(Selfish) Education
TODO Mobility report cards: The role of colleges in intergenerational mobility Income segregation and intergenerational mobility across colleges in the United States
How much does improved primary- and secondary- education increase adult income?
Before beginning to answer that question, we have to consider that there are two different avenues for this to work: education can improve human capital, thereby allow someone to generate more output, and so see greater income. The other is that by attending high-status school, signals your value in a zero-sum way. For the purposes of this page, I'm going to ignore this distinction, which makes this entire exercise take the selfish perspective ("what can better education do for me or my kids") rather than the selfless perspective ("what can better education do for society?").
Education Quality
Studies that directly estimate the effect of pre-college education-quality on income generally result in large but imprecise estimated effect sizes:
- A study used housing vouchers either with or without the requirement to move to a low-poverty neighborhood as an experiment. They found that those required to move earned ~14% more than those not required to move, but the effect was not statistically significant. However, there was a significant effect between the voucher-and-move group and the control group (public housing) of ~31% The effects of exposure to better neighborhoods on children. This is to say we can be confident that transfers combined with improved schools/neighborhoods improve adult earnings, but not confident that either does alone.
- A review of three large-scale education interventions found that
of 17 economic-outcome statistics, only one had a p-value less than 0.05. That said, 15 of the 17 outcomes were positive, including all 8 of the income-related outcomes, with an average effect equivalent to $4128 more annual income Anderson. - Project STAR had no effect on mean earnings except on white females and on blacks in certain years Wilde How does your kindergarten classroom affect your earnings? Evidence from Project STAR. However, given the number of tested hypotheses and large standard errors, this is probably just noise.
- One study used the roll-out of Title 1 as a quasi-experiment of the effect of education funding on outcomes. They find that a $100 increase in per-pupil Title 1 funding is associated with a ~7% increase in adult earnings ($100 is roughly a 3% increase in per-pupil spending) Follow the money: School spending from title I to adult earnings.
In short, 3 of the 4 studies found large effects, but only 1 was statistically significant. In short, it doesn't seem there is a single clear answer to this question. I should at least note that a review disagrees with me on this point, but it makes correlational assumption to predict earning changes based on test score changes - a practice I think is dubious.
Beyond interventions, though, it does seem clear that teacher quality matters quite a bit.
Chetty et al.
Chetty et al find that certain characteristics of the school you go to correlate with later income even after adjusting for race and parental income Where is the land of opportunity. Given that the data is purely correlation, they provide some remarkably good arguments/evidence that their estimates are causal. Given the wide standard errors of the (quasi-)experiments above, this correlation evidence is (imo) also worth examining.
Regarding education, they find that spending per student and class size don't robustly predict future income. However, they find that dropout rates and school test scores do.
The authors don't provide enough explanation to be certain, but the standard deviation of high school dropout rates at the district level was around 7.9% in the early 2000s (as they specified, but the exact number depends the definition of "dropping out") User’s Guide to Computing High School Graduation Rates. The authors also adjust for average parental income, which we'll get to in a moment.
Meanwhile, the standard deviation in child income adjusted for parental income and race is 0.076 percentiles according to the publicly available data Data Library.
The authors find a correlation of r~-0.57. Adjusting for the spreads above, this suggests that a 1pp decrease in the dropout rate of the school you attend plausibly causes a 0.55pp increase in your family income ranking. What's more, because the authors adjust for average parental income, the actual spread of the independent variable is certainly smaller, which would suggest the true slope is somewhat larger than this 0.55 estimate.
They find a correlation of similar strength for test scores (r~+0.59).
Years of Schooling
A naive correlation between income schooling and income finds that an additional year of education is associated with a ~12% increase in income Education pays. Obviously inferring causation from that is ludicrous due to large cofounders (IQ, parental income, conscientiousness, etc).
There are a number of studies that use identical twins to attempt to control for ability bias. While this does control for ability bias induced by genetics and shared environment, it does not control for all ability bias (see below). These studies generally find when one identical twin obtains one additional year of education, they're expected to earn about 9% more than the other twin earnings Rouse Krueger.
That being said, the assumption that identical twins have identical abilities before college turns out to be false - instead one twin is usually smarter, and that twin is more likely to become better educated. A Swedish study controlled for IQ found the association between education and earnings dropped from ~3.8% to ~3.0% for an extra year of education Sandewall. The association between education and earnings is much weaker in Sweden than in the US Education and earnings; if we scale the 9% return found in the US for twins by 3.0%/3.8% we find an estimated return of ~7%.
After examining the evidence, Bryan Caplan ends up concluding in Chapter 3 of his book that roughly 45% of the education-income correlation is due to ability bias, which would shrink that 12% income-gain per year of study to ~6.6%, roughly agreeing with the number suggested by the twin studies.
Finally, Bryan Caplan advises
Go to college only if you’re a strong student or special case. College is a square deal for Excellent and Good Students who follow three simple rules. First, pick a “real” major. STEM is obviously “real”; so are economics, business, and even political science. Second, go to a respected public school. It probably won’t charge list price, and even if it does, you get your money’s worth. Third, toil full time after graduation. Working irregularly after finishing college is like failing to harvest half the crops you plant. Those who stray far from these rules get burned.
For weaker students, college is normally a bad deal. If you’re a Fair Student, go only if you’re a special case. Will you major in something like engineering? Did an elite school miraculously offer a cushy scholarship? Are you a woman who firmly plans to marry? Then despite your spotty academic record, college may be for you. Otherwise, skip college and get a job. Poor Students, finally, should not go to college, period.
Don’t get a master’s degree unless the stars align. On the day they start a master’s degree, even Excellent Students can expect a lousy Degree Return of 2.6%. You should enroll, then, only if you have a great reason—or several good reasons—to believe you’ll beat the odds. For starters, your academic ability must exceed Excellent. Failure in graduate programs is so prevalent only the top 5–10% of the population can confidently expect to cross the finish line. Field also matters enormously. While data on graduate earnings by subject are scarce, there is little doubt engineering, computer science, and economics have far higher returns than fine arts, education, and anthropology. The latter degrees make sense only if you’re a gushing fan of your subject compared to your fellow master’s students. For women, finally, marital plans are also crucial. As long as she’s an Excellent Student, the master’s is a fine deal for the woman who marries, but a lousy deal for the woman who stays single.
Estimation via Test Scores
"The Production of Human Capital in Developed Countries: Evidence from 196 Randomized Field Experiments" The production of human capital in developed countries: Evidence from 196 randomized field experiments is the de-facto summary of the effects of childhood interventions on human capital. The paper has obvious strengths:
The author (Fryer) is the youngest African-American to attain tenure at Harvard, and he hasn't shied away from conclusions that reject narratives of both the left and right Roland - indeed, I agree with these controversial conclusions (although I do cite one of his papers).
The two principle weakness are (1) the use of a life-cycle model to extrapolate from effects on test scores to effects on adulthood outcomes and (2) the failure to investigate or control for fadeout.
The latter is quite important, since
Effects on test scores tend to shrink to roughly a quarter their original size over the subsequent ~3 years, after which they stop shrinking Bailey. Effects on IQ scores tend to shrink to zero within the ~5 years after the intervention Protzko, though this has been disputed Ritchie.
Given that Fryer's analysis uses standardized tests but not IQ tests, let's suppose that 75% of the gains he finds would fade out over time. This shrinks the predicted income increase from a large, systematic educational intervention from ~35% to ~8%.
Note, that Fryer's estimates do NOT account for class size or peer effects, so we examine those next.
Class Size
Reducing class size increases test scores by d~0.02 per student in the short run and by d~0.005 in the long-run.
Fryer suggests that that a 1-SD improvement in test scores likely causes a 8% increase in incomes, so this effect is miniscule.
Teachers
See here.
Peer Effects
Broadly speaking Fryer's estimates ignore peer effects while only one of the four direct studies investigates them, finding a total increase in adult income of ~14% with large standard error The effects of exposure to better neighborhoods on children.
The literature on peer effects, classifies them "exogenous" or "endogenous". Studies of the former estimate how pre-existing peer characteristics affect a child's outcomes. Studies of the later make the wrong but potentially useful assumption that peers' outcomes can affect the child's outcome.
For instance, suppose a trial randomly assigns students to different classrooms. Seeing how the economic, ethnic, and gender composition of the classroom affects child outcomes is referred to as a study of exogenous effects. Seeing how the average ACT score of peers "affects" the ACT score of the child is referred to as a study of endogenous effects. Naturally, no one thinks my score on the ACT affects yours, but the assumption is that there are peer effects on test scores not capturable by demographic data and that using peer test scores (or other outcomes) can act as a proxy for this.
I found two meta-analyses on exogenous effects: one examined peer socioeconomic status The effect of peer socioeconomic status on student achievement: A meta-analysis while the other examined peer ethnicity Peer ethnicity and achievement: A meta-analysis into the compositional effect and their scholastic achievement. Unfortunately, both rely on studies with purely correlational methodology with relatively naive controls, which makes inferring causation reckless. I also found a meta-analysis examining endogenous effects Yeung, but it also relied on studies using pure correlation.
In all, I couldn't find any meta-analyses using exclusively studies that could reasonably infer causation. However, I did find a 2011 literature review Sacerdote, which I will summarize here:
- The most common model for peer effects is that a student's outcome is a linear combination of her peers' average outcome, her background characteristics, and her peers' average background characteristics.
- Though popular, this model does not enjoy broad literature support. Many studies have found heterogenous effects, generally along the lines of students benefiting when you add students of similar-ability to their class (e.g. tracking) - though some students harm everyone (typically very low-achieving, disruptive boys).
- Having more females in a class helps quite a bit even controlling for average peer test score.
- Peer effects on outcomes besides test scores are generally larger (e.g. on drug use, attitudes, etc).
- Roommates in college have a small effect on each other's GPA.
This is all well and good, but from a pragmatic point-of-view, we want to estimate the actual size of peer effects. As I mentioned earlier, I couldn't find any good meta-analyses, so I'll do a quick-and-dirty one here. TODO
- Hoxby assumes that year-to-year changes in the composition of class gender and race composition is random to infer the causation of these variables. Looking at ~17,000 students, she finds that increasing the percent of a classroom that is female by 10pp causes an increase in test scores of d~0.013 while an increase in the black and Native American students by 10pp causes a decrease of d~0.08 in test scores Hoxby (see my convenient spreadsheet). These sex-based effects are generally much smaller than the potential non-peer effects suggested by Fryer, but the race-based effects are potentially of similar size (100% black to 0% black suggests d~0.8).
- Another study doesn't use random assignment but uses extremely thorough controls and considers hundreds of thousands of students. The authors find that a 1 SD improvement in peers is associated with a 0.02 SD improvement in a child's test scores Burke.
- A study in busing black children from (bad) urban to (good) suburban schools found a negative but statistically insignificant effect on test scores of the hosting students Angrist. That being said, the standard error terms are large enough that the study would only have reliably detected very large effects (d > 0.5).
todo Hong Hanushek Lefgren Lavy
College Selectivity
See here.
Implications for You
Recall that Fryer suggests that that a 1-SD improvement in test scores likely causes a 8% increase in incomes, so this effect is miniscule.
Assuming a 5.7% discount rate, that median income grows 0.8% per year, that children attend school from age 4 to age 22, that they then work from age 22 to age 65, and they they earn around the median income of ~$32,000 per year, the fade-out adjusted Fryer results suggest such an intervention only pays off for the child if it costs less than ~$1632 per year in inflation-adjusted terms - though this scales proportionally with the number of children and their expected incomes.
Given my housing calculator, this suggests parents should only spend ~$44,000 more on their house per child to achieve this kind of transformative educational change.
However, the standard deviation of natural-log-income is roughly 0.9. If my wife and I will earn $500k, this suggests our earning is z~2.29. Recall that the correlation between parent and child income is around 0.8, which suggests my children will earn around 5.2x more than the average, which in turn suggests I should be willing to invest 5.2 more for the above education improvement: spending $230k more on housing per child.
Fryer's work also suggests what the most effective interventions are: high-dosage tutoring (d~0.27), managed professional development for teachers (d~0.23), early childhood interventions (d~0.15), and no excuse charters (d~0.12).
That all being said, realistically whatever interventions you take, you will not improve your child's test scores by an entire standard deviation.
Remember this all ignores peer effects (TODO).
Pygmalion Effect
The Pygmalion effect basically says teacher expectations for a student can dramatically change the students IQ. In reality,