It is widely understood that diffusion of and simultaneous interactions between narratives – defined here as persistent point-of-view messaging – significantly contributes to the shaping of political discourse and public opinion. In this work, we propose a methodology based on Multi-Variate Hawkes Processes and our newly-introduced Process Influence Measures for quantifying and assessing how such narratives influence (Granger-cause) each other. Such an approach may aid social scientists enhance their understanding of socio-geopolitical phenomena as they manifest themselves and evolve in the realm of social media. In order to show its merits, we apply our methodology on Twitter narratives during the 2019 Venezuelan presidential crisis. Our analysis indicates a nuanced, evolving influence structure between 8 distinct narratives, part of which could be explained by landmark historical events.