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.

First

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.

gpa_by_asvab_income_b5

hsgpa_by_asvab_fed

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

Second

High SES people are more likely to attend relatively competitive high schools where their (average) course loads are larger and the grading standards are higher.   This stands to reason given the different average ability between different communities and relative minimal differences in average  GPA, but it can also be observed in the data.

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(The cohort of low-income students is the fraction that actually went to college, who are probably better prepared and more motivated than their average HS class mate.  It’s somewhat of a range restriction issue.  The real-world, population-wide, difference is probably considerably larger than this)

Third

Although the SAT and ASVAB are strongly correlated (r=~0.86) and predict similar outcomes for most groups, those relationships are not exactly the same for all groups at all points in the score distribution. sat_by_pred_asvab_fed

sat_by_asvab_by_parents_income_b3

(this should read 1997, not 2007 🙂

Some of this is probably regression towards the mean, some of this is apt to be the cumulative effect of differences in studying rates and motivation (independent of school “quality”), and some of this is probably due to some differences in the the competitiveness of the schools people attend (which would be less of an issue if we had more and better academic tracking).

Fourth

If we control for ASVAB, HS GPA, and HS graduation status in a simple linear model we can close much of this gap.

bachpred_by_asvab_hsgpa_hsgrad_pincomeb3 bachpred_by_asvab_hsgpa_hsgrad_pincomeb3_LM

bachrate_by_asvab_hsgpa_fed

bachrate_by_asvab_hsga_fedLM

(You might also notice that the parent education gap is much larger than the parent income gap above!)

Fifth

Even if we just control for SAT scores, the differences are quite small.

bsrate_by_sat_comp_income_b3

bachrate_by_sat_fed

It’s clearly a better predictor than ASVAB alone.  Some of that is apt to be varying levels of interest (people that aren’t even interested in college aren’t likely to sit for the SAT at all), but that goes to my point (it’s not all economics).

Sixth

If we improve the model using SAT, HS GPA, and HS graduation status (which is pretty similar to the primary criteria schools make admissions decisions with), the differences shrink further still.

bsrate_pred_by_pincomeb3

bsrate_by_sathsgpa_fed

Seventh

There are differences in propensity to even sit for the SAT in the first place.

sat_take_by_hsgpa_pincomeb3 sat_take_rate_by_iq_pincomeb3

If we combine IQ and HS GPA together (mainly) these differences largely shrink through…

sat_take_pred_by_fed sat_take_pred_by_iq_hsgpa_byincome_b3

Or in linear mode to smooth out the random noise a bit…

sat_take_by_fed_lm sat_take_pred_income_lm

(again, you might notice that the education delta is much larger than the income delta)

Eighth

There are clear differences in college aspirations by SES, even when you control for GPA or test scores.

colq_by_asvab_fed

colq_by_iq

colq_by_gpa_fed colq_by_hsgpa

Ninth

As with differences between other groups, some of this is apt to be cultural.

colq_by_iq_raceeth

bachrate_by_gpa_raceeth bachrate_by_iq_raceeth

bachrate_pred_by_rebachrate_pred_by_re_LM

bachpred_sat_hsgpa_raceeth bachpred_sat_hsgpa_raceeth_LM

Tenth

If we control directly for several key factors that we know matter, specifically race/ethnicity, sex, and the parents education level, the difference is smaller still.

bachrate_pred_6way_by_pincomeb3bachrate_pred_6way_by_pincomeb3_LM

(r=0.63 for this model)

aggregate_pred_with_ped

(Assuming the actual relationships are strictly linear throughout the entire distribution, this might be a better way of dealing with outliers/regression toward the mean)

Long story short, the maximum percentage point difference potentially attributable to income differences, holding other things roughly equal, is probably 7% or less, possibly quite a bit less.   That difference may not even be mostly economic concerns as income is also correlated with other important characteristics like actual college readiness differences (imperfect GPA comparisons), parental ability (which is relevant due to measurement error of juvenile IQ, in particular, and imperfect correlations with future ability), educational priorities, etc that aren’t perfectly controlled with parental education either [as in, a bachelors in elementary education and a BSEE have the same degree for these purposes, but the BSEE on average will be significantly more intelligent, better educated, and earn more.  The reason why the BSEE’s children are likely to perform better on average isn’t necessarily attributable to income…].

The best predictors of educational attainment are clearly, by far, cognitive ability and high school GPA, followed distantly by parental educational attainment and race/ethnicity (and probably good direct measurements of interest in pursuing higher ed).   Poor high IQ students with top grades actually attend college at very similar rates as high income students with similar stats.  Rich but low IQ students with marginal grades have similarly lousy educational attainment as their poor counterparts. The differences in average educational attainment rates between income groups is mostly attributable to large average differences in IQ/test scores, HS GPA, and the like.

That reality is a far cry from the argument in the NYTimes that the actual cause of differences between groups can almost entirely be attributed to economic concerns (never mind that their groups here are actually SES index groups, not merely income, as in, it includes and is heavily weighted towards parents education levels and their occupational categories/prestige…).

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I do not believe these differences are entirely genetic, although that is clearly a large part of it.

Google Chrome Google Chrome (1)

Google Chrome Google Chrome (1)

However, just because parents/family background probably also “matters” for some environmental reasons does not mean that that is caused by economic considerations, school “quality” (especially not in the exogenous sense), and the like or that we can readily mitigate these differences through any kind of feasible policy prescription.  Some groups clearly put a much greater emphasis on education than others, but these differences don’t just magically appear in 12th grade.  The differences run deeper and start much much earlier.  They can be found in K-12 GPA, average course loads, discipline, classroom behavior, etc.  Without actually addressing those underlying issues simply engaging in more efforts to send yet more people to college starting in 12th grade, where many people today fail out already or graduate with little, to nothing, to show for it, isn’t apt to do much to close these gaps and will likely just waste time and resources.

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3 thoughts on “On educational attainment rates and income as a causative factor

  1. I’m not arguing that it makes absolutely no difference whatsoever, but that: (1) the residual associated with income is quite small (2) that effect is likely concentrated at the very bottom of the (post-tax, post-transfer) income distribution (3) it’s likely that that much residual effect is likely a spurious relationship….

    Parental income is *also* associated with greater parental education, higher marriage/lower divorce rates, greater emphasis on education, etc in ways that are likely not causative. [Which is not to say that this is “fair” in a metaphysical sense, but that the parents’ economic means are a very small piece of this puzzle–genetics, culture, parent education, family idiosyncratic differences etc drive most of this].

    Murray’s analysis and arguments are generally consistent with mine:

    Now let’s look at the income effect in the PIAT when the mother’s IQ is statistically held constant at the national average of 100. Going to a $200,000 family income from a $1,000 family income raises the score only to the 76th percentile from the 50th—an increase of 26 percentiles. More important, almost all of the effect occurs for people making less than $125,000. Going to $200,000 from $125,000 moves the PIAT score only to the 76th percentile from the 73rd—a trivial change. Beyond $200,000, PIAT scores go down as income increases.

    In assessing the meaning of this, it is important to be realistic about the financial position of families making $125,000 who are also raising children. They were in the top quartile of income distribution in 2013, but they probably live in an unremarkable home in a middle-class neighborhood and send their children to public schools. And yet, given mothers with equal IQs, the child whose parents make $125,000 has only a trivial disadvantage, if any, when competing with children from families who are far more wealthy.

    Why should almost all of the income effect be concentrated in the first hundred thousand dollars or so? The money itself may help, but another plausible explanation is that the parents making, say, $60,000 are likely to be regularly employed, with all the things that regular employment says about a family. The parents are likely to be conveying advantages other than IQ such as self-discipline, determination and resilience—“grit,” as this cluster of hard-to-measure qualities is starting to be called in the technical literature.

    Families with an income of, say, $15,000 are much more likely to be irregularly employed or subsisting on welfare, with negative implications for that same bundle of attributes. Somewhere near $100,000 the marginal increments in grit associated with greater income taper off, and further increases in income make little difference.

    Keep in mind that I *not* arguing it is entirely genetic or that even the genetic effects are purely through IQ (there are other heritable traits that are weakly-to-moderately correlated with IQ but that effect education levels and the like). Also, Murray only has access to the mother’s IQ score, not the fathers. It’s highly likely that, holding maternal IQ equal, higher income implies a higher IQ father too (not to mention higher education, etc etc… as in, unmeasured genetic, culture, and other differences associated with the extra income).

    Btw-you might want to take a look at this quantitive genetic study on educational attainment (GCSE scores in the UK)…

    http://www.pnas.org/content/111/42/15273.full.pdf

    (Heritability of educational attainment is high and IQ only accounts for about half of it)

    Let’s throw parental education into the analysis so that we can examine the classic indictment of the SAT: the advantage a child of a well-educated and wealthy family (Sebastian, I will call him) has over the child of a modestly educated working-class family (Jane). Sebastian’s parents are part of the fabled 1%, with $400,000 in income, and his mother has a college degree. But her IQ is only average. Jane’s family has an income of just $40,000 and mom has only a high-school diploma. But mom’s IQ is 135, putting her in the top 1% of the IQ distribution.

    Which child is likely to test higher? Sebastian is predicted to be at the 68th percentile on the PIAT. Jane is predicted to be at the 78th percentile. If you want high test scores, “choose” a smart but poor mother over a rich but dumb one—or over a rich and merely ungifted one.

    ***

    If income per se causes these observed differences, we should expect exogenous wealth transfers to boost scores substantially. We generally don’t find this in practice in the first world.

    https://ideas.repec.org/p/hhs/iuiwop/1060.html

    (Study of Swedish lottery winners w/ ~0 change in child cognitive measures)

  2. Very interesting. I would honestly like to see a comprehensive large scale study that measures all of the different traits of both parents, all of the different traits of the child, the income over time, the consumption over time, the specific level of education (as in selectivity of the college, performance in college, number of years in college for dropouts), and much more. This would be a fair way to settle the debate where both sides could feel reasonably confident about the truth. At the same time, I realize that this is not likely to happen because of logistical difficulties. On your point about income, here is a White House fact sheet that cites a large number of studies that look at staggered roll out of welfare programs to conclude that there is a benefit to children from transfers. Thoughts on this? https://www.whitehouse.gov/blog/2015/05/11/six-examples-long-term-benefits-anti-poverty-programs

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