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#causality #statistics
It might seem like consistency is obviously true, but that is not always the case. For example, if the treatment specification is simply “get a dog” or “don’t get a dog,” this can be too coarse to yield consistency. It might be that if I were to get a puppy, I would observe 𝑌 = 1 (happiness) because I needed an energetic friend, but if I were to get an old, low-energy dog, I would observe 𝑌 = 0 (unhappiness). However, both of these treatments fall under the category of “get a dog,” so both correspond to 𝑇 = 1 . This means that 𝑌(1) is not well defined, since it will be 1 or 0, depending on something that is not captured by the treatment specification. In this sense, consistency encompasses the assumption that is sometimes referred to as “no multiple versions of treatment.”
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owner: crocodile - (no access) - Introduction_to_Causal_Inference-Nov19_2020-Neal.pdf, p22


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