Deriving Bounds and Inequality Constraints Using Logical Relations Among Counterfactuals

Area of Science:

• Causal inference
• Graphical causal models
• Probability theory

Background:

• Unobserved confounding can prevent precise point identification of causal parameters.
• Bounds on non-identified causal parameters can sometimes be derived from observed data.
• Existing methods may not fully exploit the information available in causal graphical models.

Purpose of the Study:

• To develop a general method for deriving bounds on causal parameters in the presence of unobserved confounding.
• To leverage rules of probability and counterfactual restrictions from causal graphical models.
• To derive inequality constraints on observed data distributions implied by causal models.

Main Methods:

• Utilizing logical relationships between identified and non-identified counterfactual events.
• Applying rules of probability to observed data.
• Incorporating restrictions on counterfactuals derived from causal graphical models.

Main Results:

• The developed method successfully recovers known sharp bounds and tight inequality constraints.
• The approach yields novel bounds and inequality constraints on causal parameters and observed data functionals.
• Demonstrates the power of combining probability rules with causal graphical model restrictions.

Conclusions:

• The new method provides a powerful framework for bounding causal parameters under unobserved confounding.
• It offers a systematic way to derive valuable information from observed data using causal models.
• The approach advances the field of causal inference by providing new tools for handling identification challenges.