Abstract(resumo):

Objective: The violence in Brazil is increasing almost all over the country. Our main purpose is to identify clusters based on the trends of male homicide rates in the 27 Brazilian states and to measure the association between the last male homicide rates and socioeconomic indicators. Methods: Ecological study to analyze the rates of male homicides by state. To measure the distances between two male homicide rate series, the Dynamic Time Warping (DTW) method aligns the series to capture that trend changes may occur before or after for some series. Then, the DTW hierarchical cluster technique identified five clusters for the 27 Brazilian states, representing distinct temporal patterns of the male homicide rates in the last 30 years. Results: Twelve states from the north and northeast regions presented sharp increases from a homicide rate around 20 per 100,000 men in 2000 to 70 in 2019. São Paulo state male homicide rate passed from 80 to 13 in the last 20 years. Other clusters presented high male homicide rates around 40 or 60 in 2019. High male homicide rates are associated with higher unemployment rates and lower Human Development Indices and Gini's indices. Conclusion: As expected, the worse socioeconomic indicators imply higher male homicide rates, with increasing trends occurring mainly in the north and northeast regions.

Keywords(palavra-chave):

Male homicide rates, Brazilian violence, Dynamic Time Warping, Cluster time series.

Content(conteúdo):

Introduction

The United Nations Office on Drugs and Crime 1 affirms that it occurred 464,000 homicides in 2017, where 37% were registered in the Americas, followed by Africa with 35%, and Asia is responsible by 23% despite its huge population (60% of population). In 2017, 38% (65,495) of all homicides in the Americas occurred in Brazil (13% of global homicides). Considering the homicide rates, only El Salvador, Honduras and Venezuela presented higher rates than Brazil in the American continent.
Considering the mortality rates due to male homicides in 2019 available in the World Bank2 database for 116 countries, Brazil is in the 13th position with 38.7 per 100,000 men, similar to the Latin American rate of 38.3 per 100,000. The countries with the 5 largest male homicide rates in 2019 are: Jamaica (86.8), Honduras (73.4), El Salvador (71.1), South Africa (66.0) and Trinidad and Tobago (63.2). Only this five countries present a rate larger than 60 homicides per 100,000 men.
In 1989 the number of homicides in Brazil was 28,736 3, it passed to 45,429 deaths in 2019, representing an increase of 58% in 20 years (2.3% a.a.). There were 1 million homicides in Brazil between 1980 and 2010 4. In the last 30 years, from 1989 to 2018, 1,287,000 male homicides occurred in Brazil. For young adults from 10 to 24, the male homicide rates increased 1% a.a. 5 from 2000 to 2019 in Brazil and this rate also increased in other American countries as in Mexico, Costa Rica, and Uruguay.
In this paper, we focus only on the study of male homicide rates since 91% of all homicides consist of male deaths and the feminicides (female homicides) deserves another detailed study due to its recent upward trend worldwide and a new Brazilian legislation 5. This pattern is similar in other Latin American countries 6.
In Brazil, the male homicide rates have been increasing every year since 1989 and this increase occurred in 12 of 27 states 7. Several states passed from a rate of 20 per 100,000 men in 1989 to more than 100 in the last decade, where most of these states are located in the Brazilian northern and northeastern regions. These rates are larger than the largest rates worldwide. Nonetheless, in the Brazilian most populous state, São Paulo, this rate reached 80 per 100,000 in 1998, decreased year after year, reaching 13 per 100,000 in 2019.
A complete review analyzing 119 different security programs in Latin America which has a direct or indirect objective to reduce homicides pointed out that 19 programs (17%) are Brazilian 8. Several programs are related to control and reduction of firearms or alcohol consumption, protection of exposed groups, police interventions and incentives, programs to monitor police actions, among others. They cited several programs in Brazil, in states who really reduced their homicide rates, and other countries with high violence rates as Trinidad and Tobago, Venezuela, Colombia, and Jamaica.
The main goal of this paper is to analyze the evolution of the male homicide rates by state from 1990 to 2019 and also to cluster these time series of rates, taking into account their different levels and local trends. To identify cluster of time series with similar characteristics, we are using the Dynamic Time Warping distances 9,10, where the time series are aligned to minimize the distances between them, since some trend changes may occur a little bit earlier or after in some states. After this time alignment, a hierarchical cluster method using the distances between the aligned time series identified different patterns of the male homicide rates. We also analyzed the correlation between the male homicide rate in 2019 and the inequality Gini's rate, the Human Development Index, and the unemployment rate in the Brazilian states.

Materials and Methods

This is an ecological study based on Brazilian male homicide data from 1989 to 2019. The national male homicide rates were obtained from the World Bank database 2. The annual male homicide rates by state from 1989 to 2019 are available at the Atlas of Violence 7. The number of homicides are available from the Mortality Information System of the Ministry of Health 3 and the annual population, the human development index (HDI), the unemployment rate, and the Gini index are obtained from the Brazilian Institute of Geography and Statistics 11. The ICD-10 codes for homicides are X85-Y09 and Y35, for ill defined causes are R0-R99, and the events of undetermined tent are classified as Y10-Y34 in the chapter of external causes. These last ill defined causes were also analyzed to investigate the recent decay of the homicide rates in 2018 and 2019.
In general, the distance between two time series with the same length are calculated using the Euclidean distance. However, the rates for some states may present similar temporal evolutions but some trend changes occurring few years earlier or after the observed change for other states. Series with the same general behavior, but with changes occurring a little before or after, should be close to each other and then allocated in the same cluster. The dynamic time warping (DTW) method finds an optimal alignment between two given time series under certain restrictions. This optimality refers to find a minimum distance between two series. For the time indices of both series, we are adopting: a boundary condition where the indices of both series begin at the first observation and end at the last observation of each series (this may be relaxed in other applications); the order of time points is maintained and we cannot come back in time; we look for adjacent time indices, not jumping several instants at once. This method was originated by dynamic optimization problems 12 and became popular in the seventies decade for language recognition 13, 14. For our purpose, we align each pair of state male homicide rates minimizing the distance between them, allowing that some trend changes occur a little before or after the other.
The analysis was done using the dwt package 10 using the statistical R software 15. Then, we identify groups of states with similar pattern with the hierarchical cluster method 16 based on the distance calculated after the DWT alignment using the dwtclust 17 in the R software 15. After the identification of the clusters, we plotted a Brazilian map with the clusters of states 18.
To measure the association between the male homicide rates and some social and economic indicators in 2019, we presented the scatter plot, the Pearson’s correlation coefficient and we fitted a linear regression model to test the significance of the effect of each social indicator to measure the association between each indicator and the homicide rate. The chosen indicators were Human Development Index (HDI), unemployment rate, and Gini index. The first one measures health, education and economic conditions 19, and the last one is an inequality indicator. After the residual analysis, the homocedastic hypothesis was rejected using the Breusch-Pagan test for the regression including the IDH index as covariate, thus we used the corrected variance using the White’s correction20 to test the significance of the indicators. The level of significance is 5% for all statistical tests.

Results
Twelve of the thirteen countries with the largest male homicide rates in the World Bank dataset in 2020 2 are from Latin America. Brazil in the 13th country with a rate of 38.7 per 100,000 men. Other large countries are Mexico in 7th position (53.2) and Colombia as the 9th (47.7). The rates presented in Figure 1 oscillate a lot for smaller countries, but most rates are around 50.0 per 100,000 men in 2021.

Figure 1: Male homicide rates per 100,000 men by country - 1990-2021.

Fig. 1

From the 27 Brazilian states, eleven presented rates larger than 60 per 100,000 in 2019 (Table 1). All the 10 greatest male homicide rates occur in states in the north and northeast regions. São Paulo, the most populous state (22% of population) and responsible for 32% of the national GDP (gross domestic product), presented the smallest rate of 13.1 homicides for each 100,000 men.

Tab. 1

Considering all the male homicide rates from 1989 to 2019, we could cluster the states according their temporal patterns, minimizing the distances of rates in the same cluster of states. The dendrogram in Figure 2 shows the hierarchical cluster of states depending on their corresponding male homicide rates.

Figure 2: Dendrogram of states minimizing the DWT distances between the state rates from 1989 to 2019.

Fig. 2

A description of the five identified clusters are presented below with the respective, plots and map in Figures 3 and 4:
1. 20 to 70: Twelve states present an upward trend passing from a male homicide rate around 20 in 2000 to rates around 70 per 100,000 in 2019 as seen in Figure 4(a,b). All these states are in the north or northeast regions with exception of GO, as shown in the map (Figure 5).
2. 60 to 60: Another group of states (RO,RR,AL,ES, PE, RJ) present erratic rates oscillating from 60 to 120 during the last 30 years, reaching rates around 60 in 2019 (Figure 4 c,d). As seen in the dendrogram, PE,ES and RJ are joined closer to each other and the AL’s time series is more distant with higher rates from 2005 to 2015.
3. 40 to 40: A third group (MS,PR,RS,DF,MT) with states of the south and central regions presented rates around 40 in 1989 and in 2019.
4. 20 to 40: The rates in the cluster of states (SC, MG, PI) were below 20 in 1989, have increased a little after 2000, but remained lower than 40, the Brazilian rate in 2019 (Figure 4e).
5. 80 to 13: The SP state presented a completely different trajectory, decreasing from 80 to 13 in the last 20 years. We included SP in this last graph only to show that its latest rate is the smallest Brazilian rate.

Figure 3: Male homicide rates by clusters of states.

Fig. 3

Fig. 4

Only in 2018 and 2019, most male homicide rates have decreased in several states. This could have happened, for example, due to an increase in the number of deaths due to ill-defined causes (chapter XVIII). The mean number of ill-defined male deaths increased only by 1% in 2018-2019 in relation to the mean number in the period 2014-2017 in Brazil. Only four states presented expressive increases in the number of ill-defined deaths, namely DF (52%), MS(44%), RJ (41%), and AC (30%). Only 8 other states presented increases in the number of ill-defined deaths and the mean increase was 11%, which could not explain the significant decrease of the male homicide rate seen in Figure 1. Another confounder could be the registration of some homicides as an event of undetermined cause, which belong to the chapter of external causes. The Brazilian number of deaths due to this cause increased 9,147 deaths in 2018 and 2019 compared to the mean annual number of deaths in 2010-2017. Meanwhile, the number of homicides fell by 15,130 deaths. Thus, most part of the drop in homicides could be explained by the higher number of deaths due to undetermined events in the chapter of external causes, but not all the recent drop.
The higher recent male homicide rates occur in the northern and northeastern regions and they are clearly associated with lower social and economic indicators. In 2019, the Pearson’s linear correlation coefficient between the male homicide rates and the indicators Human Development Index (HDI), unemployment rate and Gini index are respectively -0.67, 0.62, 0.53. Better health, education and income corresponds to higher values of HDI (19) (p<0.0001), which in turn is associated to less homicides as seen in Figure 5. Also, higher values of unemployment rate (p=0.0005) and inequality Gini (p=0.0049) indices are associated to higher male homicide rates.

Figure 5: Scatter plot of male homicide rates by HDI, unemployment rate and Gini index for the 27 Brazilian states – 2019.

Fig. 5

Discussion

The UNOCD 1 highlights that, in absolute numbers, Nigeria and Brazil, which together make up around 5 per cent of the global population, accounted for 28 per cent of global homicides. Brazil is one of the most violent countries considering the most populous countries. However, there are discrepant trends and levels of homicide rates considering the Brazilian states.
The Brazilian rate presented a significant decrease of 4.6% in 2004 21 in relation to the previous year due to the anti-gun legislation and disarmament campaigns in 2003, but, analyzing the homicide rates by state, we may conclude that this decline occurred only in SP, with its largest population. In fact, the first cluster of 12 states begins the escalation of violence in 2000, with rates passing from 20 to more than 100 per 100,000, higher than the most violent countries in the world.
National budget in security increased 80% from 2004 to 2012, but remained the same from 2012 to 2017 22. However, the homicide rates have been increasing since 2000 in most states. In 2017, the federal spending in public security amounted to 15.1 billions of reals 22 (US$ 4.0 billions, considering the prices in 2018 and one dollar corresponded to R$ 3.8 in 2018). From these total, 70% corresponds to staff payments. Some programs do not have a continuity pattern, as a program for indigenous population which presented an increased budget only during 2008 to 2011 to R$550 millions and this falls to R$94 millions in 2012. Some other programs are created and finished and there is no continuous program. We could also comment about the budget of the National Security Force, created in 2004, which support states and counties for provisory actions to defeat crisis 22. The budget of this Force increased 136% only in 2007, and then returned to the usual levels, and increased again in 2017, and depends on parliamentary amendments, which may vary a lot over time, turning impossible the evaluation of this program. Consequently, it is very hard to identify the effectiveness of security federal policies in Brazil.
The distribution of the security budget by state in 2020 23 indicates that most states spends more than 80% of the budget with general management, and only few states, namely PE, PR, RO, RS, SE and SP, registered a representative percentage budget with policing on streets. Nevertheless, as the authors discuss, this may be confounded due to different ways of registering data, since some states register almost 100% of the budget as management which may be not real. They also observed that the distribution of the budget by function change a lot for the same state over time, indicating that this corresponds to changes in the registration and this cannot be used to measure the effectiveness of the security policies. At least, SP presented a significant downward homicide trend in the last 30 years and PR, RS and RO presented lower rates in the last years. PE presented a decline but its rate rose again in the last years and SE presented a sharp rise and consists of the second largest male homicide rate of 82 per 1,000 in 2019.
Analyzing the effects of the emergence of a new criminal organization, called Família do Norte, in Manaus city, the capital of the Amazonas state, the homicide rate per 1000 inhabitants rose 76% in less than 10 years (from 31.3 in 2006 to 54.9 in 2015) 24. According to these authors, the economic effect corresponds to a loss of 2% in the per capita gross domestic product with this new criminal group. This study also discusses how the large criminal groups PCC (Primeiro Comando da Capital) and CV (Comando Vermelho) are now spread all over the country. Soares Filho et al. (2024) 25 also confirm the homicide increases in the north and northeast regions and the decrease mainly in São Paulo and Rio de Janeiro, but they highlight that the violence spread to smaller municipalities.
Friche et al. (2023) 26 analyzed 85% of all cities with 100,000 inhabitants in eight Latin American countries and they observed the heterogeneity not only between countries but also across cities within a country. They identified the association between higher education levels, higher GDP and, lower income inequality with lower homicide rates. Here, we confirm these associations with the HDI, unemployment rate, and Gini's index, where the correlation was larger between the state HDI and male homicide rates, which makes sense since the HDI measures health, education, and income conditions.
Another issue associated to the escalation of violence in most Brazilian states may be the rise in the unemployment rate, from 6.6 in Dec, 2014 to 13.9 in Mar, 2017 11. Based on data about 5565 municipalities in Brazil, higher unemployment accounted for 31,415 excess deaths between 2012 and 2017 27. To detect local effects on the homicide rates, a spatial analysis 28 identified significant negative correlations with employment rate only in SP, MA and MS. They also detected effects of the social cash transfer programs (called Bolsa Família) which were positive or negative in small regions, but they are non significant in the most part of the country. Aransiola et al. (2022) 29 also observed the increase of homicide rates in the north and northeast regions and a decrease in some areas in the southern regions, showing a reduction of the predictive strength of income inequality and an increase corresponding to unemployment from the year 2010 to 2017, reinforcing the relevance of the unemployment effect. Maybe, new proposals should involve a multidisciplinary solution, as the National Policy for the Reduction of Morbidity and Mortality resulting from Accidents and Violence 29 that not only focus on the health assistance, but evaluate and discuss the prevention involving also representatives of civil society.
About the methodology to cluster the series, it was relevant to consider the Dynamic Time Warping since it was not relevant if some trend changes occur just few years before or after for some states. The general increasing or decreasing patterns are the most important feature to cluster the series. The obtained five clusters represent the general patterns of increasing, oscillating or decreasing male homicide rates by state. The map in Figure 5 shows that more states in the north and northeast regions presented increasing trends with high rates in 2019.
The population is getting older in Brazil 31, which could result in less homicides since violence affects more young people, but even though the trend is still upwards almost everywhere.
Comparing our male homicide rates by state in 2019 with some rates worldwide2, we observe that the rate registered in São Paulo was decreasing and reached 13 per 100,000 as occurred similarly in Russia (12,2) and Ecuador (12.0). The higher rates above 60 in the cluster 20 to 70, with states in the north and northeast regions are closer to the highest rates in the world observed in Jamaica (86.8), Honduras (73.4), El Salvador (71.1), South Africa (66.0) and Trinidad and Tobago (63.2). The male homicide rate is 59.7 in Belize and 53.2 in Mexico similar to rates in the cluster called 60-60, which includes ES, PE, RJ, AL, RO and RR. The rates in Brazil (38.7) and Guatemala (42.4) are closer to the rates observed in the cluster 40 to 40 (MT, MS, PR, RS, DF) and in the cluster 20 to 40 in 2019 (SC, MG, PI). Only to compare, the rates are 8.5 in Argentina, 7.9 in the United States and are less than 2 per 100,000 men in Germany, France and United Kingdom. Brazil is really far from this stage. It is important to note that some countries do not report their homicide rates (for example, Angola, Congo and Mozambique).
Concluding, São Paulo is the only state with a sharp decreasing male homicide rate. Other 12 of 27 states are getting more violent and, in general, this increase by state is, as expected, related to worse socioeconomic conditions, with higher unemployment rates, and most of them are in the north and northeast regions. This indicates that public security politics must be developed as a continuous national plan mainly involving also economic and social development.

Acknowledgements
Airlane P. Alencar thanks FAPESP 23/12851-7 e FAPESP 23/02538-0.


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