The Explanatory Power of Causal Effects
How much of the observed variation in an outcome Y does a variable X causally explain? We propose a causal R² (CR²) to answer this question and quantify the importance of X in determining Y. CR² is the fit of a causal model, identified by combining observational and experimental data, and captures the reduction in Y’s variance from eliminating X’s causal effect. In applications, class size predicts 8% of variation in reading scores but causally explains only 3%; institutions explain one-fifth of cross-country income variation; and salt intake raises blood pressure similarly across genders, but explains far less among women.
Please cite this work as:
Stratton, James ⓡ Nicolaj Thor. 2026. “The Explanatory Power of Causal Effects.” https://www.nicolajthor.com/papers/cr2.html.