No relation between Treatment and Confounders - Can I rely on ATE estimates for causal impact ?

[bindugupta]

1. Can I rely on ATE Estimates if confounders(X) don't have any significant relation with Treatment(T) ? Would the DML approach still work ?
2. Given there is no relation between T and X, the performance of the propensity model (ml_m) is quite low. Can I rely on ATE or should I try to include more confounders in my data ?

[SvenKlaassen]

Hi @bindugupta,

1. If the features $X$ do not have any strong relation with your treatment $T$ then they are not actually confounders. The DML approach will still work. But this implies there is not much reweighting done in the method and the estimates should be somewhat close to the difference of conditional means

$$\mathbb{E}[Y|T=1] - \mathbb{E}[Y|T=0].$$

2. This completely depends on your data/problem at hand. If the treatment $T$ is actually very close/similar to a random assignment, then this would be completely fine (random treatment assignment can be still unbalanced e.g. P(T=1) = 0.05 for all units). But if you think there are some significant selection mechanisms or common causes left you should try to adjust the controls. I can recommend the article A Crash Course in Good and Bad Controls to get some insights on what to control for.

[bindugupta]

Thank you @SvenKlaassen for providing the clarity here.