Estimating causal effects with hidden confounding using instrumental variables and environments.

Area of Science:

• Econometrics
• Causal Inference
• Statistical Modeling

Background:

• Regression models invariant across data collection environments are an active area of research.
• Existing methods like Causal Dantzig (CD) offer causal interpretations but have limitations.
• Classical instrumental variable estimators, such as Two Stage Least Squares (TSLS), are widely used but can be outperformed.

Purpose of the Study:

• To derive the Causal Dantzig (CD) estimator within the Generalized Method of Moments (GMM) framework.
• To introduce novel estimators, Generalized Causal Dantzig (GCD) and a Hybrid (GCD-TSLS) combination, for enhanced causal inference.
• To provide theoretical asymptotic results for the proposed GMM-based estimators.

Main Methods:

• Derivation of the Causal Dantzig (CD) estimator as a Generalized Method of Moments (GMM) estimator.
• Development of the Generalized Causal Dantzig (GCD) estimator for continuous environments.
• Construction of a Hybrid (GCD-TSLS) estimator combining strengths of both approaches.
• Comparative analysis through simulations and a Flow Cytometry data application.

Main Results:

• The GMM representation facilitates the creation of new, practical estimators.
• The Generalized Causal Dantzig (GCD) estimator extends applicability to continuous environments.
• The Hybrid estimator demonstrates superior performance compared to GCD or TSLS individually.
• Simulations and real-world data application show the superiority of GCD and Hybrid estimators in various settings.

Conclusions:

• The GMM framework provides a robust foundation for developing advanced causal inference estimators.
• The proposed GCD and Hybrid estimators offer significant improvements over existing methods, particularly in challenging data environments.
• These novel estimators enhance the toolkit for causal discovery and analysis in econometrics and related fields.