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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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Spatial units can also change from low to high levels through hierarchical diffusion in the forms of isolated or global increases, which reflect increases (or decreases) that do not depend on contact with nearby high-level (or low-level) spatial units. Here the spread does not occur with direct contact but happens more through cultural influences (innovation or imitation) that affect the population or a particular subgroup that may be widely dispersed geographically (Cohen and Tita, 1999).

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The idea of this exercise is to compare municipalities with transitions among different significant LISA pairs in successive years. We are especially interested in exploring those yearly transitions (between time t and t+1) from low to high levels of homicide rates among statistically significant clusters.1 The case of a transition from an LH at time t to an HL or an HH at time t+1 indicates a contagious diffusion of high homicide rates, while a transition from an LL to an HL or an LH denotes a hierarchical type of diffusion process. Exhibit 1 shows other possible transition combinations.

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Data Description The data for homicides come from the vital statistics of the Instituto Nacional de Estadistica y Geografia (INEGI). These data consider all types of homicides (ICD-10: X85-Y09)2 that occurred in Mexican municipalities from 2005 through 2010. We also explore a database for homicides related to drug rivalry or organized crime released by the Presidencia de la Republica. Starting in 2007, a database on homicides related to organized crime was produced for statistical purposes only; no ministerial or judicial information was included, only the numbers of deaths in municipalities and states. These deaths are classified as homicides related to organized crime if they occur with extreme violence or as an event involving more than two victims and include at least two of the following criteria: the body had an injury that resulted from the use of a firearm; the body had severe injuries and showed signs of torture; the body was found in the interior of a vehicle; the death of the body showed use of materials characteristic of the modus operandi of organized crime; and particular facts related to the death of the body, such as if the event occurred in an ambush, was a persecution, or included the finding of a message linked to organized crime.

In this study, significance levels directly obtained from the LISA calculations differ from those of George and Tita (1990), which consider significant local pairs to be those that involve a change of at least two standard units in the value of LISA local pairs (see the reference for further details).

International Classification of Diseases, World Health Organization.

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These data exhibit some issues related to data-gathering reliability, however, given that these criteria are used when classifying the homicides and because, for some of the cases, no official death certificate is attached. These factors in turn produce an overestimate of the total counts of homicides related to organized crime or drug rivalry compared with those officially reported by INEGI (Merino and Gomez, 2012). Although we analyze both databases currently available in Mexico, the final set of results is based on mortality data from an official vital statistics report by INEGI; in this sense, the data for narcotics-related homicides are used only for comparison, given the previously mentioned problems related to such a database.3 Results Exhibit 2 shows the Moran’s I value of total homicides obtained using different weighting matrices for 5-year intervals from 1990 through 2005 and yearly from 2006 up to 2010.4 As noted, the spatial dependence of total homicide rates among municipalities does not follow a regular pattern until 2007, when thereafter a constant yearly growth is observed. This pattern indicates that high levels of homicide rates resulted in more clustering across spatial units,5 and this pattern, obtained

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Global Moran’s I Statistic of Total Homicide Rates in Mexican Municipalities, 1990–2010 0.45 0.40 0.35

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Also, Rodriguez-Oreggia and Flores (2012) detected that between 8 and 12 percent of municipalities, at some point in time, have more homicides related to narcotics than the total official account of homicides.

The respective Global Moran’s I for narcotics-related homicide rates was also calculated, but the rates are not reported here. Data availability allows for the yearly calculation of homicide rates from 2007 onward, and the results show a higher degree of spatial autocorrelation among observations, confirming the descriptive analysis shown in the previous section.

These results are available from the authors upon request.

All values show statistical significance levels of at least p 0.05.

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from comparing different weight matrixes, is consistent. The calculations also suggest that the weight matrix assessing the higher degree of spatial dependence occurred with the first order contiguity matrix. The use of this matrix is appropriate for this study because we are interested in the diffusion of homicide rates occurring primarily in contiguous municipalities. Hence, the empirical evidence shown in the subsequent sections rests on this type of weight matrix.





Exhibit 3 reports the prevalence of municipalities within each local cluster type obtained from LISA on a yearly basis during the period of 2005 through 2010 for total homicides (Panel A) and for narcotics-related homicides since 2007 (Panel B). Three main results arise and are described as follows.

First, the number of municipalities exhibiting significance levels for any local-neighbor pairs (cluster type) of total homicide rates rose during the period from 418 to 548. For narcotics-related homicides, the number increased from 191 to 353 municipalities.

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with 7 percent of total municipalities, or approximately 174 municipalities, being included in this type. This HH cluster type shows a consistent decline after reaching its peak in 2009 and 2010, although its values are still higher than the initial values in 2005.

Third, higher levels of narcotics-related homicides surrounded by municipalities with HH levels were concentrated in approximately 83 of the municipalities, or about 3.4 percent of the total, in

2007. During the following 2 years, an upward trend was observed, suggesting an increasing number of municipalities with an HH cluster of narcotics-related homicides. By 2010, HH occurred in approximately 132, or 5.4 percent, of the municipalities.

A useful way to visualize clustering patterns of homicides in Mexico is through mapping. To this end, we combine ArcGIS and GeoDa software capabilities to create a series of maps, which summarizes much of the previous discussion. As discussed previously, we prefer to use total homicides instead of drug rivalry homicides. Consequently, the rest of the analysis relies on total homicide data from INEGI. In exhibit 4, it is possible to distinguish the states with army intervention and also the distribution of only the HH clusters of total homicide rates for each year from 2005 through 2010.

The latter are displayed as centroid circles with a graduated color corresponding to each year.

As observed, much of the concentration of high homicide rates at the beginning of the period occurs in the states that will have army intervention later. This concentration in turn supports the argument that the federal government used to deploy armed forces to particular areas within the country that exhibit considerably high levels of violence.

Exhibit 4 Spatial Diffusion of High-High (LISA) Clusters of Total Homicides in Mexico, 2005–2010 (1 of 4) a. 2005

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Exhibit 4 Spatial Diffusion of High-High (LISA) Clusters of Total Homicides in Mexico, 2005–2010 (2 of 4) b. 2005–2006 High-high: 2006 High-high: 2005 c. 2005–2007 States with army intervention in 2007 High-high: 2007 High-high: 2006 High-high: 2005

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The geographic dispersion patterns followed by these HH clusters are also noteworthy. On the one hand, a greater proportion of municipalities were experiencing clusters of the HH type within the states that, at the beginning of the period, were already experiencing high homicide levels.

On the other hand, a considerable proportion of municipalities that experienced transitions from nonsignificant to significant spatial clusters, particularly to HH type, continued to experience high levels of homicide rates despite the deployment of federal forces.

Detecting the Spatial Diffusion Process: Results The analysis then considers previous results (reported in exhibit 3) to calculate local pair changes.

Exhibit 5 reports the results associated with the analysis of total homicide rates. To facilitate the explanation, we first provide the results for the proportion of municipalities that enter into each type of diffusion (contiguous or hierarchical) and have a direction change from low to high levels, and then we determine whether the local pair serves as an outcome or a source of these transitions.6 As described previously, a high incidence of homicide rates for the period of study tend to be spatially clustered within states in which army interventions actively operate; hence, the analysis also performs a t-test for mean differences of each outcome to whether the municipality belongs these states as compared with the rest.

The same analysis was performed for the transition from high to low levels of local significant clusters.

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Two main findings arise. First, the evidence suggests that transitions from low to high homicide rates follow a contiguous expansion or relocation diffusion type with significantly larger proportions in states with joint army intervention. The diffusion source of high levels of homicide rates is higher among local pairs of municipalities that are contiguous with municipalities that experience high homicide rates at the beginning of each period (year). Second, a significantly larger proportion of municipalities that stayed within the HH cluster type during each successive period occurred in states with army intervention. Approximately one-half of all the municipalities do not show statistically significant levels of any clustering type during successive periods.

As discussed previously, it is possible to identify whether a contiguous source of diffusion outcome has occurred through relocation or if an expansion type of diffusion has taken place. Exhibit 6 separates the proportion of municipalities whose local-pair transitions fit within each of these two types. The results indicate that the spread of homicides resulted from an expansion diffusion. These results provide evidence that the object being diffused (homicide rates) has spread from its original place (municipalities), while the original source of diffusion still has high incidence rates of homicides.

Furthermore, a significantly large proportion of the diffusion seems to occur in those municipalities experiencing joint army interventions, as the respective t-test shows significant levels.

The findings in this section can be summarized as follows. On the one hand, the analysis reveals that the increase in levels of homicide rates in Mexico has occurred particularly within the states facing joint army interventions. Evidence also indicates significant levels of spatial dependency

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*** p 0.001.

among municipalities that have high incidence rates of homicides. On the other hand, it appears that high levels of homicide rates are being diffused to other nearby municipalities. The mechanism through which this diffusion takes place suggests that municipalities that act as contributors to the spread of high incidence rates have not reduced their levels, but, on the contrary, continue to experience high incidence rates and that this takes place in greater proportion in municipalities that experience army intervention.

Conclusions In this article we aim to analyze the extent of the diffusion of violence, measured with the number of homicides, among Mexican municipalities from 2005 to 2010. During this period, Mexico was characterized by a rise in organized crime, and, while some army intervention was executed in some states, violence seems to have displaced to other localities. Here we look at this particular phenomenon using ESDA techniques aimed to examine the dynamics of local spatial clustering, measured by LISA transitions, and thus provide a better description of the extent to which spatial diffusion of violence occurred across the country. For a developing country immersed in an organized crime wave, the analysis and implications are relevant, not only for Mexico, but also for countries in the region facing a similar context.

The findings suggest an increase in significant spatial clusters of homicides for the period of consideration in 2 percentage points of the municipalities. Concentration tends to occur in the first years of analysis in states where army intervention took place later. Even after the army intervention, most of the municipalities in those states remained high-high clusters of violence. The significance test shows a clear contagious effect among neighbors, while HH clusters remain stationary after army interventions.

One implication of the analysis suggests that law enforcement policies applied in such hotspot areas were ineffective on spatially restraining levels of violence, at least during the period here considered, leading to the spread of violence levels to neighboring areas. Failure of law enforcement policies calls for the implementation of other actions, either to replace this action or be complementary to it, where homicides have increased and spread among areas.

Cityscape 47Flores and Villarreal



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