Some question about Instrumental Forests and Generalized Random Forests

[gnay032100-blip]

Dear authors:
Thank you for answering my question! Actually I have some questions about Instrumental Forests and Generalized Random Forests：
First，I have noticed that some authors of papers regress the Conditional Average Treatment Effect (CATE) estimated by the Generalized Random Forests model on the covariates used in building the model to indirectly explain the underlying mechanisms of their articles. However, they do not include all the covariates. I would like to ask if this approach is correct. Will there be endogeneity issues? In fact, is the approach of explaining the mechanisms of the article essentially through verifying the correlation between covariates and CATE?
Second，When my treatment variable is continuous, can I regress CATE on the treatment variable to examine how CATE changes with the variation of the treatment variable? If it is possible, do I need to include other covariates as control variables in the model?
Finally, after reading your paper “Generalized Random Forests,” I noticed that the treatment effects calculated are actually independent of the values of the covariates, right? The covariates are just used for tree splitting to calculate the similarity metrics.
Don't mind me asking some basic questions, please.

[gnay032100-blip]

And Last question：After use Instrumental Forests，Can I get the first stage outcome like 2SLS？And do I need to conduct tests for weak instruments and the validity of the instruments?

[erikcs]

Hi @gnay032100-blip, one way to summarize heterogeneity is to regress CATE on explanatory variables, as implemented in best_linear_projection. In general, grf uses covariates you supply to calculate similarity metrics. For IV, the average_treatment_effect function raises a warning if the instrument appears to be weak.

[gnay032100-blip]

你好@gnay032100-blip，总结异质性的一种方法是对解释变量进行 CATE 回归分析，如 中所述best_linear_projection。通常，grf 使用您提供的协变量来计算相似性指标。对于 IV，average_treatment_effect如果工具函数看起来较弱，该函数会发出警告。

Thank you for your response！It's helpful for me. And I wonder if I can regress CATE on treatment variable, actually I want to check if CATE and treatment variable(continuous) have inverse U-shape relationship. Does it make any sense？Can it verify the marginal effects of treatment variable on outcome variable？

And if I want to get the first-stage outcome like 2SLS, what should I do? @erikcs

Thank you again for answering these basic questions！