Economists are often disappointed by research findings that show a statistically insignificant effect. This sometimes even leads researchers to stop pursuing a topic that might otherwise engage them fruitfully. This outcome thus represents a loss to social science: knowledge and insights are not put forward to be built upon.
Null effects are often difficult to confirm because they are never estimated at exactly zero; a small negative or a small positive effect may always exist. However, if we expect to find results of considerable magnitude, but find small effects with narrow confidence intervals instead, these null effects may still be interpreted in a meaningful way.
This is the case in our recent paper “The (Non-)Effect of Violence on Education”: we find that the sharp rise in homicide rates in Mexico after 2007 during the War on Drugs did not have an effect on educational outcomes.
Because of the magnitude of the increase in violence (the homicide rate more than doubled between 2007 and 2010) and literature on the effects of this increase on employment and economic activity, we hypothesized (wrongly, as we later realized) that this increase had large effects on education. However, we found the effects to be null (statistically not different from zero), or, at the most, to be small relative to the magnitude of the increase in violence.
It is, of course, possible that there is an effect in the case of specific individuals, although we conducted our analysis at an aggregate level to detect a statistical effect. Our methodology consisted in using a fixed-effect regression model, whereby the dependent variable is one of various measures of educational outcomes (enrollment, enrollment rates, and so on), and the dependent variable of interest is a measure of the homicide rate (although we also use a measure of drug-related violence). This methodology meant that we actually estimated how the changes in educational outcomes in municipalities correlated with the changes in homicide rates in municipalities, while we controlled for municipal-specific characteristics. Our result is that the effect is at or close to zero.
It is always possible that, by looking at a more disaggregated level, one may find an association between violence and education. Indeed, it would be surprising if children who are directly affected by an increase in violence (for instance, through the loss of a family member) do not suffer an effect in their education. Nonetheless, for the purpose of understanding what the overall effects of the increase in violence are on the educational outcomes in the country, the more relevant result is the one we find: there is no statistical effect of greater violence on aggregate educational outcomes.
We contextualize our results by calculating the effect of a change similar in magnitude to the change experienced by the country as a whole. A municipality that experienced an average increase in violence (that is, an increase similar to the one experienced by the country as a whole) would see a reduction in enrollment rates of no more than 0.01 percentage points.
Our study also highlights the importance of examining the mechanisms underlying the statistical relationship in a given result. For instance, if we look at the effect of violence not on enrollment rates, but on the total number of students enrolled, we find a small, but statistically significant effect. However, we find that this effect is driven by the effect of an increase in violence on migration. Families with school-age children tend to move from the affected municipalities to less affected ones; so, although the increases in violence were associated with a lower number of students enrolled (as they moved across municipalities), the actual schooling decisions of individuals do not appear to be affected because the enrollment rates were not affected.
We also explore whether the lack of effect on enrollment may be caused by a counteracting effect on the labor force, that is, we explore whether a reduction in employment because of increased violence frees some young individuals so they may enroll in school. We find no evidence of this: increases in violence were not associated with reductions in employment or labor force participation among school-age individuals.
For other outcomes, especially those on which there are fewer observations, the confidence interval around zero presents more problems because the null effects are not so precisely estimated. In particular, we used standardized test scores as another outcome measure and also found that the increase in crime had no statistical effect on student performance, but the coefficient is less tightly estimated. In this case, more research is needed to ascertain whether the null effects we find extend to school learning as well as to educational attainment. Additionally, it is important to recall that violence appears to have had an effect on migration; so, the members of the student body taking the examinations in each municipality may have changed over time, which makes the effects we found more difficult to interpret.
Overall, our results show that the will of Mexican students to study is quite strong and that the schooling decisions of individuals have not changed as violence has increased. This is positive news: it will limit the long-term negative consequences of the increase in violence because human capital accumulation does not appear to have been undermined. Additionally, our results are encouraging in terms of the long-term effects of Mexico’s War on Drugs, as opposed to the negative—but arguably shorter-term impacts—on employment and economic activity reported in other studies, for instance, Dell (2014), Robles et al. (2013), and Velásquez (2014).
References:
Dell, Melissa (2014) “Trafficking Networks and the Mexican Drug War,” (American Economic Review, forthcoming).
Robles, G., Calderón, G., and B. Magaloni. (2013). “The Economic Consequences of Drug-Trafficking Violence in Mexico,” IADB Working Paper 426.
Velászquez, Andrea (2014). “The Economic Burden of Crime: Evidence from Mexico”. Duke University, mimeo.
Null effects are often difficult to confirm because they are never estimated at exactly zero; a small negative or a small positive effect may always exist. However, if we expect to find results of considerable magnitude, but find small effects with narrow confidence intervals instead, these null effects may still be interpreted in a meaningful way.
This is the case in our recent paper “The (Non-)Effect of Violence on Education”: we find that the sharp rise in homicide rates in Mexico after 2007 during the War on Drugs did not have an effect on educational outcomes.
Because of the magnitude of the increase in violence (the homicide rate more than doubled between 2007 and 2010) and literature on the effects of this increase on employment and economic activity, we hypothesized (wrongly, as we later realized) that this increase had large effects on education. However, we found the effects to be null (statistically not different from zero), or, at the most, to be small relative to the magnitude of the increase in violence.
It is, of course, possible that there is an effect in the case of specific individuals, although we conducted our analysis at an aggregate level to detect a statistical effect. Our methodology consisted in using a fixed-effect regression model, whereby the dependent variable is one of various measures of educational outcomes (enrollment, enrollment rates, and so on), and the dependent variable of interest is a measure of the homicide rate (although we also use a measure of drug-related violence). This methodology meant that we actually estimated how the changes in educational outcomes in municipalities correlated with the changes in homicide rates in municipalities, while we controlled for municipal-specific characteristics. Our result is that the effect is at or close to zero.
It is always possible that, by looking at a more disaggregated level, one may find an association between violence and education. Indeed, it would be surprising if children who are directly affected by an increase in violence (for instance, through the loss of a family member) do not suffer an effect in their education. Nonetheless, for the purpose of understanding what the overall effects of the increase in violence are on the educational outcomes in the country, the more relevant result is the one we find: there is no statistical effect of greater violence on aggregate educational outcomes.
We contextualize our results by calculating the effect of a change similar in magnitude to the change experienced by the country as a whole. A municipality that experienced an average increase in violence (that is, an increase similar to the one experienced by the country as a whole) would see a reduction in enrollment rates of no more than 0.01 percentage points.
Our study also highlights the importance of examining the mechanisms underlying the statistical relationship in a given result. For instance, if we look at the effect of violence not on enrollment rates, but on the total number of students enrolled, we find a small, but statistically significant effect. However, we find that this effect is driven by the effect of an increase in violence on migration. Families with school-age children tend to move from the affected municipalities to less affected ones; so, although the increases in violence were associated with a lower number of students enrolled (as they moved across municipalities), the actual schooling decisions of individuals do not appear to be affected because the enrollment rates were not affected.
We also explore whether the lack of effect on enrollment may be caused by a counteracting effect on the labor force, that is, we explore whether a reduction in employment because of increased violence frees some young individuals so they may enroll in school. We find no evidence of this: increases in violence were not associated with reductions in employment or labor force participation among school-age individuals.
For other outcomes, especially those on which there are fewer observations, the confidence interval around zero presents more problems because the null effects are not so precisely estimated. In particular, we used standardized test scores as another outcome measure and also found that the increase in crime had no statistical effect on student performance, but the coefficient is less tightly estimated. In this case, more research is needed to ascertain whether the null effects we find extend to school learning as well as to educational attainment. Additionally, it is important to recall that violence appears to have had an effect on migration; so, the members of the student body taking the examinations in each municipality may have changed over time, which makes the effects we found more difficult to interpret.
Overall, our results show that the will of Mexican students to study is quite strong and that the schooling decisions of individuals have not changed as violence has increased. This is positive news: it will limit the long-term negative consequences of the increase in violence because human capital accumulation does not appear to have been undermined. Additionally, our results are encouraging in terms of the long-term effects of Mexico’s War on Drugs, as opposed to the negative—but arguably shorter-term impacts—on employment and economic activity reported in other studies, for instance, Dell (2014), Robles et al. (2013), and Velásquez (2014).
References:
Dell, Melissa (2014) “Trafficking Networks and the Mexican Drug War,” (American Economic Review, forthcoming).
Robles, G., Calderón, G., and B. Magaloni. (2013). “The Economic Consequences of Drug-Trafficking Violence in Mexico,” IADB Working Paper 426.
Velászquez, Andrea (2014). “The Economic Burden of Crime: Evidence from Mexico”. Duke University, mimeo.
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