We consider the estimation of average
treatment effects in observational studies without the standard
assumption of unconfoundedness. We propose a new framework of robust
causal inference under the general observational study setting with
the possible existence of unobserved confounders. Our approach is
based on the method of distributionally robust optimization and
proceeds in two steps. We first specify the maximal degree to which
the distribution of unobserved potential outcomes may deviate from
that of obsered outcomes. We then derive sharp bounds on the average
treatment effects under this assumption. Our framework encompasses
the popular marginal sensitivity model as a special case and can be
extended to the difference-in-difference and regression
discontinuity designs as well as instrumental variables. Through
simulation and empirical studies, we demonstrate the applicability
of the proposed methodology to real-world settings. |