Instrumental Processes Using Integrated Covariances

Søren Wengel Mogensen

Keywords: instrumental variables, point processes, linear Hawkes processes, VAR(p), time series, causal inference, recurrent events

TL;DR: We propose a new approach to instrumental variable analysis in stochastic processes.

Abstract: Instrumental variable methods are often used for parameter estimation in the presence of confounding. They can also be applied in stochastic processes. Instrumental variable analysis exploits moment equations to obtain estimators for causal parameters. We show that in stochastic processes one can find such moment equations using an integrated covariance matrix. This provides new instrumental variable methods, instrumental variable methods in a class of continuous-time processes as well as a unified treatment of discrete- and continuous-time processes.