The ‘right’ level of mobility

26/01/2012 § 10 Comments

Oh dear. Tyler Cowen has suggested that class mobility might not be that bad, and John Quiggin has taken him to task. The underlying question is, what level of mobility would indicate a meritocracy? Or at least the level of meritocratic reward we prefer? Does low mobility in itself indicate lack of meritocracy?

In the last year or two, I have joined both Mensa and the Triple Nine Society. It turns out that high IQ societies are obsessed with IQ measurements and what they mean. For example, the last TNS newsletter had a great article on the Flynn effect (named for NZ’s own Prof Flynn, University of Otago). I have therefore been reading and thinking lately about what IQ is and what it profits a person.

This debate about mobility and meritocracy touches on three issues:

  • selection of breeding partner
  • heritability of intelligence/IQ
  • correlation of earnings and IQ.

Conceptually, if people select breeding partners with similar IQs, IQ is totally inherited, and earnings correlate perfectly with IQ, then society will be both rigid and meritocratic. Relax any of the conditions, and you introduce mobility into a meritocratic society. If we then take as given:

  • individuals are allowed to select their preferred partners
  • individuals will prefer partners similar to themselves
  • heritability is biologically determined, rather than decided by social policy,

we are left with asking, what should be the reward for a given level of IQ?

I built a small spreadsheet model to try to understand this. I generated 100 people with random IQs (mean=100, SD=15) and gave them incomes equal to exp(IQ/10). I paired them so as to minimise the sum of the squares of the differences in IQ across all breeding pairs (1000 random draws). Then, each pair had two children. Their IQs were 50% random and 50% inherited. Their incomes were also equal to exp(IQ/10).

I put both the parents and children into quintiles and calculated the class mobility of the children. Here is the result:

In this meritocratic society, 73% of children are within 1 quintile of their parents. There isn’t much mobility. Only 6% of children have the really big moves, |3| or |4| quintiles.

All the inputs to the model are subject to debate. How inheritable is IQ? How do we select mates? How much should or does income depend on IQ? What are social preferences for equality of outcomes?

The key point is that, given the right parameters, you can have both class rigidity and meritocracy.

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§ 10 Responses to The ‘right’ level of mobility

  • Ok, now tweak as follows. In first period, we have artificial class distinctions without meritocracy. Then social conventions change while geographical mobility increases so folks move from within-class assortative mating in a small sample catchment to meritocratic assortative mating in a large sample catchment. Then you get low mobility, a period of high mobility, and then low mobility again – because we’ve flipped from arbitrary classes to meritocratic assortment. The high mobility phase was just a transition.

    • Bill says:

      That’s an excellent extension. Taking it further, what happens when labour and/or jobs change from being regionally or nationally allocated to globally allocated? We should get another re-sorting. People will move up and down the rankings, with all the political and social issues that movement implies.

      • What happens? A big increase in international income mobility, a big increase in total income mobility within countries experiencing in-migration (new immigrants start poor and their kids quickly rise to where meritocratic assortment would put them), resentment among domestic underclass seeing their neighbours’ kids moving onwards and upwards while their own are idiots, increased anti-immigrant sentiment among the underclass. Then it’s a numbers game on whether anti-immigrant policy gets ramped up. And, given differential birth rates by IQ quartile, idiocracy remains a reasonable concern.

        Research implication: we really need to know more about the elasticity of births with respect to income across different IQ deciles. If high IQ decile births are inelastic (they just want 2 no matter what), deadweight costs of transfers are small; if elastic (they’d go to 3 or 4 if the tax burden were lower), deadweight costs of transfers are higher. I wouldn’t model birth increases among lower IQ / lower income cohorts consequent to transfers as any kind of loss except to the extent that the transfers attenuate birth rates among the higher IQ cohort. Then we have an opportunity cost of transfers that’s not currently factored in.

        I’m relying a lot on introspection here; were taxes lower, we could afford a bigger house and a nanny and we’d likely have more kids. If that kind of thing is common, then transfers subsidizing births among the poor induce a reallocation of births from higher income potential kids to lower income potential kids. And then Garret Jones’ work on IQ and growth rates starts looking worrying.

  • Oh, and as aside, both Mensa and Triple 9 are pretty low-brow. Did anybody really get below 2180 on the GRE combined ’94-’01? Sigh.

    • Bill says:

      Cool model. Thanks for pointing to it. I figured I wasn’t the first to toy with the ideas, but hadn’t looked for other models.

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