mathematics Article Spatial Externalities of Income Inequality on Security in Latin America Pablo Ponce 1 , José Álvarez-García 2,* , Mary Cumbicus 1 and María de la Cruz del Río-Rama 3 1 School of Economics, Universidad Nacional de Loja, Loja 11050, Ecuador; [email protected] (P.P.); [email protected] (M.C.) 2 Financial Economy and Accounting Department, Faculty of Business, Finance and Tourism, University of Extremadura, 10071 Cáceres, Spain 3 Business Management and Marketing Department, Faculty of Business Sciences and Tourism, University of Vigo, 32004 Ourense, Spain; [email protected] * Correspondence: [email protected] Abstract: The aim of this research is to analyse the effect of income inequality on the homicide rate. The study is carried out in 18 Latin American countries for the period 2005–2018. The methodology used is the Generalized Least Squares (GLS) model and the data were obtained from World Develop- ment Indicators, the World Health Organization and the Inter-American Development Bank. Thus, the dependent variable is the homicide rate and the independent variable is income inequality. In addition, some control variables are included, such as: poverty, urban population rate, unemploy- ment, schooling rate, spending on security and GDP per capita, which improve the consistency of the model. The results obtained through GLS model determine that inequality has a negative and significant effect on the homicide rate for high-income countries (HIC) and lower-middle-income countries (LMIC), whereas it is positive and significant for upper-middle-income countries (UMIC). On the other hand, the control variables show different results by group of countries. In the case Citation: Ponce, P.; Álvarez-García, of unemployment, it is not significant in any group of countries. Negative spatial dependence was J.; Cumbicus, M.; del Río-Rama, found regarding spatial models such as: the spatial lag (SAR) and spatial error (SEM) method. In the M.d.l.C. Spatial Externalities of Income Inequality on Security in spatial Durbin model (SDM), positive spatial dependence between the variables was corroborated. Latin America. Mathematics 2021, 9, However, spatial auto-regressive moving average (SARMA) identified no spatial dependence. Un- 245. https://doi.org/10.3390/ der these results it is proposed: to improve productivity, education and improve the efficiency of math9030245 security-oriented resources. Academic Editor: Keywords: inequality; homicides; Latin America; spatial models Antonio Rodríguez Fuentes Received: 29 December 2020 Accepted: 24 January 2021 Published: 27 January 2021 1. Introduction The United Nations Office on Drugs and Crime (UNODC) defines homicide as the Publisher’s Note: MDPI stays neutral intentional death that one person causes on another and considers that homicides are the with regard to jurisdictional claims in clearest reflection of the existing violence in a specific sector, country or region. According published maps and institutional affil- to the UNODC [1], in 2017, around 464,000 people were homicide victims in the world; 80% iations. of the victims were men, and 20% were women, of which the vast majority were victims of their partner, ex-partner or male relatives. In addition, it points out that 95% of murderers are male. Currently, in Latin America, the region with the highest number of homicides in the Copyright: © 2021 by the authors. world, according to the UNODC [1], in 2017 the average homicide rate was 21.5% per Licensee MDPI, Basel, Switzerland. 100,000 inhabitants. About 90.5% of homicide victims are men and 9.5% are women, and This article is an open access article 50% of victims are between 15 and 30 years old, that is, the victims come from the group distributed under the terms and with the highest labour productivity. In order to achieve well-being, the costs of crime conditions of the Creative Commons represent 3.5% of GDP. Therefore, security is Latin Americans’ main concern. Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ With regard to inequality, it has increased worldwide in recent years. In 2016, 33% 4.0/). of global income was in the hands of 1% of the wealthiest countries and 50% only had Mathematics 2021, 9, 245. https://doi.org/10.3390/math9030245 https://www.mdpi.com/journal/mathematics Mathematics 2021, 9, 245 2 of 19 10% of the wealth [2]. According to the Economic Commission for Latin America and the Caribbean [3], Latin America is the most unequal region in the world, the Gini index dropped from 0.54 in 2002 to 0.47 in 2017; between 2002–2008 the average decrease in annual inequality was 1.3%; and between 2008–2014 the average was 0.8%, while between 2014–2017 the average reduction was 0.3%. This research aims to determine the effect of income inequality on the homicide rate with a study carried out in 18 Latin American countries for the period 2005–2018. Two econometric stages are used to examine this relationship. The first through a Generalized Least Squares GLS model, which captures the determinants of homicides within each country. The second econometric stage captures spatial spillovers to explain the homicides of each country, using the spatial autoregression model (SAR), the spatial error model (SEM), the spatial auto-regressive moving average (SARMA) and spatial Durbin error (SDM). It seeks to respond to the hypothesis raised in which it is considered that an increase in income inequality leads to an increase in the homicide rate. The results show that inequality tends to decrease in the period of analysis, while the homicide rate has increasing and decreasing periods. There is also a non-significant positive correlation between inequality and the homicide rate, which means that homicides apart from inequality depend on other variables. The GLS method confirms the aforementioned, in which inequality has a significant negative effect on the homicide rate for high-income countries (HIC) and lower-middle-income countries (LMIC), whereas the effect is positive and significant for upper-middle income (UMIC). According to the control variables, the relationship varies depending on the group of countries. Through spatial models such as: the SAR model, it was also determined that countries with low homicide rates are sur- rounded by countries with high homicide rates. With the SEM model, it was found that the homicide rate of a country depends negatively on the error of neighbouring countries, that is, the homicide rate is explained by variables external to the model. Furthermore, the SDM model shows that a country’s homicide rate depends on the inequality in neighbouring countries. The contribution of the article is novel and contributes significantly to the state of the art on this problem in the region. The novelty of the study is that it takes into account the spatial effects that revolve around homicides, that is, it examines how homicides in a country are related to variables in neighboring countries. The document consists of five sections. After the introduction, the second section presents the review of the previous literature. In the third section, the methodology is collected, the data is described and the econometric models used in the development of the research are discussed. The fourth section presents the discussion of the results found according to theory and empirical evidence. Finally, the last section discusses the conclusions and practical implications of the research. 2. Literature Review There are some theories focused on the study of homicide, which include from an economic point of view the one developed by Becker [4]), who considers that criminals are individuals who reason and who adopt criminal behaviour for the expected benefit, which according to his perspective is greater than performing other legal activities. This theory is confirmed by Bourguignon [5], by arguing that violent crime arises from individual disadvantaged situations such as income inequality and poverty. The empirical evidence linking income inequality and homicides is classified into three groups. In the first group, Coccia [6], Buonanno & Vargas [7] observe a significant positive relationship between inequality and homicides. Other studies, in addition to observing a positive relationship between these variables, also find it between unemployment and homicides [8]. In this regard, homicides are inversely related to GDP [9], but they are not significantly related to the educational level, urbanization, poverty and police activity [10]. There are relevant data worldwide that show that in 2012, one in every six homicide victims were children and adolescents from zero to 19 years old. In another study, in Lithuania in the period 2004–2016 it was found that 4.2% of homicide victims were children Mathematics 2021, 9, 245 3 of 19 and 73% men [11]. Similarly, in Latin America, homicide affects mainly boys rather than girls [12]. Furthermore, in this region, in 2015 the number of homicides was four times higher than the world average [13]. On the other hand, Nadanovsky and Cunha [14] determine that countries with lower income inequality have less poverty. Similarly, in the United States, the 0.23% Gini coefficient predicts a 26% increase in crime [15]. On the other hand, Botello [16], in a study for Colombia, determines that an increase of one percentage point in the Gini coefficient results in a 4% increase in the homicide rate per 100,000 inhabitants. However, in Mexico, a one-point increase in the Gini coefficient leads to an increase of more than 36% in the number of homicides [17]. It is men aged between 20 and 49 who are the most likely to be homicide victims, with a rate of 40% per 100,000 inhabitants [18]. Meanwhile, in El Salvador it is men aged between 15 and 29 [19]. In addition, in 2016 it was identified that the homicide rate in El Salvador increased to 296 for the group of people aged 15–29 and to 205 for those aged 30–44 per 100,000 people [1].