Simple Mobility Models II


This is a sequel to the previous post exploring quantitative genetic models of income inequality motivated by the findings in Gregory Clark’s new book [1].

A simple quantitative genetic model must rely on the assumption of an underlying normal distribution of something, EQ we can call it, that is the additive genetic part of whatever determines income. We can impute this since, now, we have no way to measure it. Like IQ originally, and like our construction of AQ,’amish quotient’, here, we could come up with an estimator if we could measure what we think we ought to measure. For the moment we assume that there is such a direction in character space. An immediate problem is that income is far from normally distributed but we can impute a mapping from the observed income distribution to EQ. Income percentiles are well known and published for many countries. The figure is derived from Swedish data given by Björklund and Jäntti [2].

The the top panel shows the conventional Lorenz curve for the Swedish data: the horizontal axis is income rank and the vertical axis is the percentile of national income at that rank, i.e. it is a conventional cumulative distribution of income. The circles show data points along a green line which is a spline through the data points.

The bottom panel has the same vertical axis but the distribution along the horizontal axis is the imputed normal distribution of EQ. For example the 50th percentile of income maps to the mean of the imputed distribution, the 84th percentile maps to +1 standard deviation of a standard normal, the 16th percentile maps to –1 standard deviation, and so on. This figure gives us estimate of the income of a person given his value of an underlying normally distributed EQ, shown as superimposed on the figure. The virtue of this is that we can instantly apply a century’s worth of quantitative genetic theory and knowledge.

In each panel a computed offspring distribution is shown as a bar two standard deviations wide with a line to the parents’ EQ at each mid-quintile, i.e. at percentiles 10,30,50,70,and 90. The lines are not vertical because of regression to the mean.

Given a quantitative genetic model we know, for example, that offspring of a couple should be distributed symmetrically around the mid-parent value, regressed toward the mean.
A clear exposition of this is in a post in Steve Hsu’s blog , with a contribution from James Lee, here. This particular figure is computed with an additive heritability of 0.9 and a spousal correlation of 0.9. These are both at the high end of plausibility, as suggested by Clark’s data. We also should remember that family (cultural) transmission, of wealth or values or whatever is likely indistinguishable from genetic transmission and will increase the heritability.

From this we can compute, and perhaps derive explicit expressions, for the long term movement, i.e. EQ, of one’s descendants. It should not be difficult to derive longer term expectations from a model like that in the bottom panel. For example starting at some initial EQ the distibution of descendants’ EQ should be distributed in subsequent generations along the EQ distribution, the X axis of the bottom panel, according to some reaction-diffusion process similar to the Fisher-Komogorov equation where the diffusion is given by the the incomplete assortative mating and the heritability less than unity. The deterministic part would describe the greater number of surviving offspring with high EQ as documented in Clark’s Farewell to Alms [3].

To paraphrase what we hear often in the social sciences, there is no need to invoke any social or cultural transmission at all.

  1. Clark, G., 2014. The Son Also Rises: Surnames and the History of Social Mobility. Princeton University Press.  ↩
  2. Intergenerational income mobility in Sweden compared to the United States. A. Björklund and M. Jäntti.
    The American Economic Review (1997):1009–1018.  ↩
  3. Clark, G., 2007. A Farewell to Alms. Princeton: Princeton University Press.  ↩
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37 Responses to Simple Mobility Models II

  1. JayMan says:

    And that’s how you do it… 😉

    (Monitoring comments for post in development 🙂 )

  2. Aaron Gross says:

    But this whole EQ thing seems like question-begging. You’re assuming a big part of what needs to be shown: that the characteristics for success are reasonably constant over wide cultural and social variations in time and space. In contrast, the existence of an Amish Quotient (AQ) is more reasonable, because you’re looking at one society (one primary society – the outside society is secondary) over a relatively short period of time, and it’s a society that intentionally maintains a stable culture and social structure as well.

    Because of that, I think any edifice you build on top of an EQ assumption is going to be very shaky, unless you can somehow show the existence of a stable EQ first. (Not identify it – just show that it exists.) But if you could do that, it would in the process take away most of my – our – objection to Clark’s hereditarian implications. So showing the existence of an EQ looks like most of the hard work.

    Your final sentence is cute, but let’s keep in mind why it’s true: because there’s virtually no data available to discriminate between any types of model. In other words, we can imagine a world that matches either a purely genetic or a purely environmental model, or any model in between, and that imaginary world will be consistent with what data we actually have, which is virtually no data at all.

    • harpend says:

      This is model building. I have no interest right now in either estimating EQ or deciding how much of it is based on genes. As far as I can see family social transmission, e.g. of wealth, would behave like additive genetic transmission.

      There are data out there if someone wanted to push this. For example with huge samples in Europe of people who have had their SNPs typed and who have some socioeconomic information available, the Visscher methodology could look directly for genetic as opposed to familial contributions to an EQ.

      • Aaron Gross says:

        Point taken. Just to clarify, though: I was not talking about estimating EQ! I was talking about showing that such a thing even exists. In other words, showing that the same personality stuff that drives success (however Clark defines it) today also drove success in 12th-century England, etc. As soon as you talk about “EQ,” you’re implying that’s the case.

    • gcochran9 says:

      What nonsense. We have tons of data – contemporary data – that show beyond doubt that hereditary influences are strong as a bear. You think that genes were invented in the French Revolution or something?

      You’re boring me. That’s a very bad thing.

      • ursiform says:

        Bears are very strong. It’s hereditary …

      • Aaron Gross says:

        Sorry I’m boring you. Suggestion: don’t read my comments then.

        Still reading? OK. If by “contemporary” you mean for historical periods discussed by Clark, well, why didn’t you say so in the first place? That was the question that I asked in my very first comment on this topic.

        My whole point was that Clark was using 20th- and 21st-century behavioral genetics findings to make historical inferences. If there’s data from the time periods he’s talking about, that’s really interesting. (It’s also interesting why he didn’t cite it in his op-ed, citing current data instead.) As I’ve said, I’m obviously a layman who doesn’t know much at all about behavioral genetics. If you or anyone else would like to summarize the data, I’d appreciate that and I think other readers would, too.

        On the other hand, if by “contemporary” you mean “current,” I’ve already gone over that. Also in my first comment, I asked if there was a way to use the current data cited by Clark to support his implications. No answers, except by Henry who (as I understood it) said there wasn’t a way to do that.

      • JayMan says:

        @Aaron Gross:

        “As I’ve said, I’m obviously a layman who doesn’t know much at all about behavioral genetics. If you or anyone else would like to summarize the data, I’d appreciate that and I think other readers would, too.”

        Wait… (and not long).

      • Aaron Gross says:

        JayMan, looking forward to it, then. Just to emphasize, I’m talking about behavioral genetics data from all the places and times Clark describes (e.g., 12-th century England), not data from today.

  3. The fourth doorman of the apocalypse says:
    • melendwyr says:

      It’s an individual case, which statistical conclusions about large groups tell us very little about.

      • Sandgroper says:

        You can learn stuff from individual case studies, though. If anyone can stomach Amy Chua enough to look, culturally she is barely Chinese. She was born in the Philippines and grew up in America. She claimed her daughters ‘can speak Chinese.’ No, they picked up a smattering of Hokkien dialect from her at home. That is about as useful as speaking Welsh, and a million miles away from being literate in Chinese and fluent in standard Mandarin. Genetically she is Chinese, culturally she is not, not in the sense of any learned Chinese formal education.

      • Sandgroper says:

        Correction – she was born in America of Filipino Chinese parents.

      • Sandgroper says:

        i.e. what I’m inferring is that it looks like inherited behaviour, but regarded as ‘extreme’ by ‘normal’ Chinese people.

      • Matt says:

        I expect there’s a heritable element.

        I doubt authoritarian parenting (by those who practice it, Chinese or no) has much to do with selection for overachievers, but more a side effect of being folk high in humility and social anxieties (as both children and parents), who tend not to be particularly not permissive or uninvolved… yet who don’t have much of the capabilities for emotional warmth, feeling secure at child independence and to understand natural support seeking cues required by the authoritative parenting style.

      • The fourth doorman of the apocalypse says:

        i.e. what I’m inferring is that it looks like inherited behaviour, but regarded as ‘extreme’ by ‘normal’ Chinese people.

        Based on my experience with more than one Chinese woman (marriage to one, observation of another and discussion with the husband of another) plus feedback from offspring about how the Chinese mothers (and fathers) of their class mates push their children I think it is not “extreme” behavior at all.

        The label “extreme” might simply be being used here to assuage Caucasian feelings.

      • Sandgroper says:

        Of course, you must be right – all Chinese mothers must threaten to cut their kids’ hands off.

    • Sandgroper says:

      How to separate? As described here, a lot of it is herd behaviour, but where does that come from? A few thousand years is long enough to breed a race of over-achievers, but pushing your kid to suicide if she doesn’t have the genetic inheritance to handle the pressure is not actually useful.

      I know a lot of Chinese mothers, really a lot, and their group response to Amy Chua was that they were offended that she was representing herself as a ‘typical Chinese mother’ – many of them realise that pushing kids that hard doesn’t work if the kid just isn’t bright enough. They considered her to be borderline-abusive. In any distribution, there are going to be people in the tail like Amy Chua and that repulsive Hillsborough woman.

      I’d happily bury them both alive. The problem with Amy Chua is that far too many people take notice of her, when she doesn’t actually have anything intelligent, interesting or useful to say.

      • The fourth doorman of the apocalypse says:

        I know a lot of Chinese mothers, really a lot, and their group response to Amy Chua was that they were offended that she was representing herself as a ‘typical Chinese mother’ – many of them realise that pushing kids that hard doesn’t work if the kid just isn’t bright enough.

        I wonder if you are simply being told what they know you want to hear.

      • Sandgroper says:

        Yeah, of course – I’m an idiot.

      • The fourth doorman of the apocalypse says:

        It should be well known by now that what people say and what people actually do are two different things. They say what they think you want them to say, generally, ie, what is socially acceptable. However, they do what the genes direct them to do.

      • The fourth doorman of the apocalypse says:

        Yeah, of course – I’m an idiot.

        You are putting words into my mouth.

        Have you monitored their behavior closely enough when they think other people are not looking to know whether that they do matches what they say?

      • Sandgroper says:

        Where I live, I’m an ethnic minority of one. I have been for a long time.

    • Anonymous says:

      Once some parents in a group start using ‘extreme’ measures to ensure that their offspring will pass their genes on to the generation after, other parents have to follow suit or see their genes be purged from the gene pool.

      Pretty soon, what one group thinks is ‘extreme’, the other group thinks is ‘normal.’

  4. Sandgroper says:

    Maybe I didn’t explain this clearly enough, so I better have another try.

    Take a representative sample of Chinese mothers. Their behaviour will plot over a range, probably Bayesian – most things seem to be. So the majority who exercise moderate behaviour will fall around the middle, but you will get some whose behaviour is extreme.

    On the whole, do Chinese parents push their kids more than parents in Western societies? In my observation yes – they tend to regard academic attainment as important, and they push the kids somewhat to attain to the best of their ability, sometimes without a clear perception of what the kids’ abilities are. They will also be very supportive to their kids and help them with this.

    But these are folks in the bulge in the middle – this is normative behaviour. What about the upper tail? Well, threatening to cut a kid’s hand off for not doing his tutoring assignment, making a kid stay up all night or making her practise the piano for 3 hours non-stop are not normal, they are in the tail. They are extreme. In my view, and the views of Chinese mothers who have expressed opinions about it to me, we agree that those things are extreme, over the top, and abusive. They are not the behaviour of ‘typical Chinese mothers’. That is what they think, and having observed them, that is also what I think.

    That’s what I see.

  5. “My whole point was that Clark was using 20th- and 21st-century behavioral genetics findings to make historical inferences. If there’s data from the time periods he’s talking about, that’s really interesting. “

    I think too many people miss the point. Contemporary behavioural genetics is just icing. Clark’s own findings, by themselves, suggest a genetic transmission of status. Don’t you see it ? A persistent pattern of status transmission across many generations in countries as varied as England from the Middle Ages to the present, China from late imperial times to the post-communist era, Japan from the samurai to the salaryman, Sweden from its aristocratic 18th century to its ultra-egalitarian present, Chile one of the most unequal societies in the world, India with its extreme endogamy enforced by religion, ethnicity and caste, etc. Communist China killed off its elites or drove them abroad, yet surnames listed in imperial exam registers still show up in the upper echelons of the communist party. What possible cultural or social force can explain such persistence of status for such a time period across so many countries under so many different countries. You can throw out all of behavioural genetics and still would be powerfully impelled to conclude, the only explanation is genetic.

  6. Gottlieb says:

    ”To paraphrase what we hear often in the social sciences, there is no need to invoke any social or cultural transmission at all.”

    Social and cultural transmission are also derived by genetics but to be ‘abstractically’ specified, i mean, when genes and your collective and individual interactions with the environment to produce ”cultural artefacts” and or ”social artefacts”.
    To seems that phenotypical transmission and not genotypical transmission is most important here because we talking about ”personality traits and cognitive style”. In India i can see this ”genotypical transmission” because of the castes, but in western countries, the mobility was higher than India, absolutelly. The mobility to upper classes (psychopath places) is very difficult not only because is necessary combined psychopathic traits with higher situational and or opportunistic intelect (and this combination to seems to be rare) but also because upper classes like to be a minority because they will have less internal-social competition. ‘Cause it, today the upper western classes are ”brasilificating” the First World.
    To understand this socio-economic dynamic to be extremelly necessary understand firstly the non-direct gene factors, the social landscape produced by phenotypes genes that predominated in a upper class. If psychopaths rule the government and ”job decision niches” then they are selecting (phenotypically) themselves to aggregate power. (…and to seems that it is very older, explain the disable old and new world).

  7. Mark says:

    Fascinating stuff.

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