  Point processes are probabilistic tools for modeling event data. While there
exists a fast-growing literature studying the relationships between point
processes, it remains unexplored how such relationships connect to causal
effects. In the presence of unmeasured confounders, parameters from point
process models do not necessarily have causal interpretations. We propose an
instrumental variable method for causal inference with point process treatment
and outcome. We define causal quantities based on potential outcomes and
establish nonparametric identification results with a binary instrumental
variable. We extend the traditional Wald estimation to deal with point process
treatment and outcome, showing that it should be performed after a Fourier
transform of the intention-to-treat effects on the treatment and outcome and
thus takes the form of deconvolution. We term this as the generalised Wald
estimation and propose an estimation strategy based on well-established
deconvolution methods.
