<?xml version="1.0" encoding="UTF-8" standalone="yes"?><oembed><version><![CDATA[1.0]]></version><provider_name><![CDATA[Random Critical Analysis]]></provider_name><provider_url><![CDATA[https://randomcriticalanalysis.wordpress.com]]></provider_url><author_name><![CDATA[rcafdm]]></author_name><author_url><![CDATA[https://randomcriticalanalysis.wordpress.com/author/rcafdm/]]></author_url><title><![CDATA[On educational attainment rates and income as a causative&nbsp;factor]]></title><type><![CDATA[link]]></type><html><![CDATA[<p>As I mentioned to Robert VerBruggen in his latest piece on <a href="http://www.realclearpolicy.com/blog/2015/06/03/when_it_helps_to_have_rich_parents_1316.html" target="_blank">educational attainment and income</a>, I do not believe that economic concerns are a major <em>cause</em> of differences in education attainment rates by income.</p>
<p><a href="http://www.realclearpolicy.com/blog/2015/06/03/when_it_helps_to_have_rich_parents_1316.html"><img class="aligncenter" src="https://i1.wp.com/www.realclearpolicy.com/images/wysiwyg_images/RichParentsandBAs.jpg" alt="" /></a></p>
<p>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.</p>
<p><span style="text-decoration:underline;"><strong>First</strong></span></p>
<p>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.</p>
<p><a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/gpa_by_asvab_income_b5.png" target="_blank"><img class="aligncenter wp-image-2453 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/gpa_by_asvab_income_b5.png?w=925&#038;h=851" alt="gpa_by_asvab_income_b5" width="925" height="851" /></a></p>
<p><a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/hsgpa_by_asvab_fed.png" target="_blank"><img class="aligncenter wp-image-2454 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/hsgpa_by_asvab_fed.png?w=925&#038;h=851" alt="hsgpa_by_asvab_fed" width="925" height="851" /></a></p>
<p style="text-align:center;">(these differences would likely to be larger still if I did this as a composite SES index using education, income, occupational prestige, etc)</p>
<p style="text-align:center;"><!--more--></p>
<p><span style="text-decoration:underline;"><strong>Second</strong></span></p>
<p>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.</p>
<p><a href="https://research.collegeboard.org/sites/default/files/publications/2012/8/researchreport-2012-5-validity-academic-rigor-index-fygpa.pdf" target="_blank"><img class="aligncenter wp-image-2359 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/google-chrome8.png?w=790&#038;h=795" alt="Google Chrome" width="790" height="795" /></a></p>
<p><em>(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&#8217;s somewhat of a range restriction issue.  The real-world, population-wide, difference is probably considerably larger than this)</em></p>
<p><span style="text-decoration:underline;"><strong>Third</strong></span></p>
<p>Although the SAT and ASVAB are strongly correlated (r=~0.86) and predict <em>similar</em> outcomes for most groups, those relationships are not exactly the same for <em>all</em> groups at <em>all</em> points in the score distribution. <a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/sat_by_pred_asvab_fed1.png" target="_blank"><img class="aligncenter wp-image-2455 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/sat_by_pred_asvab_fed1.png?w=965&#038;h=998" alt="sat_by_pred_asvab_fed" width="965" height="998" /></a></p>
<p><a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/sat_by_asvab_by_parents_income_b3.png" target="_blank"><img class="aligncenter wp-image-2456 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/sat_by_asvab_by_parents_income_b3.png?w=1256&#038;h=976" alt="sat_by_asvab_by_parents_income_b3" width="1256" height="976" /></a></p>
<p style="text-align:center;">(this should read 1997, not 2007 <span class='wp-smiley wp-emoji wp-emoji-smile' title=':-)'>:-)</span></p>
<p>Some of this is probably <a href="http://emilkirkegaard.dk/understanding_statistics/" target="_blank">regression towards the mean</a>, some of this is apt to be the cumulative effect of differences in studying rates and motivation (independent of school &#8220;quality&#8221;), 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).</p>
<p><span style="text-decoration:underline;"><strong>Fourth</strong></span></p>
<p>If we control for ASVAB, HS GPA, and HS graduation status in a simple linear model we can close much of this gap.</p>
<p><a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachpred_by_asvab_hsgpa_hsgrad_pincomeb31.png" target="_blank"><img class="aligncenter wp-image-2479 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachpred_by_asvab_hsgpa_hsgrad_pincomeb31.png?w=925&#038;h=742" alt="bachpred_by_asvab_hsgpa_hsgrad_pincomeb3" width="925" height="742" /></a> <a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachpred_by_asvab_hsgpa_hsgrad_pincomeb3_lm2.png" target="_blank"><img class="aligncenter wp-image-2480 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachpred_by_asvab_hsgpa_hsgrad_pincomeb3_lm2.png?w=925&#038;h=742" alt="bachpred_by_asvab_hsgpa_hsgrad_pincomeb3_LM" width="925" height="742" /></a></p>
<p><a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachrate_by_asvab_hsgpa_fed.png" target="_blank"><img class="aligncenter wp-image-2481 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachrate_by_asvab_hsgpa_fed.png?w=925&#038;h=742" alt="bachrate_by_asvab_hsgpa_fed" width="925" height="742" /></a></p>
<p><a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachrate_by_asvab_hsga_fedlm.png" target="_blank"><img class="aligncenter wp-image-2482 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachrate_by_asvab_hsga_fedlm.png?w=925&#038;h=742" alt="bachrate_by_asvab_hsga_fedLM" width="925" height="742" /></a></p>
<p style="text-align:center;"><em>(You might also notice that the parent education gap is much larger than the parent income gap above!)</em></p>
<p><span style="text-decoration:underline;"><strong>Fifth</strong></span></p>
<p>Even if we just control for SAT scores, the differences are quite small.</p>
<p><a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/bsrate_by_sat_comp_income_b3.png" target="_blank"><img class="aligncenter wp-image-2457 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/bsrate_by_sat_comp_income_b3.png?w=1054&#038;h=819" alt="bsrate_by_sat_comp_income_b3" width="1054" height="819" /></a></p>
<p><a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachrate_by_sat_fed.png" target="_blank"><img class="aligncenter wp-image-2458 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachrate_by_sat_fed.png?w=925&#038;h=742" alt="bachrate_by_sat_fed" width="925" height="742" /></a></p>
<p>It&#8217;s clearly a better predictor than ASVAB alone.  Some of that is apt to be varying levels of interest (people that aren&#8217;t even interested in college aren&#8217;t likely to sit for the SAT at all), but that goes to my point (it&#8217;s not all economics).</p>
<p><b><u>Sixth</u></b></p>
<p>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.</p>
<p><a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/bsrate_pred_by_pincomeb3.png" target="_blank"><img class="aligncenter wp-image-2459 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/bsrate_pred_by_pincomeb3.png?w=1078&#038;h=781" alt="bsrate_pred_by_pincomeb3" width="1078" height="781" /></a></p>
<p><a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/bsrate_by_sathsgpa_fed.png" target="_blank"><img class="aligncenter wp-image-2460 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/bsrate_by_sathsgpa_fed.png?w=1083&#038;h=875" alt="bsrate_by_sathsgpa_fed" width="1083" height="875" /></a></p>
<p><span style="text-decoration:underline;"><strong>Seventh</strong></span></p>
<p>There are differences in propensity to even sit for the SAT in the first place.</p>
<p><a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/sat_take_by_hsgpa_pincomeb3.png" target="_blank"><img class="aligncenter wp-image-2461 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/sat_take_by_hsgpa_pincomeb3.png?w=1091&#038;h=808" alt="sat_take_by_hsgpa_pincomeb3" width="1091" height="808" /></a> <a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/sat_take_rate_by_iq_pincomeb3.png" target="_blank"><img class="aligncenter wp-image-2462 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/sat_take_rate_by_iq_pincomeb3.png?w=925&#038;h=742" alt="sat_take_rate_by_iq_pincomeb3" width="925" height="742" /></a></p>
<p>If we combine IQ and HS GPA together (mainly) these differences largely shrink through&#8230;</p>
<p><a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/sat_take_pred_by_fed.png" target="_blank"><img class="aligncenter wp-image-2463 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/sat_take_pred_by_fed.png?w=925&#038;h=742" alt="sat_take_pred_by_fed" width="925" height="742" /></a> <a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/sat_take_pred_by_iq_hsgpa_byincome_b3.png" target="_blank"><img class="aligncenter wp-image-2464 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/sat_take_pred_by_iq_hsgpa_byincome_b3.png?w=1011&#038;h=842" alt="sat_take_pred_by_iq_hsgpa_byincome_b3" width="1011" height="842" /></a></p>
<p>Or in linear mode to smooth out the random noise a bit&#8230;</p>
<p><a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/sat_take_by_fed_lm.png" target="_blank"><img class="aligncenter wp-image-2465 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/sat_take_by_fed_lm.png?w=925&#038;h=742" alt="sat_take_by_fed_lm" width="925" height="742" /></a> <a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/sat_take_pred_income_lm.png" target="_blank"><img class="aligncenter wp-image-2466 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/sat_take_pred_income_lm.png?w=925&#038;h=742" alt="sat_take_pred_income_lm" width="925" height="742" /></a></p>
<p style="text-align:center;"><em>(again, you might notice that the education delta is much larger than the income delta)</em></p>
<p><b><u>Eighth</u></b></p>
<p>There are clear differences in college aspirations by SES, even when you control for GPA or test scores.</p>
<p><a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/colq_by_asvab_fed.png" target="_blank"><img class="aligncenter wp-image-2468 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/colq_by_asvab_fed.png?w=925&#038;h=742" alt="colq_by_asvab_fed" width="925" height="742" /></a></p>
<p><a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/colq_by_iq.png" target="_blank"><img class="aligncenter wp-image-2471 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/colq_by_iq.png?w=1122&#038;h=842" alt="colq_by_iq" width="1122" height="842" /></a></p>
<p><a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/colq_by_gpa_fed.png" target="_blank"><img class="aligncenter wp-image-2469 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/colq_by_gpa_fed.png?w=925&#038;h=742" alt="colq_by_gpa_fed" width="925" height="742" /></a> <a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/colq_by_hsgpa.png" target="_blank"><img class="aligncenter wp-image-2470 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/colq_by_hsgpa.png?w=925&#038;h=742" alt="colq_by_hsgpa" width="925" height="742" /></a></p>
<p><b><u>Ninth</u></b></p>
<p>As with differences between other groups, some of this is apt to be cultural.</p>
<p><a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/colq_by_iq_raceeth.png" target="_blank"><img class="aligncenter wp-image-2472 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/colq_by_iq_raceeth.png?w=1252&#038;h=856" alt="colq_by_iq_raceeth" width="1252" height="856" /></a></p>
<p><a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachrate_by_gpa_raceeth.png" target="_blank"><img class="aligncenter wp-image-2473 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachrate_by_gpa_raceeth.png?w=1032&#038;h=816" alt="bachrate_by_gpa_raceeth" width="1032" height="816" /></a> <a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachrate_by_iq_raceeth.png" target="_blank"><img class="aligncenter wp-image-2474 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachrate_by_iq_raceeth.png?w=1050&#038;h=820" alt="bachrate_by_iq_raceeth" width="1050" height="820" /></a></p>
<p><a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachrate_pred_by_re.png" target="_blank"><img class="aligncenter wp-image-2484 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachrate_pred_by_re.png?w=1077&#038;h=769" alt="bachrate_pred_by_re" width="1077" height="769" /></a><a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachrate_pred_by_re_lm.png" target="_blank"><img class="aligncenter wp-image-2483 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachrate_pred_by_re_lm.png?w=925&#038;h=742" alt="bachrate_pred_by_re_LM" width="925" height="742" /></a></p>
<p><a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachpred_sat_hsgpa_raceeth.png" target="_blank"><img class="aligncenter wp-image-2485 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachpred_sat_hsgpa_raceeth.png?w=925&#038;h=742" alt="bachpred_sat_hsgpa_raceeth" width="925" height="742" /></a> <a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachpred_sat_hsgpa_raceeth_lm.png" target="_blank"><img class="aligncenter wp-image-2486 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachpred_sat_hsgpa_raceeth_lm.png?w=925&#038;h=742" alt="bachpred_sat_hsgpa_raceeth_LM" width="925" height="742" /></a></p>
<p><span style="text-decoration:underline;"><strong>Tenth</strong></span></p>
<p>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.</p>
<p><a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachrate_pred_6way_by_pincomeb3.png" target="_blank"><img class="aligncenter wp-image-2488 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachrate_pred_6way_by_pincomeb3.png?w=1055&#038;h=797" alt="bachrate_pred_6way_by_pincomeb3" width="1055" height="797" /></a><a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachrate_pred_6way_by_pincomeb3_lm.png" target="_blank"><img class="aligncenter wp-image-2487 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/bachrate_pred_6way_by_pincomeb3_lm.png?w=1012&#038;h=870" alt="bachrate_pred_6way_by_pincomeb3_LM" width="1012" height="870" /></a></p>
<p style="text-align:center;">(r=0.63 for this model)</p>
<p style="text-align:left;"><a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/aggregate_pred_with_ped1.png" target="_blank"><img class="aligncenter wp-image-2495 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/aggregate_pred_with_ped1.png?w=660&#038;h=520" alt="aggregate_pred_with_ped" width="660" height="520" /></a></p>
<p style="text-align:left;"><em>(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)</em></p>
<p style="text-align:left;">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&#8217;t perfectly controlled with parental education either<em> [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 <a href="http://blogs.discovermagazine.com/gnxp/files/2012/01/schematic.jpg" target="_blank">more intelligent</a>, better educated, and earn more.  The reason why the BSEE&#8217;s children are likely to perform better on average isn&#8217;t necessarily attributable to income&#8230;]</em>.</p>
<p style="text-align:left;">The best predictors of educational attainment are <em>clearly</em>, 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.</p>
<p style="text-align:left;">That reality is a far cry from the argument in the <a href="http://mobile.nytimes.com/2015/06/02/upshot/for-the-poor-the-graduation-gap-is-even-wider-than-the-enrollment-gap.html?referrer=&amp;_r=2" target="_blank">NYTimes</a> that the actual cause of differences between groups can almost entirely be attributed to economic concerns <em>(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&#8230;).</em></p>
<p style="text-align:left;"><a href="https://randomcriticalanalysis.files.wordpress.com/2015/06/google-chrome10.png" target="_blank"><img class="aligncenter wp-image-2489 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/google-chrome10.png?w=922&#038;h=530" alt="Google Chrome" width="922" height="530" /></a></p>
<p style="text-align:left;">I do <em>not</em> believe these differences are <em>entirely</em> genetic, although that is clearly a <a href="https://randomcriticalanalysis.wordpress.com/2015/05/20/what-blank-slate/" target="_blank">large part of it</a>.</p>
<p style="text-align:left;"><a href="http://politics.as.nyu.edu/docs/IO/5124/Sacerdote_paper.pdf" target="_blank"><img class="aligncenter wp-image-2499 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/google-chrome11.png?w=660&#038;h=602" alt="Google Chrome" width="660" height="602" /></a> <a href="http://politics.as.nyu.edu/docs/IO/5124/Sacerdote_paper.pdf" target="_blank"><img class="aligncenter wp-image-2500 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/google-chrome-1.png?w=660&#038;h=682" alt="Google Chrome (1)" width="660" height="682" /></a></p>
<p style="text-align:left;"><a href="http://politics.as.nyu.edu/docs/IO/5124/Sacerdote_paper.pdf" target="_blank"><img class="aligncenter wp-image-2502 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/google-chrome12.png?w=660&#038;h=500" alt="Google Chrome" width="660" height="500" /></a> <a href="http://politics.as.nyu.edu/docs/IO/5124/Sacerdote_paper.pdf" target="_blank"><img class="aligncenter wp-image-2503 size-full" src="https://randomcriticalanalysis.files.wordpress.com/2015/06/google-chrome-11.png?w=660&#038;h=487" alt="Google Chrome (1)" width="660" height="487" /></a></p>
<p style="text-align:left;">However, just because parents/family background <em>probably</em> also &#8220;matters&#8221; for some environmental reasons does not mean that that is caused by economic considerations, school &#8220;quality&#8221; (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&#8217;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&#8217;t apt to do much to close these gaps and will likely just waste time and resources.</p>
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