Introduction

Crime and violence have been two of the most pressing problems Mexico has faced in
the last decades. Unfortunately, the problem has dramatically worsened in recent
years mainly due to the ongoing war on drugs. A significant part of President
Calderon’s government’s efforts to fight drug violence was focused on the
persecution and removal of some notorious drug lords, but this has been typically
followed by unprecedented levels of violence amongst cartel leaders fighting for
control of territories, supply chains, and distribution networks. After federal
elections in 2012, the then new administration of President Peña Nieto announced a
new strategy to deter drug-trafficking violence.^{2} However, the new enforcement policies have proved so
far to be incomplete and the overall deterrence capacity continues to be very
limited and unable to deter the escalation of violence (^{Felbab-Brown, 2014}). Consequently, crime and violence in the
country have proven to be sturdily persistent. Official statistics indicate that
between 2003 and 2010 federal crimes, including drug-related crimes and homicides,
grew at an 8 percent annual rate. Other types of crime, usually referred to as
common crimes, have continued rising. However, common crime rates, which refer
mainly to property theft, tend to be grossly underreported. Household surveys in
Mexico indicate that the percentage of unreported property crime can be as high as
85 percent, implying that the magnitude of the problem is significantly larger than
what the official statistics would indicate.

The study of crime is important for the human, social, and economic costs associated
with it, but these costs are difficult to assess for it involves different
dimensions (^{Soares and Naritomi, 2010}).
Nonetheless, there have been some real efforts to estimate these costs. Aside from
the incalculable human costs, ^{Bourguignon
(1999a)} estimates that the economic costs of crime could be as high as
7.5% of GDP for Latin American countries, compared to 3.5% for the U.S. and 2% for
Asian countries. The higher costs of crime for Latin American countries, among the
highest in the world, compared to developed countries are mainly due to higher crime
rates (^{Bourguignon, 1999a}; ^{Soares and Naritomi, 2010}). Within Latin
America, countries like Colombia, Brazil, and Mexico have the highest crime rates
(^{Fajnzylber et al.,
2000}, ^{2002}; ^{Bourguignon, 1999a}, ^{1999b}).

Given its importance, numerous empirical studies have been conducted in order to
identify and understand the determinants of victimization and crime at the
individual, family, city, and country level. This effort has produced a large array
of variables used to predict the probability of victimization and crime rates.
However, this array can be summarized into a relatively standard set of covariates
typically used in applied studies of crime (^{Deane
et al., 2008}). Most studies consider measures of
population socio-economic disadvantage, region indicators and population size,
measures of household composition and family disruption, population instability
indicators, and measures of policing activity, including proactive measures.

Aside from the identification of the determinants of crime, some researchers have
concluded that crime is not a random activity; there tends to be important spatial
and temporal concentrations. Tobler’s first law of geography states that everything
depends on everything else, but closer things more so. In the context of crime, the
crime rate in a municipality might depend in part on the rates of all other
municipalities but especially on the rates of its closest neighbors. Empirically, it
has been shown that crime and poverty are correlated with each other and tend to
exhibit strong spatial clustering (^{Peterson and
Krivo, 2010}). Consequently, most neighborhood crime rates tend to be
similar for neighborhoods that are proximate to each other, even when crime rates
vary from one section of the city to another (^{Graif
and Sampson, 2009}). The spatial dependence of crime and victimization
rates among municipalities might be due in part to the mobile nature of crime and
criminals; research has found that up to 70% of crimes are committed by individuals
outside their neighborhoods of residence (^{Bernasco,
2010(a)}). It might also be due in part to the arbitrary nature of
neighborhood assignment, which might lead to common characteristics shared by the
neighbors in an area. This arises from the definition of neighborhood that only
considers the place of residence, and it has led to a call for a definition of
neighborhood context that takes into account individual’s daily activity patterns
(^{Cagney et al., 2013};
Matthews and Yang, 2013). In either case, ignoring spatial dependence effects might
result in a misspecified model, biased estimates, and misleading conclusions about
the determinants of property crime in Mexico (^{Anselin, 2002}).

Taking into account the clustering nature of crime and victimization, the main
mechanisms in the study of crime and victimization have been summarized under four
categories: Social ties and local interactions, norms and collective efficacy,
institutional resources, and routine activities (^{Sampson et al., 2002}).

This study utilizes data from several rounds of a nationally representative victimization survey in Mexico to consider the determinants of municipality level property crime rates. Not all municipalities are included in the samples, but this study represents an alternative to the use of government victimization statistics, which might be unreliable. This study considers several of the determinants of crime previously used in the literature, test for the presence of spatial dependence effects, and try to account for these effects explicitly in different econometric model specifications. Regression analysis is conducted for each survey year separately to account for changing characteristics and to consider variation across time in spatial dependence effects among municipalities in Mexico.

Having employed different weighting matrices, the main results indicate that population size, self-protection rates, and prior victimization rates are the strongest predictors of property crime rates in Mexico. We also find evidence that spatial dependence effects are statistically significant and are becoming stronger in more recent years, suggesting growing diffusion effects of property crime in Mexico.

The next section briefly reviews some of the existing literature on victimization and crime, including some of the literature that considers spatial dependency effects of crime. The section “Methodology” describes briefly the modeling of spatial dependence effects of crime, followed by a data description and summary statistics section. The results from the baseline and other models that consider spatial dependence effects are presented in section “Results”. Finally, the conclusions and observations about the political implications of the main results of this study are presented.

Literature review

Crime can be analyzed from the perspective of potential criminals and from the
perspective of victims. From the perspective of potential criminals and starting
with ^{Becker (1968)}, researchers typically
consider a rational individual’s decision of whether or not to commit a crime. It is
assumed then that the individual would opt to commit the crime if the expected
payoffs from committing the crime exceed the expected costs. The former depends
mainly on the economic gains, while the latter depends mainly on the probability of
apprehension and the severity of punishment.

From the perspective of victims and using aggregate units of observation, many
studies have considered the determinants of victimization across neighborhoods
(^{Smith et al., 2000}),
cities (^{Stretesky et al.,
2004}), and countries (^{Worrall,
2005}). Among the most common covariates used, measures of socio-economic
disadvantage have been found to be positively correlated with crime rates (^{Kubrin et al., 2006}; ^{Andresen, 2006}). Low opportunity costs for
socially and economically disadvantaged individuals have been cited as one of the
main drivers of crime. Higher population size and density are also positively
correlated with crime rates (^{MacDonald,
2002}), which are determined by low apprehension probabilities and higher
pecuniary gains from crime in larger areas (^{Glaeser
and Sacerdote, 1999}). Indicators of region (^{Stretesky et al., 2004}) have also been
employed to address significant differences among communities within a large area.
In terms of population instability, the literature has found the areas with high
migration and low social cohesion tend to have more crime (^{Miethe et al., 1991}). Another important
covariate used in the study of crime is the amount and extend of policing activities
(^{Kubrin et al., 2006}).
The net effect of this covariate on crime is not clear. On one side, the amount of
policing resources might reflect the amount of deterrence to crime applied in the
community, but on the other side, it might be a reflection of the extend of illegal
activities prevalent in the community. Another concern related to this covariate is
the potential endogeneity of policing resources, which might lead to biased
estimates of their effect on crime. Some studies have also considered the likelihood
of repeat victimization (^{Sagovsky and Johnson,
2007}). This literature has proposed two explanations for how prior
victimization can be correlated with current victimization probabilities. The first
one suggests that criminals might return to the victim to exploit good opportunities
further, while the second one suggests that repeat victimization might be a result
of different offenders, at different times, choosing the same victim independently
(^{Johnson, 2008}).

Social scientists have also acknowledged the importance of considering the role of
spatial effects in criminology and sociological studies (^{Weisburd et al., 2009}). It’s believed that a
place does not stand alone as an island, but rather as a part of the main (^{Dean et al., 2008}). With
regards to crime and victimization, two of the main reasons attributed for the
existence of spatial dependence effects are the potential for diffusion effects and
the use of arbitrary geographic boundaries that do not necessarily are the same for
the unit of observation and the social process being described. The potential for
diffusion effects in criminal activities in general can be best understood by
considering that criminals are mobile and their behavior would not necessarily be
constrained by geographical boundaries, especially across smaller aggregate units
like neighborhoods and municipalities (^{Bernasco and
Block, 2011}; ^{Bernasco, 2010(b)}).
Altogether, these studies propose that not controlling explicitly for spatial
dependence effects while modeling victimization and crime rates might lead to
serious identification problems.

Methodology

The municipality level property crime rate, the dependent variable, is modeled as dependent on a set of predetermined covariates commonly used in the crime literature. The baseline model has the following form:

where X contains municipality level characteristics correlated with victimization
rates, including border and rural condition indicators, internal and international
migration rates, self-protection and past victimization rates, homicide and
unemployment rates, and the percentage of households headed by females, among
others.^{3} As a start, the error
term in model (1) is assumed to have ideal standard properties, so OLS gives
appropriate coefficient estimates. Throughout the remainder of the paper, model (1)
is referred to as the baseline model.

The baseline model is commonly used in the literature but ignores the potential effects of spatial dependence in municipality level property crimes, which might result in estimation problems. This could then lead to wrong interpretations about the effects of different explanatory variables used in the model on the incidence of property crime. More importantly, misspecification in the analysis of property crime or other more general forms of crime might lead to the implementation of erroneously directed public policies that might not have the desperately needed results and even result in the exacerbation of the problem.

The use of maps depicting Mexican states or municipalities and their corresponding
crime rates has been suggested as a way to assess whether or not victimization rates
in Mexico suffer from spatial dependency. This approach might be informative and
valuable. Maps might show that crime rates in some areas are significantly
correlated with the rates of neighboring communities. However, it has been argued
that relying on visual inspection to identify data clusters and patterns might be
problematic. Human perception is typically not adequately rigorous and tends to be
biased towards finding patterns and clusters, even in spatially random data (^{Messner et al., 1999}).

Instead of relying on visual considerations to decide whether or not victimization rates across municipalities in Mexico exhibit spatial dependency, this study relies on simple econometric tests. These tests are applied to the outcome of interest, the municipality victimization rate, and to the residuals from the baseline model (1) to help in deciding whether or not spatial dependence effects are present and significant.

Generally, these tests require the computation of statistics followed by hypothesis
testing based on the statistics’ expected value. This study uses Moran’s “I” and
Geary’s “C” statistics to test the null hypothesis of no spatial correlation.^{4} Failure to reject the null
hypothesis would suggest that OLS estimates based on the baseline model would be
econometrically appropriate and that spatial dependence in the errors is not
significant. Rejecting the null hypothesis, on the other hand, implies that running
the baseline model (1) using OLS might lead to biased, inefficient estimates, or
wrong interpretations about the parameters of interest and/or their significance
level, depending on the type of spatial dependency. In this case, Maximum Likelihood
Estimation (MLE) will provide unbiased and efficient estimates and remove the
spatial dependence in the errors, provided that the model is correctly specified.
For different specifications considered in this study, the null hypothesis of
spatial independence is rejected, so the appropriate spatial econometric model to be
applied needs to be selected next.

The choices considered to model spatial dependence effects are the spatial error model (2) and the spatial lag model (3), sometimes referred to as the mixed spatial lag model.

where X is as explained before and W represents an NxN symmetric weighting matrix.
Each cell in the W matrix represents a pair of municipalities, and the matrix can
take on different forms. One form of this matrix contains zeros in the diagonal and
only zeros or ones in the off-diagonal. The values off the diagonal are ones if the
municipalities are located within a predetermined distance, the cutoff distance, and
zeros otherwise. This matrix can be easily standardized by dividing the ones in each
row by the number of neighbors, so that the sum equals to one for each row.^{5}

However, not all municipalities in Mexico are in each year sample, so there are
plenty of “islands” in the data. That is, many municipalities do not have any
neighbors within the cutoff distance. This creates computational problems, so they
must be excluded from the analysis.^{6}
To reduce the number of islands in the data, one could increase the cutoff distance.
However, if spatial dependence in property crime among close neighbors really
exists, this might effectively lower the probability of finding statistical evidence
in the results.

Another way to construct the W matrix is having the off-diagonal values of the matrix
to be the inverse of the distance between units. This approach considers the effects
of all other units in determining the municipality’s crime rate, while allowing for
larger effects from closer neighboring units.^{7} Yet another way considered for the W matrix is to
identify an arbitrary number of closest neighbors, different numbers were
considered, and have ones for those units and zeros for the rest. Regardless of the
form of the W matrix, one must first choose the appropriate way to model the spatial
dependency.

The spatial error model (2) suggests that the errors are not spatially independent.
In other words, there are unobserved variables that are associated with
victimization rates at the municipality level and they are significantly correlated
among neighbors. Trying to correct for it with standard procedures might prove
ineffective (^{Almeida, 2003}). As with omitted
variables, running the baseline model when the true model is as in model (2) might
lead to biased estimates of the regression coefficients. The covariance estimates
will be biased and might lead to incorrect inferences. If instead the true model is
the spatial lag model (3), running the baseline model will result in biased and
inefficient estimates of the regression coefficients.

The decision rule between models is based on goodness of fit criteria by comparing
the baseline model to each of the alternative models. Having a significant test
statistic for the spatial lag or the spatial error model suggests that considering
spatial dependence effects improves the model’s fit. A way to choose which spatial
dependence model is more appropriate requires the use of a robust version of the
tests (^{Anselin and Florax 1995}). The rule to
follow then is that if the robust version of the test is significant for model (2)
but not for model (3), the appropriate model is the spatial error model, and vice
versa. For most specifications of the weighting matrix and years, the appropriate
model suggested by the criteria is the spatial lag model.

Data and statistics

This study utilizes 2007, 2008, and 2010 data from Mexico’s National Survey about
Insecurity (ENSI: Encuesta Nacional Sobre Inseguridad). This survey was conducted by
the Citizen’s Institute for the Study of Insecurity (ICESI), and it contains
individual and family demographic and socio-economic characteristics, as well as
information on crime and victimization.^{8} This is not a panel data, so one cannot identify the
households that have participated in previous rounds, but one can identify which
municipalities have been surveyed in previous rounds. Not all municipalities are
included in the survey rounds, and the result is having a significantly smaller
sample size compared with the total number of municipalities in Mexico. However, the
use of this victimization survey data allows us not to rely on official crime
statistics, which might suffer from serious reliability issues.

The unit of observation in this study is the municipality, so individual and family
characteristics were aggregated at this level and were complemented with measures of
total population and internal and international migration rates computed from the
2000 and 2005 population census.^{9} A
municipality index of marginalization computed in 2000 by Mexico’s CONAPO (National
Population Council) and annual homicide rates in 2005 from INEGI are also included.

The municipality property crime victimization rate, the models’ dependent variable,
was computed by counting all households that report any household member as victim
of a property crime in their community of residence and dividing it by the total
number of households surveyed in the municipality.^{10} Regression analysis is conducted for each year
separately to account for changing characteristics and to consider variation in the
potential spatial dependence effects among municipalities.

Table 1 presents summary statistics for each of the three rounds considered. The sample size shows that only about one third of all municipalities in Mexico are present in our sample, but these municipalities represent more than two thirds of the country’s total population. Statistics show that the victimization rates increased slightly in later rounds, but it must be noted that only about half of all municipalities surveyed are present in all rounds, so some variation is expected. Also, statistics in the latter two rounds seem more similar than the first round.

ENSI Surveys | |||

2007 | 2008 | 2010 | |

Victimization Rate | 5.173 | 5.926 | 5.685 |

(6.373) | (6.794) | (6.388) | |

Border | 0.123 | 0.152 | 0.140 |

(0.328) | (0.358) | (0.347) | |

Rural | 0.225 | 0.458 | 0.443 |

(0.417) | (0.498) | (0.497) | |

Population | 106.877 | 89.960 | 77.210 |

(207.159) | (187.584) | (125.871) | |

Marginalization | -0.529 | -0.530 | -0.521 |

(0.970) | (0.920) | (0.935) | |

Internal Migration | 9.798 | 9.478 | 11.199 |

(12.090) | (11.718) | (11.322) | |

Int’l Migration | 7.717 | 7.297 | 6.981 |

(8.122) | (7.814) | (7.020) | |

Self-Protection | 30.728 | 38.641 | 27.950 |

(19.656) | (20.872) | (17.658) | |

Past Victimization | 7.705 | 8.714 | 9.296 |

(7.703) | (8.368) | (9.375) | |

Male-Female Ratio | 0.916 | 0.943 | 0.910 |

(0.794) | (0.578) | (0.521) | |

College | 9.019 | 8.640 | 10.203 |

(10.124) | (9.975) | (11.268) | |

Unemployment | 5.781 | 8.717 | 7.034 |

(6.951) | (7.498) | (6.620) | |

Homicide Rate | 9.226 | 8.940 | 10.274 |

(12.345) | (11.685) | (17.079) | |

Female Head | 17.802 | 17.559 | 17.584 |

(4.440) | (4.480) | (4.475) | |

Low Education Head | 40.584 | 40.272 | 40.546 |

(16.975) | (16.314) | (16.636) | |

Observations | 698 | 883 | 851 |

*Standard of deviation in parenthesis.

Source: Own elaboration.

Average total population and rural condition show that later rounds tend to include
smaller municipalities. Based on the literature, it is expected that total
population has a positive effect on victimization, greater economic gains and lower
probability of apprehension, but a negative effect from rural condition, higher
probability of apprehension and larger social costs. The marginalization index, a
composite measure of economic disadvantage, shows that the average municipality is
not marginalized.^{11} The expected
effect on victimization is not easy to assert, for it represents the low opportunity
cost of committing a crime, but it also represents the low economic rewards from
property crime. As measures of population instability and social cohesion, internal
and international migration rates are included. These measures represent the
percentage of adults born in another municipality and the percentage of households
with at least one migrant to the U.S. in 2000, respectively. It is expected that
municipalities with high domestic and international migration might have lower
social cohesion among its citizens, therefore, higher victimization rates.

Self-protection rates measure the percentage of households reporting taking a protective measure in the survey year. It’s suggested that this measure represents the level of awareness about insecurity and the general perception of crime in the community. Consequently, this variable is expected to have on net a positive effect on victimization. Prior victimization rate represents the percentage of households reporting at least one member has been a victim of a crime the year prior to the survey. Similar to self-protection rates, it is expected to have a positive effect on victimization. The main idea is that this variable captures the prevalence of crime in the municipality and serves as an identifier of prevalent lucrative economic opportunities to criminals.

Homicide rates are computed as per 100,000 inhabitants in 2005. We believe this
variable captures in part the amount of policing resources employed in the
municipality and the extent of criminal enterprises.^{12} This rate is smaller for our sample than for the
country as a whole. According to INEGI, the rate per 100,000 for the country in 2011
was 24. In states like Chihuahua, Guerrero, and Sinaloa, homicide rates were around
100 on average. Overall, municipalities in our sample tend to be larger compared to
the country and have lower victimization and homicide rates. It is expected that
homicide rates have a positive effect on victimization mainly because they reflect
the extent of criminal activities prevalent in the municipality. However, and as
mentioned before, this variable might also have a negative effect because it might
also capture the amount of policing resources allocated to the municipality.

The rest of the covariates refer to household composition and to the socioeconomic conditions present in the community. They include the percentage of residents with college education, the unemployment rate, the percentage of households headed by a female, the municipality average age, the average family size, the average number of children in the household, and the percentage of households headed by a low-education adult.

Results

This section presents the regression results of the municipality level victimization
rates for 2007, 2008, and 2010 separately. To illustrate the potential problems of
ignoring spatial correlation in victimization across municipalities, it begins with
typical OLS estimations based on the baseline model. Then, the results for different
tests for spatial dependence are discussed, followed by the decision on the
appropriate spatial dependence model and presentation of the main estimation results
using MLE.^{13}

Baseline regression estimates are presented in Table 2. This table shows that coefficient estimates differ to a certain extent from year to year. However, the coefficient estimates for population, self-protection rates, and prior victimization rates are consistent and statistically significant across years. The former is consistent with the existing crime literature that has found that larger municipalities tend to have more crime, while the latter two might be considered as evidence that property crime in Mexico is a familiar, widespread, and persistent problem.

Dependent Variable: Victimization Rate Dependent Variable: Victimization Rate | |||

2007 | 2008 | 2010 | |

Border | 2.004*** | 0.116 | -0.019 |

(0.733) | (0.603) | (0.642) | |

Rural | -0.793 | -1.175*** | -0.876** |

(0.546) | (0.423) | (0.444) | |

Population | 0.005*** | 0.004*** | 0.007*** |

(0.001) | (0.001) | (0.001) | |

Marginalization | -0.283 | -0.517 | 0.072 |

(0.599) | (0.516) | (0.548) | |

Internal Migration | 0.001 | 0.030** | 0.027* |

(0.016) | (0.015) | (0.015) | |

Int’l Migration | -0.053** | -0.035 | -0.018 |

(0.025) | (0.022) | (0.033) | |

Self-Protection | 0.040 *** | 0.030 *** | 0.077*** |

(0.011) | (0.009) | (0.012) | |

Past Victimization | 0.303*** | 0.258*** | 0.113*** |

(0.031) | (0.025) | (0.023) | |

Male-Female Ratio | -0.099 | -0.755** | -0.694 |

(0.283) | (0.373) | (0.430) | |

College | -0.053 | -0.030 | 0.079** |

(0.034) | (0.030) | (0.032) | |

Unemployment | -0.056* | -0.009 | -0.051* |

(0.032) | (0.024) | (0.028) | |

Homicide Rate | -0.014 | 0.050*** | 0.029*** |

(0.017) | (0.015) | (0.010) | |

Female Head | 0.040 | 0.008 | 0.156*** |

(0.055) | (0.047) | (0.051) | |

Low Education Head | -0.005 | -0.003 | 0.036 |

(0.032) | (0.026) | (0.030) | |

Constant | 1.526 | 10.501** | -9.369* |

(5.875) | (4.724) | (5.661) | |

Observations | 698 | 883 | 851 |

Notes: Robust standard errors in parenthesis. ***, **, * represent statistical significance at the 1%, 5%, and 10% respectively.

Source: Own elaboration.

Similar to summary statistics, the regression results for the last two rounds seem more similar than those for the first round. In terms of statistical significance, similar results for these years are found for rural condition, internal migration, and the homicide rate. Border condition, international migration, and unemployment rate are only statistically significant for 2007. Again, this might be due in part to sampling issues or to changing conditions related to property crime in Mexico. Nonetheless, most estimates are consistent with the existing literature on victimization.

As mentioned before, the existence of spatial dependence in municipality level victimization rates might result in reaching wrong conclusions using the baseline model’s results. The approach is then to test for the presence of spatial dependence in municipality level victimization rates and, if necessary, decide on the appropriate spatial dependence model.

To test for spatial dependence, we obtain Moran’s I and Geary’s C statistics based on the dependent variable and the residuals from baseline model (1). The null hypothesis of no spatial autocorrelation is rejected for each year separately, suggesting there is statistically significant correlation among neighboring property crime rates and the baseline residuals. The choice is then between the spatial error model (2) and the spatial lag model (3). Lagrange multiplier and modified Lagrange multiplier statistics were used to decide which model gave a more appropriate fit. The results are now presented based on different specification of the W weighting matrix.

As mentioned before, one option for the W matrix contains only zeros and ones. All diagonal elements are zeros and off-diagonal elements are ones if the municipalities are located within a predetermined distance and zero otherwise. For illustration purposes only, Table 3 presents the results using weighting matrix and a cutoff distance of 10 kilometers for each year separately. The null hypothesis of spatial independence is rejected for each year, and based on specification criteria, model (2) was used for 2008 and model (3) for 2007 and 2010. However, this approach resulted in having plenty of municipalities without neighbors, so a large proportion of municipalities were excluded and the sample size was reduced significantly. Other larger cutoff distances were used to construct the W weighting matrix, and the results vary significantly. Furthermore, spatial dependence statistics based on the longest distances suggest that the null hypothesis of spatial independence cannot be rejected.

Dependent Variable: Victimization Rate | |||

2007 | 2008 | 2010 | |

Border | 3.570** | -0.444 | -1.585 |

(1.725) | (1.872) | (1.620) | |

Rural | -1.697 | -2.066** | -0.921 |

(1.538) | (0.889) | (0.884) | |

Population | 0.004*** | 0.00316** | 0.008*** |

(0.001) | (0.001) | (0.002) | |

Marginalization | -1.361 | -0.793 | 1.330 |

(1.495) | (1.269) | (1.151) | |

Internal Migration | -0.019 | 0.020 | 0.028 |

(0.037) | (0.031) | (0.028) | |

Int’l Migration | -0.042 | -0.039 | 0.055 |

(0.052) | (0.045) | (0.078) | |

Self-Protection | 0.057 ** | 0.007 | 0.056 ** |

(0.026) | (0.018) | (0.023) | |

Past Victimization | 0.324*** | 0.266*** | 0.104*** |

(0.057) | (0.042) | (0.037) | |

Male-Female Ratio | 1.328 | -1.217 | -0.896 |

(1.114) | (0.793) | (0.782) | |

College | -0.083 | -0.142** | 0.043 |

(0.068) | (0.061) | (0.056) | |

Unemployment | -0.001 | 0.060 | 0.001 |

(0.068) | (0.047) | (0.047) | |

Homicide Rate | -0.131* | 0.121*** | 0.057*** |

(0.067) | (0.044) | (0.019) | |

Female Head | 0.079 | 0.024 | 0.137 |

(0.104) | (0.095) | (0.100) | |

Low Education Head | 0.078 | -0.017 | -0.032 |

(0.081) | (0.065) | (0.060) | |

Constant | -0.841 | 25.152*** | 1.236 |

(2.978) | (9.755) | (1.051) | |

Observations | 189 | 267 | 270 |

Rho | - | 0.024** | |

0.011) | |||

Lambda | -0.124** | 0.073*** | |

(0.061) | (0.019) |

Notes: MLE Estimates. Robust standard errors in parenthesis. ***, **, * represent statistical significance at the 1%, 5%, and 10% respectively.

Source: Own elaboration.

Having the small sample size in mind, results in Table 3 show that municipality population, self-protection rates, and previous victimization rates are positively correlated with property crime rates and continue to be statistically significant. The homicide rate variable is statistically significant for all years, but it has a negative sign for 2007. Finally, the specification for each year shows there is evidence of spatial dependence in property crime rates among municipalities in Mexico. However, and given the significantly reduced sample size, these results should be taken cautiously.

As alternative forms of the W matrix and to avoid significant sample size reductions,
the inverse of distance and the nearest five neighbors approach were also
considered.^{14} These results are
adjusted for the potential clustering effects of the standard errors at the state
level. The results are presented in Tables 4
and 5. For the most part, the results from
these two approaches are similar, except for the statistical significance level of
some covariates. Population size, self-protection rates, and previous victimization
rates continue to be statistically significant for all rounds. However, and as shown
in Table 2, the results for 2008 and 2010 are
more similar than those for 2007. Selection criteria suggest that the best model for
each year separately is the spatial lag model. However, the spatial lag variable
results for Table 5 are somewhat different
for 2007 and 2008 data.

Dependent Variable: Victimization Rate | |||

2007 | 2008 | 2010 | |

Border | 1.887** | 0.888 | 0.721 |

(0.781) | (0.680) | (0.615) | |

Rural | -0.794 | -1.165*** | -0.845* |

(0.614) | (0.371) | (0.404) | |

Population | 0.005*** | 0.004*** | 0.007*** |

(0.001) | (0.001) | (0.001) | |

Marginalization | -0.264 | -0.687 | -0.266 |

(0.590) | (0.489) | (0.503) | |

Internal Migration | 0.001 | 0.029** | 0.025* |

(0.017) | (0.015) | (0.013) | |

Int’l Migration | -0.051** | -0.039* | -0.033 |

Self-Protection Past Victimization | (0.027) 0.040*** (0.010) 0.306*** (0.031) | (0.021) 0.030*** (0.010) 0.245*** (0.034) | (0.032) 0.071*** (0.013) 0.093*** (0.025) |

Male-Female Ratio | -0.096 | -0.737** | -0.687 |

(0.284) | (0.373) | (0.430) | |

College | -0.053 | -0.026 | 0.083*** |

(0.034) | (0.040) | (0.039) | |

Unemployment | 0.056* | 0.008 | 0.049 |

(0.031) | (0.030) | (0.037) | |

Homicide Rate | -0.014 | 0.046*** | 0.028** |

(0.015) | (0.015) | (0.009) | |

Female Head | 0.042 | 0.004 | 0.151*** |

(0.054) | (0.044) | (0.051) | |

Low Education Head | -0.009 | 0.031 | 0.079** |

(0.033) | (0.027) | (0.030) | |

Constant | 1.612 | 8.410* | -11.443** |

(6.172) | (4.814) | (6.098) | |

Observations | 698 | 883 | 851 |

Rho | -0.013 | 0.051*** | 0.063*** |

(0.032) | (0.016) | (0.016) |

Notes: MLE Estimates. Robust standard errors in parenthesis. ***, **, * represent statistical significance at the 1%, 5%, and 10% respectively.

Source: Own elaboration.

Dependent Variable: Victimization Rate 2007 2008 2010 | |||

2007 | 2008 | 2010 | |

Border | 1.911** | 0.121 | 0.111 |

(0.739) | (0.649) | (0.579) | |

Rural | -0.770* | -1.157*** | -0.859** |

(0.477) | (0.372) | (0.398) | |

Population | 0.004*** | 0.004*** | 0.006*** |

(0.001) | (0.001) | (0.001) | |

Marginalization | -0.252 | -0.513 | 0.220 |

(0.592) | (0.471) | (0.499) | |

Internal Migration | -0.001 | 0.029 | 0.024 |

(0.016) | (0.018) | (0.014) | |

Int’l Migration | -0.055** | -0.037* | -0.018 |

Self-Protection Past Victimization | (0.022) 0.038*** (0.011) 0.294*** (0.046) | (0.021) 0.031*** (0.010) 0.252*** (0.042) | (0.032) 0.074*** (0.014) 0.093*** (0.032) |

Male-Female Ratio | -0.099 | -0.761** | -0.655 |

(0.206) | (0.384) | (0.438) | |

College | -0.048 | -0.025 | 0.085* |

(0.039) | (0.039) | (0.047) | |

Unemployment | -0.057 | -0.009 | 0.049* |

(0.038) | (0.027) | (0.027) | |

Homicide Rate | -0.014 | 0.049*** | 0.025*** |

(0.014) | (0.015) | (0.008) | |

Female Head | 0.042 | 0.006 | 0.152*** |

(0.053) | (0.046) | (0.049) | |

Low Education Head | -0.002 | 0.003 | 0.041 |

(0.033) | (0.026) | (0.029) | |

Constant | 0.788 | 9.725** | -11.851* |

(6.282) | (4.821) | (6.233) | |

Observations Rho | 698 0.016* (0.009) | 883 0.016* (0.009) | 851 0.050*** (0.010) |

Notes: MLE Estimates. Robust standard errors in parenthesis. ***, **, * represent statistical significance at the 1%, 5%, and 10% respectively.

Source: Own elaboration.

Some results are expected to vary between years in part because the sample for each
year does not necessarily include the same households or municipalities. To account
partially for this, the spatial dependence model using the inverse of distance and
the nearest five neighbors approach is applied using only municipalities surveyed in
all 3 rounds. Table A1 in the appendix lists the municipalities included in
this restricted sample. This intentional truncation renders the working sample no
longer representative and the sample size is reduced significantly, but the results
might be used to discuss whether or not the spillover effects of crime are
intensifying, constant, or disappearing.^{15} As before, the inverse of distance and the nearest five
neighbors approach result in similar results, so we present only the results using
the inverse of distance.

Table 6 shows that the estimates for population size, self-protection rates, and previous victimization rates continue to be statistically significant and very consistent across years. The main differences in results are for the latest round, 2010. Table 6 shows significant differences with respect to rural condition, internal and international migration, male-female ratio, college rate, homicide rate, and the female head rate. Again, the restricted sample includes only municipalities surveyed in all rounds, so these differences might be due to different households being surveyed in different years or to changing conditions related to property crime in Mexico. As mentioned before, self-protection rate measures the level of awareness about insecurity and the general perception of crime in the community. Prior victimization rate, on the other hand, represents the percentage of households reporting at least one member has been a victim of a crime the year prior to the survey and represents in part the presence of good crime opportunities for criminals. Taken together, the policy implications of the results might be that crime fighting resources are allocated more efficiently when directed toward large communities and to communities with high percentage of prior victims and to communities with large incidence of self-protection measures.

Dependent Variable: Victimization Rate | |||

2007 | 2008 | 2010 | |

Border | 2.773*** | 0.357 | 1.036 |

(0.981) | (1.049) | (0.954) | |

Rural | -0.734 | -0.685 | -1.803*** |

(0.700) | (0.602) | (0.643) | |

Population | 0.004*** | 0.002* | 0.005** |

(0.001) | (0.001) | (0.001) | |

Marginalization | -1.040 | -0.337 | 1.690* |

(0.957) | (1.039) | (1.009) | |

Internal Migration | -0.003 | 0.017 | 0.035* |

(0.026) | (0.023) | (0.020) | |

Int’l Migration | -0.060* | -0.113*** | 0.005 |

(0.031) | (0.030) | (0.060) | |

Self-Protection | 0.057*** | 0.041** | 0.086*** |

(0.017) | (0.017) | (0.021) | |

Male-Female Ratio | 1.329** | -0.935 | -1.595** |

(0.681) | (0.654) | (0.812) | |

College | -0.033 | -0.042 | 0.152*** |

(0.049) | (0.054) | (0.060) | |

Unemployment | 0.058 | 0.014 | -0.061 |

(0.049) | (0.047) | (0.054) | |

Homicide Rate | -0.013 | 0.032 | 0.024** |

(0.018) | (0.023) | (0.012) | |

Female Head | 0.080 | -0.023 | 0.215*** |

(0.072) | (0.079) | (0.084) | |

Low Education Head | 0.020 | 0.043 | 0.035 |

(0.059) | (0.052) | (0.057) | |

Constant | -3.597 | 9.857 | -0.989 |

(8.232) | (8.056) | (10.721) | |

Observations | 411 | 411 | 411 |

Rho | -0.030 | 0.066** | 0.100*** |

(0.041) | (0.030) | (0.028) |

Notes: MLE Estimates. Robust standard errors in parenthesis. ***, **, * represent statistical significance at the

1%, 5%, and 10% respectively.

Source: Own elaboration.

Finally, the estimate for the spatial dependence coefficient estimate is not statistically significant for 2007. The coefficient estimate is only statistically significant for 2008 and 2010, but it’s significantly larger for 2010. It should be noted here that, for the most part, the decision rule for the presence of spatial dependence effects in municipality level property crime in Mexico do not depend on the choice of the weighting matrix or the set of covariates used. Taken together, these results can be interpreted as evidence that property crime in Mexico is becoming more prevalent and there is a diffusion mechanism that appears to be growing stronger in more recent years. Furthermore, the coefficient for the homicide rate is statistically significant only for 2010, suggesting that the changing conditions in Mexico regarding property crime rates is also significantly correlated with increasing levels of more serious types of crime.

Conclusions

Using nationally representative victimization data for several years, this study considers the determinants of municipality level property crime rates in Mexico. Baseline results show that population size, self-protection rates, and prior victimization rates are the stronger predictors of victimization rates. These covariates are consistently, positively, and statistically correlated with property crime rates for all years and specifications. Different tests are applied for each round to consider the presence of spatial dependency in crime rates. All tests for each year reject the null hypothesis of spatial independence.

We explore different ways to define the weighting matrix W, but the hypothesis testing rule for spatial dependency for the most part does not depend on the form of the weighting matrix or the set of covariates used. Having rejected the null hypothesis of spatial independence for each year, we consider the appropriate way to model municipality level property crime in Mexico, while controlling explicitly for the presence of spatial dependence effects. In most cases and based on model selection criteria, the spatial lag model is preferred over the spatial error model for each year separately.

The main spatial lag model results show that population size, self-protection rates, and prior victimization rates continue to be positively and statistically correlated with municipality level property crime rates. In terms of spatial dependency, the results suggest that spatial dependence effects are present and are becoming stronger, suggesting growing spillover effects in property crime in Mexico.

The results from this study might help policy makers to develop and implement more efficient measures to fight property crime and other forms of crime in Mexico. The main specification results suggest that areas with high homicide rates and prior victimization rates are significantly more likely to continue suffering from high property crime rates. Moreover, the evidence suggests that spillover effects are getting stronger, which gives a special sense of urgency to the need to address the problem of crime and victimization in Mexico. Failing to act effectively and promptly will result most likely in significant economic and social losses for Mexico.