Varying adaptive weighting function

[liaochris]

Hi! I am trying to apply causal forest to a panel data setting. I have two questions in bold.

Is there a way to modify the adaptive weighting function (${\alpha }_i(x)$ from equation 2 of Athey et. al 2019) such that it varies by categorical attributes in the data? The reason is that since I'm interested in estimating the CATE for $Y_i$ (relative to the pre-treatment period $g$) in multiple time periods ($Y_{i,s}-Y_{i,g},Y_{i,s+1}-Y_g,...Y_{i,s+k}-Y_g$), and I want to ensure that when the CATE for ${\delta }_{s-g}(x)$, one of my parameters of interest is calculated, that only observations from where $t=s$, not $t=s+1$ have non-zero weights (according to the adaptive weighting function).

This is to ensure that when comparing the treatment and control, I'm only comparing observations with the same $t-g$ value.

Please let me know if anything is unclear! I had originally thought of using a separate causal forest for each $Y_{i,t}-Y_{i,g}$ for $t\in [s,\cdots ,s+k]$ but since I want to cluster SEs at the individual level inference is difficult under that procedure. Is there a way to combine each iteration of a bootstrapped CATE from multiple forests (assuming bootstrap seeds are the same in all forests) for the purposes of inference?

[erikcs]

Hi @liaochris, the causal forest setup is a cross section of covariates. If you had only two time periods you could collapse this to a standard cross section by looking at the first-differenced outcomes. It is typically easier to try and translate your problem to a standard cross section than to modify the underlying weight function, which would involve creating a custom grf forest from scratch. This paper might be useful: https://arxiv.org/abs/1905.11622 (there's also some applied work in various outlets applying causal forests to first-differenced outcomes).