How to interpret high predictive error on estimating Y.hat for causal forests

[qpmnguyen]

Dear authors,

I was wondering if you can help with interpreting the results of estimating the CATE under the paradigm where there is limited predictive power to estimate $\hat{Y}$. In other words, it seems that baseline characteristics doesn't necessarily well predict the outcome ($Y$ is continuous, predictive $R^2$ is ~2-3%). This was replicated with or without including treatment as a covariate using regression_forest, as well as using other methods (like standard random forest).

However, results look okay for test_calibration(), where the coefficients are close to 1 (but no significant p-values, although my sample size is small).

Would the variance of the CATE "incorporate" the predictive/estimation error for $\hat{Y}$ such that I can report the CATE and associated confidence interval and not have to worry about the "validity" of the estimate? Additional diagnostics I've done include comparing the CATE point estimate against the observed treatment difference and they seem to match okay(-ish).

If there are existing guidance on this that has been published by your group, I would love to know (I wasn't able to find any through google).

Thank you so much for your patience.