Amazing content as always. So we can assess the relevance assumption through an empirical or a statistical test but we don't do the same with the validity assumption. Why? I mean somebody can come and suggest "Let's run a regression Y ~ Z + X so we essentially block the path Z -> X -> Y. If we found no association, the instrument is valid (no path between Z and Y). I know this reasoning is invalid but not sure if I have good reasoning for it.
You could use an empirical test to assess the validity assumption *under some theoretical assumptions that cannot be verified*. For example, you could use a test like that to check the validity of Z *if you are very certain that Z -> X -> Y is the only possible path violating validity*. However, note that this assumes no other possible pathway like Z->X2->Y, or that X is potentially a collider - that test also doesn't work if the path Z->XY is on the diagram. So you can use an empirical test to *support* some of the assumptions you're making (like if cor(X, Z) is near 0 then your assumption that the path Z->X->Y is not on the diagram is more plausible, supporting your validity assumption), but since validity is inherently a causal assumption and not a predictive one, you can't test it using data alone.
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amazing video! thank you so much for this breakdown
Amazing content as always. So we can assess the relevance assumption through an empirical or a statistical test but we don't do the same with the validity assumption. Why? I mean somebody can come and suggest "Let's run a regression Y ~ Z + X so we essentially block the path Z -> X -> Y. If we found no association, the instrument is valid (no path between Z and Y). I know this reasoning is invalid but not sure if I have good reasoning for it.
You could use an empirical test to assess the validity assumption *under some theoretical assumptions that cannot be verified*. For example, you could use a test like that to check the validity of Z *if you are very certain that Z -> X -> Y is the only possible path violating validity*. However, note that this assumes no other possible pathway like Z->X2->Y, or that X is potentially a collider - that test also doesn't work if the path Z->XY is on the diagram.
So you can use an empirical test to *support* some of the assumptions you're making (like if cor(X, Z) is near 0 then your assumption that the path Z->X->Y is not on the diagram is more plausible, supporting your validity assumption), but since validity is inherently a causal assumption and not a predictive one, you can't test it using data alone.
relevant section of the book theeffectbook.net/ch-InstrumentalVariables.html#checking-the-instrumental-variables-assumptions