Now, why might that be?
Why would levels of subjective status differ substantially from status inferred from the objective markers? A number of explanations are based on the possibility that the subjective status measure just does a better job of measuring social standing. First, subjective social status may reflect the success or failure to meet one’s educational potential, while the objective measures do not. Second, subjective status allows the respondent to weigh income, education, and occupation in proportion to the importance of each marker in the respondent’s own social context. For example, education may be a more important determinant of status for a college professor and income for an entrepreneur. [emphasis added] Third, the objective measures of SES are crude and the ladder may be capturing finer gradations of the objective indicators than the objective markers. For example, years of education does not distinguish between the quality and status of the school attended (e.g., community college versus Ivy League school), but the respondents know that education scores have different meanings depending on school. Finally, subjective ratings probably capture a broader range of SES markers, including wealth, living locations and conditions, and parental SES, that are not measured by our more limited range of objective markers.I'd take the measurement error response reasonably seriously. But I'd really love to see work helping to distinguish the second hypothesis from the third. Unfortunately, their data was collected 2000-2004, so it would be impossible to go back to the subjects with a couple of follow-up questions. I'd ask subjects where they went to school and for their zip-plus-four at the time they were in the study. The former would allow tighter control for objective education; the latter, for neighbourhood characteristics that would correlate with other unmeasured parts of SES.
What I really like about the approach in the paper is that it mostly avoids the problems of IQ as a confounding variable. Many studies finding bad health outcomes from low status control for education but few control for IQ. Linda Gottfredson finds IQ, when it's available, strongly reduces the effect of income on health status. Why? IQ determines both income and health behaviours. But in this case, there isn't really much that IQ can do in helping the quarantined subjects avoid catching the cold to which they've been exposed.
If people are status-seeking and they seek status over more dimensions than just income, then income redistribution doesn't really help in equalizing status outcomes as status-seeking behaviour then just pushes onto other margins and we're still left with inequality leading to status-based health differences. Instead, facilitating the creation of more ladders lets more folks achieve higher subjective status.
In any case, we ought be upweighting the likelihood that we're in the choose-your-ladder world.