Bounded, efficient and multiply robust estimation of average treatment effects using instrumental variables (1611.09925v4)

Abstract: Instrumental variables (IVs) are widely used for estimating causal effects in the presence of unmeasured confounding. Under the standard IV model, however, the average treatment effect (ATE) is only partially identifiable. To address this, we propose novel assumptions that allow for identification of the ATE. Our identification assumptions are clearly separated from model assumptions needed for estimation, so that researchers are not required to commit to a specific observed data model in establishing identification. We then construct multiple estimators that are consistent under three different observed data models, and multiply robust estimators that are consistent in the union of these observed data models. We pay special attention to the case of binary outcomes, for which we obtain bounded estimators of the ATE that are guaranteed to lie between -1 and 1. Our approaches are illustrated with simulations and a data analysis evaluating the causal effect of education on earnings.

Overview of Estimation Techniques Using Instrumental Variables

The paper entitled "Bounded, efficient and multiply robust estimation of average treatment effects using instrumental variables," authored by Linbo Wang and Eric Tchetgen Tchetgen, addresses an essential aspect of causal inference in observational studies where unmeasured confounding poses significant challenges. Instrumental variable (IV) methods have long been established as a solution to estimate causal effects in such settings. However, traditional methods often fall short in precisely identifying the average treatment effect (ATE), primarily due to model assumptions that intertwine identification and estimation processes.

Methodological Contributions

The paper introduces novel assumptions facilitating the identification of the ATE, separating these assumptions from estimation models to avoid commitment to specific observational data structures. This segmentation allows for the construction of multiple estimators consistent across different model assumptions, offering a significant advancement over traditional single-model approaches.

The authors propose two assumptions for identification:

1. No-additive interaction in treatment assignment: This assumption generalizes prior linear models and suggests that upon conditioning on covariates, unmeasured confounders should not modify the effect of the instrument on the exposure linearly.
2. No-additive interaction in treatment effects: A similar assumption is extended to the outcome, ensuring that unobserved confounders do not modify the causal effect of the treatment.

These assumptions allow for the identification of the ATE by establishing its equivalence to the conditional Wald estimand. The estimators developed under these assumptions are multiply robust and consistent, if at least one of the assumed models is correct. This multiply robust feature is pivotal, offering resilience against possible model misspecifications.

Bounded and Efficient Estimation

The estimation approaches discussed are bounded, particularly effective for binary outcomes, ensuring the estimated ATE lies within feasible limits, specifically between -1 and 1. Three key estimation strategies are detailed:

1. Regression-Based Estimation: Directly models the ATE, avoiding indirect inference through separate components liable to model misspecification.
2. Inverse Probability Weighting (IPW): Separates design and outcome assessments to mitigate post-design biases, yet constrained in handling binary outcomes.
3. G-estimation: Provides a consistent estimation even under partial adherence to model assumptions.

The authors further introduce a multiply robust estimator that maintains validity across varied model surfaces, maximizing efficiency when models intersect correctly.

Numerical and Practical Evaluations

Simulations within the paper reveal promising results, showcasing the robustness and efficiency of the proposed estimators, even under various settings of model misspecification. Additionally, real-world data application concerning the effect of education on earnings illustrates the practical relevance of these methods. The empirical results highlight the merits of addressing unmeasured confounding with robust methodologies provided herein.

Implications and Future Developments

This paper's methodologies significantly impact practical econometrics and epidemiology, allowing more accurate causal inferences from observational data where confounders lurk unobserved. The multiply robust approach, allowing the relaxation of stringent model assumptions, is particularly appealing for studies where model validity is perpetually in question.

Future research could explore extending these strategies to non-binary treatments or outcomes and further refine methodologies to cater to broader assumptions and models. Incorporating machine learning techniques for model estimation within the IV framework could also enhance the robustness and applicability of these innovations in complex data environments.

In conclusion, this paper enriches the IV literature with its innovative methodologies for robust causal inference, effectively bridging identification and estimation between traditionally segregated domains. The bounded, efficient, and multiply robust methodologies offer substantive advancements for dealing with unmeasured confounding, promising more reliable estimates in observational settings.