Causal Inference in High-dimensional Generalized Linear Models with Binary Outcomes

Abstract This paper proposes a debiased estimator for causal effects in high-dimensional generalized linear models with binary outcomes and general link functions. The estimator augments a regularized regression plug-in with weights computed from a single convex optimization that approximately balances link-derivative-weighted covariates and controls variance; it does not rely on estimated propensity scores. Under standard conditions, the estimator is $\sqrt{n}$-consistent and asymptotically normal for dense linear contrasts and causal parameters. Simulation results show the superior performance of our approach in comparison to alternatives such as inverse propensity score estimators and double machine learning estimators in finite samples. In an application to the National Supported Work training data, our estimates and confidence intervals are close to the experimental benchmark.