Inter-generational mean reversion

Tyler Cowen, among many others, is intrigued by a study by Raj Chetty and others showing downward mobility of black males.

My view, which I came to in the process of reading Gregory Clark’s study of long-term heritability of income, is that inter-generational income has a large heritable component and a large random component. Over several generations, the random component washes out. But for the difference across a single generation, the random component matters.

This model suggests that when someone’s income is far above (below) the heritable component, it will revert to the mean. Children will do worse than parents who have enjoyed a positive shock and they will do better than parents who have suffered a negative shock.

If the shocks to income were normally distributed, then mean reversion would not produce any systematic pattern of children falling below parents or rising above them. So you would not expect the Chetty result in that case.

But what if the random component is not normally distributed? Suppose that what you observe in one generation are a few really large shocks on the up side, with a lot of smaller negative shocks on the down side. The next generation will then have some apparent big losers and a lot of apparent small winners. Depending on how you sort the data (Chetty appears to be looking at measures of income based on rank rather than absolute level), Chetty’s result could be an artifact of the random component. It might be that if he were to measure incomes three or four generations apart, the apparent downward mobility would disappear.

21 thoughts on “Inter-generational mean reversion

  1. “It might be that if he were to measure incomes three or four generations apart, the apparent downward mobility would disappear.”

    But then, of course, you have the problem that if you look back 3 or 4 generations, you’re dealing with 8 great-grandparents and 16 great-great grandparents. My great-grandparents were a mixed bag economically (including a lawyer, a house-painter, and a general store owner), and going back farther than that, I have little idea really (several were born outside the US).

    And, BTW, if you look at the NY Times link in the same MR post, you can see black males aren’t showing any more downward mobility than white or black women. White men are actually the unusual case is showing less reversion to the mean than other 3 groups.

  2. I think the un-PC way of reading the data: (1) the previous generation of successful black males were greater beneficiaries of affirmative action. The children of these successful men do not benefit from affirmative action as much because either (a) affirmative action benefits for males has declined a lot (possibly because of dilution; in the old days, affirmative action just went to blacks, which mostly meant black males; now it goes to blacks, women, the poor, Hispanics, the disabled, etc.) or because (b) affirmative action benefits poor blacks much more than wealthy blacks. Or it could be (2) Successful black men are disproportionately successful in fields where luck plays a huge role. In other words, a much higher percentage of successful black males are athletes, actors, or musicians.

    Explaining it by cognitive ability isn’t going to help unless there’s been some decline in the cognitive ability (though if there’s lower assortative mating in black men than in whites it could lead to a greater decline in cognitive ability; that is, if smart, successful black men prefer dim-witted wives, then it could lead to stronger reversion to the mean) or some change in the correlation between cognitive ability and success.

    The more PC way of reading the data is that (1) education is moving more towards helping female students succeed and not male students. Black males are hurt by this whereas white males are not because the white males have so much more support from their parents, so that quality of education is unimportant. Or it’s (2) the War on Drugs is leading to the arrests and convictions of more black children of affluent parents than white children of affluent parents.

  3. The random component washes out under normal distribution, but it leaves its effect in segmenting incomes.
    Each generation knows what the random variations are in income, and agents are unable to plan except that the plan indicates a gain above random. The effect of the random is to leave a wedge between income tiers.

  4. Then again, reading through the comments on Marginal Revolution, some people suggest that it’s white males that are the outliers. In other words, the regression to the mean for black males, white females, and black females are all about the same. It’s just unusually low for white males. Why would that be? Maybe whites have much higher assortative mating than blacks. Combine that with differences in the heritability of intelligence between men and women (that is, that male intelligence correlates much more closely to the intelligence of the mother, whereas female intelligence correlates much more closely to the average intelligence of both parents).

    • If intelligence is more heritable along the female line (X chromosome), then you should still see reversion to the mean of white men, since the women aren’t usually the breadwinners (although in a few years we might see black male children of successful black women showing up as another uptick). There’s probably a few families where a white women is the breadwinner to look at, but it’s going to be hard to separate from assortive mating. it also possible that there’s a lot more assortive mating among whites than blacks, which might be another explanation. Possibly successful black women are forced to “marry down” or not at all so their male children suffer more from the effects of being in a single parent family and/or lack of male role models.

    • One aspect I really wonder about with the dataset for white males is being the outlier is the timing of the 1970 – 2000 generation. So we see:

      1) White parents tended to have less children and therefore put more time and money into those children. Notice the various Asian populations this would be true and they had the upward mobility. (Yes I assume there are other variables at play here.)

      2) Being born in 1970 – 2000 there was still some parenting sexism occurring. So white couple put more emphasis on the male education etc. (This aspect probably diminished a lot after 1980.)

  5. Its no real mystery why black women are not handicapped by ability differences in the same way as are black men: employment in government. More than in any other sector, government’s use de facto hiring quotas and black women are especially desirable as two-fers. This is demonstrated by the fact that black women are disproportionately employed in government. You don’t have to get into any fancy reversion to mean theorizing to see that the male offspring of a winner in the token employment lottery faces longer odds than a female two-fer.

    Chetty’s claim in the abstract to demonstrate that differences in ability do not account for the results is a canard directly contradicted by pages 26 and 27 of the paper itself which states that there is no way to control for ability differences.

    Academics really need to get out more. It might help them avoid these embarrassing disconnects from reality that any regular joe standing down on the corner could have explained to them in 3 minutes.

    • If black females are being used as two-fers in the employment statistics game, that is actually evidence FOR continuing discrimination against black males.

  6. I think there a lot of moving pieces here and some of the multi generational impact of the past was reality that rich people had 5 children and wealth gets divided and used.
    And I do believe long term there will a race mean revision as minorities will catch up to white citizens. (Note the wages for minorities has increased more since 2012 than for white workers.) Several thoughts:

    1) Considering we are measuring African-American males of the 1970s – 2000, I assume they suffered from residual racism that increases their chances of downward mobility. We forget how hard desegreation really was and I remember in 1979 Maryland the murmuring of a good African-American moving into the neighborhood. (The family paid my friend $.50 weekly to walk with their 1st grade child to school!) Police forces searched and arrested an A-A with marijuana while turned their back to white teenage behavior. (Or schools treated them differently.) I suspect this reality diminishes over time.

    2) African-American families had more kids and less wealth to distribute. And family giving to children is not just inheritance but more likely paying for college etc.

    3) My guess African-Americans did not assortative marry as much as white people did post 1970. (I think that is the primary mover for the African-American women here.) So in many services jobs, say nurse, willingness to work unusual hours and circumstances impacts their income a lot more.

  7. This reminds me of the origins of the word ‘regression’. Francis Galton used the term because when he measured a similar phenomenon, how children compare to their parents in height, he found a heritable and random component. His insight, or what I found interesting at least, was that in a context where there are somewhat normal random shocks, the population estimate must be below one (i.e. mean-regressing) for the trend not to be explosive over generations.

    Perhaps that maps onto this example, I’m not entirely sure given your point about non-random shocks.

  8. RandomCriticalAnalysis has been tweeting out some great work on this one; definitely worth checking out. And Sailer is indispensible on anything involving Chetty.

    It really is an embarassing shame and indictment of the state of the profession and our current intellectual environment that a quasi-charlatan like Chetty who behaved like a Party propaganidst and whose claims can be reasonably rejected and dismissed at cursory inspection by perceptive amateur bloggers applying ordinary common sense is treated as some kind of celebrity wunderkind. “Market for confirmation bias,” indeed.

    Let me explain what Chetty is all about in plain language. Everybody knows that there are big and long-standing disparities between ethnic groups in America in many important variables, but given that Chetty’s working from an IRS dataset, he focuses on reported income. The question is why. Now, obviously, it’s a combination of lots of things, but there are two rival candidates for the major contributing factor, and the question really is, to put it bluntly, “Race or Racism?”

    Unless you’ve been living in a cave for the last 100 years, you know that race is the evil-person answer and racism is the right-thinking person answer, but unfortunately that doesn’t map well to “actually true in fact.”

    Which creates an enormous demand for some genius illusionist with world class data legerdemain skills to confirm the bias of right-thinking people that racism is the problem, race presents no obstacle to eradicating statistical disparities when racism is finally conquered, and that the disparities themselves providing evidence of the persistence of racism.

    And in order to do that, one must try to reject at least one theory of where “reported income” comes from that has race as a primary factor. But how does one do that if race actually is a primary factor? Easy, by rejecting a false, naive version of a race-based income model.

    For instance, let’s say the “true” model is that average income is a combination of heritable factors related to innate human capital which correlates with income, and also highly significant race-specific but inter-generationally inconsistent and dynamic cultural conditions and social promotion policies (i.e., unlike genes, one doesn’t reliably inherit the culture and social promotion advantages ones parents had), but one is testing a theory based on results being purely a result of heritable factors.

    One would be able to properly reject that particular hypothesis, sure, but the technical scientific objection is, “who cares?” because it would then be improper to then jump to the inaccurate conclusion that one had therefore produced evidence sufficient to reject all heritage-based models of income, which we can all therefore rest assured knowing that only evil people believe, despite all this scientific proof to the contrary.

    What a farce.

    • living in a cave for the last 100 years

      You mean past 100,000 years, and yes we have, but nothing wrong with cave living.

  9. One theory I have always believed is the black man’s athletic ability is a curse, in a way the opioid of the black male. Talk to any school counselor, and every black male is going to the NBA or NFL. And if that black male has a father, he will encourage that dream. But that dream is a long shot, and 99.9% do not make it, so instead of being focused on school so they can be lawyers, doctors, MBAs, or accountants they have fallen behind in school and can not catch up by the time the athletic dream fades.
    Explains why black females have done OK, but not black males.

  10. Arnold, this was my first thought as soon as I heard the results of the study! I’m glad somebody thought of this and made it known. (Though I hadn’t thought of the effect of ranking, which you mention in the last paragraph. Interesting stuff.)

    I think this might be too deep for your average talking head to explain.

  11. “Chetty’s result could be an artifact of the random component. It might be that if he were to measure incomes three or four generations apart, the apparent downward mobility would disappear.”

    This is not correct. Mean reversion would not explain Chetty’s black white gap results. The rate of mean reversion would determine the slope of the parent-child ranks but not the level of black-white difference. In the extreme case of perfect mean reversion the curve would be flat with everyone converging to the mean after one generation.

    You need to come up with a highly convoluted argument to explain the black-white gap. E.g. the last generation of blacks had an extremely positive idiosyncratic shocks or the last generation of whites had an extremely negative idiosyncratic shock. Moreover, this shock would have affected only man but not women.

  12. It’s long been known that blacks from wealthy families score lower on the SAT’s than whites from poor families. Likewise, it’s long been known that SAT scores are highly g-loaded and therefore capture cognitive ability, the most predictive single trait for success we currently know of. And the simplest explanation for this is regression to the mean. Black and white IQ means are different, so these two populations don’t regress to the same mean. This is the most parsimonious explanation for these results, imo.

  13. When an average person refuses to acknowledge a blindingly obvious reality I ask myself “Is this person an idiot, or a liar?” When it’s an academic, I ask “Is this a person who has lead such a cloistered existence their entire life that they are genuinely oblivious to this reality, or is it that the consequences of doing so will be so personally and professionally catastrophic that there’s no limit to the amount of hand-waving-kabuki-theater they’ll do to avoid acknowledging it.”

    I went to very economically and ethnically diverse public schools that were roughly 25% black, 35% everything else, and 40% white. The problem is a deeply pathological set of norms, attitudes, and behaviors embedded in black culture that there are extremely high social penalties for shunning, no matter how prosperous your parents are.

    It takes an almost superhuman level of self assurance in a young person to resist adopting a personae that will spare you from exclusion, ostracization, and abuse that awaits anyone who conspicuously fails to comply with a set of norms that satisfy peer expectations that you have sufficiently internalized an authentically black identity. The said identity has requirements, ranging from pressure to immediately and violently avenge any slight, no matter how trivial to a positive hostility towards academic achievement that essentially preclude achieving life-outcomes consistent with the American mainstream.

    The black peers that I had that were able to resist these pressures fell into three groups. Being a successful athlete, particularly in football, gave some kids enough street cred to be left alone – and being big and strong enough to beat the hell out of anyone who messed with them didn’t hurt. Then there were the kids with enough savvy and personal charisma to convince their peers that they were “down” while still maintaining good enough grades, behavior, etc to prepare themselves for a successful adulthood. There were the kids who were so hopelessly awkward, nerdy, and otherwise “white” that attempting to adopt a “hard” persona would have just invited more abuse, so they essentially just kept their heads down, suffered, and prayed for college to start.

    We didn’t have any in my school – but my perception based on african-immigrant adults is that they are able to provide a distinct identity and set of cultural norms that can effectively shield their children from the malignant social pressures that their children are exposed to as a consequence of being black. An African colleague of mine wasted no time removing his children from public schools and doing whatever was necessary to get them admitted to private religious schools. Other strategies include quietly scolding themselves for behaving like the “akata” etc. I had to struggle to avoid erupting in laughter when he described his bafflement upon seeing black teenagers idling on the street near his home after school, and very earnestly asking them “What is it that you are doing? Have you no chores? Why are you not tending to your studies?”

    I haven’t kept in touch with any of the black guys I went to junior high or high-school with, but based on what I’ve heard from classmates, what I’ve seen at high-school reunions, and here and there on social media is that all of the guys who avoided the cultural traps I described above have achieved at least a standard level of personal success and are leading happy, productive lives. Even those who were flirting with very destructive behaviors like loosely affiliating with gang members, but managed to get into the military were able to course-correct enough to get back on track and lead the same sort of lives.

    The upshot of this is that the fate of black men will improve when the set of norms, behaviors, attitudes, beliefs, etc that define the prevailing cultural archetypes for black men change. If someone were able to flip a switch and change these norms to those that prevail amongst the Nigerian Igbo who immigrate to the US, black outcomes would instantaneously become superior to those that prevail in white Americans in almost every measureable dimension. To believe otherwise is to be an idiot, a liar, or an academic hybrid of both.

    • An interesting comment, though a bit harsh.

      You can learn a lot by reading memoirs etc. written by male Black Americans who have escaped ghetto life. Old timers such as Thomas Sowell and Walter E Williams have written on it, as have slightly younger men such as Shelby Steele and a younger generation like John McWhorter, Wes Moore, and Jason Riley. Not all of those individuals came up from “the ‘hood,” and some (McWhorter, Riley) had some professional middle class family background if I recall correctly. Maybe Steele as well, though Steele has poignant tales of being terrorized by a dysfunctional teacher in his all Black suburb of Chicago, and become briefly so depressed that he could not read.

      Jason Riley has some provocative observations toward the beginning of _Please stop helping us_ about what his father did to keep him out of trouble. For one thing, his father moved the family out of the Buffalo ‘hood (“too many knuckleheads,” said he) to a neighborhood near the SUNY Buffalo Main Street campus. It also helped that Riley’s mother and sister were devout Jehovah’s Witnesses.

      I have gone to several “consciousness raising” round table encounter sessions in the Rochester area run by trained professionals. Typically they are in a public library and sponsored by the YWCA among a long list of other groups. You will hear some interesting things at those groups. A topic for another post.

      I mention those groups in part because they provide reading lists for those who like to read more about racial issues. Last I checked none of the authors I mention above were on the list, except maybe the Wes Moore title which has become popular among some book groups.

      I suspect that one big problem is there is a supply of accurate information on racial dynamics, life chances, and how to stay out of trouble but also a large supply of and strong demand for in-accurate information, well-meaning falsehoods, comfortable myths, and self-serving excuses.

      P.S.: Come to think of it, Ben Carson in his memoir / presidential aspirant book mentions making friends with the toughest athletes at his high school and helping them with their homework so that the other people at school would leave him alone.

      P.P.S. Ogbu’s research set in Shaker Heights is still significant. He has a useful theoretical/analytical distinction between caste-like groups, sectarian groups, and immigrant groups in American life. If I recall correctly, Black Americans tend toward behaving with the customs and mores and world view of a oppressed caste. Immigrants (including most Black Africans) act differently. To oversimplify.

  14. @Charles:

    As far as my tone is concerned – frank, direct, and realistic is the tone I was going for. Part of what I find maddening about the “national dialogue on race,” at least as it concerns white commentators, is that it tends to be either disingenuous or clueless. To the extent that it’s the former – it’s clear that the objective is to broadcast and validate their own personal righteousness to their peers, rather than engage in a realistic assessment of what’s keeping blacks down and therefore do something that might actually help. To the extent that it’s the latter – my conjecture is that the white people who are part of the commentariat with any kind of a mainstream platform haven’t gone to public schools or lived in areas where they’ve had any kind of sustained, un-filtered experience with black-culture.

    One vivid example of both dynamics played out at the lunch table at the research institute that I was working at. Half the table were foreign PhDs, the other half-were off-the-shelf progressive (OTSP) white women from the US. They were collectively lamenting the achievement gap between blacks and whites in the local schools. I briefly forgot myself and mentioned the social pressures that the black kids in my “college prep” classes had to negotiate over and above what white “nerd” types had to deal with. Oreo, sellout, Uncle-Tom, house negro, etc. One of the OTSPs at the table, a product of an expensive east-Coast prep-school who had spent about as much of her formative years with black people as I had spent exploring the depths of the Mariana Trench proceed to tell me that none of my lived experience was real because she had read a study informing me that it wasn’t a factor in black underperformance. This was literally less than a month after Obama’s “Acting White Speech.” Nevermind the idiocy of the notion of thinking that society would have coined and maintained an array of terms for social phenomena that no one had ever experienced.

    Finally – when you have experienced some of these pathologies first-hand it has a profound impact on your perspective and your patience. To take but one example, having your best friend (to this day) show up ashen-faced describing his escape from a shootout that erupted over a “40”* leave 12 wounded and two dead leaves you feeling slightly less indulgent, both towards the pathological behaviors and those that indulge in them, and their cloistered apologists in the media and academia.

    *40oz bottle of malt-liquor for the uber-cloistered types.

    • Thanks for your reply, and your honesty. Your tone is fine with me, by the way.

      Lord have mercy on our country!

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