  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.
