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.

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. In such models, there may be so many free parameters that the model fits the training data perfectly. We first investigate high-dimensional linear regression for imputing wage data and estimating average treatment effects, where we find that models with many more covariates than sample size can outperform simple ones.

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.

The Synthetic Control method (SC) has become a valuable tool for estimating causal effects. Originally designed for single-treated unit scenarios, it has recently found applications in high-dimensional disaggregated settings with multiple treated units. However, challenges in practical implementation and computational efficiency arise in such scenarios. To tackle these challenges, we propose a novel approach that integrates the Multivariate Square-root Lasso method into the synthetic control framework. We rigorously establish the estimation error bounds for fitting the Synthetic Control weights using Multivariate Square-root Lasso, accommodating high-dimensionality and time series dependencies. Additionally, we quantify the estimation error for the Average Treatment Effect on the Treated (ATT). Through simulation studies, we demonstrate that our method offers superior computational efficiency without compromising estimation accuracy. We apply our method to assess the causal impact of COVID-19 Stay-at-Home Orders on the monthly unemployment rate in the United States at the county level.

Event causality identification (ECI), a process that extracts causal relations between events from text, is crucial for distinguishing causation from correlation. Traditional approaches to ECI have primarily utilized linguistic patterns and multi-hop relational inference, risking false causality identification due to informal usage of causality and specious graphical inference. In this paper, we adopt the Rubin Causal Model to identify event causality: given two temporally ordered events, we see the first event as the treatment and the second one as the observed outcome. Determining their causality involves manipulating the treatment and estimating the resultant change in the likelihood of the outcome. Given that it is only possible to implement manipulation conceptually in the text domain, as a work-around, we try to find a'twin' for the protagonist from existing corpora. This'twin' should have identical life experiences with the protagonist before the treatment but undergoes an intervention of treatment. However, the practical difficulty of locating such a match limits its feasibility. Addressing this issue, we use the synthetic control method to generate such a'twin' from relevant historical data, leveraging text embedding synthesis and inversion techniques. This approach allows us to identify causal relations more robustly than previous methods, including GPT -4, which is demonstrated on a causality benchmark, COPES-hard.

In causal inference, whether through randomized controlled trials or observational studies, access to both treated and control units is essential for estimating the effect of a treatment on an outcome of interest. When treatment assignment is random, the average treatment effect (ATE) can be estimated directly by comparing outcomes between groups. In non-randomized settings, various techniques are employed to adjust for confounding and approximate the counterfactual scenario to recover an unbiased ATE. A common challenge, especially in observational studies, is the absence of units clearly labeled as controls-that is, units known not to have received the treatment. To address this, we propose positive-unlabeled (PU) learning as a framework for identifying, with high confidence, control units from a pool of unlabeled ones, using only the available treated (positive) units. We evaluate this approach using both simulated and real-world data. We construct a causal graph with diverse relationships and use it to generate synthetic data under various scenarios, assessing how reliably the method recovers control groups that allow estimates of true ATE. We also apply our approach to real-world data on optimal sowing and fertilizer treatments in sustainable agriculture. Our findings show that PU learning can successfully identify control (negative) units from unlabeled data based only on treated units and, through the resulting control group, estimate an ATE that closely approximates the true value. This work has important implications for observational causal inference, especially in fields where randomized experiments are difficult or costly. In domains such as earth, environmental, and agricultural sciences, it enables a plethora of quasi-experiments by leveraging available earth observation and climate data, particularly when treated units are available but control units are lacking.