Gender bias in the convergence dynamics of the regional homicide rates in Mexico

Applied Geography 45 (2013) 280e291

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Applied Geography journal homepage: www.elsevier.com/locate/apgeog

Gender bias in the convergence dynamics of the regional homicide rates in Mexicoq Marcos Valdivia*, Roberto Castro Researchers at Regional Center for Multidisciplinary Research (CRIM), National University of Mexico (UNAM), Av. Universidad s/n, Circuito 2, 62210, Col. Chamilpa, Cuernavaca, Morelos, Mexico

a b s t r a c t Keywords: Convergence of crimes Modernizationeconflict hypotheses Spatial panel models Gender gap

The geography of violence in Mexico has changed in recent years because of an explosive increase in regional homicide rates since 2006. This study relies on spatial statistical data analysis to address the issue of convergence in homicide victim rates across Mexican municipalities from 2001 to 2010. Based on the results of spatial panel modeling, we conclude that despite strong regional disparities in murders, municipal-level homicide growth rates display a pattern of convergence with spatial interaction features. This convergent pattern is gender-specific; the homicide growth rates for females show stronger convergence than those for males when local and regional factors are not considered. We postulate that homicide growth dynamics among females more closely follow the predictions of the “modernization hypothesis” than do the dynamics among males. This finding suggests that violence (specifically, homicides) against women in Mexico is driven by underlying factors other than short-term factors, such as drug cartel dynamics, and regional factors, such as local institutions and governments. The data might support the long-established feminist hypothesis that contends that violence against women follows specific dynamics that are different from the dynamics of violence against men.
2013 Elsevier Ltd. All rights reserved.

Introduction Mexico experienced a consistent reduction in homicide rates from the mid-1980s to the early 2000s, to an extent that the country was on pace to reach average growth rates observed in many developed countries. However, in 2006, the trend reversed; since that year, Mexico has undergone an explosive increase in homicide rates. Some reports attribute the drastic changes in the homicide trends to the negative effects of government crime policies meant to combat drug cartels (Astorga & Shrik, 2010). However, few studies have systematically addressed the regional features of the contemporary dynamics of homicide growth in

q The authors wish to thank the National Commission for Preventing and Eradicating Violence against Women (CONAVIM) for providing the funds that made it possible to conduct the original study on which this paper is based. They also want to express their gratitude to Martha Hijar for her kind disposition to share the mortality data set for Mexico 2001e2010 and to Juan Manuel Castañeda for his technical support. * Corresponding author. Extremadura 30, Dpto. 601, Insurgentes Mixcoac, 03740 Mexico City, Mexico. Tel.: þ52 5555630966, þ52 5532597254 (mobile), þ52 777 3130555/3175299x306 (work). E-mail addresses: [email protected], [email protected] (M. Valdivia), [email protected] (R. Castro). 0143-6228/$ e see front matter
2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apgeog.2013.09.015

Mexico (Widner, L-Reyes, & Enomoto, 2011). In addition, to the best of our knowledge, no study has analyzed such regional patterns along the lines of crime convergence or divergence. The convergence in homicide rates would be important because it would mean that national or international (structural) forces shape regional trends in homicide rates. In contrast, divergence would imply that regional or local factors are more influential. Standard approaches analyze convergence in homicide rates by contrasting rich and poor countries. In particular, these studies test whether, as income disparities decrease among countries in the long run, the homicide rates in less-developed countries reach those observed in developed countries (LaFree, 2005). Nevertheless, convergence is rarely studied within a single country, where inherent regional inequalities can also shape local violent behavior in important ways. One exception to this is the study by Cook and Winfield (2013), which was focused on the USA. They showed that even though the USA exhibits strong variation in criminal activity across its states, there has been a clear national tendency toward convergence for a wide array of crimes in recent decades. That is, “national underlying factors” can be more important than regional factors in shaping crime behavior across states. In contrast, some influential economic research on crime, such as that by Levitt (2004), suggests that the sharp decline in crime in the USA since the 1990s was more driven by local or regional factors. Regardless

M. Valdivia, R. Castro / Applied Geography 45 (2013) 280e291

of which set of factorsdnational or localdare more influential in shaping criminal behavior in a single country, a discussion of convergence in regional crime can shed some light on the appropriate weight of each of those factors on violent crime. It is also worth noting that there is another line of thought in empirical criminal studies that analyze convergence along the dimension of gender. This focus is an important track of contemporary research in violence studies. Specifically, this approach consists of evaluating whether the gap between male and female homicide rates is narrowing (Simon, 1975). According to this line of thought, convergence is understood as a reduction in the gender gap in crime. Such a reduction is generally considered an indicator of greater equality (Steffensmeir & Allen, 1996). However, to some extent, if divergence by gender prevails, it would mean that there are structural gender differences in crime that cannot be reduced to common general dynamics for both genders. To the best of our knowledge, there have not been any studies of convergence in a single country that have simultaneously considered both dimensions of convergence referred to above (the regional and gender dimensions). In this study, we address this gap in the literature by studying homicide growth rates in Mexico at the municipality level. It is important to note that in this research, we are focusing on the homicide rates of victims. We rely on spatial panel econometric techniques along the lines of a convergence model that is used to analyze regional growth under the interaction of spatial effects (Ertur & Le Gallo, 2009). Focusing on the Mexican case is interesting not only because of the recent dramatic increase in the homicide growth rate but also because Mexico is a setting with interesting spatial features; in particular, the dynamics of homicide rates in recent years have generated important hot spots across the country. In the second section, we review the relevant literature. In Section 3, we present some empirical facts that characterize the dynamics of homicide rates in Mexico. First, we compare the Mexican national data to those of other countries; then, we address the regional dynamics of the homicide rates at the municipality level. In Section 4, we study the convergence dynamics of the homicide growth rates through a beta convergence model that relies on spatial panel regressions. Lastly, the paper concludes with final remarks. The literature on crime convergence and this research In the comparative criminology literature, the idea of convergence is discussed at the country level in terms of two main rival theories: modernization and conflict (LaFree, 2005). Broadly speaking, the “modernization hypothesis” posits convergence in crime rates across countries, while the “conflict hypothesis” predicts divergence. The modernization hypothesis assumes that all countries are on the same historical track of development transformations, which induce crime rates to converge as disparities between countries are reduced. Eisner (2001) provides the most comprehensive empirical study of the modernization hypothesis as it applies to industrialized European countries over many centuries and demonstrates convergence in (declining) homicide rates among these countries. From the modernization perspective, the gradual equalization of crime rates among developed countries is expected, as is the eventual generation by developing countries of crime rates similar to those observed in the developed world. In contrast, the “conflict perspective” stresses the structural differences that the global economy has produced between highly industrialized core nations and developing peripheral countries (LaFree, 2005). Based on perspectives such as the world-systems perspective put forth by Wallerstein (among others), the conflict perspective predicts divergence in crime rates between highly

281

industrialized countries and poor developing countries. Unfortunately, few studies have been conducted to test the convergence hypothesis empirically. Convergence in crime is generally discussed across countries, and it is empirically treated at the macro level using modern time series techniques (LaFree, 2005; O’Brien, 1999). What is less frequently discussed is whether the modernization and conflict hypotheses can be applied to a single country in which regional socioeconomic differences could affect criminal behavior. As mentioned earlier, Cook and Winfield’s study (2013) is one of the few that considers this perspective. They found robust empirical support for the regional convergence hypothesis in an analysis of several crime variables at the state level in the USA over the period from 1960 to 2009. A relevant technical feature of the authors’ approach was their reliance on standard measurements of (beta or sigma) convergence used in the regional economic literature (Barro & Sala-i-Martin, 1992). This approach allowed the authors to postulate that states in the USA with lower initial crime rates tended to experience more rapid increases in crime rates than regions with higher initial crime rates. As a consequence, it is also expected that crime rates in states with higher initial crime rates would grow more slowly than in regions with lower initial crime rates. There is another branch of the empirical literature that analyzes crime convergence in terms of the evolution of the gender gap. Authors such as Adler (1975) and Simon (1975) proposed a convergence hypothesis that argues that as the roles of men and women become more similar, so too do the rates of crime against men and women. The historical empirical literature on violence for European countries shows that the ratio of male to female victims decreased during the period 1800e1950 (Eisner, 2008). O’Brien (1999) used time series methods to test for convergence of various serious crimes of males and females in the USA during the period 1960e1965. The analysis results provide evidence of convergence in male and female arrests for robbery, burglary and motor vehicle theft, but divergence for homicide arrests. In contrast, Steffensmeier, Zhong, Ackerman, Schwartz, and Agha (2006) did not find empirical support for convergence (or what they called a “narrowing gender gap”) over the period 1980e2003 in any of the common violence indicators. Based on their findings, they rejected the general perception that the actual rise in arrests of women in the USA was really a widening of the “gender gap” in crimes. To the best of our knowledge, there have not been any systematic studies of regional convergence by the gender of the victims. Substantive empirical research on spatial crime patterns has been conducted in recent years, focusing on patterns of agglomeration and the emergence of crime hot spots (Andresen, 2011; Ye & Wu, 2011; Porter & Purser, 2010). A Mexican example is Vilalta (2010), who used local indicators of spatial autocorrelation to identify spatial patterns of drug possession crimes in Mexico City. Another spatial analysis approach used in crime mapping focuses specifically on the geometry component of crime. For example, some authors have relied on mobility triangle classifications to study the geodiversity of crime within cities (Frank, Andresen, & Felson, 2012). Unfortunately, there have been no studies that have attempted to link this spatial perspective on crime with the homicide convergence literature that we have mentioned above. From our perspective, this is an important shortcoming of regional studies on crime because it omits the dynamic and equilibrium aspects of homicide rates from what has traditionally been discussed in the empirical literature on homicides. In this research, we studied homicide rates in Mexico from the perspective of the gender and regional convergence approaches mentioned above. We simultaneously emphasized the regional and

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Table 1 Comparative statistics in homicide rates (victims). Male

Female

Ratio

Homicide rates per 100,000 Mexico (1985e2008) 15.0 USA (1980e2008) 7.4

Total

25.2 11.6

2.9 3.4

8.6 3.4

2008 Homicide rates per 100,000 World 7.95 Africa 20.12 America 17.18 Europe 5.14 High income 2.71 Upper-middle income 17.13 Lower-middle income 5.26 Low income 16.08

13.09 33.43 30.91 7.85 4.08 30.15 8.28 27.21

2.72 6.91 3.78 2.61 1.37 4.56 2.11 5.01

4.81 4.84 8.18 3.01 2.98 6.61 3.92 5.43

Mexico USA

24.26 8.50

2.65 2.30

9.15 3.70

13.28 5.40

Fig. 1. Time series of homicide rates.

Source: ONU-Mujeres (2011), Cooper and Smith (2011) and World Wealth Organization.

spatial components of these processes. To formally treat both convergence approaches related to homicide rates, we borrowed from the conditional regional convergence model, which is a standard tool in the economic growth literature, to econometrically model both convergence forces (i.e., modernization and the gender gap). In doing so, we recognized that the observed heterogeneity in homicide rates in Mexico is contingent on the regions’ dynamics; however, we also assessed whether homicide rates are converging, regardless of actual regional discrepancies in homicides. The results of this study of convergence in homicide crimes can shed light on the underlying factors shaping homicide rates in Mexico beyond those “short-term” or “conventional-wisdom” factors (such as drug cartels and drug war policy) commonly cited to explain the current trends in homicide crimes in Mexico. The underlying factors in which we were interested can be associated with the variables invoked by the “modernization approach” to predict convergence in homicide rates. Still, we were concerned with evaluating whether such factors are conditioned by regional or gender forces that would account for the different convergence patterns in homicide rates between the genders. Comparative and regional description of the homicide rates in Mexico Comparative figures and recent tendencies This research relied on data from death certificates of the National Health Ministry of Mexico (INEGI y Secretaría de Salud). Table 1 shows some comparative statistics for the homicide rates (victims) per 100 thousand persons between Mexico and other parts of the world. In the upper panel of the table, we contrast Mexico’s homicide rates during the period 1985e2008 against the USA’s rates during 1980e2008. Mexico had a higher average homicide rate (15) than the USA (7.4) over these comparable periods of time. This disparity can be explained by Mexico’s homicide rate for males (25.2), which was more than twice that of the USA (11.6). In contrast, Mexico’s homicide rate for females (2.9) was only slightly lower than the USA’s rate for females (3.4). In comparing Mexico’s homicide rates for 2008 with those of other world regions, we observe that the homicide rate for females (2.65) was roughly the same as the world (2.72) and European (2.61) averages; however, it was just over half the average rate among upper-middleincome countries (4.56), which is Mexico’s peer group, as classified by the World Health Organization. In contrast, Mexico’s homicide rate for males (24.26) was closer to those of their regional

Fig. 2. Male-to-female ratio of homicide rates.

(America, 30.9) and income-based peers (middle-income countries, 30.15). Mexico’s male-to-female ratio in homicide rates was the highest among the aggregate regions of the world. Fig. 1 presents the time series of annual homicide rates by gender during the period 1985e2010. The figure clearly shows that homicide rates trended downward for both series between 1985 and 2006. However, a turning point occurred, such that the trends in both series begin to increase between 2007 and 2010. This increase was so dramatic that by the end of the decade, homicide rates reached the high levels of the mid-1980s. The robust increase in the homicide rates can be attributed to the drug war policy that the Mexican government implemented during the Calderon presidential administration.1 Fig. 2 presents the annual male-to-female ratio of homicide rates in Mexico from 1985 to 2010. The series demonstrates the decreasing trend in the ratio during the period from 1985 to 2004 and the shift to a steady increase from 2005 to 2010. The data indicate that the high ratio that Mexico has experienced in recent years, compared to other regions (see Table 1), reflects a recent rebound from a long-standing decrease in which the rates in Mexico seemed to converge to those of developed countries. Exploratory spatial data analysis One of the prevalent explanations for the dramatic recent increase in homicide rates in Mexico is the implementation of a drug war policy beginning in 2006 (Astorga & Shrik, 2010). It is well known that drug cartels in Mexico have geographical

1 Some authors argue that the drug war strategy against the drug cartel was not a cause of this increase (Sota & Mesmacher, 2012); instead, they argue that the increase in violence began prior to the implementation of the government’s policy interventions.

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283

Fig. 3. Coefficient of variation of homicide rates (sigma convergence).

concentrations (Alvarado, 2010; Guerrero, 2011; Simser, 2011); thus, it is expected that homicide rates would be responsive to those regional dynamics. In this research, we approached the analysis of the regional dynamics of homicide rates by considering the municipalities to be regional units. There were a total of 2456 municipalities across the country during the period 2001e2010. We decided to normalize the homicides with respect to the populations of the municipalities, regardless of gender. This was done because the estimates available for municipal populations for the period 2001e2010 were more reliable than those segmented by gender. In regional economics, convergence is invoked in the context of a discussion about the reduction in spatial disparities among regions. A widely used measurement is sigma convergence, which is a decline in the dispersion of per capita income (or productivity) among regions over time (Capello & Nijkamp, 2009). It is common to find empirical studies focused on regional crime (or any other socioeconomic variable) that adopt this approach to analyzing convergence in such indicators (Cook & Winfield, 2013; Liargovas & Fotopoulos, 2009). Fig. 3 displays the coefficient of variation of homicide rates for both genders across municipalities in Mexico as a measure of (sigma) convergence.2 The value of the coefficient of variation was calculated for each year during the period 2001e2010, and the values were scaled so that the initial value was 1, to facilitate comparison of values in the series. Fig. 3 suggests that homicide rates for both genders were relatively stable between 2001 and 2006, but the male series started to display a clear divergence pattern in 2007 that is not borne out in the female series. Moreover, homicide rates for females tended to display more convergence beginning in 2008. As mentioned above, there is an important branch of the empirical literature that focuses on the spatially interactive features of the dynamics of violence; in particular, the literature emphasizes the identification of hot spots (Andresen, 2011; Ye & Wu, 2011). Therefore, any serious attempt to perform regional analyses (in the context of convergence) must also address this topic. The presence of hot spots can be associated with neighborhoodesocial interaction effects on the dynamics of crime (Glaeser, Sacerdote, & Scheinkman, 1996). Hot spots may also be associated with the social disorganization approach, which emphasizes the mechanisms of social control in neighborhoods (Sampson, Raudenbush, & Earls, 1997). Wang and Arnold (2008), for example, adopted this last perspective in explaining the intraurban variation in homicide rates

2 The coefficient of variation (CV) of the homicide rates is calculated as follows: CV ¼ s/m where s is the standard deviation of the homicide rates across municipalities and m is the statistical mean of such observations.

Fig. 4. Spatial autocorrelation of homicide rates. aA first-order Queen contiguity matrix was used to calculate the values of Moran’s index. All measurements were found to be statistically significant at levels above 99%, as determined using permutation tests.

in Chicago using, among other factors, a localized income inequality index that measures income inequality between contiguous areas. Fig. 4 shows the spatial autocorrelation of the homicide rates by gender using values of Moran’s index, calculated with a spatial firstorder contiguity weight matrix. The series shows that the homicide rates against both females and males at the municipality level displayed spatial autocorrelation during the period 2001e2010. Hence, homicides are not randomly allocated across municipalities; on the contrary, the homicide rate in one municipality is statistically correlated with the rates of its neighbors. The homicide rates against males have more than twice the global spatial autocorrelation of the homicide rates against females. The behavior of the index for both series was relatively stable during the period 2001e 2007, but the index values increased drastically beginning in 2007 for males and in 2008 for females. It is important to note that the Moran’s index for females shows a lag time of 1 year with respect to the male index. This suggests that if the dynamics of regional contagion exist in the homicide rates of males, they would influence the homicide rates against females as well. Therefore, the trends in the Moran’s index values shown in Fig. 4 indicate that the implementation of the government policy against drug crimes, which began in 2006, was associated with a strong increase in the homicide rates and an increase in the regional concentration of homicide. The agglomerations in crime rates by gender are presented in Maps 1e4, where local indicators of spatial autocorrelation (LISA) of homicide rates are used to show the evolution of hot spots of high crime rates between 2001 and 2010 (in particular, note the highehigh municipalities in the maps).3 The maps for 2001 indicate that hot spots for crime were well established in 2001 in the case of males: the northwestern and southwestern coasts of Mexico were hot spots years before the explosion of the aggregate crime rate across the country. In the case of females, the hot spots were more scattered and smaller in 2001. Hot spots for homicide rates for males become more prominent in 2010. In particular, the agglomeration of the northwestern coast in 2001 extended toward the north central region of the country by

3 LISA analysis in this research relies on the Anselin (1995) calculation of local Moran index values. Values of LISA were used to generate four statistically significant spatial clusters (or hot spots), and a first-order Queen contiguity matrix was used for the calculations. In particular, in this research, these hot spots (see Maps 1e4) are the following: HigheHigh, which are municipalities with high crime rates surrounded by municipalities with high crime rates; LoweLow, which are municipalities with low crime rates surrounded by municipalities with low crime rates; HigheLow, which are municipalities with high crime rates surrounded by municipalities with low crime rates; and LoweHigh, which are municipalities with low crime rates surrounded by municipalities with high crime rates.

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Table 2 Descriptive statistics of the homicide growth rate (2001e2010). Growth rate pooleda Observations

Mean

Std

Min

Max

Females 22,104 1.00% 0.94 594% 594% Males 22,104 2.40% 1.568 658% 772% Municipalities without violent event are excluded Females 4594 94.36% 1.153 196% 594% Males 11,764 72.20% 1.417 258% 772% Municipalities with more than 100 thousand people and violent event Females 1410 14.31% 0.482 124% 182% Males 1702 5.86% 0.496 198% 233% a Growth rate is yearly per municipality. Pooled information implies nine times the number of observations during the 2001e2010 period, i.e., 9  2456 ¼ 22,104 (obs.).

2010. This agglomeration incorporated many municipalities of Chihuahua and Durango. The hot spots of the southwestern coast remained as strong as in 2001. In addition, a new agglomeration emerged along the northeastern coast that covered the municipalities of Tamaulipas and Nuevo Leon. This cluster corresponded to the rise of drug cartel violence in that region. Nevertheless, the most important change in spatial agglomerations corresponded to females; their hot spots became more defined in terms of size and localization, compared to 2001. In general, the crime rates for females seem to confirm that they are reactions to the spatial dynamics of the crime rates against males.

homicide rates for both genders, as discussed above. Consequently, the polarization in the homicide rates is associated with specific regional agglomerations in the country (see Maps 1e4). In particular, the right tail of the distribution tends to be larger and wider in the case of male victims; in contrast, the densities for females at the beginning of the decade display a clear bimodal shape that seems to diminish over time. Fig. 6 also displays kernel estimates by year, but in this figure, municipalities with more than 100 thousand people are excluded. Clearly, both distributions show two modes over time; however, the female densities have two peaks that are more similar. Nevertheless, in the case of the female densities, the twin peaks tend to converge toward the center (implying that they will converge to a single mode in the long run), while the second mode of the males tends to prevail throughout the decade. The results of this nonparametric analysis suggest that the growth in homicide rates against both women and men tend to converge in municipalities with more than 100 thousand people. In contrast, the growth in homicides for males in the least urbanized municipalities tend to be more polarized than that for females. The wave of violence that Mexico has experienced since 2006 suggests two different dynamics of growth for males and females. Specifically, the trend for females demonstrates more characteristics of convergence. We discuss this issue in detail in the next section.

Distributions of homicide growth rates

Modeling beta convergence with a spatial panel approach

Table 2 presents basic statistics of the pooled homicide growth rate by gender. The homicide rate for males grew by 2.4% annually, while the homicide rate for females grew by 1%. The maximum and minimum values were similar for both genders. However, if we exclude municipalities without violent events (i.e., municipalities with homicide rates of zero), the average growth rate for females was 94%, while the growth rate for males was only 72%. However, in both cases, the substantial increase was partially due to the bias that population size introduces into the growth rates. To correct for that bias, Table 2 also presents the descriptive statistics for the municipalities with more than 100 thousand people only. For these municipalities, the average annual growth rate was 14.3% for females and 5.9% for males. That is, the growth of violence against women (in terms of homicides) was two and a half times larger than it was for males in the more urbanized areas of the country. Gaussian kernel densities of the homicide growth rates were estimated for the purpose of evaluating multimodality.4 Multimodality would be indicative of convergence dynamics being constrained or absent. To evaluate the distribution of the growth of homicide rates, we present Gaussian kernel density estimates of the homicide growth rates by year in Fig. 5. The estimates do not include municipalities with zero homicides, and it should be noted that the data are log-transformed. Both distributions have modes that are consistently present throughout the whole period. These results suggest a pattern of polarization that is consistent with the spatial autocorrelation of

We discussed earlier the fact that homicide rates display different patterns of dispersion across municipalities when the gender of the victim is considered (Fig. 3). In particular, the socalled sigma convergence indicates that a divergent pattern arises only for the case of males during the period 2006e2010. Following Cook and Winfield (2013), we adopted a beta convergence approach to addressing whether convergence dynamics are conditioned by the victim’s gender. One of the main advantages of using this approach is the possibility of introducing explanatory variables that account for the dynamics of homicide growth rates. Consistent with the beta convergence literature in economics (Baumol, 1986), the objective was to estimate the following linear model of the homicide growth rate in a panel setting:5

4 As is recognized in the nonparametric statistical literature, the lack of smoothness of a histogram can be addressed using nonparametric procedures such as the kernel method. Given a sample population X1, X2, . Xn with a density P function f, the kernel estimate is b f ðxÞ ¼ ðnhÞ1 nj¼ 1 Kððx  Xj Þ=hÞ; x˛
gi;t ¼ a þ blogðhr Þi;t1 þ εi;t

(1)

In this expression, g is the average growth rate in homicide rates, i is the municipality, hr is the rate of homicides per 100 thousand persons, t represents the temporal period (in this case, 9 years are considered, from 2001 to 2010), and epsilon is a stochastic perturbation. The key statistical hypothesis associated with this model is that b < 0, which indicates convergence; that is, the homicide rates in regions (or municipalities) that had the lowest homicide rates at the beginning of the period grew at faster rates during the period than their counterparts with higher initial homicide rates. Conversely, an absence of convergence implies that b ¼ 0 or b > 0. The latter case implies divergence; that is, that the homicide rates in regions (or municipalities) that had the lowest homicide rates at the beginning of the period grew more slowly during the sample period than their higher-rate counterparts.

5 Violence studies have analyzed beta (absolute) convergence in cross-sectional settings, as in Cook and Winfield (2013). In contrast, our approach follows modern methods in growth theory (Islam, 1995), using cross-section panel regressions, as in equation (1).

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285

Fig. 5. Gaussian kernel density of the homicide growth rates by year. aMunicipalities with zero homicides are excluded.

We must introduce a caveat with respect to the estimation of equation (1). As is widely acknowledged in the beta convergence literature, beta parameter estimation can be biased in the presence of spatial dependence of the dependent variable. This bias arises because the stochastic term could be autocorrelated (Rey & Montouri, 1999). We show in Subsection 3.2 that homicide growth rates displayed a strong pattern of spatial dependence during the period 2001e2010. This spatial dependence can bias the beta parameter estimate. A traditional panel approach could

eliminate the bias induced by spatial dependence in the crosssection because it introduces regional heterogeneity in a dynamic setting. Nevertheless, we preferred to rely on a spatial panel approach to estimate beta convergence because we have enough elements to consider the spatial interactions (among regional units) that could be present in the dynamics of homicide growth rates. These elements were discussed in Subsection 3.2. We proceeded with two main specifications to incorporate spatial interactions among regional units in a panel setting. The

Fig. 6. Gaussian kernel densities of the homicide growth rates in municipalities with less than 100 thousand people. aMunicipalities with zero homicides are excluded.

0.42 0.01 0.54 0.41 0.00 0.54 0.42 0.01 0.54 0.42 0.00 0.54

22,104 22,104

0.31 0.01 0.52 Note: standard errors are in parenthesis and they are robust. *p < 0.01. **p < 0.10.

0.29 0.00 0.52 0.29 0.00 0.52

22,104 22,104

Statistics Observations r2 r2 overall r2 between r2 within

22,104 0.29

22,104

0.28 0.00 0.51

22,104

22,104 0.42

0.299* (0.031) 0.181* (0.009) 0.065* (0.010) 1.241* (0.077) 0.683* (0.020)

0.683* (0.020)

0.198* (0.077) 0.208* (0.077)

0.151* (0.014)

22,104

22,104

0.034* (0.008) 0.181* (0.009)

0.052 (0.032) 0.098* (0.008) 0.053 (0.032) 0.098* (0.008)

1.097* (0.009) 0.856* (0.011) 1.098* (0.009) 0.856* (0.011)

0.151* (0.014)

Pooled

FE

RE

SAR, FE

SDM, FE

Pooled

Females Coefficients

Males

6 Levitt (2004) analyzed the sharp decline in crime in the USA in the 1990s and addressed each of the possible explanations suggested by conventional wisdom to account for the decline (changing demographics, a strong economy in the 1990s, better policing strategies, laws allowing carrying of weapons, and increased use of capital punishment). Levitt concluded that these rationales explained little of the sharp decline in homicide rates. Levitt argued that the increasing number of police, the huge number of prisoners, the decline of the crack epidemic and the legalization of abortion actually drove the decrease. These findings are relevant not for the explanations per se but because they conflict with traditional economic models of crime that consider homicidal behavior to be linearly responsive to labor market opportunities (Becker, 1968) or macroeconomic performance (Freeman, 1995). Levitt put appropriate emphasis on regional factors (controlled by local government actors) that have a greater impact on criminal behavior. In this same sense, we consider that a spatial regression approach such as the one taken in this research can be an appropriate modeling strategy for indirectly accounting for the institutional and regional factors that shape criminal behavior. 7 The spatial panel econometric regressions were estimated in STATA using the algorithms (commands "xsmle") generated by Federico Belloti, Andrea Piano Mortari, and Gordon Hughes. The algorithms are available at http://www. econometrics.it/stata.

Table 3 Convergence models of the homicide growth rate (2001e2010).

In this specification, x is the parameter associated with the spatial lag variable of the homicide rate among regional neighbors, and j is the vector of parameters associated with the spatial lag variables used in the model to condition the convergence dynamics of homicide growth. Equation (3) can be estimated with fixed or random effects. To consider the two approaches to convergence that we discussed in the introduction, i.e., the modernizationeconflict approach (LaFree, 2005) and the gender gap approach à la Adler (1975), we proceeded econometrically by estimating separate regression equations for males and females. The idea was to evaluate whether beta convergence differed between males and females under different spatial and regional specifications, as a way of introducing possible heterogeneity due to gender factors. We used the gross domestic product (GDP) per capita as a unique additional covariate that conditions the homicide growth rate. In doing so, we relied on unobserved regional heterogeneity (under a fixed or random effects assumption) to be consistent with the elements discussed in footnote.6 In Table 3, we present the econometric estimates for all models.7 The second column presents the OLS estimates of equation (1) for the males without subscript t and adding only GDP per capita. The analogous results for females are in the ninth column. These pooled estimates indicate that convergence prevails for both genders. However, the beta coefficient is lower for females (0.86) than for males (0.60). This indicates that the rate of convergence toward the stationary state is higher for females.

FE

(3)

1.063* (0.009) 0.337* 0.025 0.124** (0.074) 0.485* (0.133) 0.170* (0.012)

þ m þ εi;t

1.049* (0.009)

RE

gi;t ¼ rWgi;t þ blog hri;t1 þ xWlog hrj;t1 þ Xi;t1 G þ WXt1 j

0.596* (0.012)

SAR, FE

In this specification, r is the spatial interaction parameter of the endogenous homicide growth rate, W is the spatial weight matrix, and X is a vector of exogenous variables that can condition the homicide growth rate (these variables can rely on what the literature has used to explain homicides dynamics).6 We selected a first-order contiguity weight matrix for the estimation. Equation (2) can be estimated with fixed or random effects. Equation (3) represents the SDM model:

1.049* (0.009)

(2)

0.596* (0.012)

gi;t ¼ rWgi;t þ blog hri;t1 þ Xi;t1 G þ m þ εi;t

SDM, FE

first specification relies on a spatial autoregression model (SAR) (Anselin, Le Gallo, & Jayet, 2008; Elhorst, 2009) and the second relies on a spatial Durbin model (SDM). Equation (2) represents the SAR model:

1.099* (0.009) 0.127* 0.023 0.030 (0.032) 0.179* (0.069) 0.079* (0.011)

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Variables log hr, t-1 XW log hr, t-1 log GDPc, t-1 XW log GDPc, t-1 Wg, t Constant

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287

Map 1. LISA of homicide rates for females in 2001.

Fixed and random effects estimates (FE and RE, respectively) are presented in columns 3 and 4, respectively, for males and in columns 7 and 8, respectively, for females. Compared to the pooled estimates, it is clear that the beta coefficient decreases substantially for males in the FE model, from 0.6 to 1.04; the beta estimates do not change in the RE models. There is a similar effect in the case of females: the FE model strengthens the beta coefficient to 1.09, while the RE model does not affect it. GDP per capita has a statistically significant positive impact on the rates for both genders, but the coefficient is greater and more significant for males (GDP per capita is only significant at the 10% percent level for females). The use of the Hausman test to discriminate between the FE and RE models is traditional. The null hypothesis is that individual effects are random (and RE produces consistent estimates), while the alternative hypothesis is that these estimators differ. Our results indicate that in both cases (females and males), the FE model is preferred. Therefore, once we considered an FE model as an alternative to the pooled OLS estimation, the main result was that beta convergence was equal for homicide for both genders. This result was expected, as regional heterogeneity at the municipality level is accounted for in an FE model. Estimates of equation (2) (the SAR model) with fixed effects are presented in columns 5 and 10 for males and females, respectively. The beta coefficients are quite similar in both cases (1.06 for males and 1.09 for females), and the parameter associated with GDP per capita is only significant at conventional levels for males. It is important to note that the estimate of the spatial interaction parameter (r) is significant for both genders, although it is stronger

in the case of males (0.06) than in the case of females (0.03). This is an important result because it supports the hypothesis of the contagion of the growth rate of homicides among municipalities that is suggested in Maps 1e4. Columns 6 and 11 of Table 3 show the estimates for equation (3) (the SDM model). This model produces estimates of the beta coefficients and the coefficients of GDP per capita that are similar to those estimated for the SAR model. However, the value of the parameter r is greater for both genders and, again, is stronger for males (0.17) than for females (0.08). These results for the SDM model confirm the spillover effect detected with the SAR model, making clear that the dynamics of convergence in the homicide growth rates depend on the spatial interaction between municipalities. That is, the average homicide growth rate of neighboring municipalities positively affects the process by which municipalities equalize their homicide growth rates. It is important to note that in the SDM model, it is possible to estimate the spatial lag parameter of the ratio of homicides and GDP per capita. In this case, the homicide rates of neighbors produce a positive effect on the growth of homicide rates for both genders. The GDP per capita of neighbors also has a significant positive effect on the growth of homicide rates for both genders. That is, there are positive spatial spillovers of the homicide rates and GDP per capita on the growth of homicide rates. This means that the level of economic development (proxied by the GDP per capita) of neighboring municipalities contributes positively to the equalization of homicide growth rates for both genders.

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Map 2. LISA of homicide rates for males in 2001.

To see the full effects that spatial spillovers have on homicide growth rates, Table 4 shows the direct and total effects produced by the elasticities of the variables in the SAR and SDM models. The direct effect is measured as the impact of a one-unit change in variable X in municipality i on the growth of the homicide rate in municipality i, averaged over all municipalities i’s. The total effect is measured as the impact of a one-unit change in all municipalities on the growth rate of municipality i, averaged over all municipalities i’s. The results shown in Table 4 indicate that the SAR model suggests a small but significant indirect effect of the homicide growth rate for both genders, decreasing the total convergence effects to 1.12 and 1.14 for males and females, respectively. Nevertheless, if the SDM model is considered, the indirect convergence effect for males is relatively larger but positive (0.18). Thus, the total convergence effect (see log hr, t-1) increases from 1.06 to 0.88. In contrast, the indirect effect for women is also positive but small (0.04), and it produces only a slight reduction in the total convergence effect (1.06). These findings are relevant because they suggest that convergence is counterbalanced by local spatial interactions among municipalities. This effect seems to be much stronger in the case of males. Another important finding is that the GDP per capita does not have a significant direct effect in the case of females in either the SAR or the SDM model, although it has a significant indirect effect in the SDM model, generating a total effect of 0.23. In the case of males, GDP per capita produces significant direct effects in both models, but the indirect effects are quite strong in the SDM model (0.59), in contrast to the effect in the SAR

model (0.01). These results indicate that the effect of GDP per capita on homicide growth rates is derived mainly from the neighboring municipalities; in the case of females, the GDP per capita of a municipality does not have any impact on homicide growth. These results suggest that a region’s economy has a more important effect on homicide growth rates than the economy of a municipality per se at this is more true for males than for females. Hence, even when spatial interaction exists in homicide growth dynamics, beta convergence for females is less conditioned by local regional factors than for males. These results are consistent with the results we obtained in the sigma exercise (see Fig. 3) and in the kernel-smoothed distributions (see Figs. 5 and 6 4); that is, there is evidence that the dynamics of the homicide rates for women differ from the dynamics observed for males because they are headed toward much more homogeneous and convergent regional behavior. Lastly, the econometric results described in this section are relevant because, to the best of our knowledge no other study has addressed the effects of externalities on the convergence dynamics of homicides. This is relevant because it implies that there is a multiplier effectdwhich operates across regionsdof the factors that explain homicide growth rates. Final remarks In this study, we used a spatial empirical modeling strategy to examine two of the common approaches to studying homicide convergence discussed in the literature: the modernizatione

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Map 3. LISA of homicide rates for females in 2010.

conflict and gender gap hypotheses. In doing so, we addressed the issue of properly weighting structural and local (or institutional) factors that together explain homicide rate variation across regions, in a methodological setting in which spatial externalities play a central role in shaping homicide dynamics. The results of our study are particularly illustrative because Mexico has experienced a significant increase in homicide rates in recent years, after a long period of sustained decreases. In only a couple of years, Mexico fell off a path leading toward homicide levels comparable to those observed in developed countries. Nevertheless, few analyses have focused on whether the underlying forces that made homicide rates diminish are the same that made them rise (i.e., whether the escalation of crime also operates in a context of convergence). We propose that this phenomenon can be addressed in the context of a discussion of convergence of homicide rates. In particular, we have shown that there are some other underlying factors, beyond the components suggested by conventional wisdom (such as drug cartels, drug war policy or inequality conditions), that shape the convergence dynamics in the homicide rates in contemporary Mexico. Homicide of males is more responsive to local dynamics (such as drug cartels and the local economy), which translates into stronger cluster formation of hot spots. Our findings reveal that homicide rates for females demonstrate a stronger convergence pattern than those for males, when local and regional factors are not considered. The conventional interpretation of this finding would be that the “modernization hypothesis” fits better for female homicides. However, it is difficult to accept this hypothesis without explaining

why the “modernization hypothesis” works well for women but not for men. We need to turn to the feminist literature that focuses on the differential effects that specific social forces (such as patriarchy) and specific social arrangements (such as the absolute status of women and relative gender inequality) have on regional homicide rates by gender (Vieraitis, Britto, & Kovandzic, 2007). Accordingly, we might have obtained in this study evidence to support some of the hypotheses currently being explored in feminist research, i.e., that homicide victimization rates for females grow faster than those for males when women are in disadvantaged positions relative to their male counterparts (Sanday, 1981) or that greater levels of gender equality may lead to a temporal “backlash” whereby men try to regain control by force (Brewer & Smith, 1995). Further research on these topics is needed, taking into special consideration the literature on specific patterns of female victimization in times of social unrest (ONU Mujeres et al., 2011; Russell & Harmes, 2001). We maintain that the empirical approach to the analysis of convergence used in regional economicsdand in particular, beta convergencedis useful for incorporating the issues involved in debating the modernizationeconflict hypothesis and the gender gap approach to studying violence within a country. Our results appear to be relevant to the gender literature on violence because they reveal that regional convergence seems to be conditioned by gender. In the case of Mexico, this finding implies that fatal violence toward women responds more to general (socioeconomic and/or cultural) development factors and less to local or regional factors, which makes the growth in homicide rates for women a much

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Map 4. LISA of homicide rates for males in 2010.

Table 4 Direct and total elasticities of homicide growth rate. Males

log hr, t-1 SAR, FE SDM, FE log GDPc, t-1 SAR, FE SDM, FE

Females

Direct

Indirect

Total

Direct

Indirect

Total

1.050* (0.008) 1.058* (0.008)

0.072* (0.012) 0.182* (0.027)

1.122* (0.015) 0.876* (0.029)

1.098* (0.008) 1.099* (0.008)

0.039* (0.010) 0.043* (0.021)

1.137* (0.012) 1.056* (0.023)

0.203* (0.085) 0.145 (0.082)

0.014* (0.007) 0.597* (0.148)

0.218* (0.091) 0.743* (0.173)

0.054 (0.036) 0.035 (0.036)

0.002 (0.001) 0.194* (0.070)

0.056 (0.037) 0.229* (0.077)

Note: standard errors are in parenthesis. *p < 0.01.

more homogenized and universalized phenomenon than in the case of males. References Adler, F. (1975). Sisters in crime. New York: McGraweHill. Alvarado, A. (2010). Seguridad Nacional y Seguridad Interior. In Serie: Los grandes problemas de México, Tomo XV. México: El Colegio de México. Andresen, M. (2011). Estimating the probability of local crime clusters: the impact of immediate spatial neighbors. Journal of Criminal Justice, 39, 394e404. Anselin, L. (1995). Local indicators of spatial association LISA. Geographical Analysis, 27, 93e115. Anselin, L., Le Gallo, J., & Jayet, H. (2008). Spatial panel econometrics. In L. Matyas, & P. Sevestre (Eds.), The econometrics of panel data (3rd ed.). Berlin: Springer. Astorga, L., & Shrik, D. (2010). Drug trafficking organizations and counter-drug strategies in the U.S.-Mexican context. In Shared responsibility. U.S.-Mexico

policy options for confronting organized crime (pp. 31e61). Woodrow Wilson Center for Scholars y University of San Diego. Barro, R., & Sala-i-Martin, X. (1992). Convergence. Journal of Political Economy, 100(2), 223e251. Baumol, W. (1986). Productivity growth, convergence, and welfare: what the longrun data show. American Economic Review, 76(5), 1072e1085. Becker, G. (1968). Crime and punishment: an economic approach. Journal of Political Economy, 76(2), 169e217. Brewer, V., & Smith, M. (1995). Gender inequality and rates of female homicide victimization across U.S. cities. Journal of Research in Crime and Delinquency, 32, 175e190. Capello, R., & Nijkamp, P. (2009). Introduction: regional growth and development theories in the twenty-first century e recent theoretical advances and futures challenges. In R. Capello, & P. Nijkamp (Eds.), Handbook of regional growth and development theories (pp. 1e32). Cheltenham, UK: Edward Elgar. Cook, S., & Winfield, T. (2013). Crime across the states: are US crime rates converging? Urban Studies, 50(9), 1724e1741.

M. Valdivia, R. Castro / Applied Geography 45 (2013) 280e291 Cooper, A., & Smith. (2011, November). Homicide trends in the United States, 1980e 2008, annual rates for 2009 and 2010. Bureau of Justice Statistics, U.S. Department of Justice. NCJ 236018, 1–35. Eisner, M. (2001). Modernization, self-control and lethal violence: the long-term dynamics of European homicide rates in theoretical perspective. British Journal of Criminology, 41, 618e638. Eisner, M. (2008). Modernity strikes back? A historical perspective on the latest increase in interpersonal violence (1960e1990). International Journal of Conflict and Crime, 2(2), 288e316. Elhorst, P. (2009). Spatial panel data. In M. Fischer, & A. Getis (Eds.), Handbook of applied spatial analysis (pp. 377e407). Berlin: Springer. Ertur, C., & Le Gallo, J. (2009). Regional growth and convergence: heterogeneous reaction versus interaction in spatial econometric approaches. In R. Capello, & P. Nijkamp (Eds.), Handbook of regional growth and development theories (pp. 374e388). Cheltenham, UK: Edward Elgar. Frank, R., Andresen, M., & Felson, M. (2012). Applied Geography, 34, 180e188. Freeman, R. (1995). The labor market. In J. Wilson, & J. Petersilia (Eds.), Crime (pp. 171e192). San Francisco: ICS Press. Glaeser, E., Sacerdote, B., & Scheinkman, J. (1996). Crime and social interactions. The Quarterly Journal of Economics, 111(2), 507e548. Guerrero, E. (2011). La raíz de la violencia. Revista Nexos. June. INEGI y Secretaría de Salud de México. Mortality statistics. At http://www.inegi.org.mx. Islam, N. (1995). Growth empirics: a panel data approach. The Quarterly Journal of Economics, 110, 1127e1170. LaFree, G. (2005). Evidence for elite convergence in cross-national homicide victimization trends, 1956 to 2000. Sociology Quarterly, 46, 191e211. Levitt, S. D. (2004). Understanding why crime fell in the 1990s: four factors that explain the decline and six that do not. Journal of Economic Perspectives, 18(1), 163e190. Liargovas, P., & Fotopoulos, G. (2009). Socioeconomic indicators for analyzing convergence: the case of Greece: 1960e2004. Social Indicators Research, 93(2), 315e330. ONU Mujeres, INMujeres, LXI Legislatura Cámara de Diputados. (2011). Feminicidio en México, aproximación, tendencias y cambios, 1985e2009. México. O’Brien, R. (1999). Measuring the convergence/divergence of ‘serious crime’, arrest rates for males and females: 1960e1995. Journal of Quantitative Criminology, 15, 97e114.

291

Porter, J., & Purser, C. (2010). Social disorganization, marriage, and reported crime: a spatial econometrics examination of family formation and criminal offending. Journal of Criminal Justice, 38, 942e950. Rey, S., & Montouri, B. (1999). US regional income convergence: a spatial econometric perspective. Regional Studies, 33(2), 143e156. Russell, D., & Harmes, R. (2001). Femicide in global perspective. New York: Teachers College Press. Sampson, R. J., Raudenbush, S. W., & Earls, F. (1997). Neighborhoods and violent crime: a multilevel study of collective efficacy. Science, 277, 918e924. Sanday, P. (1981). The socio-cultural context of rape: a cross-cultural study. Journal of Social Issues, 37, 5e27. Silverman, B. W. (1986). Density estimation for statistics and data analysis. London: Chapman and Hall. Simon, R. (1975). Women and crime. Lexington, MA: D.C. Heath. Simser, J. (2011). Plata o plomo: penetration, the purchase of power and the Mexican drug cartels. Journal of Money Laundering Control, 14(3), 266e 278. Sota and Mesmacher. (2012). Operativos y violencia. Revista Nexos. December. Steffensmeier, D., Zhong, H., Ackerman, J., Schwartz, J., & Agha, S. (2006). Gender gap trends for violent crimes, 1980 to 2003: a UCR-NCVS comparison. Feminist Criminology, 1, 72e98. Steffensmeier, D., & Allen, E. (1996). Gender and crime: toward a gendered theory of female offending. Annual Review of Sociology, 22, 459e487. Vieraitis, L., Britto, S., & Kovandzic, T. (2007). The impact of women’s status and gender inequality of female homicide victimization rates. Feminist Criminology, 2, 57e73. Vilalta, C. (2010). The spatial dynamics and socioeconomic correlates of drug arrests in Mexico city. Applied Geography, 30, 263e270. Wang, F., & Arnold, M. (2008). Localized income inequality, concentrated disadvantage and homicide. Applied Geography, 28, 259e270. Widner, B., L-Reyes, M., & Enomoto, C. (2011). Crimes and violence in Mexico: evidence from panel data. The Social Science Journal, 48, 604e611. Ye, X., & Wu, L. (2011). Analyzing the dynamics of homicide patterns in Chicago: ESDA and spatial panel approaches. Applied Geography, 31, 800e807.