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matheusfacure / python-causality-handbook

Causal Inference for the Brave and True. A light-hearted yet rigorous approach to learning about impact estimation and causality.
https://matheusfacure.github.io/python-causality-handbook/landing-page.html
MIT License
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Issue in ATT = ATE in chapter 1 #230

Closed JacksonRudd closed 2 years ago

JacksonRudd commented 2 years ago

There is an issue on chapter 01, in the following paragraph """ Not only that, but E(Y1-Y0 | T=1) = E(Y1-Y0 | T=0), simply because the treated and untreated are exchangeable. Hence, in this case, the difference in means BECOMES the causal effect: """ At this point we only know that E(Y0|T=1) = E(Y0|T=0). aka we know there is no bais.

Therefore we still need to prove that E(Y1| T=1) = E(Y1 | T=0) to show that E(Y1-Y0 | T=1) = E(Y1-Y0 | T=0). Maybe this is obvious and I'm missing something, but I think the section would be improved by proving this. I am somewhat doubtful this is true.

MichaelPfeuti commented 2 years ago

I agree An example would be where the group T=0 reacts more strongly on the treatment than group T=1. So the differences wouldn't be equal, even though thenon bias equation still holds. I think you need a stronger assumptions (maybe on the distribution and not just the expected value).

matheusfacure commented 2 years ago

You are right. Beyond E[Y0 | T=0] = E[Y0 | T=1], you also need E[Y1 | T=0] = E[Y1 | T=1]. Both are satisfied under randomization, but this isn't clearly state in the chapter. Thanks!