Heterogeneous causal effects deep dive
Understanding and identifying heterogeneity in causal effects is central to tailoring interventions and policies more effectively. Several strategies are employed in statistical analysis to detect and estimate heterogeneous effects, each with its mathematical framework and application.
Interaction terms in regression models
Interaction terms are a powerful tool for causal inference scholars to explore how an intervention’s impact changes based on another variable.
Consider a linear regression model examining the effect of a treatment 
on an outcome 
. We suspect this effect might vary by a covariate 
. To capture this, we extend the model with an interaction term:
(6)
Here, 
is the intercept, 
is the ATE, 
captures the effect of 
on 
, and the key term β₃ is the interaction effect. It reveals how the treatment effect (
) varies with changes in the covariate . Finally, &...
