partial causal identification

Causal inference often relies on strong, unverifiable assumptions—such as no unmeasured confounding and perfect compliance—leading to unreliable effect estimates. This paper systematically investigates bounding causal effects and counterfactual queries (e.g., the probability of necessity and sufficiency, PNS) under partial identification. We extend entropy-constrained methods for the first time to bound necessity and sufficiency probabilities, and develop a unified evaluation framework integrating symbolic reasoning, optimization, and information theory. We propose a decision-tree– and machine-learning–guided algorithm selection strategy, validated through large-scale discrete and continuous simulations (thousands of runs) assessing tightness, computational efficiency, and robustness of bounds. We release CausalBoundingEngine, an open-source Python toolkit enabling integrated invocation and comparative benchmarking of multiple bounding methods. Our approach significantly enhances the reliability and practicality of causal inference under realistic, non-ideal conditions.

To address inaccurate parameter estimation and poor confidence interval coverage under weak identification, this paper proposes a robust inference method within the minimum distance framework that incorporates parameter boundary information. Methodologically, it unifies asymptotic theory for weak identification with limit distribution theory for parameters lying on boundaries, thereby constructing a boundary-constrained identification-robust estimation and inference system. The approach builds upon minimum distance estimation, integrated with factor model identification analysis and boundary-constrained inference techniques. Simulation studies and an empirical application to parental educational investment demonstrate that the method substantially improves confidence interval coverage—bringing it close to the nominal level—and enhances estimation precision under weak identification. It overcomes the failure of conventional methods near parameter boundaries and establishes a novel paradigm for weak-identification inference in structural models featuring inequality constraints.

This paper addresses point estimation and uncertainty quantification for treatment effect paths—such as dynamic effects and event-study designs—in policy evaluation. To overcome the looseness of conventional uniform confidence bands, which ignore correlations among path estimators, we propose two data-driven feasible bound methods. Our novel framework jointly enforces average-effect coverage guarantees and path smoothness constraints, integrating post-selection inference, smooth regularization, Monte Carlo simulation, and robust point estimation. The resulting confidence bands are substantially narrower while maintaining valid coverage, especially under high estimator correlation; our point estimator also demonstrates superior performance across diverse simulation settings. The key contribution is the first systematic incorporation of smoothness priors into path inference, thereby unifying statistical rigor with economic interpretability.

This paper addresses the robustness challenge of average treatment effect on the treated (ATT) estimation under the no-unconfoundedness assumption when high-dimensional covariates or poor overlap undermine conventional methods. We propose a finite-information aggregation estimation framework situated between Manski’s bounds and inverse probability weighting (IPW). Our approach integrates a constrained dependence function design with a variant of IPW to jointly achieve robustness against model misspecification and efficiency in information utilization. We establish asymptotically valid interval estimation theory for the resulting estimator. Simulation studies and empirical applications demonstrate that the proposed method substantially tightens the identification bounds, exhibits superior robustness to increasing covariate dimensionality and overlap deficiency, and consistently outperforms both classical Manski bounds and standard IPW estimators in finite-sample performance.

This work addresses the fundamental tension between in-sample fit and out-of-sample generalization: while ordinary least squares (OLS) minimizes training error, it lacks robustness to distributional shifts; conversely, causal models offer strong out-of-distribution guarantees but sacrifice in-sample accuracy. To bridge this gap, we propose **causal regularization**, the first framework to formally characterize a continuous trade-off between causal strength and empirical risk. Grounded in structural causal models, our approach unifies regularization, subsample stability analysis, and finite-sample generalization theory, yielding a tight risk upper bound. We further prove that cross-validation adaptively achieves this bound. Both theoretical analysis and empirical evaluation demonstrate that our method preserves high in-sample fidelity while substantially improving robustness and reliability under distributional shift.

This study addresses the inferential bias arising from misspecification of a single causal model under model uncertainty. The authors propose a weighted triangulation framework that integrates identification functionals from multiple candidate causal models through a data-driven measure of model validity, enabling robust causal effect estimation without explicit model selection. This approach uniquely bridges testability in causal discovery with semiparametric inference, formalizing robustness under causal pluralism without requiring consensus among models or reliance on any single specification. Theoretically, the proposed functional is shown to converge to the true causal effect with high probability. Both simulation studies and empirical analyses demonstrate the method’s robustness and effectiveness.

This work proposes an efficient method for estimating sharp bounds on causal effects when point identification is precluded by unobserved confounding. The approach uniquely integrates the conditional independence constraints implied by the causal graph into a sensitivity analysis framework, leveraging influence function projections and semiparametric estimation theory to substantially improve the statistical efficiency of bound estimation. Empirical evaluations on both simulated data and real-world applications—including the effect of job training on earnings and the impact of ejection fraction on heart failure mortality—demonstrate that the method achieves high efficiency and robustness under non-identifiable settings.

This study addresses the computational challenge of efficiently deriving sharp analytical bounds on average treatment effects in discrete instrumental variable models. We establish a theoretical lower bound on computational complexity by proving that any sharp analytical bound must involve an exponential number of linear terms, and that the corresponding instrumental variable inequalities likewise grow exponentially in number. Leveraging tools from probability theory, linear programming, and combinatorial analysis, we develop an efficient constructive algorithm that matches this lower bound. We further provide open-source implementations in Python and R, which optimally generate sharp bounds and associated inequalities, thereby empirically validating our theoretical results.

This study addresses the joint optimization of experimental design and estimation to minimize worst-case mean squared error (MSE) in finite populations with bounded potential outcomes, such as binary outcomes. By analyzing all assignment mechanisms within the class of affine estimators, the authors demonstrate that independent randomization coupled with an intercept-free regression using midpoint-centered covariates achieves optimal performance. This approach reduces the worst-case MSE by 50% compared to classical paired randomization with fixed-effects regression. Moreover, the optimality of this method is shown to extend beyond the affine class, establishing the theoretical superiority of independent random assignment in minimizing worst-case estimation error under bounded potential outcomes.