C-Learner: Constrained Learning for Causal Inference
This addresses a key problem in causal inference for researchers and practitioners by providing a more robust estimator in scenarios with limited overlap, though it is an incremental improvement over existing methods.
The paper tackles the instability of debiased causal inference methods under limited treatment-control overlap by proposing a constrained learning framework that produces stable plug-in estimates with desirable asymptotic properties, outperforming basic one-step and targeting methods in challenging settings.
Popular debiased estimation methods for causal inference -- such as augmented inverse propensity weighting and targeted maximum likelihood estimation -- enjoy desirable asymptotic properties like statistical efficiency and double robustness but they can produce unstable estimates when there is limited overlap between treatment and control, requiring additional assumptions or ad hoc adjustments in practice (e.g., truncating propensity scores). In contrast, simple plug-in estimators are stable but lack desirable asymptotic properties. We propose a novel debiasing approach that achieves the best of both worlds, producing stable plug-in estimates with desirable asymptotic properties. Our constrained learning framework solves for the best plug-in estimator under the constraint that the first-order error with respect to the plugged-in quantity is zero, and can leverage flexible model classes including neural networks and tree ensembles. In several experimental settings, including ones in which we handle text-based covariates by fine-tuning language models, our constrained learning-based estimator outperforms basic versions of one-step estimation and targeting in challenging settings with limited overlap between treatment and control, and performs similarly otherwise.