Mobility Report Cards: The Role of Colleges in Intergenerational Mobility

Many of the highest mobility rate colleges, such as California State colleges and a number of community colleges, are not highly selective in terms of student observables such as SAT scores or revealed preferences.

“In particular, many of the highest mobility rate colleges -such as the California State colleges and a number of community colleges -are not highly selective institutions in terms of student observables such as SAT scores or based on students' revealed preferences (Avery et al. 2013).”

• cites Avery et al. 2013 sourcePartly supported

  Section I (p. 4) supports the use of students’ revealed preferences to rank colleges. But the paper says its ranking covers only about a hundred undergraduate programs, and the cited passages do not establish that California State colleges or community colleges have low selectivity by SAT scores or revealed preferences. It also does not address which colleges have the highest mobility rates. (LLM, conf=0.78)

  Experimental — accuracy not yet measured

Because low-income students pay very little tuition at elite private colleges, tuition costs are not the primary explanation for the under-representation of low- and middle-income students at those colleges.

“Since students from the lowest-income families pay very little tuition to attend elite private colleges, this result suggests that tuition costs are not the primary explanation for the under-representation of low-and middle-income students at elite private colleges, consistent with work examining the determinants of students' application decisions (Hoxby and Avery 2013).”

• cites Hoxby and Avery 2013 sourceSupported

The median income segregation across Census tracts within the 100 largest commuting zones is H = 0.084, with an interquartile range of 0.067 to 0.099.

“the median level of income segregation (at the 25th percentile) across Census tracts within the 100 largest commuting zones in America is H = 0.084, with an interquartile range of 0.067 to 0.099 (Chetty et al. 2014, Online Data Table 8).”

• cites Chetty et al. 2014 sourcePartly supported

  Section VI.B defines income segregation using a two-group Theil index H(p) across census tracts within commuting zones, including a measure at the 25th percentile. The passages in our copy do not give the claimed median of 0.084, interquartile range of 0.067–0.099, or summary for the 100 largest commuting zones; those figures cannot be verified from this copy. (LLM, conf=0.78)

  Experimental — accuracy not yet measured

Measuring children's incomes too young can yield misleading estimates of lifetime income because children with high lifetime incomes have steeper earnings profiles.

“Measuring children's incomes when they are too young can potentially yield misleading estimates of lifetime income because children with high lifetime incomes have steeper earnings profiles (e.g., Haider and Solon 2006; Solon 1999).”

• cites Haider and Solon 2006 sourceSupported
• cites Solon 1999 sourceNot checked — no full text of the source

There is considerable variance within the for-profit sector in terms of success rates and access.

“there is considerable variance within the for-profit sector in terms of success rates and access, consistent with the findings of Deming et al. (2012).”

• cites Deming et al. (2012) sourceSupported

Tax returns leave few children unclaimed, since claiming them brings sizable refundable credits.

“Very few children are unclaimed on tax returns (Chetty et al. 2014) because claiming children yields substantial refundable tax credits.”

• cites Chetty et al. 2014 sourceSupported

At Harvard, the bottom-quintile student share increased starting in 2006, from an average of 3.1% in 2000-2005 to 4.8% in 2006-2011.

“the fraction of students from the bottom quintile of families increased at Harvard starting in 2006, from an average of 3.1% from 2000-2005 to 4.8% from 2006-2011.”

• cites Avery et al. 2006 sourcePartly supported

  Section III reports that the share of Harvard students from families earning under $40,000 rose from 6.6% in the Class of 2008 to 7.9% in the Class of 2009. That supports the direction of an increase among lower-income students, but the paper does not report a bottom-quintile measure or the claimed 3.1% and 4.8% averages for 2000–2005 and 2006–2011. (LLM, conf=0.88)

  Experimental — accuracy not yet measured

Real incomes for low-income households have declined in recent years.

“The second factor that drives a wedge between trends in Pell shares and our percentile-based measures of access is the well-known fact that real incomes have fallen for low-income households in recent years (e.g., Piketty et al. 2016).”

• cites Piketty et al. 2016 sourcePartly supported

  Section 4.3 reports that average pre-tax income fell since 1980 for working-age adults in the bottom 50%. But it says income for the bottom 50% overall stagnated, while post-tax income rose for low-income seniors. The unqualified claim that real incomes fell for low-income households therefore overstates the finding. Page numbers are unavailable in our copy. (LLM, conf=0.88)

  Experimental — accuracy not yet measured

Aggregate trends mask substantial heterogeneity across colleges within selectivity tiers.

“These aggregate trends mask substantial heterogeneity across colleges within selectivity tiers.”

Even at Ivy-Plus colleges, the fraction of students from lower quintiles of the parent income distribution did not increase significantly.

“Even at the Ivy-Plus colleges, which enacted substantial tuition reductions and other outreach policies during this period, the fraction of students from lower quintiles of the parent income distribution does not increase significantly.”

The standard deviation of access conditional on having a success rate in the top quartile of colleges is nearly two-thirds as large as the raw standard deviation of access across all colleges.

“More generally, the standard deviation of access conditional on having a success rate in the top quartile of colleges is nearly two-thirds as large as the raw standard deviation of access across all colleges.”

If success is measured as reaching the top 1% of the earnings distribution instead of the top 20%, the patterns found are very different.

“If we measure “success” in earnings as reaching the top 1% of the earnings distribution instead of the top 20%, we find very different patterns.”

Conditional on the college attended, children from low- and high-income families have similar earnings outcomes.

“Second, children from low-and high-income families have similar earnings outcomes conditional on the college they attend, indicating that low-income students are not mismatched at selective colleges.”

• Also stated in: § I Introduction · plain

  “Second, children from low-and high-income families have very similar earnings outcomes conditional on the college they attend.”

The fraction of students from low-income families at institutions with the highest mobility rates, such as SUNY-Stony Brook and Glendale Community College, fell sharply over the 2000s.

“Most importantly, the fraction of students from low-income families at the institutions with the highest mobility rates -for instance, SUNY-Stony Brook and Glendale Community College -fell sharply over the 2000s.”

Bottom-to-top-quintile mobility rates range from 0.9% at the 10th percentile to 3.5% at the 90th percentile across colleges.

“Mobility rates range from 0.9% at the 10th percentile to 3.5% at the 90th percentile across colleges.”

Colleges with the highest bottom-to-top-quintile mobility rates are typically mid-tier public institutions.

“The colleges that have the highest bottom-to-top-quintile mobility rates -i.e., those that offer both high success rates and low-income access -are typically mid-tier public institutions.”

Children from top-1% families are 77 times more likely to attend an Ivy-Plus college than children from bottom-quintile families.

“children from families in the top 1% are 77 times more likely to attend an Ivy-Plus college than children from the bottom quintile.”

Many campuses of the City University of New York, certain California State colleges, and several campuses in the University of Texas system have mobility rates above 6%.

“For instance, many campuses of the City University of New York (CUNY), certain California State colleges, and several campuses in the University of Texas system have mobility rates above 6%.”

College attendees come from richer families than non-attendees.

“Children who attend college come from richer families and earn more themselves.”

Nationally, children from the highest-income families end up 30 percentiles higher in the earnings distribution on average than children from the lowest-income families.

“In the nation as a whole, children from the highest-income families end up 30 percentiles higher in the earnings distribution on average than those from the lowest-income families.”

On net, recent trends left low-income access to elite private colleges largely unchanged.

“Our analysis simply shows that on net, recent trends have left low-income access to elite private colleges largely unchanged.”

Only 3.8% of students at Ivy-Plus colleges come from the bottom quintile of the income distribution.

“Only 3.8% of students come from the bottom quintile of the income distribution at Ivy-Plus colleges.”

The share of students from bottom-quintile families at four-year colleges and selective colleges did not change significantly.

“The share of students from bottom-quintile families at four-year colleges and selective colleges did not change significantly.”

At Ivy-Plus colleges, more students come from families in the top 1% of the income distribution (14.5%) than from the bottom half of the income distribution (13.5%).

“Among “Ivy-Plus” colleges (the eight Ivy League colleges, University of Chicago, Stanford, MIT, and Duke), more students come from families in the top 1% of the income distribution (14.5%) than the bottom half of the income distribution (13.5%).”

The highest upper-tail mobility rates are concentrated at highly selective colleges with large endowments and high levels of expenditures.

“More generally, the highest upper-tail mobility rates are concentrated at highly selective colleges with large endowments and high levels of expenditures.”

At the State University of New York at Stony Brook, 51% of students from the bottom quintile reach the top quintile.

“For example, 51% of students from the bottom quintile reach the top quintile at the State University of New York at Stony Brook.”

At the twelve Ivy-Plus colleges, more students come from top-1% families (14.5%) than from the bottom half of the parent income distribution (13.5%).

“There are more students who come from families in the top one percent (14.5%) than the bottom half of the parent income distribution (13.5%).”

Among college-goers with bottom-quintile parents, 18.3% reach the top quintile by 2014, when they are ages 32-34.

“Conditional on having parents in the bottom quintile, 18.3% of college-goers reach the top quintile of the distribution (in 2014, when they are between the ages of 32-34).”

Colleges that channel the most children from low- or middle-income families to the top 1% are almost exclusively highly selective institutions, such as UC-Berkeley and the Ivy-Plus colleges.

“The colleges that channel the most children from low-or middle-income families to the top 1% are almost exclusively highly selective institutions, such as UC-Berkeley and the Ivy-Plus colleges.”

Children from families in the top 1% of the income distribution are 77 times more likely to attend an Ivy-Plus college than children from families in the bottom quintile.

“As a result, children from families in the top 1% are 77 times more likely to attend an Ivy-Plus college compared to the children from families in the bottom quintile.3”

Among students at a given elite college (Tier 1 of Barron's 2009 selectivity ranking), the gap between students from the highest- and lowest-income families is only 7.2 percentiles, 76% smaller than the national gradient.

“In contrast, among students attending a given elite college (defined as one of the colleges in Tier 1 of Barron's 2009 ranking of selectivity), the gap between students from the highest-and lowest-income families is only 7.2 percentiles, 76% smaller than the national gradient.”

Colleges with mobility rates in the top decile have mean annual instructional expenditure of approximately $8,000 per student.

“From a policy perspective, the colleges with mobility rates in the top decile are of particular interest because their mean annual instructional expenditure is approximately $8,000 per student.”

Gaps in earnings outcomes at lower-ranked colleges are relatively small as well.

“Gaps in outcomes at lower-ranked colleges are relatively small as well.”

Access to colleges varies greatly by parent income.

“First, access to colleges varies greatly by parent income.”

• Also stated in: § I Introduction · plain

  “First, access to colleges varies substantially across the income distribution.”

The average bottom-to-top-quintile mobility rate in the United States is 1.7%.

“To put these numbers in perspective, the average bottom-to-top-quintile mobility rate in U.S. is currently 1.7%.”

Among children attending college between ages 19 and 22, 83.2% attend a college included in the public data release based exclusively on 1980-82 cohorts.

“Among those who attend a college between 19 and 22, 83.2% attend a college that is included in the public data release based exclusively on data from the 1980-82 cohorts.”

61.8% of the 10.8 million children in the 1980-82 birth cohorts attend college between ages 19 and 22.

“61.8% of the 10.8 million children in 1980-82 birth cohorts attend college at some point between the ages of 19 and 22.”

Mobility rates are not strongly correlated with differences in the distribution of college majors, endowments, instructional expenditures, or other institutional characteristics.

“Mobility rates are not strongly correlated with differences in the distribution of college majors, endowments, instructional expenditures, or other institutional characteristics.”

The college-level estimates of average student earnings have a mean enrollment-weighted absolute error of $266.

“the estimates of average student earnings by college have a mean (enrollment-weighted) absolute error of $266”

Including colleges with imputed data based on 1983-84 cohorts raises the fraction of students with publicly available college-level statistics to 93.9%.

“When we include colleges for which we impute data based on the 1983-84 cohorts, the fraction of students for whom college-level statistics are publicly available rises to 93.9%.”

Only 3.8% of students at Ivy-Plus colleges come from bottom-quintile families.

“Only 3.8% of students at these colleges come from families in the bottom quintile”

Children from high-income families are slightly more likely to work, even within elite colleges.

“In practice, children from high-income families are slightly more likely to work, even within elite colleges.”

The correlation between access and success rates is -0.50.

“Colleges with greater low-income access tend to have lower success rates on average (correlation = -0.50).”

Children from low-income families tend to attend college at later ages than children from higher-income families.

“Children from low-income families tend to attend college at later ages than children from higher-income families”

The top-1% share falls from 14.5% to 2.4% and 0.4% across the selectivity tiers.

“Conversely, the fraction of students coming from the top 1% falls from 14.5% to 2.4% and 0.4% across these tiers.”

Stony Brook's low-income access is 16.4%.

“a much higher level of low-income access (16.4%)”

An OLS regression estimates that a one percentage point increase in parent rank is associated with a 0.288 percentage point increase in the child's mean rank.

“Using an OLS regression, we estimate that a one percentage point (pp) increase in parent rank is associated with a 0.288 pp increase in the child's mean rank.”

Columbia's upper-tail mobility rate is 0.75%.

“Columbia's upper-tail mobility rate -the fraction of students it channels from the bottom quintile to the top 1% -is 0.75%”

No university in the U.S. currently offers both high rates of upper-tail success and substantial low-income access.

“no university in the U.S. currently offers both high rates of upper-tail success and substantial low-income access.”

As parental income falls, the likelihood that a child attends Berkeley rather than Harvard rises monotonically.

“As parental income falls, the likelihood that a child attends Berkeley rather than Harvard rises monotonically.”

Students from the lowest-income families are less likely to attend the most selective private colleges than the most selective public colleges.

“students from the lowest-income families are less likely to attend the nation's most selective private colleges than its most selective public colleges.”

For individuals who attended elite colleges, especially Ivy-Plus colleges, earnings ranks rise sharply from age 25 to 30.

“For individuals who attended elite colleges, and especially Ivy-Plus colleges, earnings ranks rise sharply from age 25 to 30.”

Nationally, children from the richest families are 37.2 percentage points more likely to be married than children from the poorest families.

“Nationally, children from the richest families are 37.2 pp more likely to be married than those from the poorest families.”

At Columbia, low-income access is 5.0%.

“at Columbia, access is 5.0%”

Among elite colleges, the average within-college rank-rank slope is 0.065.

“Among elite colleges, the average rank-rank slope is 0.065 on average within each college.”

Children from top-0.1% families with income above $2.2 million are 117 times more likely to attend Ivy-Plus colleges than children from bottom-quintile families.

“children born to families in the top 0.1% (income > $2.2 million) are 117 times more likely to attend such colleges than those in the bottom quintile.”

Within elite colleges, the marriage-rate gap between richest and poorest family backgrounds remains 15.1 percentage points.

“Within elite colleges, the gap in marriage rates remains at 15.1 pp.”

Columbia's mobility rate is 3.1%.

“the mobility rate at Columbia is 5.0% × 61.2% = 3.1%.”

Stony Brook channels nearly three times as many children from the bottom to the top of the income distribution as Columbia, as a fraction of total enrollment.

“channeling nearly three times as many children (as a fraction of total enrollment) from the bottom to the top of the income distribution as Columbia.”

Columbia's upper-tail success rate is 15%.

“15% of students at Columbia from the bottom quintile reach the top 1%”

Mean earnings ranks at elite colleges stabilize at about the 80th percentile after age 30, with little change starting at age 32.

“Mean ranks at elite colleges stabilize at approximately the 80th percentile after age 30, with very little change starting at age 32.”

Children from the highest-income families end up 29 percentiles higher on average than children from the poorest families.

“children from the highest-income families end up 29 percentiles higher in the income distribution on average relative to children from the poorest families in the nation.”

The estimated rank-rank slope for Harvard is 0.112 with a standard error of 0.018.

“the estimated rank-rank slope for Harvard is 0.112 (s.e.= 0.018).”

2-year non-profit community colleges have a mean top-quintile success rate of 12.3%.

“2-year non-profit (community) colleges have a mean top-quintile success rate of 12.3%.”

UC-Berkeley has fewer students from high-income families than Harvard.

“Berkeley, one of the most selective public colleges in the U.S., has fewer students from high-income families than Harvard.”

Age profiles at lower-tier colleges are virtually constant from ages 25 to 36, at about the 60th percentile for two-year colleges and the 70th percentile for non-elite four-year colleges.

“In contrast, the age profiles at lower-tier colleges are virtually constant from ages 25 to 36, at approximately the 60th percentile for 2-year colleges and the 70th percentile for non-elite 4-year colleges.”

Several high-mobility-rate colleges like Stony Brook exist.

“our analysis below uncovers several high-mobility-rate colleges like Stony Brook”

At Columbia, the success rate is 61.2%.

“the success rate is 61.2%”

There is considerable variation in mobility rates across colleges.

“there is still considerable variation in mobility rates -the product of access and success rates -across colleges.”

If earnings were measured at age 25, Ivy-Plus attendees would have lower income ranks than attendees of less selective four-year colleges.

“If we were to measure children's earnings at age 25, we would find that children at Ivy-Plus colleges have lower income ranks than those who attend less selective 4 year colleges.”

Stony Brook's upper-tail success rate is 2%.

“compared with 2% at Stony Brook.”

Stony Brook's upper-tail mobility rate is 0.32%.

“where the upper-tail mobility rate is 0.32%.”

The estimated degree of income segregation across colleges in the cross-sectional sample is H = 0.075.

“We estimate that H = 0.075 across the colleges in our cross-sectional sample.”

Ivy-Plus colleges have a mean top-quintile success rate of 58.0%.

“Ivy-Plus colleges have a mean top-quintile success rate of 58.0%”

Nationally, children from the highest-income families are about 40 percentage points more likely to reach the top quintile than children from the poorest families.

“Nationally, children from the highest-income families are about 40 pp more likely to reach the top quintile than children from the poorest families.”

Columbia's upper-tail mobility rate is more than twice as large as Stony Brook's.

“more than twice as large as at Stony Brook”

Mobility rates vary substantially across colleges because there are large differences in access across colleges with relatively similar success rates.

“mobility rates vary substantially across colleges because there are large differences in access across colleges with relatively similar success rates.”

Stony Brook's mobility rate is 8.4%.

“Stony Brook has a bottom-to-top-quintile mobility rate of 8.4%”

The bottom-quintile share varies greatly across colleges, from 3.8% at the 10th percentile to 24.7% at the 90th percentile.

“The fraction of students coming from the bottom quintile varies greatly across colleges, ranging from 3.8% at the 10th percentile to 24.7% at the 90th percentile.”

Children from low- and high-income families at a given college have similar earnings distributions across all percentiles, not just similar mean ranks.

“Children from low-and high-income families at a given college not only have similar mean rank outcomes but also a similar distribution of earnings outcomes across all percentiles.”

Conditioning on the specific college a child attends further reduces the correlation between children's and parents' incomes, even at elite colleges.

“Our data show that conditioning on the specific college a child attends further reduces the correlation between children's and parents' incomes, and that this holds true even at elite colleges”

The bottom-quintile share rises monotonically as selectivity tier decreases, from 3.8% at Ivy-Plus colleges to 7.1% at Selective Private colleges to about 21% at for-profit colleges.

“The fraction of students from families in the bottom quintile rises monotonically as one moves down selectivity tiers, ranging from 3.8% at Ivy-Plus colleges to 7.1% at”

Upper-tail success is highly concentrated at elite colleges like Columbia with very high levels of instructional expenditure and large endowments.

“we find that upper-tail success is highly concentrated at elite colleges like Columbia with very high levels of instructional expenditure and large endowments”

Stony Brook's success rate is 51%.

“Stony Brook has a slightly lower success rate (51%) than Columbia”

There is substantial variation in access and success rates across colleges.

“There is substantial variation in both of these dimensions across colleges.”

Students from low- and high-income families have very similar earnings outcomes in practice, especially at highly selective colleges.

“Since students from low-and high-income families have very similar earnings outcomes in practice (y AR -y AP 0), especially at highly selective colleges”

The colleges with the lowest mobility rates consist primarily of certain non-selective colleges at which a very small share of students reach the top quintile.

“the colleges with the lowest mobility rates consist primarily of certain non-selective colleges at which a very small share of students reach the top quintile.”

Even if every Asian student ended up in the top quintile, the fraction of students in the top quintile would rise by a maximum of 5 pp over this range.

“Even if every Asian student ended up in the top quintile of the earnings distribution, the fraction of students in the top quintile would rise by a maximum of 5 pp over this range”

Asian students from low-income families have success rates that are at most 23.5 pp higher than non-Asians.

“we use Census data to estimate that Asian students from low-income families have success rates that are at most 23.5 pp higher than non-Asians.”

California State University-Los Angeles has the highest mobility rate among colleges with 300 or more students per year.

“The college with the highest mobility rate is California State University-Los Angeles”

Eight out of the ten colleges with the highest mobility rates are public institutions.

“Eight out of the ten are public institutions”

The SD of access among all colleges with upper-tail success rates comparable to the Ivy-Plus colleges is 1.3%.

“The SD of access among all colleges with upper-tail success rates comparable to the Ivy-Plus colleges is just 1.3% (Table V, Row 4, Column 3)”

There are several colleges that offer access to a large number of low-income students along with outcomes similar to highly selective colleges.

“there are several colleges that offer access to a large number of low-income students along with outcomes similar to highly selective colleges.”

Mobility rates at the 10th percentile, median, and 90th percentile of the enrollment-weighted distribution across colleges are 0.9%, 1.6%, and 3.5%, respectively.

“mobility rates at the 10th percentile (0.9%), median (1.6%), and 90th percentile (3.5%) of the enrollment-weighted distribution across colleges.”

Across colleges around the 75th percentile of success rates, the SD of access is 6.9%, compared with an unconditional SD of access across all colleges of 7.6%.

“Across this slice of colleges, the SD of access is 6.9%, just 10% smaller than the unconditional SD of access across all colleges of 7.6% (Table V, row 1).”

Differences in the racial and ethnic makeup of colleges' student bodies are highly predictive of their mobility rates.

“differences in the racial and ethnic makeup of colleges' student bodies are highly predictive of their mobility rates.”

Colleges with higher upper-tail mobility tend to have higher average faculty salary.

“Spending is also strongly related to upper-tail mobility rates, as measured by higher tuition, instructional cost per student, and average faculty salary.”

Colleges with the highest mobility rates tend to be mid-tier public colleges that combine moderate success rates with high levels of access.

“the colleges with the highest mobility rates tend to be mid-tier public colleges that combine moderate success rates with high levels of access.”

Very little of the variance in mobility rates is explained by instructional expenditures or faculty salaries.

“very little of the variance in mobility rates is explained by these characteristics.”

Nine of the top ten colleges in Table IVa have success rates above the median (14.4%).

“Nine of the top ten colleges in Table IVa have success rates above the median (14.4%)”

The fraction of students majoring in business is approximately 20% in both high mobility rate colleges and other colleges.

“the fraction of students majoring in business is approximately 20% in both groups.”

Public control is not significantly correlated with mobility rates on average.

“public control is not significantly correlated with mobility rates on average.”

For Ivy-Plus levels of top-quintile success, the standard deviation of access is 3.6%.

“the SD of access conditional on Ivy-Plus levels of top-quintile success is much higher, at 3.6%.”

Differences in majors have opposite-signed correlations with success rates and access.

“differences in majors have opposite-signed correlations with success rates and access”

The mean annual instructional expenditure per student across colleges in the top 10% of mobility rates is $8,155, compared with $7,483 across all colleges.

“the mean annual instructional expenditure per student across colleges in the top 10% of mobility rates is $8,155, only slightly higher than the mean instructional expenditure across all colleges of $7,483.”

The fraction of students in STEM fields is 17.9% at high mobility rate colleges, compared with 14.9% at other colleges.

“The fraction of students in STEM fields is 17.9% at high mobility rate colleges, compared with 14.9% at other colleges”

A number of Ivy-Plus colleges appear in the top ten for upper-tail mobility even though their low-income access is relatively low.

“many Ivy-Plus colleges rank among the top ten colleges in terms of upper-tail mobility rates despite their relatively low levels of low-income access (Table IVb).”

There is little correlation between college completion rates and mobility rates.

“We also find little correlation between college completion rates and mobility rates”

Colleges with higher upper-tail mobility tend to have greater STEM shares.

“Colleges that have higher mobility rates tend to be smaller, have larger endowments, higher completion rates, and greater STEM shares.”

Colleges with higher upper-tail mobility tend to be smaller.

“Colleges that have higher mobility rates tend to be smaller, have larger endowments, higher completion rates, and greater STEM shares.”

Most of the variation in mobility rates is across colleges within rather than between selectivity tiers.

“most of the variation in mobility rates is across colleges within rather than between tiers.”

At California State University-Los Angeles, nearly 10% of students come from a family in the bottom quintile and reach the top quintile.

“where nearly 10% of students come from a family in the bottom quintile of the income distribution and reach the top quintile.”

Mobility rates are only weakly correlated with the distribution of majors.

“mobility rates end up being only weakly correlated with the distribution of majors.”

These correlations nearly cancel each other out in the full sample.

“These correlations nearly cancel each other out in the full sample.”

The shares of Hispanic and Black undergraduates are positively correlated with mobility rates.

“The shares of Hispanic and Black undergraduates are also positively correlated with mobility rates”

Among colleges around the 75th percentile of success rates, access varies widely, with examples including Bowling Green State University (3.6%), Louisiana Tech University (10.7%), and Glendale Community College (32.4%).

“This group includes colleges such as Bowling Green State University (access = 3.6%), Louisiana Tech University (access = 10.7%), and Glendale Community College (access = 32.4%).”

Colleges with higher upper-tail mobility tend to have higher completion rates.

“Colleges that have higher mobility rates tend to be smaller, have larger endowments, higher completion rates, and greater STEM shares.”

Differences in fields of study do not account for much of the variation in mobility rates even among colleges with very high success rates.

“Differences in fields of study do not account for much of the variation in mobility rates even among colleges with very high success rates.”

Selectivity tiers have a rank correlation of 0.55 with upper-tail mobility rates.

“College's selectivity tiers have a rank correlation of 0.55 with upper-tail mobility rates.”

The success rates at these colleges are below those of children who do not attend college between the ages of 19-22 (4.1%).

“the success rates at these colleges are below those of children who do not attend college between the ages of 19-22 (4.1%).”

Pace University is the only private not-for-profit college among the top ten.

“with Pace University in New York as the only private not-for-profit college”

The Asian-adjusted mobility rates have a correlation of 0.43 with Asian shares.

“The Asian-adjusted mobility rates continue to have a correlation of 0.43 with Asian shares”

There is no strong pattern in the mobility rates across the tiers.

“There is no strong pattern in the mobility rates across the tiers.”

The average mobility rate in the U.S. is 1.7%.

“the average mobility rate in the U.S. is 1.7%.”

A 1 pp increase in the share of Hispanic students is associated with a 0.34 pp increase in the share of students from the bottom quintile.

“we estimate that a 1 pp increase in the share of Hispanic students is associated with a 0.34 pp increase in the share of students from the bottom quintile using an OLS regression across colleges.”

Many public colleges have much lower success and mobility rates than private colleges.

“there are many public colleges that have much lower success and mobility rates than private colleges.”

Even among colleges with success rates comparable to the Ivy-Plus colleges, the SD of access is 3.6%.

“Even among colleges with success rates comparable to the Ivy-Plus colleges, the SD of access is 3.6%.”

Upper-tail mobility rates are much higher at highly selective four-year colleges than at other college types.

“Highly selective four-year colleges have much higher upper-tail mobility rates than other types of colleges (Table II, Column 10).”

A regression of mobility rates on the share of students in each of eight majors yields an R-squared of 2.2%.

“A regression of mobility rates on the share of students in each of the eight majors listed in Figure VIa (weighted by enrollment) yields an R-squared of just 2.2%.”

There are much stronger correlations between mobility rates and the demographic characteristics of the undergraduate student body at each college.

“We find much stronger correlations between mobility rates and the demographic characteristics of the undergraduate student body at each college.”

No college on the top ten list for bottom-to-top quintile mobility also appears on the top ten list for upper-tail mobility.

“Interestingly, none of the colleges that appear on the top ten list in terms of bottom-to-top quintile mobility in Table IVa appear on the top ten list in terms of upper-tail mobility in Table IVb.”

Public control does not correlate strongly with mobility rates because it correlates in opposite directions with access and success.

“public control does not correlate strongly with mobility rates because it correlates in opposite directions with access and success.”

The SD of access between the Ivy-Plus colleges themselves is 0.94%.

“which is essentially the same as the SD of access between the Ivy-Plus colleges themselves (equal to 0.94%).”

Mobility rates are not correlated with the cost of attending a college, measured either by sticker prices or net costs to low-income students.

“mobility rates are not correlated with the cost of attending a college, measured either by sticker prices or net costs to low-income students.”

There is substantial variation in mobility rates between colleges within the Los Angeles commuting zone.

“There is substantial variation in mobility rates between colleges within LA”

These correlations are not just driven by individual-level differences across racial and ethnic groups.

“these correlations are not just driven by individual-level differences across racial and ethnic groups.”

The distribution of majors is very similar between colleges in the top decile of mobility rates and all other colleges.

“The distribution is very similar.”

There are no colleges with upper-tail success rates comparable to the Ivy-Plus colleges that offer much higher levels of access.

“there are no colleges with upper-tail success rates comparable to the Ivy-Plus colleges that offer much higher levels of access.”

The share of Asian undergraduates has a correlation of 0.53 with mobility rates.

“The share of Asian undergraduates has a correlation of 0.53 with mobility rates”

Colleges with higher upper-tail mobility tend to have larger endowments.

“Colleges that have higher mobility rates tend to be smaller, have larger endowments, higher completion rates, and greater STEM shares.”

There is considerable variation in access across colleges even conditional on having a high success rate.

“there is considerable variation in access across colleges even conditional on having a high success rate.”

As Asian shares rise from 0% to 5%, the percentage of students who reach the top quintile rises by nearly 15 percentage points.

“As Asian shares rise from 0% to 5%, the percentage of students who reach the top quintile rises by nearly 15 percentage points (pp).”

Most colleges have success rates well above 3.9%.

“most colleges have success rates well above 3.9%.”

Colleges with higher upper-tail mobility tend to have higher instructional cost per student.

“Spending is also strongly related to upper-tail mobility rates, as measured by higher tuition, instructional cost per student, and average faculty salary.”

Technical Career Institutes is the only for-profit college among the top ten.

“and Technical Career Institutes as the only for-profit college.”

Almost all selectivity tiers have a mean top-quintile mobility rate of around 2%, with a range of 1.5% to 2.7% across tiers.

“almost all tiers have a mean top-quintile mobility rate of around 2%, with a range of 1.5% to 2.7% across tiers”

Colleges with higher upper-tail mobility tend to have higher tuition.

“Spending is also strongly related to upper-tail mobility rates, as measured by higher tuition, instructional cost per student, and average faculty salary.”

For-profit colleges have slightly higher average mobility rates than public and private non-profit colleges.

“for-profit colleges have slightly higher average mobility rates than public and private non-profit colleges.”

The colleges with the highest mobility rates listed in Table IVa do not achieve high mobility rates by combining very high access with very low success rates.

“the colleges with the highest mobility rates listed in Table IVa do not achieve high mobility rates by combining very high access with very low success rates.”

Among colleges with success rates at or above the 75th percentile, the conditional SD of access is 4.6%.

“among colleges with success rates at or above the 75th percentile, the conditional SD of access is 4.6% (Table V, row 2).”

Across the distribution, access changes are weakly negatively related to success-rate changes.

“Changes in access have a weak negative association with changes in success rates throughout the distribution.”

Colleges with higher mobility rates experienced larger access declines.

“One pattern suggested by the preceding examples is that access has fallen more at colleges with relatively high mobility rates.”

Ivy-Plus Pell receipt grew from 12.1% to 16.8% over 2000-2011.

“At Ivy-Plus colleges, the fraction of students receiving Pell grants increased from 12.1% to 16.8% between 2000-2011”

Because they are small, Ivy-Plus and other elite colleges make up an even smaller fraction of those who reach the top 20%.

“Ivy-Plus colleges (and elite colleges more generally) account for an even smaller share of children who reach the top 20%, simply by virtue of their relatively small size.”

The low-income student fraction fell sharply at Stony Brook.

“the fraction of low-income students fell sharply at Stony Brook, one of the selective public colleges with the highest mobility rates (based on data from the 1980-82 cohorts).”

Access declined sharply at Glendale Community College.

“Finally, we see a sharp decline in access at Glendale Community College, another one of the colleges with the highest mobility rates in our data.”

Compared with other colleges, top mobility-rate colleges saw access decline by 2.8 percentage points over 2000-2011.

“Relative to other colleges, access fell at the highest mobility rate colleges by 2.8 pp between 2000 and 2011.”

Real income declines added about 2.5 percentage points to Ivy-Plus Pell shares.

“while the decline in real incomes increased Pell shares by approximately 2.5 pp (Online Appendix Figure IX).”

• AssumptionRests on an assumption: Real incomes fell sharply during the 2000s at the bottom of the distribution.

Harvard's 1.7 percentage point access rise implies a success-rate drop below 0.3 percentage points from a 58% baseline.

“these estimates imply that the 1.7 pp increase in access at Harvard documented above would be associated with less than a 0.3 pp decline in success rates, relative to a baseline success rate of 58%.”

Once these factors are accounted for, Pell data show no significant shift in Ivy-Plus students' parental income distribution over 2000-2011.

“Accounting for these factors, the Pell data imply that there was no significant change in the parental income distribution of students at Ivy-Plus colleges between 2000-2011, consistent with our conclusions in Figure Xa.”

UC-Berkeley's access was roughly flat over 2000-2011.

“access remained relatively constant at UC-Berkeley between 2000-2011.”

Two factors explain why Pell trends differ from the paper's percentile-based access measures.

“In Online Appendix F, we show that the apparent discrepancy between trends in Pell shares and our percentile-based statistics, which show little or no change in lowincome access, is driven by two factors.”

Adding controls for above-median access and success leaves the high-mobility colleges' downward trend essentially unchanged.

“These controls do not significantly affect the estimated downward trend at high mobility rate colleges, confirming that the decline is a phenomenon specific to that group rather than trends at all colleges that have either high levels of access or success rates.”

Overall, elite private colleges saw little net change in low-income access.

“What the data show is that on net, the combination of changes that occurred -which included college-level policy reforms, macroeconomic trends in inequality, and various other factors -left low-income access to elite private colleges largely unchanged.”

Success-above-median colleges outside the top mobility decile had no access change over the sample.

“Likewise, colleges that have above-median success rates (but are not in the top decile of mobility rates) exhibit no change in access over our sample period.”

The bottom-quintile share at Ivy-Plus colleges increased by 0.65 percentage points between 2000 and 2011.

“Even at Ivy-Plus colleges, which enacted substantial tuition reductions and other outreach policies during this period, the fraction of students from the bottom quintile increased by only 0.65 pp from 2000-2011.”

Eligibility-rule changes added roughly 2.9 percentage points to Ivy-Plus Pell shares over 2000-2011.

“We estimate that the changes in eligibility rules mechanically increased Pell shares at Ivy-Plus colleges by approximately 2.9 pp from 2000-2011”

• AssumptionRests on an assumption: Congress raised the Pell Grant income eligibility threshold significantly between 2000 and 2011.

Among poor children who reach the top 1%, 5.0% attended Ivy-Plus colleges.

“Just 5.0% of children from poor families who reach the top 1% come from Ivy-Plus colleges.”

The within-tier estimate is similar, at -0.18 with a standard error of 0.08.

“Identifying this coefficient from within-tier variation across colleges by including tier fixed effects yields a very similar coefficient of -0.18 (s.e.= 0.08).”

Declining access is most strongly linked to having both high access and high success rates.

“Importantly, it is the combination of high access and success rates that is most strongly associated with declining access over time.”

Top-quintile success rates fall by 0.17 for each 1 percentage point rise in access.

“Using an OLS regression, we estimate that a 1 pp increase in access is associated with a 0.17 reduction in top-quintile success rates.”

At top-decile mobility colleges, access dropped 0.97 percentage points over 2000-2011.

“Using an OLS regression, we estimate that access fell by 0.97 pp at the colleges with the highest mobility rates from 2000-2011.”

The observed rise in Pell shares is fully explained by these two changes combined.

“Together, these changes fully account for the observed increase in Pell shares.”

Access-above-median colleges outside the top mobility decile gained 2 percentage points in low-income representation.

“Colleges that are above the median just in terms of access (based on mean access over the sample period) but are not in the top decile of mobility rates exhibit a 2 pp increase in the representation of low-income students, mirroring national trends (Figure Xc, open circles).”

Including college tier fixed effects yields similar results.

“Column 4 shows that the results remain similar when we compare colleges within tiers by including college tier fixed effects.”

On average, two-year colleges saw a significant rise in low-income enrollment over this period.

“This decline is especially striking since the fraction of low-income students at two-year colleges increased significantly on average during this period.”

The fraction of students receiving a Pell grant rose sharply from 2000 to 2011, particularly among students with parental AGI in the middle of the income distribution.

“As expected, we find that the fraction of students receiving a Pell grant increased sharply from 2000 to 2011, especially for students with parental AGI in the middle of the income distribution (Appendix Figure IXb).”

Across the ten high-mobility colleges, average mobility fell from 7.7% to 5.9% over 2000-2011, a drop of nearly 25%.

“These changes led to a change in mobility rates from 7.7% in 2000 to 5.9% in 2011 -nearly a 25% decline -on average across these ten colleges.”

• AssumptionThe authors state this as an assumption: Each college's success rate is fixed at levels observed in the 1980-82 cohorts for predicting mobility changes.

Under the most-attended measure, 4.1% of analysis-sample students were missing from 1098-T data and initially appeared only in NSLDS Pell data.

“Using our most-attended college attendance measure, 4.1% of the students in our analysis sample were not in the 1098-T data and originally appeared only in the NSLDS Pell data.”

Ivy-Plus colleges' points in Figure XIb show little movement over 2000-2011.

“The points for the Ivy-Plus colleges in Figure XIb generally move very little between 2000 and 2011.”

Ivy-Plus average mobility stayed near 2.25% over 2000-2011.

“As a result, the average mobility rate at Ivy-Plus colleges remained essentially unchanged at 2.25% between 2000 and 2011.”

• AssumptionThe authors state this as an assumption: Each college's success rate is fixed at levels observed in the 1980-82 cohorts for predicting mobility changes.

The average Pell share at Ivy-Plus colleges rose from 12.1% to 16.8% between 2000 and 2011.

“Ivy-Plus colleges, for instance, have seen their average Pell share increase from 12.1% to 16.8% between 2000 and 2011.”

Substantial access declines occurred at nearly every high-mobility-rate college.

“In contrast, almost all of the high-mobility-rate colleges experienced substantial declines in access, shifting their points significantly to the left in Figure XIb.”

Most student-college-year attendance observations come from 1098-T records, which record attendance by calendar year.

“The vast majority of studentcollege-year attendance observations appear in the 1098-T data, which measure attendance by calendar year.”

Despite major efforts, Ivy-Plus low-income access did not change significantly.

“As noted above, low-income access at these colleges did not change significantly despite their substantial efforts to increase access during this period.”

Across all colleges, the mean absolute error of mean earnings estimates is $266.

“The mean absolute error is $266.”

The predicted change in Pell shares at Ivy-Plus colleges from changes in eligibility rules is 2.9 percentage points.

“We obtain a predicted change in Pell shares at Ivy-Plus colleges of 2.9 pp due to changes in eligibility rules.69”

Nearly every EIN-ZIP pair corresponds to one OPEID.

“In almost all cases, each EIN-ZIP pair maps to a single OPEID.”

For colleges with many Pell students, the imputation adds nearly zero net students to 1098-T attendance counts.

“at colleges with substantial numbers of students on Pell grants, the imputation algorithm adds almost no net students to 1098-T attendance records”

Observable characteristics explain much of the gap between College Scorecard earnings and earnings for all students.

“Second, the discrepancy between the earnings estimates from the College Scorecard and the earnings for the full set of students is well explained by differences in observable characteristics.”

In the 29 Illinois community colleges model, higher College Scorecard student earnings predict higher overall earnings.

“The estimated relationships are intuitive: for instance, colleges with higher student earnings on the College Scorecard (by several measures) are predicted to have higher earnings overall.”

Among Title IV students with parental income of $50,000, the share receiving a Pell grant increased from 17.4% in 2000 to 60.6% in 2011.

“For instance, the fraction of Title IV students with parental income of $50,000 (as reported on the FAFSA form) who received a Pell grant increased from 17.4% in 2000 to 60.6% in 2011.”

For students aged 19-22, 9.2% of annual attendance records were absent from 1098-T data and appeared only in NSLDS Pell data.

“9.2% of our annual attendance records for students aged 19-22 were not in the 1098-T data and appeared only in the NSLDS Pell data.”

A few college-year observations lack complete 1098-T data because of administrative errors or changes in EINs and reporting practices.

“A small number of college-year observations have incomplete 1098-T data, either because of errors in administrative records or because of changes in EIN's and reporting procedures.”

Glendale's 10 percentage point access decline predicts a success-rate gain under 2 percentage points from a 22% baseline.

“Conversely, at Glendale Community College, where access fell by 10 percentage points from 2000-2011, we predict that success rates would increase by less than 2 pp relative to a baseline of 22%.”

The main analysis core sample contains 11.3 million children.

“This leaves us with 11.3 million children in our core sample underlying our main analysis.”

For the 1980 birth cohort, average earnings among students at Illinois community colleges, a 29-college group, are $36,316.

“For example, the average earnings for students in the 1980 birth cohort who attended community colleges in Illinois -a group of 29 colleges -is $36,316.”

The model finds a negative correlation between the share of students receiving financial aid and earnings.

“The percentage of students receiving financial aid is correlated with lower earnings”

In most cases flagged by the 10% rule, the 1098-T count is zero, suggesting the college filed no 1098-T forms.

“In the vast majority of these cases, the 1098-T counts are exactly zero, implying that the college did not report any 1098-T form”

A regression of the paper's median earnings on College Scorecard median earnings has an R2 of 0.92.

“regressing median earnings in our data on median earnings in the College Scorecard (the main earnings measure reported in the Scorecard) yields an R 2 of 0.92 (Looney 2017).”

• cites Looney 2017Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

High-mobility colleges' mobility decline is about ten times larger than any Ivy-Plus change.

“The decline in mobility rates at these high mobility rate colleges is an order of magnitude larger than the changes at any of the Ivy-Plus colleges.”

The share of students from the bottom 40% of the parental income distribution at Ivy-Plus colleges rose by only 0.6 percentage points between 2000 and 2011, according to a linear regression.

“We find that the fraction of students from the bottom 40% of the parental income distribution at Ivy-Plus colleges increased by just 0.6 percentage points (based on a linear regression) between 2000 and 2011.”

At selective colleges, low-income admits do not look over-placed; their earnings resemble those of higher-income peers.

“First, low-income students admitted to selective colleges do not appear over-placed, as their earnings outcomes are similar to those of their peers from higher income families.”

At Stony Brook and Glendale, the count of low-income students did not change significantly.

“The number of low-income students did not change significantly at Stony Brook or Glendale”

Students at Columbia have much higher chances of reaching the top 1% of the earnings distribution than those at Stony Brook.

“We show below that students at Columbia have much higher chances of reaching the upper-tail (top 1%) of the earnings distribution than those at Stony Brook”

Mobility rates are strongly correlated with the racial and ethnic composition of the student body, such as the fraction of Asian and Hispanic students.

“We do find that mobility rates are strongly correlated with the racial and ethnic composition of the student body -e.g., the fraction of Asian and Hispanic students”

When broken out by campus, six CUNY campuses rank among the top 10 colleges by mobility rates.

“When broken out separately by campus, six of the CUNY campuses are ranked amongst the top 10 colleges in terms of mobility rates.”

The predicted 5.4 percentage point increase is similar to the observed 4.7 percentage point increase.

“This predicted change is similar to the observed increase of 4.7 pp.”

At Stony Brook and Glendale, the proportion of low-income students declined over time.

“the share of lowincome students fell over time”

The maximum Pell Grant increased by more than 33% between 2000 and 2011.

“The cap increased by more than 33% between 2000 and 2011.”

The SD of access declines gradually, with a sharp reduction from 2.4% to 1.3% when success is defined as reaching the top 5% instead of the top 1%.

“It then begins to decline gradually, with a sharp reduction from 2.4% to 1.3% even when defining success as reaching the top 5% instead of the top 1%.”

There is no pattern in the SD of access conditional on success rates above the 75th percentile as the income threshold varies.

“In contrast, there is no pattern in the SD of access conditional on having success rates above the 75th percentile of the distribution across colleges as one varies the income threshold.”

The share of students in the 10th income ventile who were Pell-eligible rose by 17.1 percentage points from 2000 to 2011.

“For instance, the fraction of students in the 10th ventile who are Pell-eligible increased by 17.1 percentage points from 2000 to 2011, and 2.1% of students at Ivy-Plus institutions are in the 10th ventile.”

Other Ivy-Plus colleges that enacted similar policy changes did not show significant changes in the low- or middle-income student share, unlike Harvard.

“Unlike at Harvard, we do not observe significant changes in the fraction of low-or middle-income students at other Ivy-Plus colleges that enacted similar policy changes (as shown in Figure Xa).”

• cites Figure XaNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

There is an increasing trend in the share of Pell-eligible students at Ivy-Plus colleges that is generated solely by national income distribution trends.

“Appendix Figure IXc shows that there is an increasing trend in the fraction of Pell-eligible students at Ivy-Plus colleges that is generated purely by national trends in the income distribution.”

The decline in real incomes accounts for about a 2.5 percentage point increase in Pell-eligible students at Ivy-Plus colleges between 2000 and 2011.

“The decline in real incomes accounts for roughly a 2.5 pp increase in Pell-eligible students at Ivy-Plus colleges between 2000 and 2011.70”

2.1% of students at Ivy-Plus institutions are in the 10th ventile of the income distribution.

“For instance, the fraction of students in the 10th ventile who are Pell-eligible increased by 17.1 percentage points from 2000 to 2011, and 2.1% of students at Ivy-Plus institutions are in the 10th ventile.”

About one-fifth of children in the 1980 cohort had zero individual earnings in 2014.

“Roughly 20% of children have $0 in individual earnings.”

Between 2000 and 2011, the share of low-income children among college students rose by 2.15 percentage points, from 10.6% to 12.8%.

“Between 2000 and 2011, the fraction of low-income children among college students increased by 2.15 percentage points, from 10.6% to 12.8%.”

The rise in college attendance among low-income students was concentrated at for-profit institutions and two-year colleges.

“The growth in college attendance among low-income students was concentrated at for-profit institutions and two-year colleges.”

The SD of access conditional on success rates comparable to Ivy-Plus colleges remains stable at roughly 3.7% from the top 40% to the top 20% threshold.

“The SD of access remains stable at roughly 3.7% from the top 40% to the top 20% threshold.”

The share of low- and middle-income students (bottom 60%) increased by only 0.86 pp at Ivy-Plus colleges.

“the fraction of low-and middle-income students (bottom 60%) increased by only 0.86 pp at Ivy-Plus colleges.”

Children's earnings outcomes do not vary significantly with parents' incomes at Columbia and SUNY-Stony Brook.

“Children's earnings outcomes do not vary significantly with their parents' incomes:”

Among Ivy-Plus colleges and top-decile mobility colleges with similar success rates, differences in major distribution explain 10% of the variance in mobility rates.

“among this set of colleges, differences in the distribution of majors explain 10% of the variance in mobility rates.”

At four-year colleges and elite colleges on average, the low-income student share showed no significant change.

“The fraction of low-income students did not change significantly at four-year colleges and elite colleges on average.”

In the paper's data, the 40th percentile of parental income among parents with college-age children fell from $45,600 for the 1980 cohort to $36,300 for the 1991 cohort.

“For example, in our data, the 40th percentile of the income distribution among parents with college-age children fell from $45,600 for parents of children in the 1980 cohort to $36,300 in the 1991 cohort.”

Mobility rates at colleges where many female students do not participate in the labor market in their mid-thirties, such as Brigham Young University, change significantly under alternative measures.

“Mobility rates at certain colleges where a large fraction of female students do not participate in the labor market in their mid-thirties, such as Brigham Young University in Utah, do change significantly when we use these alternative measures.”

Changes in Pell eligibility thresholds and the decline in real incomes together produce roughly a 5.4 percentage point increase in the share of Pell-eligible students at Ivy-Plus colleges.

“In sum, we estimate that the changes in the Pell eligibility thresholds and the decline in real incomes together lead to roughly a 5.4 pp increase in the share of Pell-eligible students at Ivy-Plus colleges.”

• AssumptionRests on an assumption: In the sample period, Pell eligibility required an Expected Family Contribution below 95% of the Maximum Pell Grant, so increases in the Maximum Pell Grant expanded both award size and the eligible set.

Changes in Pell eligibility raised Pell shares by 17 percentage points among Ivy-Plus students with parents in the 10th income ventile.

“Changes in Pell eligibility thus increased Pell shares by 17 percentage points among students at Ivy-Plus colleges with parents in the 10th ventile of the income distribution.”

The success rate for individuals who do not attend college by age 28 is 3.9%.

“minus 3.9%, which is the success rate of those who do not attend college by age 28.”

Across all quantiles, including the probability of reaching the top quintile or top 1%, stabilization occurs by the early 30s.

“We find analogous stabilization across all quantiles of the distribution by the early 30s, including the probability that children reach the top quintile or the top 1% of their age-specific income distribution (Online Appendix FigureIV).”

• cites Online Appendix FigureIVNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

About one-third of students at both Columbia and Stony Brook major in STEM or business.

“approximately one-third of students at both Columbia and Stony Brook major in science, technology, engineering, or mathematics (STEM) or business, two of the highest-paying fields.”

At Harvard, the share of students from the bottom 60% rose from 16.1% in 2000-2005 to 20.9% in 2006-2011.

“whose share at Harvard increased from 16.1% from 2000-2005 to 20.9% from 2006-2011 (Online Appendix Figure VIII).”

• cites Online Appendix Figure VIIINot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Higher top 1% mobility rates are linked to greater instructional expenditure per student in 2000 across the distribution, even when Ivy-Plus colleges are excluded.

“Greater instructional expenditure is associated with higher top 1% mobility rates throughout the distribution, even excluding the Ivy-Plus colleges, which all fall within the top expenditure bin.”

The 1980 cohort's median individual earnings at age 34 (2014) were $28,000.

“For children in the 1980 cohort, median individual earnings in 2014 (at age 34) are $28,000.”

At Stanford, the low-income student share was essentially constant from 2000-2011.

“the fraction of low-income students at Stanford was essentially constant from 2000-2011 (Figure Xb).”

• cites Figure XbNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The estimated Pell-eligible share at Ivy-Plus colleges in 2011 (16.7%) closely matches the 16.8% figure obtained from actual Pell data at those colleges.

“This estimate matches closely the 16.8% figure that one would get from using the actual Pell data at these colleges”

Most cases of assignment to Super OPEID -1 are college-year cells with no 1098-T records in the database.

“Most of these cases are college-year cells with zero 1098-Ts in the database.”

Some universities changed from reporting data separately for each campus to using one EIN-ZIP for all campuses, producing inconsistencies in their data across years.

“some universities switch from reporting data separately for each campus to using a single EIN-ZIP for all their campuses, which creates inconsistencies in their data across years.”

The highly skewed parental income distribution at Harvard is representative of other elite private colleges.

“This highly skewed parental income distribution is representative of other elite private colleges.”

The paper's conclusions do not change when excluding the 85 EIN-ZIP clusters that aggregate multiple campuses.

“We include these clusters in our baseline analysis, but confirm that our conclusions do not change when excluding them.”

If high-income children earn more by attending a more selective college, the potential earnings loss from attending a selective college cannot be large for low-income students.

“In particular, we show using a stylized model that if children from high-income families earn more by attending a more selective college, the potential earnings loss from attending a selective college cannot be large for low-income students.”

• AssumptionThe authors state this as an assumption: More selective colleges produce better outcomes for high-income students.

Ivy-Plus educational models are less scalable.

“In comparison, the mean instructional expenditure at Ivy-Plus colleges -which are often the focus of efforts to increase access to high-quality higher education -is around $54,000, making their educational models less scalable.6”

Using exact values instead of the blurred public estimates yields virtually identical results.

“However, using the exact values for our analysis yields virtually identical results.”

Among highly selective colleges (176 colleges in the top two tiers of the Barron's 2009 selectivity index), the correlation between the paper's enrollment counts and IPEDS first-time, full-time undergraduate counts is 0.99.

“Among these colleges, the correlation between our enrollment counts and the number of first-time, full-time undergraduates in IPEDS is 0.99.15”

The number of children for whom parents are identified exceeds 98% of children born in the United States between 1980 and 1991.

“Thus, the number of children for whom we identify parents exceeds 98% of children born in the U. S. between 1980 and 1991 (Online Appendix Table I).”

All main findings of the paper hold when restricting attention to colleges with no imputed data.

“However, all of the main findings of the paper hold if we restrict attention to the set of colleges with no imputed data.”

Colleges that offered many low-income students pathways to success are becoming less accessible over time.

“In short, the colleges that offered many low-income students pathways to success are becoming less accessible over time.”

The estimation error in the college-level statistics does not meaningfully affect comparisons across colleges.

“Hence, the estimation error does not meaningfully affect comparisons across colleges.”

The earnings ranks of children in the primary cross-sectional analysis sample stabilize by 2014.

“We show in Section IV.A that the earnings ranks of children in our primary cross-sectional analysis sample stabilize by 2014.”

The range of mobility rates across colleges is substantial relative to the 2.3 percentage point difference between perfect mobility (4%) and the U.S. average (1.7%).

“Relative to the 2.3 percentage point difference between these benchmarks, the range of mobility rates across colleges is quite substantial.”

Colleges with both high success rates and substantial low-income access must either have particularly high value-added for students or have a technology to select particularly high-ability students from low-income families.

“Using a stylized model, we show that such colleges must either have particularly high value-added for their students or have a technology to select particularly high-ability students from low-income families.”

Children's incomes are measured in 2014 to minimize lifecycle bias from measuring earnings at too early an age.

“We measure children's incomes in 2014 -the most recent year in which we observe earningsto minimize the degree of lifecycle bias that arises from measuring children's earnings at too early an age.”

The paper does not identify each college's causal effect on a given student (value-added).

“Unlike this prior work, we do not identify each college's causal effect on a given student (“value-added”).”

The cross-sectional sample focuses on the 1980-82 cohorts so that incomes can be measured at age 32 or older in 2014, the age at which children's income ranks stabilize at all colleges.

“We focus on children in the earliest birth cohorts (1980-82) in the cross-sectional sample so that their incomes can be measured at age 32 or older in 2014, the age at which children's income ranks stabilize at all colleges (see Section IV.A).”

Low-income students who do nearly as well as high-income peers at selective colleges would not do much better by attending less selective colleges.

“Hence, the fact that low-income students do nearly as well as their high-income peers at selective colleges implies that they would not do much better by attending less selective colleges.”

Characteristics positively correlated with children's earnings outcomes (such as selectivity or expenditures) correlate negatively with access, leading to little or no correlation with mobility rates.

“This is because the characteristics that correlate positively with children's earnings outcomes (e.g., selectivity or expenditures) correlate negatively with access, leading to little or no correlation with mobility rates.”

These findings challenge the common perception that colleges foster greater interaction between children from diverse socioeconomic backgrounds than the environments in which they grow up.

“These findings challenge the common perception that colleges foster greater interaction between children from diverse socioeconomic backgrounds than the environments in which they grow up.”

Low-income students are not mismatched at selective colleges.

“indicating that low-income students are not mismatched at selective colleges.”

• Also stated in: § I Introduction · hedged

  “this finding implies that students from low-income families are not over-placed (or “mismatched”) at selective colleges.”

Mobility rates vary substantially across colleges because there are large differences in access across colleges with similar success rates.

“Mobility rates vary substantially across colleges because there are large differences in access across colleges with similar success rates.”

The four example colleges illustrate large differences in parental income distributions across colleges with different selectivity levels.

“These four examples are more broadly illustrative of the large differences in parental income distributions across colleges with different levels of selectivity.”

Differences in labor force participation rates do not mask latent differences in earnings potentials between low- and high-income children within elite colleges.

“These results suggest that differences in labor force participation rates do not mask latent differences in the earnings potentials of children from low-vs.high-income families within elite colleges.”

The finding that low- and high-income students within a given college have similar earnings outcomes provides evidence against the concern that low-income students are mismatched at selective colleges.

“The result that students from low-and high-income families within a given college have very similar earnings outcomes provides evidence against the concern that students from low-income families may be”

If a rich child earns more by attending college A than college B, then the potential earnings gain from attending the less selective college for a poor student must be smaller than the earnings difference between poor and rich students within the selective college.

“If a child from a rich family earns more by attending college A than college B (y AR ≥ y BR ), then the potential earnings gain from attending the less selective college for a poor student must be smaller than the difference in earnings between students from poor and rich families within the selective college:”

• AssumptionThe authors state this as an assumption: Among students admitted to a given college, children from low-income families do not have higher ability levels than children from high-income families.
• AssumptionThe authors state this as an assumption: Children's incomes are weakly increasing in parents' incomes, holding all else equal.

Children from low-income and high-income families who attend the same college have very similar earnings outcomes.

“children from low-income and high-income families who attend the same college have very similar earnings outcomes.”

Low-income students admitted to highly selective colleges cannot be significantly over-placed on average relative to their high-income peers.

“(1) implies that low-income students who are admitted to highly selective colleges cannot be significantly over-placed on average (relative to their high-income peers).34”

Alternative definitions of college attendance produce very similar parental income distribution estimates, with correlations of 0.99 for the bottom-quintile share across colleges.

“We find very similar estimates of parental income distributions using these alternative definitions of college attendance, with correlations of 0.99 of the bottom-quintile share across colleges using the three measures”

If high-income students are well-matched at selective colleges, they cannot earn less than low-income students of comparable or lower ability would earn by attending less selective colleges.

“Intuitively, if high-income students are well-matched at selective colleges, they cannot earn less than low-income students of comparable or lower ability would earn by attending less selective colleges.”

All statistics reported below are not sensitive to the way students are assigned to colleges.

“More generally, all of the statistics reported below are not sensitive to the way in which we assign students to colleges.”

The problem of measuring earnings too young may be especially acute at elite colleges, where many students pursue advanced degrees.

“This issue may be especially acute at elite colleges, where many students go on to pursue advanced degrees.”

Income segregation across colleges is comparable to income segregation across Census tracts in the average American city.

“The degree of income segregation across colleges is thus comparable to income segregation across census tracts in the average American city.”

Colleges in America are just as segregated as the neighborhoods in which children grow up.

“colleges in America are just as segregated as the neighborhoods in which children grow up.”

There is substantial income segregation across colleges, with rich students concentrated in certain institutions and poor students in others.

“Figure Ic implies that there is substantial income segregation across colleges, with students from rich families predominantly attending certain institutions while students from poor families attend others.”

Stony Brook admits students with weaker academic qualifications than Columbia, at least based on observables.

“In practice, Stony Brook admits students with weaker academic qualifications than Columbia, at least based on observables.”

• AssumptionRests on an assumption: SAT scores and admissions rates are valid measures of academic qualifications.

Colleges do not pay a large cost in terms of reduced earnings outcomes for their students for any affirmative action policies currently in place that favor the admission of low-income students.

“A related implication of the results in this section is that colleges do not pay a large cost -in terms of reduced earnings outcomes for their students -for any affirmative action policies currently in place that favor the admission of low-income students.”

Much of the increase in intergenerational persistence when using household income is driven by high-income children being more likely to be married, even conditional on attending the same college.

“Hence, much of the increase in intergenerational persistence when measuring income at the household level is driven by the fact that children from high-income families are more likely to be married, even conditional on attending the same college.”

Measuring children's earnings between ages 32 and 34 is sufficiently late to obtain a reliable measure of children's ranks at all colleges.

“The preceding evidence indicates that this is sufficiently late in a child's life to obtain a reliable measure of children's ranks at all colleges.”

The degree of mismatch can be bounded by the differences in earnings between low- and high-income students within a college.

“we show that the degree of such mismatch can be bounded by the differences in earnings between low-and high-income students within a college.”

Stony Brook may be more effective in helping students of a given ability level reach the top earnings quintile than Columbia.

“These statistics point in favor of the second explanation, namely that Stony Brook may be more effective in helping students of a given ability level reach the top earnings quintile than Columbia.”

• AssumptionRests on an assumption: SAT scores and admissions rates are valid measures of academic qualifications.

If all colleges had mobility rates comparable to those at the 10th percentile, the U.S. would have about half as much bottom-to-top-quintile income mobility among those who attend college as it currently does.

“If all colleges had mobility rates comparable to those at the 10th percentile, we would have about half as much bottom-to-top-quintile income mobility among those who attend college as we currently do in the U.S.”

The educational model linked to the highest upper-tail mobility rates shows little heterogeneity.

“In sum, these findings show that there is little heterogeneity in the educational model that is associated with the highest rates of upper-tail mobility.”

Only 43% of the association between Hispanic shares and access is explained by the lower incomes of Hispanics themselves.

“implying that only 43% of the association between Hispanic shares and access is explained by the lower incomes of Hispanics themselves.”

The correlations between alternative mobility measures and baseline measures exceed 0.8.

“they all have (enrollment-weighted) correlations with our baseline measures exceeding 0.8 (Online Appendix Table VI).”

The broad patterns in mobility rates are not sensitive to using income measures that are less influenced by labor force participation choices.

“the broad patterns in mobility rates are not sensitive to using income measures that are less influenced by labor force participation choices.”

The within-CZ SD of access among colleges with a success rate above the 75th percentile is 3.44%.

“the within-CZ SD of access among colleges with a success rate above the 75th percentile remains substantial, at 3.44% (Table V, row 3).”

Differences in labor market conditions or prices across areas explain relatively little of the variation in mobility rates across colleges.

“we conclude that differences in labor market conditions or prices across areas explain relatively little of the variation in mobility rates across colleges.”

Differences in bottom-to-top-quintile mobility rates across colleges cannot be systematically predicted based on colleges' observable characteristics.

“differences in bottom-to-top-quintile mobility rates across colleges cannot be systematically predicted based on colleges' observable characteristics, such as whether a college is a public or private institution or its selectivity rate.”

Colleges that move many low-income students into the top earnings distribution are all highly selective, high-expenditure, elite institutions.

“The colleges that channel many of their students from low-income families to the top of the distribution are uniformly highly selective, high expenditure, elite colleges.”

The correlation between baseline and cost-of-living-adjusted mobility rates is 0.96.

“the (enrollment-weighted) correlation of our baseline and cost-of-living-adjusted mobility rates is 0.96 (Online Appendix Table IV).”

Hispanic parents are 14.8 pp more likely than non-Hispanics to be in the bottom income quintile.

“Hispanic parents are only 14.8 pp more likely than non-Hispanics to be in the bottom income quintile (based on the 2003 Current Population Survey)”

• cites 2003 Current Population SurveyNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The correlation between baseline estimates of mobility rates and alternative measures using male students or household income exceeds 0.92.

“The correlation between our baseline estimates of mobility rates and all of these alternative measures exceed 0.92 (Online Appendix Table IV).”

The normalized mobility rates have a correlation of 0.98 with baseline estimates.

“The normalized mobility rates have a correlation of 0.98 with our baseline estimates.”

The educational models linked to broad upward mobility are different from those linked to upper-tail mobility.

“Hence, the educational models associated with broadly defined upward mobility are distinct from those associated with upper-tail mobility”

Most of the baseline correlation of 0.54 between mobility rates and Asian shares is due to ecological factors.

“implying that most of the baseline correlation of 0.54 between mobility rates and Asian shares is due to ecological factors.”

The colleges with the highest mobility rates remain very similar when focusing on male students or using household earnings.

“The colleges that have the highest mobility rates when we focus just on male students or use household earnings also remain very similar (Online Appendix Table V).”