  Causal mediation analysis is routinely conducted by applied researchers in a
variety of disciplines. The goal of such an analysis is to investigate
alternative causal mechanisms by examining the roles of intermediate variables
that lie in the causal paths between the treatment and outcome variables. In
this paper we first prove that under a particular version of sequential
ignorability assumption, the average causal mediation effect (ACME) is
nonparametrically identified. We compare our identification assumption with
those proposed in the literature. Some practical implications of our
identification result are also discussed. In particular, the popular estimator
based on the linear structural equation model (LSEM) can be interpreted as an
ACME estimator once additional parametric assumptions are made. We show that
these assumptions can easily be relaxed within and outside of the LSEM
framework and propose simple nonparametric estimation strategies. Second, and
perhaps most importantly, we propose a new sensitivity analysis that can be
easily implemented by applied researchers within the LSEM framework. Like the
existing identifying assumptions, the proposed sequential ignorability
assumption may be too strong in many applied settings. Thus, sensitivity
analysis is essential in order to examine the robustness of empirical findings
to the possible existence of an unmeasured confounder. Finally, we apply the
proposed methods to a randomized experiment from political psychology. We also
make easy-to-use software available to implement the proposed methods.
