On the Irregular Behavior of Regularized Calibration in High Dimensions

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Propensity-score weighting is widely used for treatment effect estimation, and calibrated estimation has been advocated as an alternative to maximum-likelihood fitting of logistic propensity score models, particularly with $\ell_{1}$-regularization in high dimensions and with claims of favorable robustness properties. We show that regularized calibration exhibits intrinsic high-dimensional failures that can invalidate these guarantees. In regimes where the number of controls $p$ is large relative to the sample size $n$—including sparse data-generating processes—regularized calibration can (i) yield inconsistent fitted propensity scores/weights, (ii) fail to admit a finite (parameter) solution, or (iii) become infeasible, depending on whether regularization is imposed via constraints, penalties, or relaxed calibration equations. Moreover, these pathologies do not depend on the specific norm used for regularization, pointing to a general incompatibility between calibration-based fitting and high-dimensional geometry. Consequently, treatment effect estimators that rely on calibrated propensity scores may lack existence and/or consistency precisely in settings where sparsity-inducing regularization is intended to help.