The Model to Beat: Status Rank

There’s been much discussion of income inequality over the last few years. However, I just randomly came across what should be a seminal related result, published in 2010 but mostly ignored. Let me do my bit to fix that.

People often presume that policy can mostly ignore income inequality if key individual outcomes like health or happiness depend mainly on individual income. Yes, there may be some room for promoting insurance against income risk, but not much room. However, people often presume that policy should pay a lot more attention to inequality if individual outcomes depend more directly on the income of others, such as via envy or discouragement.

However, there’s a simple and plausible income interdependence scenario where inequality matters little for policy: when outcomes depend on rank. If individual outcomes are a function of each person’s percentile income rank, and if social welfare just adds up those individual outcomes, then income policy becomes irrelevant, because this social welfare sum is guaranteed to always add up to the same constant. Income-related policy may influence outcomes via other channels, but not via this channel. This applies whether the relevant rank is global, comparing each person to the entire world, or local, comparing each person only to a local community.

That 2010 paper, by Christopher Boyce, Gordon Brown, and Simon Moore, makes a strong case that in fact the outcome of life satisfaction depends on the incomes of others only via income rank. (Two followup papers find the same result for outcomes of psychological distress and nine measures of health.) They looked at 87,000 Brits, and found that while income rank strongly predicted outcomes, neither individual (log) income nor an average (log) income of their reference group predicted outcomes, after controlling for rank (and also for age, gender, education, marital status, children, housing ownership, labor-force status, and disabilities). These seem to me remarkably strong and robust results. (Confirmed here.)

The irrelevance of individual income and reference group income remained true whether the group within which a person was ranked was the entire sample, one of 19 geographic regions, one of 12 age groups, or one of six gender-schooling groups. This suggests that the actual relevant comparison group is relatively narrow. If people cared mainly about their global rank in the whole sample, then analyses of rank within groups should have missed an effect of the rank of the group, which should have appeared as an effect of reference group income. But such effects weren’t seen.

It these statistical models were the correct model of the world, then income policy could only include influence social welfare via the control variables of age, gender, education, marital status, children, housing ownership, labor-force status, and disabilities. You couldn’t improve social welfare directly by redistributing income, though redistribution or taxation might help by changing control variables.

But even that conclusion seems premature. The key idea here is that people care about their social status rank, and income should only be one of many factors contributing to social status. So we should really be looking at models where all of a person’s observable features can contribute to their status. For each feature, such as personality or marital status, we should ask if our data is best described as that factor contributing directly to social status, which is then ranked to produce individual outcomes, or whether that factor also influences individual outcomes via some other channel, that doesn’t pass through social status. It is only effects via those other channels that might change overall social welfare.

This seems a straightforward statistical exercise, at least for someone with access to relevant data. Who’s up for it?

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