I’m agnostic on the right functional form for the VSLY, just as I’m agnostic on the right η. My point was just that you cannot have it be independent of u′(c).
You need to impose some structure to get an exact identification of η, but that should not be interpreted as meaning that we can be fully agnostic about how η affects valuations, the way you describe. So I don’t think that puts us at the point you stated. Specifically, I think the framework you describe where the VSLY relative to income doublings is constant while you shift η is still inconsistent with utility maximization, and still not a valid way to interpret how η affects the value of health vs income.
I’m agnostic on the right functional form for the VSLY, just as I’m agnostic on the right η. My point was just that you cannot have it be independent of u′(c).
You need to impose some structure to get an exact identification of η, but that should not be interpreted as meaning that we can be fully agnostic about how η affects valuations, the way you describe. So I don’t think that puts us at the point you stated. Specifically, I think the framework you describe where the VSLY relative to income doublings is constant while you shift η is still inconsistent with utility maximization, and still not a valid way to interpret how η affects the value of health vs income.