*** (0.08) 0.43*** (0.11) 0.44*** (0.08)
24–212 0.44*** (0.08) 0.44*** (0.10) 0.41*** (0.08)
Business type (base: retail)
Mining −0.33 (0.44) −0.33 (0.32) −0.31 (0.44)
Construction −0.02 (0.14) 0.02 (0.14) 0.02 (0.14)
Manufacturing −0.21* (0.08) −0.21** (0.08) −0.18* (0.08)
Wholesale 0.06 (0.10) 0.06 (0.15) −0.00 (0.10)
Transport −0.03 (0.15) −0.03 (0.14) 0.01 (0.15)
Media −1.54*** (0.37) −1.54*** (0.31) −1.49*** (0.37)
Finance 0.20 (0.24) 0.20 (0.27) 0.21 (0.23)
Real estate 0.18 (0.21) 0.18 (0.15) 0.18 (0.20)
Prof. services 0.23 (0.15) 0.23 (0.20) 0.23 (0.15)
Maintenance −0.32* (0.15) −0.32 (0.20) −0.29 (0.15)
Education −0.15 (0.14) −0.15 (0.18) −0.12 (0.14)
Health 0.14 (0.13) 0.14 (0.12) 0.15 (0.13)
Leisure −0.20 (0.25) −0.20 (0.24) −0.20 (0.25)
Hotels Rest Bar 0.39*** (0.08) 0.39*** (0.09) 0.36*** (0.08)
Other −0.15 (0.10) −0.15 (0.12) −0.15 (0.09)
Business size (base = large)
Medium 0.11 (0.09) 0.11 (0.12) 0.07 (0.09)
Small 0.02 (0.09) 0.02 (0.10) 0.07 (0.09)
Micro −0.69*** (0.08) −0.69*** (0.10) −0.64*** (0.08)
State-level variables
Corruption prevalence (log) 0.36* (0.17) 0.36*** (0.09) 0.40* (0.17)
Weapon crimes (log) 0.45*** (0.11) 0.45*** (0.06) 0.44*** (0.11)
Drug crimes (log) −0.31*** (0.08) −0.31*** (0.04) −0.31*** (0.08)
N businesses (log) −0.45 (0.29) −0.45** (0.15) −0.49 (0.29)
Population (log) −0.10 (0.11) −0.10 (0.05) −0.11 (0.11)
Competitiveness index −0.02** (0.01) −0.02*** (0.00) −0.02** (0.01)
‘Rule of law’ index −0.00 (0.01) −0.00 (0.00) −0.00 (0.01)
n 28161 28161 28158
Groups 32 32 32
Journal of Quantitative Criminology (2021) 37:1115–1157
1146
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1 3
Table 7 Model estimates (log scale) and robustness checks for multilevel logit (ML) models
∗∗∗p
<
0.001
,
∗∗p
<
0.01
,
∗p
<
0.05
. Bootstrap repetitions: 99
Hurdle: ML
Original (SE) Bootstrap (SE) Excluding outliers (SE)
Intercept −2.84*** (0.12) −2.84*** (0.09) −2.84*** (0.12)
Business-level variables
Corruption victimizations 0.11*** (0.02) 0.11** (0.04) 0.11*** (0.02)
Business age (base: 0–5)
6–9 0.33*** (0.07) 0.33*** (0.08) 0.33*** (0.07)
10–14 0.36*** (0.08) 0.36*** (0.07) 0.35*** (0.08)
15–23 0.45*** (0.07) 0.45*** (0.07) 0.45*** (0.07)
24–212 0.35*** (0.08) 0.35*** (0.07) 0.35*** (0.08)
Business type (base: retail)
Mining −0.14 (0.40) −0.14 (0.41) −0.14 (0.40)
Construction 0.08 (0.12) 0.08 (0.12) 0.08 (0.12)
Manufacturing −0.17* (0.08) −0.17** (0.07) −0.17* (0.08)
Wholesale 0.07 (0.09) 0.07 (0.10) 0.07 (0.09)
Transport 0.23 (0.12) 0.23 (0.13) 0.23 (0.12)
Media −1.19** (0.36) −1.19** (0.38) −1.19** (0.36)
Finance 0.15 (0.21) 0.15 (0.19) 0.15 (0.21)
Real estate 0.26 (0.18) 0.26 (0.17) 0.26 (0.18)
Prof. services 0.18 (0.13) 0.18 (0.11) 0.18 (0.13)
Maintenance −0.04 (0.14) −0.04 (0.12) −0.04 (0.14)
Education −0.14 (0.12) −0.14 (0.12) −0.14 (0.12)
Health 0.11 (0.11) 0.11 (0.12) 0.11 (0.11)
Leisure −0.11 (0.23) −0.11 (0.17) −0.11 (0.23)
Hotels rest bar 0.36*** (0.07) 0.36*** (0.07) 0.36*** (0.07)
Other −0.15 (0.09) −0.15 (0.11) −0.15 (0.09)
Business size (base = large)
Medium 0.21* (0.09) 0.21* (0.09) 0.21* (0.09)
Small 0.35*** (0.08) 0.35*** (0.08) 0.35*** (0.08)
Micro −0.35*** (0.08) −0.35*** (0.09) −0.35*** (0.08)
State-level variables
Corruption prevalence (log) 0.48** (0.18) 0.48*** (0.08) 0.48** (0.18)
Weapon crimes (log) 0.44*** (0.12) 0.44*** (0.05) 0.44*** (0.12)
Drug crimes (log) −0.26** (0.09) −0.26*** (0.04) −0.26** (0.09)
N businesses (log) −0.53 (0.31) −0.53*** (0.14) −0.53 (0.31)
Population (log) −0.15 (0.12) −0.15** (0.06) −0.15 (0.12)
Competitiveness index −0.02* (0.01) −0.02*** (0.00) −0.02* (0.01)
‘Rule of law’ index −0.00 (0.01) −0.00 (0.00) −0.00 (0.01)
n 28161 28161 28158
Groups 32 32 32
Journal of Quantitative Criminology (2021) 37:1115–1157 1147
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1 3
Table 8 Model estimates (log scale) and robustness checks for multilevel truncated negative binomial
(MTNB) models
∗∗∗p
<
0.001
,
∗∗p
<
0.01
,
∗p
<
0.05
. Bootstrap repetitions: 99
Hurdle: MTNB
Original (SE) Bootstrap (SE) Excluding outliers (SE)
Intercept −4.37*** (0.22) −4.37*** (0.31) −4.45*** (0.22)
Business-level variables
Corruption victimizations 0.14*** (0.04) 0.14* (0.07) 0.15*** (0.04)
Business age (base: 0–5)
6–9 0.09 (0.16) 0.09 (0.21) 0.08 (0.16)
10–14 0.14 (0.17) 0.14 (0.20) 0.01 (0.17)
15–23 0.18 (0.16) 0.18 (0.20) 0.16 (0.16)
24–212 0.31 (0.16) 0.31 (0.24) 0.22 (0.16)
Business type (base: retail)
Mining −0.29 (0.85) −0.29 (0.87) −0.31 (0.85)
Construction −0.41 (0.26) −0.41 (0.29) −0.29 (0.26)
Manufacturing −0.14 (0.16) −0.14 (0.21) −0.08 (0.16)
Wholesale 0.05 (0.18) −0.05 (0.32) −0.09 (0.18)
Transport −0.71** (0.27) −0.71* (0.31) −0.58* (0.27)
Media −1.41 (0.85) −1.41 (0.72) −1.31 (0.85)
Finance −0.25 (0.47) −0.25 (0.49) −0.21 (0.46)
Real estate −0.03 (0.39) −0.03 (0.40) −0.04 (0.39)
Prof. services −0.14 (0.29) −0.14 (0.28) −0.13 (0.29)
Maintenance −0.93** (0.31) −0.93* (0.43) −0.83** (0.31)
Education −0.24 (0.26) −0.24 (0.38) −0.17 (0.26)
Health 0.05 (0.24) 0.05 (0.30) 0.06 (0.24)
Leisure −0.04 (0.51) −0.04 (0.71) −0.05 (0.50)
Hotels rest bar 0.30 (0.16) 0.30 (0.21) 0.26 (0.16)
Other 0.08 (0.20) 0.08 (0.31) 0.08 (0.20)
Business size (base = large)
Medium −0.25 (0.18) −0.25 (0.24) −0.33 (0.18)
Small −0.72*** (0.16) −0.72*** (0.21) −0.61*** (0.16)
Micro −1.08*** (0.16) −1.08*** (0.19) −0.96*** (0.16)
State-level variables
Corruption prevalence (log) −0.27 (0.29) −0.27 (0.19) −0.13 (0.28)
Weapon crimes (log) 0.14 (0.19) 0.14 (0.13) 0.14 (0.18)
Drug crimes (log) −0.28 (0.15) −0.28** (0.10) −0.29* (0.15)
N businesses (log) 0.31 (0.51) 0.31 (0.35) 0.13 (0.50)
Population (log) 0.15 (0.20) 0.15 (0.08) 0.14 (0.19)
Competitiveness index −0.02 (0.01) −0.02** (0.01) −0.02 (0.01)
‘Rule of law’ index 0.01 (0.01) 0.01 (0.01) 0.01 (0.01)
n 2266 2266 2263
Groups 32 32 32
Journal of Quantitative Criminology (2021) 37:1115–1157
1148
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