Socioeconomic Noiselessness

I’m currently reading, and almost through, The Signal and the Noise by Nate Silver. I’ll probably write more about my personal takeaway after I’ve had a chance to finish and think, but one particular phrase in the third chapter struck me:

Imagine you walked into an average high school classroom, got to observe the students for a few days, and were asked to predict which of them would become doctors, lawyers, and entrepreneurs, and which ones would struggle to make ends meet. I suppose you could look at their grades and SAT scores and who seemed to have more friends, but you’d have to make some pretty wild guesses.

Now Silver was trying to explain the difficulty of prediction, though this is unfortunately not a great example. A question popped up in my mind: how confident am I that I would be where I am today, if not for inequality. That is, how lucky am I that life sucks for everyone else. (Part of this post is simply chronicling my thoughts for future reference – feel free to skip if uninterested)

It’s a difficult question to define quantitatively but, I think, the answer is an overwhelming “yes”. You can define “inequality” quantitatively to be a whole host of indicators. GINI is obviously the most common one. And, I’ve shown (to little surprise), this tracks with a (slightly modified) difference between mean and median incomes extremely well. The most sophisticated indicator is Theil, and I’ll get back to that later in this post – as the derivation actually flows well from our intuition of inequality: better than GINI at least.

I’m too young for “where I am today” to be defined well in any objective context like income. I’ll use my admission to a selective university as proxy. The admissions committee has certainly aggregated a bunch of information, and their “stamp” signals a fair amount of information to a clueless onlooker (and, honestly, that’s probably what I’m paying for). You don’t have to believe in the importance of prestigious universities, or whatever, for this to be a fair definition. You only have to accept that there is at least correlation between students at a good university and what society might call “success”.

Now, read this damning document from the Brookings Institution, titled “The Missing ‘One Offs: The Hidden Supply of High-achieving Low Income Students”, which says:

We show that the vast majority of very high-achieving students who are low-income do not apply to any selective college or university. This is despite the fact that selective institutions would often cost them less, owing to generous financial aid, than the resource-poor two-year and non-selective four-year institutions to which they actually apply. Moreover, high-achieving, low-income students who do apply to selective institutions are admitted and graduate at high rates. We demonstrate that these low-income students’ application behavior differs greatly from that of their high-income counterparts who have similar achievement.

Also let’s note that, other things equal, a low income student has an above-average chance of acceptance than me. They are more likely to be black or Latino and colleges favor socioeconomic diversity: both shifting the admission result fairly in their favor.

Finally, know that aside from exceptional circumstance, a low income student – by official university policy – will be given enough money to ensure academic success, along with preference for more comfortable on-campus jobs and the guarantee that this will not affect chances of admission. Financial aid is offered to families who would in no other context be considered “needy”, for example some well-endowed colleges help families earning well into the six-figure range.

You will read many admissions counselors say something along the lines of “we expect that nearly 60% of the students admitted to the class of 2017 will need financial aid”. Usually at the information sessions where such statements are made there will be a knowing nod admiring such generous policy. And it is generous. But what should strike you – as it does me – is the 40% of people who clearly do not need financial aid come from maybe 2% of the country.

That means the total number of applicants, if in a country of approximately equal opportunity, would be much larger. By simple calculation you can see that if the whole country applied to top colleges as much as the top 2% do, the admitted class – at the same admission rate – would be 20x higher. Clearly impossible. That means my little lower than 10% acceptance rate would be translated to about 0.5%.

Now go back to my question: “What are the chances, if not for inequality, I would not be where I am today”. To answer this, all you need to do are answer the question “Do you think if the admissions officers took their pool of admitted students, cut it in half, then cut it in half again, and then again, and lopped off 25% of that for fun your application would remain in the pool“.

I would have to be supremely arrogant to think this to be the case. The chances of this happening, of course are about thrice as unlikely as my admission in the first place. Indeed, my chance at this is worse than a Gallup poll over a year in advance of a primary election. None of this even accounts for the fact that each progressive halving puts me against increasingly competitive students, or the preference for minorities.

And so my university admission is overwhelmingly a consequence of inequality. It is not because I have been endowed with books, enrichment “programs” and, above all, educated parents – which I have – but the chance of it all. There is nothing distinctive about my application, and any objective respondent to my initial question would be lying if they answered otherwise. The stagnation of life for 98% of America works so deeply in my favor that just educational programs, or whatever, can’t explain it.

Now let me answer Nate Silver’s question. There is literally no chance that I will have problems making ends meet. I, first, have an entitlement well beyond what the government provides the poor, which is the promise that if luck and God conspire against me my parents will help out. But more than that, I know for a damned fact that people in the top quintile of America rarely ever fall out. And what of that quntile within the quintile?

And I am willing to bet – on good odds – that if Nate Silver took me to a random high school and instead of giving me a bunch of SAT scores, gave me parental occupation (as a proxy for income) I would make money – in a market where everyone else was flipping a coin. A lot of it. I am willing to bet, for example, on 300:1 odds that the son of a Yale educated lawyer and Berkley educated computer scientist (not me, by the way, but who cares same point) will never except of his own choice earn less than $50,000 a year. I’ll take 150:1 odds that he earns more than $100,000. And if I was betting against a random market, I’d make ten times as much in a tenth of the time. [In retrospect: I would not place 300:1 odds on the second bet, that is just me lying. I might place 10:1 odds, on the bet that inequality is getting worse. Regardless, this isn’t the point as much as the chance that someone in the top quintile will fall to the median, especially near the top 5%. There I am willing to place very high odds].

This is bad for all the reasons evident from moral philosophy and basic humanity. But it has deeper consequence. It engenders deep rot and complacence among those who benefit. My dad’s professor, once, told him “if your GPA falls below 3.8 [voiding your fellowship], don’t ask me for any leeway, the only thing I can give you is a free ride to the airport”. That is the stress under which people without any money study and work. Do you have any doubt that I, in that position today, would work a tenth as hard? (Not to mention the fact that both my parents worked jobs at odd hours when I am more likely to be sleeping or studying in comfort).

I would never will it upon myself, but I wish the politicians would. Say I believed there’s a 50% chance that I would earn less than $40,000 a year. That’s a high chance and would be a big drop from [the latter part of] my upbringing. I would work hard as hell to avoid that. People talk too much about inequality without the economic rot emerging from predictability: too much signal, and too little noise.

If you think that complacence doesn’t affect productivity riddle this. Each person has a normal distribution of their earning potential. The mean will be the fundamentals – IQ, attractiveness, height, charm, parental income – and the variance uncertainty thereof. Now, be careful in interpreting this, it is not the aggregate normal distribution. That means richer people may have just as high, or even higher, variance – but just from a much higher mean.

There is also reason to believe that the distribution is log-normal at the tail, implying a right skew. This is because income has a zero lower bound, but a more or less infinite upper bound (Bill Gates is effectively, if not technically, “arbitrarily” rich). Even if you believe, too optimistically, the the median American has a mean chance of success – that is he has a 1% chance of earning more than $350,000 you would see rot in the system. Because the log-normal distribution has a right skew, the 1% quantile for someone in the 1% should be higher than the .01% of the country as a whole. How high depends on your variance. But my odds would be lower than this statistical sample. By the way, if this weren’t the case, inequality would be higher. I call that good inequality. You could measure this, if you had a way of forming a good prior, as the difference between potential variance and observed variance. Of course potential is too hard to define!

Clearly the more accurately I can predict your income, the sadder meritocratic conditions are. You might put it another way: we want entropy in our socioeconomic system. We want noise. Something called the Theil Index of inequality does just this. As I explained earlier:

The math behind the measure (between 0 and 1) requires a fair understanding of information theory but the idea is lower index implies a higher economic “entropy”.

Your physics teacher might tell you that this is a bad thing (heat death and all) but, economically, it’s a little more complex. As Boltzmann showed, entropy increases as predictability of an event decreases. This means the entropy of a fair coin is higher than a biased one. Similarly, in a very equal economy it is very difficult to distinguish between two earners based only on their income. Indeed in a perfectly equal society this is impossible. However, as society stratifies itself, knowledge of ones income conveys far more information (redundancy), thereby decreasing entropy.

Within a system, Theil makes it easy for econometricians to understand the amount of total inequality due to within-group inequality and across-group inequality. If this is a little hard to grasp, think about it this way. If the total differences in economic output remained constant between countries (that is, India is still poor and Norway rich) but income was equally distributed within each country the residual inequality would be the “across-country” inequality. The residual from the converse, where all countries remain as unequal as they were, but world economic output is distributed equally to countries (not people), represents the “within-country” inequality.

It’s not the same as what I describe, but intutional similarities are clear. My bluster in making such strong bets on future income – proved through college admission – is a sign of a rotting economic system. I’ll end with a story of post-Revolution America. Divorced from British classism of lords and whatever the hell else you see on Downton Abbey, suddenly candlemakers and peasants felt good about working hard. Because class was determined by income, and gentrified Americans were suddenly at risk of loosing it all. As it ought to have been. Entropy was high in America, and low across the pond. That vibrancy crumbles every time someone like me is unfairly admitted into an institution of choice. It crumbles as the future distribution becomes so certain, that no one would believe that I may have to fry cook at McDonald’s. Part of the evil in this is that someone has the fry cook at McDonald’s (or do some other shitty job if robots take over). And because it’s not me – or anyone in the top 30% of American society – the risk is disproportionate on the bottom 30%. The rot does not come from lack of upward mobility. It comes from lack of downward mobility. I want John Boehner to make a big bet on my future potential. And I dare him not to change it once I give him my background. Because that’s the kind of society he thinks we live in.

By the way, it should come as no surprise that after 1776 American productivity shot well above Britain’s and the rest is history.

  1. This is interesting, but your essay rather skips over the “hidden priors”. For example, if intelligence is 100% genetic, and 100% meritocratic (more intelligent people earn more) then society would become very static very quickly. Big disruptions come when the skills that define a meritocracy change, because then your chance of success suddenly does become normally distributed.

    Twin studies (where twins are split up and adopted in separate families)suggest that something like 70-80% of intelligence (g-factor) is strictly genetic, and nearly all of the rest is heritable (attitude to work, availability of books etc). As feminism increased woman in the workforce, and people started to look for partners who were `more equal’, the assortivity of mating has increasingly been based on intelligence. When I read in Lincon’s biography that his mother was highly intelligent but his father not so much, I realise that that really never happens anymore. I don’t know any graduate who has married a non graduate. As in, not a single one.

    Its clear that under such circumstances inequality will rise, and its hard to see what to do about it.

    It gets even worse if intelligence is dynamic, such that working hard actually increases your intelligence, rather than just teaching you more stuff. In that case, the fact that (upper) middle-class are pretty much guaranteed a quiet place to work and parents who force them do to their homework and help them with their questions will be able to cement a cumulative advantage that may well be unassailable by the age of 18. Many studies suggest that the difference in performance by the age of five years is already pretty large. Since IQ scores are normally distributed going from 100 to 105 is not nearly as impressive as going from 130 to 135 – a point that is often overlooked.

    There are now a large variety of supposedly knowledge-neutral aptitude tests, and they all seem to show that the children of high earners are just smarter than children of the bottom quintile – even at very young ages.

    The question of how to think about this depends crucially on how much catchup is possible. I.e., how much of this is a permanent increase in capacity due to environmental factors that can seldom be replicated at a later date, and how much is strictly dynamic such that learning can catch you up.

    Sweden has an education system to die for, and much lower levels of inequality, but not really all that much more social mobility in the long run. Its true that in a more equal society, random fluctuations in earnings matter more, and so on some measures sweden looks a lot better than the US, but here over a longer period is clear that social inequality in the 18th century still determines earnings now in sweden, despite seventy years of really quite good equality of opportunity at the school level.

    So, we can do better, but if intelligence remains the determining factor in the meritocracy for a long time to come, expect more inequality of opportunity, even if we can do much better at inequality of income.

    • I am not confident about genetics one way or the other. For example, racial differences in IQ are negligible at very young ages but emerge at statistically significant levels later on. How do we make of this we know that African Americans, in general, are poorer and the kids are exposed to fewer words, books, etc.

      A progressive tax system can encourage people to work more, but let’s say it doesn’t. Let’s also say a tax system is either “progressive” or “regressive”. This is an incredibly generous simplification, but follow me for a second. If absolutely no hidden prior derives from intelligence, that is a good reason for progressive taxation to equalize opportunity we would all be a lot richer off if the many “little Einsteins” weren’t deprived of knowledge at a young age.

      Now think about a society where all hidden priors derive from genetics. I argue that for a rich society, like America, redistribution is also good, because it increases overall welfare (utilitarianism) and we just don’t want poor people. You must have similar ethics to reach this conclusion, so that’s a stumbling block. Still, in this scenario I doubt even most republicans would disagree with me. Americans hate fatalism, across the political spectrum.

      There may be a sweet spot, somewhere in between, in which the efficient option is not “progressive”. Where this is, and what it means is obscured by our definition of “progressive” and “regressive”. Are we at that spot? Near it? I don’t think so.

      By the way, it’s not scientific, and purely anecdotal but tell me what you make of this:

      • So sure, I am also quite unsure about genetic intelligence, I did not mean to come across as having a super strong view on it, more to demonstrate that it is not obvious how much inequality is about “having a silver spoon”. Sweden is a progressive’s dream, and on many (some) measures of social inequality, it is not that much better than the US. I agree with you that the US is not near “the sweetspot”, but it is a huge outlier on surveys of developed countries – I am a UK citizen, and I am much less sure about the social democracies of Europe. Schemes like the NHS are extremely progressive measures, which are often hidden from the income inequality statistics (free universal healthcare is easily worth £3000 per person of direct transfer), also since our state sector is largely state funded there is much more regulatory pressure to pick socially diverse mixes, and it seems to make almost no difference to the social mix.

        If I wanted to form a counter story to the genetic one, I think the network effect is massive. Being brought up surrounded by successful/moneyed people breeds confidence, and an articulate and engaging manner etc, all of which grooms you to succeed at interview by being “like” your successful interviewer (for high status jobs), who likely belongs to that class now, even if (s)he didn’t then. Then again, having been to Helsinki, I felt out-intellectualled by the person serving me at McDonalds, who was fluent in four languages. I have no idea if they can as easily pick class out of accent and manner as you can in the UK, or if this is a UK cultural oddity.

        I would guess that as india’s casts system breaks down, they are about to enter the golden age of social mobility that the US and UK had at the end of the nineteenth century – or possibly even earlier. Since the prior arrangements (cast/social status/etc) were largely independent of merit, merit starts off distributed equally among the classes, so you get extremely large social mobility at the change over, and then declining mobility as the new elite entrenches themselves. Although this would be the store whether that entrenchment is genetic or otherwise.

        My basic thesis is that disruption breeds social mobility, by upsetting the established order, and rendering the old pecking order, based on intelligence, martial skill, whatever, irrelevant to the new paradigm, and you find that the new skill is equally distributed across every class. Perhaps the next one will be cybernetics, or genetic enhancement, or intelligence increasing drugs, that mean that everyone will become functionally identical, operating near the limit of human potential, and character traits will become the dominant way to order society. 🙂 A man can dream eh……

  2. I also liked this graph.

    Equality of opportunity on the Y, equality of income on the X, so there is a correlation, but the real story is how all the developed nations (shown i.e. EU+USA) are down on the bottom left, but those in the process of making the transition are up in the top right. This is pretty much what I would expect – in the transition the old skills and paradigm and social statuses pass away, and there is a golden age of mobility, until the new meritocracy establishes itself.

  3. Good to see that you now agree that, Complacent, arrogant and ignorant is no way to go through life. But, speaking of making ‘wild guesses’, how do you know that everyone else’s life ‘sucks’?

    Also, do you know who Aaron Hernandez is? Scotty Pippen, Dennis Rodman? Paula Deen? They were all millionaires at one time, but no longer. Probably also happened to the guy who invented the hula hoop, the 8 track tape and the typewriter.

  4. Copy editing error: “`How confident would I be that I am where I am today, if not for inequality’ . . . the answer is an overwhelming `yes'” The answer to a non-boolean question should not be a boolean value.

    (I’d email this instead of posting as a comment, but I can’t find your email.)

    • You’re right, will edit out when I get the chance. Thanks!

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