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«Urban Problems and sPatial methods VolUme 17, nUmber 1 • 2015 U.S. Department of Housing and Urban Development | Office of Policy Development and ...»

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Abstract In this article, we explore the spatial dimension of violence in Mexico by investigating the existence of spatial diffusion patterns associated with the increase in homicides. We specifically use exploratory spatial data analysis, or ESDA, techniques during the 2005through-2010 period to measure the extent to which Mexican municipalities have experienced an increase in violence levels that have diffused to contiguous municipalities. The findings indicate significant levels of spatial dependency leading to spatial clustering of high-incidence rates of homicides in specific regions of the country, with diffusion patterns of high levels of homicide rates to other nearby municipalities. Furthermore, it has been found that, during the period of analysis, municipalities that acted as contributors to the spread of high-incidence rates have not reduced their levels but are still experiencing high-incidence rates during the period of study.

Introduction Mexico witnessed a dramatic increase in violence levels during the second half of the 2000s. The most violent scenarios arose in areas with a high level of drug-trafficking activities and a longstanding presence of drug-trafficking organizations (DTOs, or cartels). It has been argued that the dispute among the DTOs concerning taking control of specific territories has been a major contributing factor in terms of the steep increase in violence when compared with previous periods of relatively stable trends in violence.

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The role of geography is a crucial aspect when analyzing recent violence levels in the country. This cruciality is because of well-defined patterns across the country of the distribution of past and contemporary violence levels and also the presence of DTOs. On the one hand, drug-trafficking activities routing from Mexico to the United States have very longstanding roots. Such activities date back to at least the mid-1980s, when Colombian cartels extended their influence to the United States via drug-trafficking networks, particularly after the successful enforcement efforts by Colombian authorities against the Colombian Cali and Medellin cartels that eventually gave rise to the emergence of Mexican DTOs. Colombians previously trafficked cocaine through Florida (Payan, 2006). Mexican smugglers made ties with Colombian traffickers and relocated the activity to the northern border.

On the other hand, DTOs have taken advantage of the rugged terrain of the mountains to plant marijuana and opium and, more recently, to produce synthetic drugs. The region referred to as the Golden Triangle, formed by the states of Chihuahua, Durango, and Sinaloa, historically has been a major producer of illicit drugs. Evidence suggests that, in fact, mountainous terrain has a positive relationship with proliferation of armed conflict, which eventually translates to rising homicide rates (Fearon and Laitin, 2003).

Although drug-trafficking and related violence have become serious problems and have hindered the government and national security, the concerns do not apply to the whole territory but only to particular areas. In such areas, the levels of violence, as measured by the number of homicides, have soared dramatically since the end of 2006. The unprecedented increasing levels of violence have been attributed to the confrontation among DTOs, especially after the deployment of federal armed forces to combat these organizations and to eliminate criminal control of public spaces.

These operations were coordinated by military and federal police forces and were backed by state and local security forces. The strategy included the dismantling of criminal organizations, the arrest of the largest possible number of criminals and the confiscation of drug shipments, the deployment of military operations in several regions of the country, and a permanent increase in resources devoted to the military forces. The states exposed to these joint operations were Michoacán (December 2006), Guerrero and Baja California (January 2007), Nuevo León and Tamaulipas (January 2008), Chihuahua (April 2008), and Sinaloa and Durango (May 2008). These states, with the exception of Nuevo León, not coincidentally have a long tradition of being involved in either drug trafficking or the production of illicit drugs. The map in exhibit A1 in the appendix depicts these regions.

These factors may certainly play an important role in explaining the rise in violence and, in particular, the location in which violence became noticeable. The areas with creation and expansion of illegal markets will produce extra murders when contextual factors conducive to lethal violence exist (Zimring and Hawkins, 1997).

In this article, we focus on the spatial dimension of this phenomenon by investigating the existence of spatial diffusion patterns associated with the increase in homicides in Mexican municipalities.

We specifically use exploratory spatial data analysis (ESDA) techniques during the 2005-throughperiod to measure the extent to which Mexican municipalities have experienced an increase in violence levels that have diffused to contiguous municipalities.

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Our contribution in this study consists of characterizing the type of spatial diffusion process in municipalities with low or high incidence levels. Using official, publicly available data of homicide records at the municipal level, the analysis employs global and local ESDA techniques to provide a descriptive analysis of the spatial distribution of homicides as well as dynamic changes that enable us to look for patterns across space in spatial dependencies. The analysis aims to answer the following research questions: How does the spatial distribution of homicides depict significant hotspot areas of high violence levels across the country? To what extent is spatial diffusion of high violence focalized within and between those states with longstanding drug-trafficking activities and where the joint operations took place.

Identification of concentrations or clusters of greater criminal activity has appeared as a central mechanism to targeting law enforcement efforts and crime prevention response to crime problems.

These clusters of crime are commonly referred to as hotspots—geographic locations “of high crime concentration, relative to the distribution of crime across the whole region of interest” (Chainey and Ratcliffe, 2005: 147). The main interest of the present study is to better understand the existence of hotspots of contemporary violence in the country; nonetheless, the identification of crime hotspots should be considered as the starting point of a more detailed analysis. The conclusion section of this article addresses further research venues on the topic.

The article is structured as follows. The next section, which introduces the methodology based on the ESDA techniques and describes the data used in the analysis, is followed by a section that outlines the results and the final section that draws some conclusions.

Methodology The methods described in this section are based on the use of ESDA, which helps visualize and describe the spatial distribution of homicides and also helps identify global and local spatial dependencies in the distribution of homicides across municipalities.

When exploring the distribution of homicides through ESDA, a common global indicator of spatial autocorrelation is the Global Moran’s I. It indicates the extent to which our variable of interest is clustered, dispersed, or randomly distributed across municipalities by formulating a null hypothesis of randomness in the entire data (Anselin, 1995). The Global Moran’s I is denoted in the following equation— (1), where N is the number of cases, x is the mean of the variable, xi is the variable value at a particular location, xj is the variable value at another location, and wij is a weight spatial matrix specifying the spatial interdependency of i relative to j. Positive values of this statistic indicate spatial clustering (for example, high homicide rates are found in close neighbors), while negative values indicate dispersion in the variable of interest.

Cityscape 37Flores and Villarreal

The significance of this statistic is influenced by the specification of the spatial relationship among the units of analysis or, in other words, by the choice of the spatial weight matrix. In the present analysis, four different standardized weight matrices are considered in the calculation of this indicator: (1) the first order contiguity matrix, (2) the second order contiguity matrix, (3) the k-4 nearest neighbors, and (4) the inverse distance.

Although global spatial measures help to assess the strength of spatial autocorrelation across all spatial units, generating one global statistic, local spatial variations may also exist in the degree of spatial dependency. The latter can be tackled through the computation of local measures of spatial autocorrelation. The use of local statistics can inform us about spatial nonstationarity or spatially varying relationships in our variable of interest, thus identifying statistically significant clusters (Fotheringham, 2009).

To analyze the nature of the local distribution of homicides, a local version of Moran’s I or local indicator of spatial autocorrelation (LISA) is employed. This statistic assesses a null hypothesis of spatial randomness by comparing the values of local pairs (that is, the values of each specific location with the values in neighboring locations; Anselin, 1995). It is particularly useful because

it allows for the decomposition of spatial association into four categories (HH, LL, HL, and LH):

(1) HH, or high-high—when a location with an above-average value is surrounded by neighbors whose values are also above average; (2) LL, or low-low—when a location with a below-average value is surrounded by neighbors whose values are also below average; (3) HL, or high-low—when a location with an above-average value is surrounded by neighbors whose values are below average;

and (4) LH, or low-high—when a location with a below-average value is surrounded by neighbors whose values are above average. See Anselin (1993) for a detailed description of the statistical properties of LISA statistics.

Detecting the Spatial Diffusion Process To explore the possible mechanisms associated with the diffusion process of homicide rates in the municipalities, this section develops an exercise that is useful for studying spatial clusters in a dynamic framework. Cohen and Tita (1999) identified changes in the levels of local-neighbor pairs (LISA clusters), looking at the type of diffusion process of homicide rates within spatial units. Within this framework, it is possible to identify four different mechanisms that may lead to changes from low to high levels (or vice versa) in local spatial units. Expansion and relocation are forms of contagious diffusion in which the status among neighboring spatial units affects the future status of adjoining units, by increasing the level either locally or for the neighbors located in the same local-neighbor pair. A distinction between these two forms is that with relocation the object that is being diffused leaves the point of origin and spreads outward from that point, and with expansion diffusion also spreads from the center but continues to experience high incidence rates of the diffusing phenomenon.

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