The Instrumental Variable Method for Estimating Local Average Treatment Regime Effects

We propose the instrumental variable regime (IVR) method to estimate the causal effects of multiple sequential treatments. This method serves to address the problem of endogenous selections of sequential treatments. An IVR is a sequence of instrumental variables in which each IV instruments for an endogenous treatment variable. Our proposed method generalizes the LATE model in Imbens and Angrist (1994) from a single treatment to many treatments applied sequentially. More precisely, with the IVR this model allows for estimating the local average treatment regime effects (LATRE), possibly conditional on a set of initial covariates. Though there exist studies in this area that use IVR, all of them require a structural functional form assumption. Our method is novel in that we do not require any such assumption. Thus unlike previous approaches, ours is robust to model misspecifications, which usually occur in treatment regime settings. The ideas and estimators in this paper are motivated and illustrated through a contextual example showing the use of IVR in estimating the treatment regime effect of advertisements on purchasing behaviors when advertisements are displayed in multiple periods. We demonstrate the performance of the proposed method with simulations.