  This paper presents methods for analyzing spatial experiments when complex
spillovers, displacement effects, and other types of "interference" are
present. We present a robust, design-based approach to analyzing effects in
such settings. The design-based approach derives inferential properties for
causal effect estimators from known features of the experimental design, in a
manner analogous to inference in sample surveys. The methods presented here
target a quantity of interest called the "average marginalized response," which
is equal to the average effect of activating a treatment at an intervention
node that is a given distance away, averaging ambient effects emanating from
other intervention nodes. We provide a step-by-step tutorial based on the
SpatialEffect package for R. We apply the methods to a randomized experiment on
payments for community forest conservation in Uganda, showing how our methods
reveal possibly substantial spatial spillovers that more conventional analyses
cannot detect.
