An instrumental variable method for point processes: generalised Wald estimation based on deconvolution

TL;DR

This paper introduces a novel instrumental variable approach for causal inference in point processes, extending Wald estimation through Fourier transform-based deconvolution to handle unmeasured confounders.

Contribution

It develops a generalized Wald estimation method for point processes using deconvolution, enabling causal interpretation despite unmeasured confounders.

Findings

Nonparametric identification of causal effects with binary IV

Extension of Wald estimation to point processes via Fourier transform

Proposed deconvolution-based estimation strategy

Abstract

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.