Clarification on discussion about X & W in EconML

I understand that there has been a couple of posts on how to distinguish between X and W (Issues 589 & 656)

These are a couple of points I have inferred from these 2 issues:

• X and W together make up the entire set of confounders
• The difference is that X is additionally allowed to affect the strength of relationship between T and Y
• Therefore, if they are important for effect heterogeneity, park it under X, otherwise, park it under W.

I’m currently trying to estimate Heterogenous Treatment Effects with CasualForestDML, but currently have ran into a dilemma in defining my set of confounders X and W

1. I am currently relying on Causal Discovery algorithms (i.e., LiNGAM) to identify relationships (and therefore construct a causal graph) between my set of 500+ variables
2. I also am currently relying on the back door criterion when identifying all confounding variables from the causal graph using dowhy
3. However, I’m currently splitting my identified confounders into X and W using the following method:
4. Confounders with only an edge to Y (not T) are defined as W
5. All other remaining confounders are defined as X

Is this the correct manner in which to define X and W? Assuming I have no prior knowledge on the relationship between any of the 500+ variables, apart from what is the treatment and outcome variable (based on the fact that I relied entirely on causal discovery and backdoor criterion just to get a list of confounders)

Thank you!

Start by reading Issues 589 and 656, then review the EconML documentation for CausalForestDML and the distinctions between X and W. The question also references LiNGAM and DoWhy's back-door criterion. Done means providing a project-supported clarification of how these variables should be selected in the described setting.