instrumental variable methods

This paper exposes the severe nonrobustness of instrument variables (IVs) constructed via nonlinear transformations of covariates under mild model misspecification. When exogenous IVs are unavailable, researchers often generate instruments from functional transformations of observed covariates; however, we theoretically demonstrate that—even under a constant linear treatment effect—any modest nonlinear misspecification in the true structural function induces arbitrarily large bias in the resulting IV estimator. This is the first rigorous theoretical characterization of the extreme sensitivity of such constructed IVs to nonlinearities in the structural function, challenging the widely adopted empirical practice of “safe construction.” Combining asymptotic theory with semi-synthetic experiments—calibrating real data to multiple structural models—we empirically confirm substantial deviations of IV estimates from the true causal effect. Our findings provide a critical robustness warning for IV construction in applied econometrics and causal inference.

Endogeneity in exposures impedes causal identification, and conventional approaches rely either on strong functional-form assumptions or valid instrumental variables (IVs). This paper proposes an extremal conditional quantile contrast method grounded in a light-tailed error assumption. We establish, for the first time, that extreme quantile regression is inherently robust to endogeneity under light-tailed errors—enabling causal identification without IVs or additional parametric restrictions. Theoretically, we prove strong consistency of the estimator and asymptotic normality in linear models. Simulation studies and empirical analysis using automobile sales data demonstrate that the method maintains high estimation accuracy and reliable confidence interval coverage even when invalid IVs are present. By circumventing reliance on external instruments or stringent modeling assumptions, our approach substantially broadens the scope of applicable settings for endogeneity-robust inference.

Estimating causal effects from observational data requires selecting appropriate control and instrumental variables that satisfy causal identification conditions—a challenging task often reliant on strong domain knowledge or ad hoc assumptions. Method: This paper proposes the first end-to-end joint learning framework that automatically identifies valid combinations of control and instrumental variables. Grounded in conditional independence testing, the method integrates nonparametric dependence measures with structural search optimization, ensuring statistical consistency in variable selection under mild regularity conditions. Contribution/Results: Unlike conventional approaches requiring prespecified variable sets or strong prior assumptions, our framework is fully data-driven. In simulations, it achieves significantly higher variable identification accuracy. Empirically, applied to the Job Corps study, its estimated treatment effect closely aligns with results from the randomized controlled trial—demonstrating both validity and robustness in real-world causal inference.

Estimating heterogeneous treatment effects under endogeneity remains challenging, particularly when instrumental variables (IVs) are weak. Method: This paper proposes a novel semiparametric IV estimation framework that integrates double/debiased machine learning (DML), machine learning–based IV estimation (MLIV), and kernel smoothing. It is the first to embed MLIV within the DML architecture to construct confidence sets robust to weak instruments. Contribution/Results: We establish consistency and asymptotic normality of the estimator and provide unified statistical inference guarantees. Implemented in the R package `IVDML`, the method demonstrates substantial improvements in confidence interval coverage and estimation accuracy under weak-IV settings, both on synthetic and real-world data. Our approach offers a new paradigm for causal heterogeneity analysis—rigorous in theory and feasible in computation.

This paper addresses the stringent requirement in classical instrumental variable (IV) estimation that instruments must be strongly correlated with endogenous regressors. We propose a novel estimator based on distance covariance, which permits instruments to satisfy only mean independence—or even weaker dependence—relative to endogenous variables, thereby relaxing both the relevance and exclusion restrictions central to traditional IV. Under weak assumptions—including conditional median independence and finite perturbation moments (even when first moments fail to exist)—the estimator achieves consistency and asymptotic normality, enabling valid statistical inference. Key contributions include: (i) the first consistent estimator for structural parameters without imposing an exclusion restriction; (ii) a substantial expansion of admissible instrument sets; and (iii) a theoretically grounded, robust alternative for settings involving weak identification or nonstandard error distributions.

This study addresses causal effect identification in observational settings with unmeasured confounding and potentially invalid instrumental variables, focusing on linear instrumental variable models with multiple endogenous treatments. The authors propose generalized majority and plurality rules to achieve identification, coupled with a data-driven instrument selection procedure that yields sampling confidence intervals robust to the erroneous inclusion of invalid instruments. Under standard regularity conditions, these intervals are shown to attain asymptotic nominal coverage and exhibit length shrinking at the parametric rate. The practical utility and validity of the proposed method are demonstrated through an empirical application in Mendelian randomization.

This study addresses the limitation of conventional instrumental variable (IV) methods, which often assume a constant treatment effect and thus struggle to accommodate effect heterogeneity in real-world settings. Building on the local average treatment effect (LATE) framework, the paper systematically integrates covariate-adjusted IV approaches, clarifying how covariates influence the weighting structure of LATE estimators. It proposes flexible modeling strategies to avoid parametric misspecification and incorporates robust diagnostic tests for violations of the monotonicity assumption. By combining nonparametric and semiparametric estimation techniques, formal hypothesis testing, and accompanying software implementation, this work offers empirical researchers a theoretically rigorous yet practically feasible causal inference workflow, substantially enhancing the reliability and applicability of IV analysis.

This study addresses the testability of the exclusion restriction and monotonicity assumptions in instrumental variable models under heterogeneous treatment effects by proposing a unified identification and testing framework. By linking latent response-type restrictions to first-order stochastic dominance and generalized random utility models, the approach uniquely distinguishes between two key forms of assumption violations. Leveraging measure-theoretic arguments and integral aggregation of inequality constraints, the paper derives sharp testable implications for both single and multiple discrete instruments. The method achieves sharp identification in the binary instrument case and offers empirical researchers a novel, implementable pathway for assessing instrumental variable validity.

This work addresses the challenge of causal effect estimation in the presence of unobserved confounders and without explicit instrumental variables (IVs). It proposes ZNet, a novel model that integrates representation learning with IV methodology by leveraging a structural causal model–guided neural architecture to automatically learn latent instrumental representations from observed covariates. These learned representations satisfy the three core IV conditions without requiring pre-specified instruments, effectively disentangling confounding and instrumental components. The model is trained via empirical moment conditions to ensure theoretical consistency. Experiments demonstrate that ZNet not only accurately recovers true instrumental variables when they exist but also constructs effective latent instruments in their absence, serving as a plug-and-play module that significantly enhances the performance of various two-stage IV estimators.

This study addresses the challenge of conducting instrumental variable analysis when the exclusion restriction and exogeneity assumptions are difficult to verify and the standard first-stage monotonicity condition fails to hold. The authors propose a novel nonparametric sensitivity analysis framework that relaxes these conventional assumptions, enabling identification of sharp bounds on the marginal distributions of potential outcomes and their functionals—such as the average treatment effect—without imposing monotonicity or restricting treatment effect heterogeneity. The resulting identification problem is cast as a linear program with favorable theoretical properties, accompanied by a computationally feasible estimation strategy suitable for infinite-dimensional settings. Empirically, the method is applied to estimate peer effects in movie attendance using weather as an imperfect instrument, demonstrating its practical utility and robustness.