Inequality and Schools

by Harry on December 12, 2011

Helen Ladd and Ted Fiske have an excellent piece in today’s Times explaining the relationship between educational inequality and income inequality, drawing on Sean Reardon’s contribution to Whither Opportunity?: Rising Inequality, Schools, and Children’s Life Chances. An excerpt:

The Occupy movement has catalyzed rising anxiety over income inequality; we desperately need a similar reminder of the relationship between economic advantage and student performance.

The correlation has been abundantly documented, notably by the famous Coleman Report in 1966. New research by Sean F. Reardon of Stanford University traces the achievement gap between children from high- and low-income families over the last 50 years and finds that it now far exceeds the gap between white and black students.

Data from the National Assessment of Educational Progress show that more than 40 percent of the variation in average reading scores and 46 percent of the variation in average math scores across states is associated with variation in child poverty rates.

International research tells the same story. Results of the 2009 reading tests conducted by the Program for International Student Assessment show that, among 15-year-olds in the United States and the 13 countries whose students outperformed ours, students with lower economic and social status had far lower test scores than their more advantaged counterparts within every country. Can anyone credibly believe that the mediocre overall performance of American students on international tests is unrelated to the fact that one-fifth of American children live in poverty?

The most striking graph in Reardon’s chapter shows the change in achievement gaps between black and white students (which declines from Brown on) against the change in gaps between children from the highest and lowest income deciles (which starts to rise as income inequality starts to rise, perhaps unsurprisingly):

More on Whither Opportunity? another time, but for now read the whole thing.



William Timberman 12.12.11 at 6:46 pm

A tragedy, isn’t it, that something so glaringly obvious needs to be tiptoed through like this? No, we can’t at the moment call down fire and brimstone on the conservative, expletive-deleted misanthropes who’re at the root of all this misery, but it would be nice to say that we ought to before proceeding on to discuss the impoverished alternatives that they’ve left us with.


mpowell 12.12.11 at 6:46 pm

Does the Black-White gap plotted here attempt to correct for income inequality between those two groups?


SamChevre 12.12.11 at 6:47 pm

The initial article seems to switch back and forth between saying “family background” and saying “poverty.” They aren’t the same thing.

I’d really like to see a study by family structure; it’s my anecdotal experience that children from stable, 2-parent families–even very low-income families–do much better than children from unstable or single-parent families. But stable families are more and more rare in lower-income demographics.


Harry 12.12.11 at 7:07 pm

absolutely true (you’ll find all this and more in the book). Your last sentence is the giveaway though.

I don’t think so, I think the black white gap is much narrower when you do that.


Watson Ladd 12.12.11 at 7:19 pm

One thing I would like to see is what the causes of this disparity are. The article blames access to extracurriculars and nutrition, but I think (as many CT commentators know already) that quite a bit of this is the result of the ability to purchase access to public schools through the real estate market, together with the political allocation of resources to schools.


Claude Fischer 12.12.11 at 11:51 pm

Nice catch, but did you have to wait for the Times?
The Reardon study was reported on this blog post in April: (and re-posted on The Berkeley Blog the next day).


lemmy caution 12.13.11 at 12:17 am

I was thinking that this had something to do with the hispanization of child poverty, but the online appendix to Reardon’s chapter shows that similar changes in the 90/10 effect exist for whites, blacks and hispanics considered separately.


joe koss 12.13.11 at 1:48 am

Interesting to read/compare this piece to the Hess/Darling-Hamilton piece that came out about a week ago.

At the time, I was left wondering if FH/LD-H deliberately narrowed their focus to really, explicitly K-12, or they just couldn’t agree on the importance of family background (at least I find it hard to believe D-H would minimize it’s importance). Now I am wondering if Ladd/Fiske’s piece is an indirect reply to them, or just a happy coincidence (knowing that op-ed pieces are usually crafted over a time-frame of greater than 5 days).

The Hess/ D-H op-ed does brilliantly underscore Ladd/ Fiske’s point though, even if it is just a happy coincidence, viz that focused policy on the family-background/ achievement matrix isn’t on “what the federal government can do well” list.

Pretty disheartening.


Watson Ladd 12.13.11 at 2:08 am

joe, there is a dead link with no url given. And I’m not sure that the feds are powerless over child poverty. They fund WIC, TANF, etc. Increasing the scope of these programs would reduce the material deprivation of those in poverty.


joe koss 12.13.11 at 2:35 am

One of these days I’ll figure out those tags:

Oh, I should have added “but ought to be” to the end of my penultimate sentence, because I absolutely agree that the fed isn’t powerless, and that alleviating family background/ child poverty is the glaring omission from Hess/ Darling-Hamilton’s “list.”

I guess more to the point on federal programs would directed policy, specific to education, especially years 3-8, the type Ladd/ Fiske talk about on page 2. Tons of research out there on this, as I am sure we are both aware of; no reason to believe funding can’t be federally driven, and outcomes federally overseen, but specifics locally driven and directed, right?


Tom T. 12.13.11 at 4:09 am

What are the units of the y-axis in that graph?


FredR 12.13.11 at 4:46 am

Is cognitive sorting a possibility, or is the conclusion that this is because, to quote from the link Claude Fischer provides, “money is “buying” more and more cognitive development” pretty robust?


Salient 12.13.11 at 5:01 am

What are the units of the y-axis in that graph?

It’s fairly standard to report aggregated test score differences in “standard deviations from the mean” (Z-scores in stats lexicon). This method normalizes the units and also normalizes the variable degree of disparity we see in test scores (one kind of test might have more widely varying scores than another). I say “it’s fairly standard” because I haven’t been able to specifically verify that Reardon does this in this instance. It just feels safe to me to assume so ’cause I’ve seen that practice elsewhere.

If my “Reardon’s using Z-scores” assumption is correct, a score of “1.00” on the vertical axis of the graph would mean that approximately 84% of all students scored better than 50% of the students in the subpopulation. (This does assume a normal distribution of test scores, which is not necessarily always in evidence. I assume that because Reardon is using Z-scores there is ample reason for me to believe the data is roughly normally distributed, but that’s piling assumptions on assumptions.) A score of 0 is parity (50% of students overall scored better than 50% of the students in the subpopulation, which is kinda sorta what you’d expect if you plucked a sufficiently large but completely random and arbitrary subpopulation out of the general population). A score of 2.00 means about 98% of students in the general population scored better than 50% of the students in the subpopulation.

My apologies if you’re familiar with Z-scores and that last paragraph was unnecessary clarification, I just didn’t want to give an unexplained answer; also my apologies to stats folks who are possibly currently tearing their hair out at my errors and abuse of everything statistics.


SamChevre 12.13.11 at 2:31 pm

And I’m not sure that the feds are powerless over child poverty. They fund WIC, TANF, etc. Increasing the scope of these programs would reduce the material deprivation of those in poverty.

And if the problem is material deprivation, this will help. If the problem is that the adults can’t help the children because the adults are illiterate, it will not help much. If the problem is that the family structures are unstable, it may well make the problem worse.


Tedra Osell 12.13.11 at 4:27 pm

SamChevre, the distinction between “poverty” and “single-parent families” strikes me as question-begging. Surely the main reason single-parent families have worse outcomes is because single-parent families are far, far more likely to be poor–and the main reason that’s true is that we’ve decided, in our collective wisdom, that single parents, the vast majority of whom are women, should live lives of enormous stress and anxiety.

E.g., trying to collect child support from non-custodial fathers–or jumping through court hoops every time non-custodial dad switches jobs to evade child support. “Owing” their child support payments back to “the system” to reimburse for welfare payments received due to not getting child support. Having to have your eligibility for said payments reassessed quarterly, which is especially ridiculous if your income fluctuates. Having to constantly juggle child care while you go out to work. Feeling shamed and beholden to your friends and family because you are constantly having to ask them to watch your kids, or pick up your kids, or loan you some money to tide you over. Having utilities turned off and on. Trying to be an involved parent at your kids’ school without compromising your paid job. Occasionally taking extortionate payday loans. Not being able to afford health care. And all without the support of another adult in the house who can help you shoulder the burden. (I believe that poverty is also a major factor in causing divorce.)

All of those examples, by the way, are real-life examples I have witnessed my close friends and family going through.


Tedra Osell 12.13.11 at 4:28 pm

Also, how does receiving financial support make unstable families *worse* off?!?


Barry 12.13.11 at 4:37 pm

Tedra, though the Magic of the Market – poor people receiving money makes them lazy.


Steve LaBonne 12.13.11 at 4:39 pm

It’s been a conservative talking point forever that giving money to rich people makes them behave better, but giving money to poor people makes them behave worse.


Watson Ladd 12.13.11 at 4:46 pm

Salient, are Z scores acceptable here? It seems like we are assuming equal variances, which is a strong assumption given that it isn’t true across genders. The sorting hypothesis would also make it not apply: the two halves of a Gaussian are not themselves Gaussian , a factor in honors course grading.

Tedra, Sam’s argument goes something as follows: let’s say two adults want to have a family and file taxes. Well, because of the bias in the tax code and welfare system for single provider families, Mommy going out to work is less good then Daddy working more. Also, some welfare benefits used to require recipients to have no one who could theoretically work in the house. But an expansion of welfare isn’t likely to change these provisions. That argument has some merit, but really if welfare isn’t working ripping it apart will make it work less.

Sam, even if adults are illiterate why should their children be? Besides, I’m sure having bread in the house helps make for a stable family: hungry people are no fun to be around.


Uncle Kvetch 12.13.11 at 5:10 pm

Also, how does receiving financial support make unstable families worse off?!?

Nothing says family stability like “Mommy and Daddy are in it for the money.”


Uncle Kvetch 12.13.11 at 5:20 pm

In case that wasn’t clear, I think the answer to Tedra’s question is that if you make life as economically difficult as possible for single parents, more people will get and stay married.

Now, how using the threat of deprivation as a way to essentially scare people into staying married promotes “family stability” is beyond me.


Tedra Osell 12.13.11 at 5:20 pm

“because of the bias in the tax code and welfare system for single provider families, Mommy going out to work is less good then Daddy working more.”

Yeah, I’m familiar with this argument. Speaking as a mommy who stays home married to a daddy who works long hours (and travels frequently), the tax code was not a really big part of our decision-making process. In fact, I would say that it never even entered our minds.

And I’m gonna go way out on a limb and say we’re probably a little more aware of financial planning and tax code bullshit than most Americans.


Tedra Osell 12.13.11 at 5:25 pm

“if you make life as economically difficult as possible for single parents, more people will get and stay married”

Translation: if women have no other options, they will stay in miserable situations longer than they should.

Which is kinda true, although again, everyone in my friends/family circle who has been in that “I can’t afford to leave” situation has been thinking in terms of how much money they make at work (or how much they think it’s reasonable to expect to make once they start working). Welfare benefits, food stamps, TANF are not on people’s radar until *after* things have gotten so bad that they’re thinking in terms of immediate survival. Then once they’ve showed up at the DV shelter the shelter folks start explaining to them how they are going to manage to feed their kids. At which point they’re able to calm down enough to start planning and doing socially approved things like “looking for a job” and “finding affordable housing”.


Watson Ladd 12.13.11 at 6:07 pm

Let’s say two people work full time at minimum wage with a single child. This gives each parent the ability to sustain the family at the poverty line for a family of three, and slightly over for a family of two. But if they are counting both incomes then they suddenly become ineligible for many programs, including SCHIP. That’s a very significant incentive to play the system. Don’t forget wealth effects and marginal utility: gaming our taxes isn’t worth it in terms of time as our time is valuable. But for a minimum wage working taking an hour to save thousands of dollars in benefits and taxes is a very valuable thing to do.


SamChevre 12.13.11 at 7:48 pm

Watson in 24 gets the main argument–if marrying, or even living together, will cost you and your family benefits eligibility, that’s a severe disincentive to living together. It’s a problem with any means-tested system that uses family income.

And Watson @ 21–if the adults are illiterate, and thus can’t read to their children, help them with schoolwork, and so forth, that’s a significant disadvantage to the children.


Salient 12.13.11 at 8:34 pm

Salient, are Z scores acceptable here?

Well, heck, I’m neither an arbiter of what’s acceptable practice nor any kind of stats authority, but Z scores seem pretty standard… Do you have a suggestion for an alternative way to report test scores in the aggregate, for comparative purposes?

It seems like we are assuming equal variances

No, we’re not. You might be thinking of standard normal distributions, with independently normalized variance. Consider this alternative: normalize the entire population’s variance, and apply that same transformation to the subpopulation, which will not normalize the subpopulation’s variance. Now we have the entire data set matching a perfect standard Gaussian, and the subset matching a nonstandard Gaussian with who knows what variance.

The weird transformation of subpopulation variance doesn’t matter at all because the only information we retrieve from that data is the median score of the subpopulation, and for normal distributions the median (= mean) is insensitive to variance transformation. Now, if I started saying something like “62% of the subpopulation scored worse than 55% of the population” you would be absolutely correct in demanding the comparison take the variances into account. But for what I said, all I need from the subpopulation is the median, and all I need to assume is that mean ≈ median in the subpopulation.

Anyhow, if this still bugs you, presumably the variance is known completely for test-takers, we have a comprehensive data set from all students (somewhere) so we could go check for discrepancies there and fiddle with that to derive statements that might better satisfy you.

The sorting hypothesis would also make it not apply: the two halves of a Gaussian are not themselves Gaussian , a factor in honors course grading.

I’m not sure I gather why you assume the subpopulation would fall entirely within the first half of the Gaussian, or whatever it is you’re saying here. Let’s assume our subpopulation sample is sufficiently large to ensure that, if it had been collected completely arbitrarily and randomly, the distribution would be close enough to identically the distribution of the whole population, with subpopulation mean ≈ entire population mean, etc. Instead, we find the subpopulation’s mean is below where we’d expect. How far below? One standard deviation from the mean, where the italicized phrases are entirely in terms of the Gaussian of the whole population.

All of this works equally well if, instead of taking a subset of a whole population, we just compare two different populations’ distributions.


StevenAttewell 12.13.11 at 8:55 pm

In terms of what the government can do about poverty and its effects on education, it’s actually quite a lot. Adult education programs for parents so they can help their kids would be one example, providing more access to child care, paid family leave, and boosting EITC/minimum wage would make it easier for parents (even single parents) to help their kids with school instead of working every hour they have, etc.

And of course, severing the property tax from education funding and establishing class-based affirmative action would also help.


Watson Ladd 12.13.11 at 9:18 pm

Salient, if we take two Gaussians, slam them on top of each other, and then create an instrument that makes that look Gaussian, neither distribution will look Gaussian. Test scores are Gaussian by convention, not nature. That makes me skeptical about statistics on subpopulations, particularly subpopulations with distinct dialects. Of course, given that this is about educational skilling it might be less of a problem: the test could be objectively measuring skill competencies. Then again they said that about Stanford-Binnet.

Sam, that wasn’t a question about causation but morality. You seem to be naturalizing the consequences of poverty to a remarkable extent. Of course what Ladd and Fiske are missing is that overall wealth was increasing over the last 50 years, yet performance wasn’t to the same extent. Instrumenting this is going to be a PITA, and possibly impossible: what is being taught has changed dramatically.


Tedra Osell 12.13.11 at 9:31 pm

“if marrying, or even living together, will cost you and your family benefits eligibility, that’s a severe disincentive to living together. ”

Bollocks. I could receive TANF, etc., if I lived alone, sure; and yet I stay married.

Because marriage/living together isn’t primarily an economic decision. I’m going to assume that the claim that a single adult “work[ing] full time at minimum wage with a single child” can “sustain the family at the poverty line for a family of three, and slightly over for a family of two” is correct–although I seriously doubt it–but, as we all know, the poverty line is not, actually, a sustainable standard of living. Especially if we are assuming that a minimum wage job isn’t providing things like health insurance, which they mostly don’t. So your single parent working a f-t minimum wage job has zero backup if they lose their job, has almost no ability to switch jobs if they are unhappy (when, exactly, are you supposed to job hunt if you work full time and have a couple of kids?), certainly isn’t able to save for a rainy day or a kid’s education, and is royally fucked if they *or their kid* get sick (someone has to stay home with the sick kid).

If you have a halfway decent partner (who also makes minimum wage), otoh, you have emotional support, some kind of income even if you lose your own job, someone else who can hopefully take an occasional sick day so that you guys can collectively manage not to lose your jobs if your kid(s) get sick, and *maybe* you’re making enough money that you can manage to save a few hundred bucks for Xmas at the end of the year. You still probably lack health insurance, but it’s a little easier for one of you to look for a job that provides it. You’re still going to have a devil of a time saving, and any unexpected expense (car problems, needing to move, backed-up toilet) is going to be a crisis, but it crises are a lot easier to handle if there’s another adult around to do some of the heavy lifting.

The problem with the “incentives against marriage” argument is that it’s wildly unrealistic about why people get married. Even if you’re not liberal enough (I am) to think that people who work between them two full-time jobs might should be able to make enough money to live a modest comfortable existence, have a nest egg and health insurance and be able to save enough to send their kids to a state college (and that if they can’t do those things, then why the fuck *not* provide benefits that make those things possible?), you ought at least to recognize that financial “disincentives to marriage” are ridiculously out of touch with how people live their lives.


Daniel 12.13.11 at 9:41 pm

I don’t think the method of z-scores does assume equal variance. Surely the point of transforming the data to a z-score is to normalise each sample by its own variance?


Watson Ladd 12.13.11 at 10:03 pm

Daniel, that’s the problem. If we normalize the whole population it doesn’t normalize the subgroups. Note also that many skills have a pretty big ceiling not many reach: if the Sistine Chapel is a 10, most good art isn’t even a 4. So normalization is really an artifice to make the test easy to analyze.

Tedra, I went and looked those numbers up and did the calculation of how much someone on minimum wage makes if they work 46 weeks at 40 hours each. Medicare covers the child health insurance only if the family is at or below the poverty line. In your situation being together isn’t materially affecting your quality of life: for the hypothetical 2 person 1 child family it is. The value of TANF isn’t more then love when you have a lot of food. When starving it is. So comparisons to your situation or viewing your decisions as normative are very misleading.

Sam, it was a question of morality, not causation. Why do we let a cycle of illiteracy persist?


Salient 12.13.11 at 10:07 pm

Salient, if we take two Gaussians, slam them on top of each other, and then create an instrument that makes that look Gaussian, neither distribution will look Gaussian.

You’re misrepresenting what I described, possibly ’cause you’re misunderstanding. We don’t slam one Gaussian on top of another. I don’t even have the slightest clue what that could mean. We don’t create an instrument that makes “that” look Gaussian. I don’t even know what the “that” in your sentence is, and it’s unclear to me what this “instrument” is you’re envisioning. Never, at any time, did I combine two distributions. Not in any way, shape, or form. Whatever gave you that impression was misunderstood.

Now, if you’re “skeptical about statistics on subpopulations” to the extent that you do not acknowledge the validity of comparing two means from two different populations, period, then your beef isn’t with me or with Reardon or with me, it’s with, I dunno, statistics as a discipline. Computing a mean is of rather limited value if it’s impossible to reasonably compare it to another mean, don’t you think?

On the other hand, if you’re not using skepticism to mean “blanket disapproval” then this practice is really fairly robust against your complaints:

Say you have two numbers. They are some distance apart. You want to describe how far apart they are. Specifically you want to describe “How far away from A is B?” where we think of A as a kind of central value, maybe from a control group, whatever. Ok, so you measure the horizontal distance from A to B. It’s 12. But, 12 what? That means what? You realize the horizontal units are problematic. You need some unit of measurement that somehow “naturally arises” from A, so that “distance from A” is meaningful in terms of A, hopefully independent of the existing horizontal units, which we are assuming are arbitrary and not intrinsically meaningful.

You discover that A is the mean of {something}. This implies the existence of a metric that is meaningful in terms of A: the Z-score of the number B, with respect to the standard deviation in {something}. It actually doesn’t matter where B came from (so long as it’s in the same units as A so that “distance from A to B” makes sense).

Now you have a way of describing the distance from A to whatever. You have a horizontal unit. Use that unit to measure the distance from A to B. Report the result. Why is this a problem? Moreover, why is “a point is one unit from mean A if it is one standard deviation away from A” any more problematic than any other unit you could possibly use — what units should we be using?


Watson Ladd 12.14.11 at 12:00 am

Salient, these are test scores. The test is designed to give Gaussian answers. And in your A and B example the answer depends on the distributions of A and B, not just on A. Any answer should be symmetric. My point is simple: since the test gives Gaussian answers when administered to everyone, if the population is composed out of two separate subpopulations at least one of the subpopulations is not Gaussian. That’s what the issue is.

As for resizing why is variance in skill the relevant criterion for sizing skill imbalances? It seems that the disadvantages faced by someone not being able to do math are not changed by the variance in that skill.


Salient 12.14.11 at 12:56 am

Salient, these are test scores.

I did not know that. Why, that changes everything.

Comments on this entry are closed.