  Causal evidence is needed to act and it is often enough for the evidence to
point towards a direction of the effect of an action. For example, policymakers
might be interested in estimating the effect of slightly increasing taxes on
private spending across the whole population. We study identifiability and
estimation of causal effects, where a continuous treatment is slightly shifted
across the whole population (termed average partial effect or incremental
causal effect). We show that incremental effects are identified under local
ignorability and local overlap assumptions, where exchangeability and
positivity only hold in a neighborhood of units. Average treatment effects are
not identified under these assumptions. In this case, and under a smoothness
condition, the incremental effect can be estimated via the average derivative.
Moreover, we prove that in certain finite-sample observational settings,
estimating the incremental effect is easier than estimating the average
treatment effect in terms of asymptotic variance. For high-dimensional
settings, we develop a simple feature transformation that allows for
doubly-robust estimation and inference of incremental causal effects. Finally,
we compare the behaviour of estimators of the incremental treatment effect and
average treatment effect in experiments including data-inspired simulations.
