When something unpleasant is happening around you, the most natural reaction you might have is to try and get away from it. For instance, if you live in Mexico and there is a lot of criminal activity in the neighborhood, you might want to move, if you can afford to. This seems intuitive, but is it true? Science is often the process of systematically testing whether our intuitions about the world are true; you never know when the easy answer is wrong if you never investigate it!
This is what I did with Roxana Gutiérrez-Romero: I went back to my old love – the investigation of Mexican drug trafficking – and this resulted in the paper “Displacement and disconnection: the impact of violence on migration networks and highway traffic in Mexico” which was recently published in the Spatial Economic Analysis journal.
The question is simple: do we see a disproportionate increase in emigration (whether local within Mexico or international) from municipalities that experience spikes of criminal violence? Answering this question is quite hard, and it involves controlling for many other potential explanations that might drive emigration. Roxana did a remarkable job in figuring out how to control for those other factors, leaving me to worry about a simpler, networky question. Let’s focus on local internal migration for now.

We can take a snapshot of internal migration by creating a network of municipalities. Two municipalities are connected by a directed edge weighted by the number of people who change their residence from one to the other. The picture above depicts just that.
A single network doesn’t tell us much, we need two different points in time. For each pair of municipalities, we have data about the migration links for several five-year intervals (2005-2010, 2010-2015, 2015-2020). We cannot simply compare the edge weights in two subsequent snapshots, as the change we observe might be just a random fluctuation. Moreover, how do we know whether a change is significant when there are many migration links? Immigration from a municipality might have increased at the same time as all other incoming links have decreased. For this reason, the question morphs into a network science one: if we have an edge observed across two different five-year intervals with two different weights, how do we know the edge weight changed in a statistically significant way?
We got help from an unexpected ally: network backboning. Normally, network backboning is the process of determining whether an edge measured with a noisy process exists. However, by using the Noise-Corrected approach I developed with Frank Neffke a while ago, we can do more than that.
See, noise-corrected backboning achieves the task of verifying an edge’s existence by modeling it, estimating its expected weight and variance. The same edge at different times will have different weights and different variances. By using bootstrapping, a fancy word that means “draw many random numbers from a distribution characterized by the edge’s weight and standard deviation,” we can create an edge weight distribution and figure out whether the edge’s weight truly increased, decreased, or stayed the same.
This is what you see in the picture above: green edges showed an increase in migration, red edges a decrease, and yellow ones stayed about the same. We can aggregate a municipality’s net migration change, which we use for the node’s color. As a robustness check, we create the same network, but using highway traffic instead of migration:
We can use this estimation of increased/decreased migration/traffic as the variable we want to predict in a big and complicated regression that takes into account many possible alternative explanations – ask Roxana for the painfully precise details, she worked literal years on it.
What Roxana found was that our intuition is accurate: violence indeed is associated with increased emigration. We also checked international emigration to the US (which accounts for 90% of Mexican emigration) and found a similar effect: violence is associated with a 5% rise in emigration to the US and a 3% drop in return migration from the US.
So, for once, we don’t have a puzzling counter-intuitive result: we indeed see violence and criminal activity discouraging people to stay around. It would be interesting to see whether this holds in different contexts and scenarios.






























