Quantifying the Escalation of Cartel Violence: A Hawkes Process vs. Poisson Process Analysis

Music City Center 

Cartel violence in Mexico remains a critical issue, affecting millions. Understanding its escalation is key for public policy and law enforcement. This study applies the Univariate Hawkes Process to analyze the self-excitation of cartel conflicts, revealing how violent events increase the likelihood of future incidents. Using UCDP data (1989 - 2021), we identify key dyads, with Jalisco-Sinaloa accounting for 20.06% of all conflicts. The half-life of cartel violence varies, from 1.89 days (Government vs. Civilians) to 59.75 days (Los Ardillos vs. Los Rojos).
To enhance accuracy, we implement a Hierarchical Hawkes Process, estimating global parameters: μ ≈ 0 (low background violence), α= 0.98 (high self-excitation), and β = 0.03 (moderate decay). This model improves predictive accuracy by capturing global patterns in violence escalation. We plan to compare the results from the Hawkes Process against the Poisson Point Process, which assumes that violent events occur independently over time, without any triggering effect. Future work will refine this comparison, integrate a Multivariate Hawkes Model, and assess external factors such as law enforcement actions and economic conditions.

Cartel Conflicts

Univariate Hawkes Process

Hierarchical Hawkes Process

Jalisco-Sinaloa

Self-excitation

Poisson Point Process 

Social Statistics Section