  This paper studies local asymptotic relationship between two scalar
estimates. We define sensitivity of a target estimate to a control estimate to
be the directional derivative of the target functional with respect to the
gradient direction of the control functional. Sensitivity according to the
information metric on the model manifold is the asymptotic covariance of
regular efficient estimators. Sensitivity according to a general policy metric
on the model manifold can be obtained from influence functions of regular
efficient estimators. Policy sensitivity has a local counterfactual
interpretation, where the ceteris paribus change to a counterfactual
distribution is specified by the combination of a control parameter and a
Riemannian metric on the model manifold.
