Including pre-treatment covariates in difference-in-differences: what if my covariates determine treatment but are outcomes of treatment? I have the following question: What should I do with covariates that affect treatment in the pre-treatment period but are affected by treatment once the treatment is in place in a difference-in-differences model?

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*Should I exclude them because they are outcomes of the treatment?


*Is there a way to use the variation of the pre-treatment period in the difference-in-differences formulation without including the post-treatment variation?
A potential (please comment on it) solution: including the pre-treatment values of the covariates, but for the post-treatment period include the average of the pre-treatment period. In this way, the covariates can explain the treatment in the pre-treatment period, without being affected by the treatment in the post-treatment period.

It is not possible for a covariate to affect treatment and be affected by treatment, unless the covariate changes its value in time. You should never adjust for post-treatment variables unless you are doing G-computation and know what you are doing. If you are using time-dependent cox (or something similar), then introducing post-treatment variables completely destroys any causal interpretation the coefficients in the model may have had.
Can you clarify your data-structure? It is a bit unclear. Why do you care about post-treatment variables? Is your treatment changing in time? What exactly are you trying to estimate? What model?
If you treatment is not changing in time, you can and should ignore all post-treatment information.
