Motivated by a recent literature on the double-descent phenomenon in machine learning, we consider highly over-parameterized models in causal inference, including synthetic control with many control units.

The synthetic control method (SCM) estimates causal effects in panel data with a single-treated unit by constructing a counterfactual outcome as a weighted combination of untreated control units that matches the pre-treatment trajectory. In this paper, we introduce the targeted synthetic control (TSC) method, a new two-stage estimator that directly estimates the counterfactual outcome. Specifically, our TSC method (1) yields a targeted debiasing estimator, in the sense that the targeted updating refines the initial weights to produce more stable weights; and (2) ensures that the final counterfactual estimation is a convex combination of observed control outcomes to enable direct interpretation of the synthetic control weights. TSC is flexible and can be instantiated with arbitrary machine learning models. Methodologically, TSC starts from an initial set of synthetic-control weights via a one-dimensional targeted update through the weight-tilting submodel, which calibrates the weights to reduce bias of weights estimation arising from pre-treatment fit. Furthermore, TSC avoids key shortcomings of existing methods (e.g., the augmented SCM), which can produce unbounded counterfactual estimates. Across extensive synthetic and real-world experiments, TSC consistently improves estimation accuracy over state-of-the-art SCM baselines.

The synthetic control (SC) framework is widely used for observational causal inference with time-series panel data. SC has been successful in diverse applications, but existing methods typically treat the ordering of pre-intervention time indices interchangeable. This invariance means they may not fully take advantage of temporal structure when strong trends are present. We propose Time-Aware Synthetic Control (TASC), which employs a state-space model with a constant trend while preserving a low-rank structure of the signal. TASC uses the Kalman filter and Rauch-Tung-Striebel smoother: it first fits a generative time-series model with expectation-maximization and then performs counterfactual inference. We evaluate TASC on both simulated and real-world datasets, including policy evaluation and sports prediction. Our results suggest that TASC offers advantages in settings with strong temporal trends and high levels of observation noise.

Estimating causal effects on time-to-event outcomes from observational data is particularly challenging due to censoring, limited sample sizes, and non-random treatment assignment. The need for answering such "when-if" questions--how the timing of an event would change under a specified intervention--commonly arises in real-world settings with heterogeneous treatment adoption and confounding. To address these challenges, we propose Synthetic Survival Control (SSC) to estimate counterfactual hazard trajectories in a panel data setting where multiple units experience potentially different treatments over multiple periods. In such a setting, SSC estimates the counterfactual hazard trajectory for a unit of interest as a weighted combination of the observed trajectories from other units. To provide formal justification, we introduce a panel framework with a low-rank structure for causal survival analysis. Indeed, such a structure naturally arises under classical parametric survival models. Within this framework, for the causal estimand of interest, we establish identification and finite sample guarantees for SSC. We validate our approach using a multi-country clinical dataset of cancer treatment outcomes, where the staggered introduction of new therapies creates a quasi-experimental setting. Empirically, we find that access to novel treatments is associated with improved survival, as reflected by lower post-intervention hazard trajectories relative to their synthetic counterparts. Given the broad relevance of survival analysis across medicine, economics, and public policy, our framework offers a general and interpretable tool for counterfactual survival inference using observational data.

We begin by thanking all reviewers for their extremely encouraging and helpful responses. We agree that the fact we do PCR on both the training and testing covariates should be more explicitly placed in the context of transductive semi-supervised learning. We have strived to interpret our major theorem results (Thm 4.2 & Thm 5.1) by: (i) providing examples of natural generating Proposition 4.2, should be tight). Their empirical results support our theoretical guarantees.