On the relationship between school suspensions, race, single-motherhood, and more.

As a follow up to my prior post on single-motherhood and mobility and in response to various assertions of discrimination against blacks in the school system, I decided to take a data-driven look into the relationship between race and school suspension rates.

There is, of course, ample evidence that discipline rates vary dramatically between racial/ethnic groups.

Microsoft Excel

Blacks get suspended at vastly disproportionate rates whereas “asians” (census/OMB definition), on the other hand, are about half as likely as whites are to get suspended.  Contrary to conventional wisdom, though, this pattern tends to be pretty consistent nation wide and the south is not notably “worse” with respect to disparities here.

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On Philip Cohen’s knee-jerk response to Chetty’s “causal mobility” data and its association with single-motherhood

Philip Cohen, a sociologist that blogs at Family Inequality, recently argued, in response to the proposition that single-motherhood is strongly associated with economic mobility, that the single-motherhood effect is “entirely in the % black effect”.

While I do not necessarily disagree with the notion that racial demographics are strong predictors (albeit probably for different reasons than he does) and I do not necessarily believe that the single-motherhood association is (mostly) causal, his strong language is clearly at odds with the data.  In fact, his statements are not even well supported by his own stats.

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On educational attainment rates and income as a causative factor

As I mentioned to Robert VerBruggen in his latest piece on educational attainment and income, I do not believe that economic concerns are a major cause of differences in education attainment rates by income.

I previously analyzed this and related issues using the ELS:2002 data, but I decided to extend my analysis with NLSY97 and clarify my views, now that I have marshaled a fair amount of data to support my arguments.


Although the IQ (ASVAB) is an excellent predictor and generally mediates these differences fairly well, there are other systematic differences that are not fully accounted for when you control for IQ.   High SES people, whether measured by income or educational attainment, typically have higher GPAs even with the same test scores.



(these differences would likely to be larger still if I did this as a composite SES index using education, income, occupational prestige, etc)

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Understanding socioeconomic mobility

Although it may not seem like it at first blush, given the apparently modest correlations, the socioeconomic figures that I blogged about earlier largely agree with the published data on economic mobility.

They are measuring income (or earnings) whereas I am measuring with the ELS SES index (which is an equally weighted average of the respondents own earnings as of 2011, educational attainment, and occupational prestige), but the systematic income differences between classes (however measured) are almost certainly virtually fully mediated by this more comprehensive SES measure.

ELS data, students 2011 SES by 2002 SES of parents


The correlation between parent SES and child SES is 0.35.  This may not sound like much, but if you bin child SES and parent SES into quintiles the mobility estimates are very similar to the widely publicized economic mobility estimates.

Microsoft Excel (1)

Microsoft Excel

The average person born at the top of the SES distribution has little chance of ending up at the bottom and vice versa, but there is clearly a great deal of mobility that happens amongst less extreme groupings.

[Note: I didn’t correct these figures for oversampling, so I won’t claim they’re a perfect representation of reality, but they are generally pretty close in practice and they still are good for illustrative purposes.]

Mobility delta (child SES – parent SES) by parent SES


On average, as compared to their parents, high SES people are downward mobile and low SES people are upward mobile.  This may seem counter-intuitive to some, but this makes sense because r < 1, i.e., there is non-trivial mobility, and this must be true for there to be meaningful relative mobility.  Of course, just because there is mobility doesn’t imply that all people have an equal chance of ending up in any place in the SES distribution.

As I mentioned in my last post, there are other differences between groups besides just propensity to end up in particular SES bins and many of these differences are highly predictive of mobility — see test scores, HS GPA, etc.  Indeed, they almost fully mediate outcomes, so talking in terms of “mobility” here can be a bit misleading because relative starting position (parent SES) tells you relatively little about what is likely once you have better information (e.g., test scores, HS GPA, etc).

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Predicting economic mobility from 10th grade test scores

In my last post I briefly touched upon economic mobility vis-a-vis the link between test scores and subsequent adult incomes.  Because these individuals were still pretty young, just a few years out of college (if they graduated), the earnings correlations were weaker than one might have expected.  Since then I discovered an interesting continuous SES variable (F3SES) in the ELS:2002 data set that is probably a better measure of future earnings or mobility.

F3SES is the average of 3 inputs (2011 earnings from employment, the prestige score associated with the respondents current/most recent job, and educational attainment), each of which is standardized to a mean of 0 and a standard deviation of 1 prior to averaging.

Data users should note that, as of the third follow-up, socioeconomic status may be less-than fully stable for some third follow-up respondents, e.g., respondents with graduate-level education who are just beginning or have yet to begin their careers.  Users should also note that F3SES does not account for the income, occupation, or education of the respondents spouse/partner, and therefore may not be fully indicative of household socioeconomic status as of the third follow-up.

NOTE: While the two versions of the BY family SES composites (BYSES1 and BYSES2) were created by differential assignment of prestige scores based on the 16-category BY occupation variables, F3SES is created by assigning prestige scores based on the 2-digit ONET code associated with the respondents current/most recent job as of the third follow-up.

While I am sure I could derive my own formula to produce a similar composite score, I’ll just use theirs for the time being.



There is no statistically significance difference between blacks and whites here.


Asian SES is higher than white SES for most of the distribution, but that’s not statistically significant either.

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Exploring ELS 2002 data

The NYTimes turned me onto a new data source in a recent article on college graduation rates by SES.  They implied that college graduation rates are better predicted by “wealth” than by the students test scores (10th grade ELS scores taken in 2002).

Google Chrome

Being both curious about the underlying data and somewhat skeptical of the particular claims (or, at least, its interpretation) I decided to investigate it for myself.  Having done so now, I can tell you that it’s a pretty rich data set.  Unfortunately, a few key data points (e.g., SAT scores, HS GPA, etc) are censored or rounded/binned to protect anonymity, but there are still a lot of interesting data there to analyze.


Update (6/6/15):

As in my follow-up post on economic mobility, I realized that they actually provided 9th-12th grade high school GPA as a non-continuous variable in the publicly accessible file.  I have updated my post to reflect this new information in a few places!

First point

The parent’s educational attainment is a much better predictor of both test scores and subsequent child educational attainment than economic measures…..

 (Bachelor degree) Attainment rate by test scores, grouped by parent income levels


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