C-Learner: Constrained Learning for Causal Inference

TL;DR

This paper introduces C-Learner, a constrained learning method for causal inference that combines the stability of plug-in estimators with the desirable asymptotic properties of debiased estimators, especially effective with limited overlap.

Contribution

The paper proposes a novel constrained learning framework that produces stable, asymptotically efficient causal estimates using flexible models like neural networks and trees.

Findings

Outperforms basic one-step and targeting estimators in limited overlap scenarios.

Achieves stable estimates with desirable asymptotic properties.

Effective with complex data such as text via language model fine-tuning.

Abstract

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.