How does armed conflict influence tropical forest loss? For Colombia, both enhancing and reducing effect estimates have been reported. However, a lack of causal methodology has prevented establishing clear causal links between these two variables. In this work, we propose a class of causal models for spatio-temporal stochastic processes which allows us to formally define and quantify the causal effect of a vector of covariates X on a real-valued response Y. We introduce a procedure for estimating causal effects and a nonparametric hypothesis test for these effects being zero. Our application is based on geospatial information on conflict events and remote-sensing-based data on forest loss between 2000 and 2018 in Colombia. Across the entire country, we estimate the effect to be slightly negative (conflict reduces forest loss) but insignificant (P = 0.578), while at the provincial level, we find both positive effects (e.g., La Guajira, P = 0.047) and negative effects (e.g., Magdalena, P = 0.004). The proposed methods do not make strong distributional assumptions, and allow for arbitrarily many latent confounders, given that these confounders do not vary across time. Our theoretical findings are supported by simulations, and code is available online.