Incremental causal effects
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This is a draft. The ignorability assumption is a key assumption in causal inference. It is commonly made, but often violated in observational studies. In this paper, we investigate a local version of this assumption for continuous treatments, where potential outcomes are independent of the treatment assignment only in a neighborhood of the current treatment assignment. Similarly, we introduce a local version of the overlap condition, where the positivity assumption only holds in a neighborhood of observations. Under these local assumptions, we show that the effect of shifting a continuous treatment variable by a small amount across the whole population (termed incremental treatment effect) is still identifiable, and that the incremental treatment effect is equal to the average derivative or average partial effect. Moreover, we prove that in certain regression settings, estimating the incremental effect is easier than estimating the average treatment effect in terms of asymptotic variance and more robust to additive confounding. For high-dimensional settings, we develop a simple feature transformation that allows for doubly-robust estimation and doubly-robust inference of incremental causal effects. Finally, we compare the behaviour of estimators of the incremental treatment effect and average treatment effect on simulated data.
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