Great video! Thanks! Two quick questions: first, isn't there redundancy in saying Average Treatment Effect "on the treated"? Treatment effect will _always_ be on the treated by definition, isn't it? It makes me think if there can be something like Average Treatment Effect on the untreated which is absurd. Second, if we have a large enough sample, and the observable covariates balance, does it also guarantee that the unobservables would also balance?
If we had statistical independence then in the first example then why did the treatment variable coefficient changed so drastically? Does it means we had a omitted variable bias problem when we were regressing wage on treatment variable alone though we proved that we had statistical independence? Thanks
