  Unobserved spatial confounding variables are prevalent in environmental and
ecological applications where the system under study is complex and the data
are often observational. Instrumental variables (IVs) are a common way to
address unobserved confounding; however, the efficacy of using IVs on spatial
confounding is largely unknown. This paper explores the effectiveness of IVs in
this situation -- with particular attention paid to the spatial scale of the
instrument. We show that, in case of spatially-dependent treatments, IVs are
most effective when they vary at a finer spatial resolution than the treatment.
We investigate IV performance in extensive simulations and apply the model in
the example of long term trends in the air pollution and cardiovascular
mortality in the United States over 1990-2010. Finally, the IV approach is also
extended to the spatial interference setting, in which treatments can affect
nearby responses.
