Identification in Nonparametric Models for Dynamic Treatment Effects

Abstract

This paper develops a nonparametric model that represents how sequences of outcomes and treatment choices influence one another in a dynamic manner. In this setting, we are interested in identifying the average outcome for individuals in each period, had a particular treatment sequence been assigned. The identification of this quantity allows us to identify the average treatment effects (ATE's) and the ATE's on transitions, as well as the optimal treatment regimes, namely, the regimes that maximize the (weighted) sum of the average potential outcomes, possibly less the cost of the treatments. The main contribution of this paper is to relax the sequential randomization assumption widely used in the biostatistics literature by introducing a flexible choice-theoretic framework for a sequence of endogenous treatments. We show that the parameters of interest are identified under each period's two-way exclusion restriction, i.e., with instruments excluded from the outcome-determining process and other exogenous variables excluded from the treatment-selection process. We also consider partial identification in the case where the latter variables are not available. Lastly, we extend our results to a setting where treatments do not appear in every period.

Keywords: Dynamic Treatment Effect, Optimal Treatment Regime, Dynamic Model, Endogenous Treatment, Average Treatment Effect, Instrumental Variable

JEL Classification: C14, C32, C33, C36