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In many data scientific problems, we are interested in inferring causal relationships in the data generating mechanism. Here, we consider the following real-world question: how has the Colombian conflict influenced tropical forest loss? There is evidence for both enhancing and reducing impacts. Answering such questions requires the use of causal models. In this work, we propose a class of causal models for spatio-temporal stochastic processes. It allows us to formally define and quantify the causal effect of a vector of covariates $X$ on a real-valued response $Y$, even if the causal background knowledge is incomplete. We introduce a procedure for estimating causal effects, and a non-parametric hypothesis test for these effects being zero. 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 (or, alternatively, they do not vary across space). When applying our causal methodology to the problem of conflict and forest loss, using data from 2000 to 2018, we find a reducing but insignificant causal effect of conflict on forest loss. Regionally, both enhancing and reducing effects can be identified. Our theoretical findings are supported by simulations, and code is available online.