3.1 Data

This study uses annual data from 2006 to 2012. Educational outcomes are measured at the school level and homicide rates at the municipal level. There are 59,673 and 22,932 elementary and middle schools, respectively, in the sample, each observed for six periods. The schools are located across 1,697 municipalities, which represent approximately 69.1% of México’s 2,456 municipalities in 2010.

Academic performance is measured using the scores obtained in the ENLACE standardised test. ENLACE evaluates students’ abilities in the subjects of Spanish and Mathematics. Beginning in 2008, it also included a third subject which changes on a rotating basis. The test was initially implemented with the purpose of providing information on how to better structure and improve course outlines, and to help identify the skills and training needed by teachers. While elementary school in Mexico covers grades 1 through 6, ENLACE is taken by students in grades 3 through 6, and by middle school students in grades 7 through 9.³ The test is measured on a scale ranging from 200 to 800, with a mean of 500. ENLACE scores in Spanish and Mathematics are available by grade and subject. However, in the empirical analysis, they are used at the school level by averaging the scores obtained in each subject across different grades. An advantage of ENLACE is that it allows for a single and direct comparison between all evaluated students and schools. School level figures on ENLACE scores were obtained from the Ministry of Public Education (SEP).

Information on grade failure rates was taken from the Statistics 911 school census. The dataset includes information on students, teachers, school characteristics and other elements of the educational system from all the elementary and middle schools in Mexico.⁴

Statistics on the number of homicides at the municipal level were obtained from SIMBAD. Homicides per 10,000 inhabitants were constructed using population data from the 2005 Population Count and the 2010 Population Census. For year with unavailable information on population figures, the data was extrapolated assuming a constant yearly population growth-rate. Data on drug-related homicides was taken from ^{Policía Federal (2015)} and only includes information from December 1, 2006 onwards. While the homicide rate-like other crime related variables- is potentially subject to measurement error, as argued by ^{Caudillo and Torche (2014: 90)}, it is the most noticeable type of violent crime and provides a more reliable measurement than other types of crimes (^{Sampson, Raudenbush and Earls, 1997}).

To identify the effect of crime exposure on educational outcomes, a series of school, municipal, and state-level controls are introduced. Data on narcotics related charges at the municipal-level and the unemployment rate and GDP per capita at the state-level was taken from SIMBAD. Data on school characteristics such as the number of students, groups, and the student-teacher ratio, among others, was obtained from Statistics 911. Information on whether the school participates in the Quality School Program (PEC), Full-Time School Program (PETC) or the Safe School Program (PES) was taken from SEP.⁵ Data on the Seguro Popular coverage rate was obtained from the National Commission of Social Protection in Health. Information regarding the Prospera coverage rate was taken from the National Coordination of Prospera Social Inclusion Program.⁶

3.2 Descriptive statistics

Table 2 displays the means and standard deviations of selected variables. Regarding the variables of interest, every year ENLACE scores in Mathematics are higher than those in Spanish. With respect to grade failure rates, they gradually decreased each year during the period of analysis.

Among school-level controls, on one hand, the average number of students per school decreased between 2006 and 2012, dropping from 192.9 to 188.1, respectively. On the other hand, the number of groups per school remained relatively constant at around 7.9. The fact that the number of groups is highly correlated with the number of classrooms used signals that classrooms are generally not shared among different groups. Focusing on the different school-level programs, the coverage rate of both the PETC and PES increased each year between 2006 and 2012. Specifically, while the coverage of the PETC was 0.4% in 2009, by 2012 this figure had increased to 2.2%. Furthermore, the PES which started in 2007 increased its coverage rate from 1.1% in its initial year to 35.0% in 2012. The PEC followed a less predictable pattern, where its coverage rate varied between 22.4% and 30.5%.

Turning our attention to municipal-level characteristics, the number of homicides per 10,000 inhabitants more than doubled during the period of analysis. While this figure stood at 0.9 in 2006, it escalated to 2.1 in 2011 and 2012. The increase in the total homicide rate was driven by a rise in drug-related homicides, which stood at 0.2 in 2007 and reached 1.5 in 2011. While not as pronounced, there was also an increase in the number of narcotics related charges per 10,000 inhabitants, which rose from 1.2 in 2006 to 1.7 in 2011. Regarding different social assistance programs, the expansion of Seguro Popular is seen within the period analysed. In 2006, 21.6% of the population were enrolled in Seguro Popular. By 2012, this figure stood at 55.9%. On the contrary, the coverage rate of Prospera remained stable, between 30.9% and 33.4%, as its main enrolment surge occurred before 2006. With respect to state-level characteristics, the unemployment rate fluctuated between 3.6% in 2006 and 5.6% in 2010, while GDP per capita reached its lowest point in 2009, when it dropped to 102,100 pesos per year. The reduction in GDP per capita was driven by the global economic crisis, when in 2009 Mexico’s GDP contracted by 4.7% (^{World Bank, 2014}).

5.1 Homicides and academic performance

Table 3 presents the effects of homicides on ENLACE scores in Spanish and Mathematics for elementary and middle school students. Columns (1) and (2) show that among elementary school students, a one-unit increase in the homicide rate per 10,000 inhabitants is associated with lower scores in Spanish and Mathematics exams between 0.0035 and 0.0039 standard deviations. Both effects are statistically significant at the 5.0% level. Regarding middle school students, columns (3) and (4) show that the effect of homicides is negative and significant at the 1.0% level. Specifically, a one-unit increase in the homicide rate per 10,000 inhabitants is associated with lower scores in Spanish and Mathematics ENLACE exams 0.0089 and 0.0142 standard deviations, respectively.⁸

Moreover, it is observed that in all cases an increase in the number of students at the school and in the number of classrooms used is associated with a rise in standardised test scores. On the contrary, an increase in the number of groups at the school decreases the ENLACE scores in elementary schools but is not significant for middle schools. A rise in the number of teachers per 100 students is positively associated with an increment in standardised test scores, where this variable is significant at the 1.0% for both elementary and middle schools. This implies that students improve their academic performance when the student-teacher ratio decreases. With respect to the school’s principal also being a teacher, under this scenario middle school students tend to perform worse in both Spanish and Mathematics, whereas for elementary schools there is no effect. The fact that the principal is also a teacher may be signalling that there is a shortage of teachers in the school. Focusing on the different federal programs, in all four columns the PEC and PETC are associated with an increase in ENLACE scores. Finally, the PES is associated with a decrease in standardised test scores, although this variable is generally not significant.

Table 4 presents how the effects of homicides vary depending on their timing and how close they occur to the date the ENLACE test was taken. In general, the effects of an increase in the homicide rate grow stronger if they occur closer to the examination date. For elementary schools, whereas a rise in the homicides registered during the entire academic year is associated with a decrease in Spanish test scores of 0.0043 standard deviations, an increase in the homicides committed during the week prior to the test being taken decreases average scores by 0.0214 standard deviations. A similar relationship is observed for scores in Mathematics, where a rise in the number of homicides committed the week before the exam is associated with a decrease on average scores of 0.0325 standard deviations, compared to 0.0048 for homicides committed during the entire academic year. Among middle schools, the relationship between Spanish scores and the timing of the homicides remains stable over the different time periods. Conversely, the effect of an increase in the homicide rate on Mathematics scores stands at 0.0155 standard deviations for homicides committed during the entire academic year and rises to 0.0203 for homicides registered during the 3 months prior to the ENLACE test. On one hand, the larger impact of homicides as they occur closer to the examination date may be indicating that the emotional and psychological effects of being exposed to a violent crime gradually decrease over time. On the other hand, it could also be signalling that classes missed closer to the examination date have a stronger effect on test performance than classes that were cancelled earlier in the academic year.

In elementary schools, the largest effects on test scores can be attributed to homicides that occurred during the week prior to the examination date. And in middle schools the largest effects are homicides that occurred during the 3 months prior to the exam. In middle schools, the non-effect of homicides that occurred during the week before the exam is partly a result of the coefficients’ larger standard errors. Nonetheless, this also reflects that the factors through which violence affects elementary and middle school students are different.⁹

To examine if there are heterogeneous effects, Table 5 focuses on different subsamples, where separate regressions were estimated for the different groups of schools. It can be seen that for both elementary and middle schools, the negative effect of a rise in the homicide rate is strongest among those based in a locality with high marginality levels or in highly deprived areas.¹⁰ Moreover, the decrease in ENLACE scores generated by an increase in the homicide rate is larger in schools located in rural areas compared to those registered in urban localities, where for the latter there is generally no significant effect.¹¹ Additionally, the effects of an increase in the homicide rate tend to be greater among schools teaching in the morning session compared to those that teach in the afternoon session. Among elementary schools, an increase in the homicide rate negatively affects test scores in public schools; while among private schools, a rise in the homicide rate increases ENLACE scores in both subjects, although the coefficient is only significant for Spanish. This result may be signalling that pupils studying in private schools, due to their generally privileged socioeconomic status, are being compensated in some manner (for example, by being given private tutoring) to minimise the adverse effects of being exposed to homicides or to keep them away from the perceived dangers brought by an increase in the levels of violent crime. On the other hand, due to hesitation driven by economic constraints or because some parents may not perceive their children to be aware of the situation or to be at risk due to their young age, it may be that students attending public schools are not being compensated in the same way. Nonetheless, academic performance in indigenous schools appears to be greatly affected by increases in violent crime levels, where a one-unit rise in the homicide rate per 10,000 inhabitants is associated with a reduction in Spanish and Mathematics ENLACE scores of 0.0264 and 0.0236 standard deviations, respectively. These effects are statistically significant at the 1.0% level.

Among middle schools, the estimated coefficients of the effect of a rise in homicides on test scores are positive for public and private schools but are negative for telesecundarias, which are distance learning middle schools that provide classes mainly through television broadcasts in rural or difficult to access areas in Mexico. On one hand, the positive effect for public and private middle schools may arise because an increase in violence is likely to lead some students to drop out of school and enter the labour force to help support their families through the negative economic consequences of a more violent context. Hence, this may be a result of changes in the composition of students within schools. This is also consistent with the positive estimate for afternoon middle schools, which tend to focus on students who often work and therefore might be less attached to school. On the other hand, the negative effect for telesecundarias may be driven by the fact that, like indigenous schools, they tend to be in small communities in isolated areas with prevalent poverty rates and low levels of schooling. It may be that in these communities there are higher levels of kinship or affinity among its residents, where the effects of an increase in the homicide rate are more widely felt among its inhabitants compared to schools located in larger or more densely populated areas. Furthermore, due to a lack of economic resources or geographical isolation, there may not be any type of compensating mechanisms in place for pupils attending telesecundarias.

The lagged effects of an increase in homicides are small for elementary schools and completely disappear after two years. Lagged effects are strong for middle schools, where these only become non-significant after three years.¹² Lastly, the cumulative effects of the homicides that occurred during the two and three years prior to the exam date are more noticeable in middle schools than in elementary schools, and are strongly significant.¹³

5.2 Homicides and grade failure

As Table 6 shows, a one-unit increase in the homicide rate per 10,000 inhabitants is associated with a rise in the grade failure rate of 0.028 percentage points for elementary schools and 0.027 percentage points for secondary schools, where both effects are significant at the 1.0% level.

Column (1) shows that for elementary schools, the effect of homicides is only significant for schools located in areas with low marginality levels. Nevertheless, although not significant, the estimated coefficient is the largest for schools situated in high marginality areas. Concerning the locality size, the effect of a rise in violent crime is significant at the 1.0% level in schools located in both urban and rural localities, where the effect of an increment in homicides is stronger among schools located in rural settings. With respect to whether classes are taught in the morning or afternoon session, the effect of a rise in homicides is slightly larger for schools that teach in the afternoon. Regarding the school type, the effect of crime exposure is stronger in public schools compared to private schools. In indigenous schools an increase in the homicide rate is associated with a decrease in the grade failure rate. On the contrary, a rise in the lagged homicide rate is related with an increase in the grade failure rates for up to two periods.

Focusing on middle schools, it can be seen in column (2) that the effect of a rise in homicides on grade failure rates is larger in schools based in localities with high marginality levels. Once again, the negative effect of violent crime is stronger in rural areas compared to urban settings. Further, the effect of an increase in homicides on grade failure rates is stronger for middle schools that teach in the morning session. While there is no significant effect for private schools, a rise in crime does increase the grade failure rate for public schools and telesecundarias or distance learning middle schools, where this effect is significant at the 1.0% level. One- and two-year lagged values of the homicide rate significantly affect current grade failure rates. Finally, cumulative effects of the homicides that occurred during the last two and three years show that a one-unit rise in the homicide rate per 10,000 inhabitants is associated with an increase in the grade failure rate that ranges from 0.0138 to 0.0173 percentage points, where these effects are statistically significant at the 1.0% level.¹⁴

6.1 Drug-related homicides and instrumental variable estimations

Since the increase in homicide levels was driven by a rise in drug-related homicides, this section examines their effect on educational outcomes. Obtained from ^{Policía Federal (2015)}, data on drug-related homicides is available at the municipal-level on an annual basis starting in 2006.

This section also addresses the challenges of identification that arise when attempting to estimate the effect that crime exposure has on educational outcomes. First, regardless of the inclusion of a wide range of schools, municipal and state level controls, unobserved variables may jointly determine educational outcomes and variations in the homicide rate. Factors such as institutions may generate a downward bias on the coefficient if municipalities with weak institutions offer lower quality schooling and have poorer educational outcomes, while also being exposed to larger increases in crimes levels due to less effective police and judicial services (^{Basu and Pearlman, 2017}). Second, the potential reverse causality between educational outcomes and violent crime levels cannot be disregarded. Whereas an increase in the homicide rate is likely to negatively affect academic performance and grade failure rates, it is plausible to assume that violent crime levels are higher where educational outcomes are worse. This is likely to arise because DTOs may more easily employ adolescents who study at badly-performing schools (^{Michaelsen and Salardi, 2015}). Lastly, while measurement error in homicide variables is not generally considered a serious problem compared to other types of crime, evidence suggests that this could be a problematic issue for the case of Mexico. According to official government data, between 2006 and 2013 an estimated 1,273 bodies were found in different clandestine graveyards throughout the country (^{PGR, 2014}). Moreover, it is probable that there many other illegal graveyards that have not yet been discovered and never will be. Measurement error in the homicide rate biases the coefficient towards zero. That is, it leads to attenuation bias by overestimating or estimating a negative coefficient to be more positive. Considering all these factors, the potential direction of the bias is uncertain.

To address the potential endogeneity issues, this study follows a similar strategy to the one put forward by ^{Castillo et al. (2014)}. Specifically, an instrumental variable (IV) model is estimated using the interaction of a municipality’s proximity to the U.S. border with the percentage of cocaine seized in Colombia as a source of exogenous variation. ^{Castillo et al. (2014)} states that when the Colombia government seizes large quantities of cocaine, its price rises due to a reduction in supply. This increases the market value of cocaine, even more so in localities close to the U.S. border. Mexican municipalities that are close to the border have a comparative advantage due to their strategic geographic location since the U.S. is the final market. It is assumed that it will be these municipalities that see the highest increase in homicide levels because the control of these places is more valuable to the DTOs (^{Robles et al., 2015}).¹⁵

However, the instrument presents a couple of limitations. First, according to ^{Castillo et al. (2014)} the large reduction in Colombian cocaine supply accounts for up to 25.0% of the increase of violence in northern Mexico, where this figure drops to 15.7% for Puebla, a municipality that has an approximate national mean distance from the U.S. border of 760 kilometres. Hence, the instrument has a stronger relationship to violence in northern municipalities than in the rest of the country. Second, the instrument proposed by ^{Castillo et al. (2014)} is related to drug-trafficking violence and therefore does not consider the channels through which violence in Mexico affected civilians.

Table 7 presents the first stage results of the IV estimations. In all cases, the coefficient on the interaction of the municipality’s proximity to the U.S. border and the percentage of cocaine seized in Colombia is positive. This relationship is the expected sign, since it is assumed that if a municipality is closer to the U.S. its homicide rate will be higher. It is also expected that if the percentage of cocaine seized increases, more homicides will occur. Furthermore, the interaction term is a strong predictor of the homicide rate at the municipal level, where the coefficient, at 1%, is significant in all models. The value of the F statistic is above ten, which is commonly used in literature, and above the Stock-Yogo critical values at the 10.0% significance level.

FE and IV estimations of the effects of drug-related homicides on educational outcomes are presented in Table 8. Results for the effects of total homicides during the last calendar year have a directly comparable measurement of the two violent crime variables. Table 8 shows in columns (1) and (3) that among elementary school students, concerning ENLACE scores in Spanish and Mathematics, the decrease generated by a rise in total homicides is larger than the one generated by an increase in drug-related homicides. For grade failure the same pattern is observed, where the effect of drug homicides is smaller relative to that of total homicides. Among middle school students, FE results suggest that ENLACE scores do not decrease when drug-related homicides rise. Nonetheless, grade failure rates increase when drug homicide rise, where this coefficient is significant at the 1.0% level. With respect to the IV estimations presented in columns (2) and (4), when instruments are employed for the homicide variables, using the interaction of a municipality’s proximity to the U.S. border with the percentage of cocaine seized in Colombia, the effect is again negative and significant. For middle school students, the relationship between a rise in drug-related homicides and a decrease in ENLACE scores in Spanish and Mathematics is now significant at the 1.0% level. The larger size of homicides and drug homicides coefficients when using IV models suggest that the FE estimations may be downwardly biased.

6.2 Mechanisms

It is hypothesised that exposure to violent crime affects academic performance and grade failure rates partly because it leads to a reduction in contact hours. To examine this, data from the National Time-Use Survey (ENUT) from 2002, 2009 and 2014 is used. Table 9 explores the relationship between attending school, the number of contact hours, engaging in school related work at home, the number of hours doing schoolwork at home, and homicide rates. The analysis is performed for individuals in: a) elementary or middle school age (6 to 18 years); b) elementary school age (6 to 12 years); and c) lower middle school age (13 to 16 years). Estimation results for both OLS and IV models are presented.

Row A column (1) shows that homicide rates are not associated with the decision to attend school. Nonetheless, it can be seen in column (2) that for both the OLS and IV models, higher homicide rates are indeed related with a fewer number of hours spent at school, where these effects are significant at the 5.0% level. Because of fewer contact hours, families could compensate for this by spending more time performing school related activities at home. Column (3) shows that the homicide rate is not associated with whether children and adolescents perform schoolwork at home. However, it can be seen in column (4) that higher homicide rates are negatively associated with the number of hours students spend performing school related activities at home. The coefficients in both the OLS and IV models are statistically significant. Thus, families do not compensate for fewer contact hours by making their children study more outside of the classroom. On the contrary, these two mechanisms appear to reinforce one another. When the analysis is focused exclusively on either the elementary or the middle school age population, rows B and C also show a similar relationship.

High levels of violent crime in a municipality are also likely to affect the characteristics of the schools located within their limits. Table 10 explores the relationship between homicides, teacher and student mobility and teachers’ education levels. Row A presents results based on all elementary and middle schools. It can be seen in column (1) that an increase in the homicide rate is associated with a decrease in the number of teachers per school. Moreover, column (2) shows that a rise in homicide levels is also associated with a reduction in the number of students enrolled per school. The estimated coefficients are statistically significant at the 1.0% level and suggest that crime exposure affects both teacher and student composition. Column (3) presents the effects of the homicide rate on the student-teacher ratio, where an increase in the homicide rate is associated with a reduction in the number of students per teacher. This may be partly a result of the higher mobility that students have in changing schools relative to teachers. Column (4) shows that the relationship between homicides and the percentage of teachers with graduate studies, interpreted here as a broad measure of teacher quality, is not statistically significant. Row B separates elementary schools and lower middle schools. Among elementary schools, an increase in the homicide rate is associated with a statistically significant reduction in the number of teachers, students and the student-teacher ratio. Among lower middle schools, it is associated with a drop in the number of students and in the number of teachers with graduate studies.

Focusing on different subgroups of schools, an increase in the homicide rate is always statistically associated with a decrease in the number of teachers in all the different groups of schools, except in those located in high marginality areas. A similar relationship is observed for students, where a rise in the homicide rate is always associated with a decrease in the number of teachers, where these coefficients are statistically significant at the 1.0% level.

Moreover, by locality size, the reduction in the number of students is almost double in urban schools relative to rural schools. This may be reflecting differences in the supply of schools and hence the number of options available to parents depending on the size of the locality of residence. By school type, a rise in the homicide rate has a larger effect in private schools relative to public schools, which may be signalling the higher income capacity of parents to move their children to a different school. Additionally, when the homicide rate increases the student-teacher ratio decreases in schools of: low marginality levels, in schools that have sessions in the afternoon and in public schools.

Lastly, previous evidence suggests that the rise in homicides influenced the migration behaviour and mental health status of different segments of the population. ^{Rios (2014)} observes that a one-unit increase in the drug-related homicide rate per 10,000 inhabitants is associated with 63.34 Mexicans fleeing their municipality of residency. Changes in the student body composition may have important effects on the results, since the findings depend on which students are changing schools. The effects found in the empirical analysis could be partially or completely explained by these changes. For example, if the brightest students from municipalities that encounter high homicide rates move to safer municipalities, then the negative effects of homicides on educational outcomes would be at least partially driven by the migration of the smartest students. To minimise the effects of this phenomenon, Eq. (1) was estimated for schools where the difference in the total number of students in any two periods was never larger than 15, 20 or 25. The results obtained from these subsamples were similar to those reported in Table 3. Moreover, ^{Márquez-Padilla et al. (2015)} show that, for the 2007-2010 period, the rise in homicide levels did not affect the enrolment rates of elementary and middle school students.

Finally, ^{Balmori (2014)} examines the effect of drug-related violence on depression in Mexico. The author observes a statistically significant increase in clinical and non-clinical depression among women, but not men, because of drug-related violence. The fact that the rise in homicide rates is associated with some segments of the population being displaced from their municipality of residence as well as with an increase in the prevalence of depression, a common symptom of PTSD, implies that, besides the reduction in contact hours, these two factors are also likely to explain why being exposed to violent crimes is negatively associated with educational outcomes.