That’s exactly right. The fact that for treatment T, and outcome Y, there is generally an unobserved common cause U of T and Y is in some sense the fundamental problem of causal inference. The way out is either:
(a) Make parametric assumptions and find instrumental variables (econometrics, mendelian randomization)
(b) Try to observe U (epidemiology, etc.)
(c) Randomize T (statistics, empirical science)
There are some other lesser known ways as well:
(d) Find an unconfounded mediator W that intercepts all causal influence from T to Y:
That’s exactly right. The fact that for treatment T, and outcome Y, there is generally an unobserved common cause U of T and Y is in some sense the fundamental problem of causal inference. The way out is either:
(a) Make parametric assumptions and find instrumental variables (econometrics, mendelian randomization)
(b) Try to observe U (epidemiology, etc.)
(c) Randomize T (statistics, empirical science)
There are some other lesser known ways as well:
(d) Find an unconfounded mediator W that intercepts all causal influence from T to Y:
T → W → Y
Then use the “front-door criterion.”