07 October 2016

Graduation Rates In Four Year Programs In Colorado

The latest available data on the six year graduation rate for full time four year first degree bachelor's degree program students at Colorado institutions is as follows:
  1. United States Air Force Academy (Federal) 86%
  2. Colorado College (Non-Profit) 86%
  3. U. of Denver (Non-Profit) 76%
  4. Colorado School of Mines (State) 76%
  5. U. of Colorado at Boulder (State) 70%
  6. Colorado State U. at Fort Collins (State) 67% 
  7. Regis U. (Non-Profit) 60% 
  8. Rocky Mountain College of Art + Design (For Profit) 48%
  9. Johnson and Wales U. at Denver (Non-Profit) 47%
  10. U. of Colorado at Colorado Springs (State) 47%
  11. U. of Northern Colorado (State) 46% 
  12. Colorado Christian U. (Non-Profit) 40%
  13. U. of Colorado at Denver (State) 40% 
  14. Nazarene Bible College at Colorado Spring (Non-Profit) 40%
  15. Fort Lewis College (State) 38%
  16. Western State Colorado U. (State) 37%
  17. Naropa U. (Non-Profit) 33%
  18. Colorado Mesa U. (State) 32%
  19. Colorado State U. at Pueblo (State) 32% 
  20. College America at Colorado Springs, Denver and Fort Collins (Non-Profit) 31%
  21. Art Institute of Colorado (For Profit) 29%
  22. National American U. at Centennial, Colorado Springs and Denver (For Profit) 29%
  23. Colorado Technical U. at Colorado Springs (For Profit) 27%
  24. Metropolitan State U. (State) 25%
  25. Adams State U. (State) 24% 
  26. U. of Phoenix at Colorado Springs, Lone Tree and Westminster (For Profit) 18%
  27. Colorado Technical U. at Aurora (For Profit) 14% 
  28. DeVry U. at Colorado Springs, Denver and Westminster (For Profit) 12%
  29. Denver School of Nursing (For Profit) 11%
  30. Colorado Heights U. (Non-Profit) 11%
Notable Conclusion

Students who are below a 22 on the ACT composite, a 1073 on the new SAT composite, a 1610 on the older SAT composite, are not in the top 35% of his high school class (in a high school that is representative of the general population), or have below a B+ GPA, have a significantly impaired, low chance of graduating with a four year degree.  This cutoff is not very sensitive to the selectivity or to the type of institution attended, although certain programs (e.g. some STEM programs such as math, physics and engineering) may have a higher effective minimum threshold for a student to have a reasonable chance of graduating.

The threshold for any ordinary college program corresponds to an IQ of about 110 on a 15-point standard deviation scale or 111 on a 16-point standard deviation scale which is about the 75th percentile of the general population (a higher percentage because the general population includes high school dropouts who aren't included in SAT and ACT percentiles). Under 15-point standard deviation WAIS IQ scaling standard, an IQ of 100 is average for the population as a whole, an IQ of 105 is average for a high school graduate, and an IQ of 115 is average for a college graduate. So, an effective cutoff IQ of about 110 for a reasonable likelihood of graduating from college, fits with the concept that one must be discernibly better than average high school student to be likely to graduate from a college or university with a four year degree.


Non-Academic Factors

Now, obviously, reality is complicated. Someone with a good work habits and good interpersonal skills who probably overachieves on his or her grade point average and class rank relative to his test scores may be able to graduate with test scores below this cutoff.  On the other hand, someone with bad work habits and poor social skills with test scores above this cutoff may be likely to fail to graduate. Indeed, I wouldn't be surprised if measured of work habits quality were more predictive of college success than test scores.

Accuracy of Academic Factors

Similarly, if there was good reason to think that the student's test scores or grades were not accurate for some reason that would matter. Somebody who takes the ACT while sick with the flu, for example, may underperform relative to their true ability. And, the high school grades of someone who was experiencing disruptive issues in their personal life while in high school, may similarly not reflect their abilities. And, trying to learn in a language other than your native language could also pose issues that would confound typical measures of academic ability. Any system controlling access to higher education should have some safety valves for these kinds of issues.

Gradual Variation In Graduation Likelihood

More fundamentally, at any given level of academic ability, the likelihood of not graduating in six years is almost never either 0% or 100%. It is perhaps 4% at the highest level of academic ability and gradually increases as one moves down the academic ability scale. I can't even tell you what the percentage would be exactly at the cutoff, although it would almost certainly be significantly below 50% and wouldn't be 100% either. There is a substantial literature on college retention rates, but much of it is pretty dubious, relying on economic models rather than hard data. The central facts driving this inquiry are as follows:
Among individuals aged twenty-three in 1970, 23 percent of high school graduates had completed a BA degree, while about 51 percent had enrolled in college for some period since high school graduation. For the same age group in 1999, the share of high school graduates who had enrolled in college at some point rose substantially, to 67 percent, while the share receiving a BA degree rose only slightly, to 24 percent of the cohort. Thus, for college participants measured in their early twenties, completion rates fell by more than 25 percent over this interval. Completion rates measured at older ages are closer to stagnant, implying an overall increase in the time to degree.
A related issue is that the growth in degrees awarded between 1984 and 2009 was heavily concentrated in majors that provide the lowest post-graduation salaries.

One summary of the literature explains that:
The American literature includes Bound and Turner (2011), who survey the economics literature on college enrolment and completion with a focus on the limited US growth in college enrolment and áat college completion rates over time. The empirical analysis includes issues such as student preparedness, student funding, parental background, college resources and the costs and gains of college education. Bowen et al. (2009) study completion in US public colleges. One of the results of their empirical analysis is that high school grades are much better for predicting college completion than the Scholastic Assessment Test (SAT) scores. Another strand of the American literature deals with the ability of the SAT test to predict college admission (e.g. Manski and Wise 1983) and freshman grades (e.g. Rothstein 2004). In combination with high school grades, US colleges and universities use the SAT score for determining admission. For example, the University of California constructs an admission index consisting of a weighted average of SAT scores and high school grades. If a student from a public secondary school in California has a score above a certain threshold on this index, this student is automatically admitted to the University of California system. In addition to pre-college grades learning about academic performance during college plays a role according to Stinebrickner and Stinebrickner (2014) who assess that 45 per cent of dropout in the first two years of college can be attributed to what students learn about their academic performance. The problem of attrition in the US higher educational system figures prominently in the educational and sociological literature, where the seminal contribution is Tinto (1993).
Thus, about half of students drop out of college because they are not getting good grades in the classes that they are taking.

Economists know that a student's personal chance of graduating greatly impacts the return that a student can get on an investment in higher education: 
The return to trying to get a degree is far lower than the return to successfully getting a degree. Why? Because marginal students routinely fail to graduate. 
But, a close examination of the "single best paper on this theme" demonstrates that the economists are making little more than crude guesses about how the probability of graduating relates to one's academic ability with no detailed data upon which to base their suppositions. It estimates the marginal probability as follows:
[T]o map SAT scored into failure risk, we use observed data on institution-level failure rates by SAT score to estimate a linear map that takes the percentile of the test scores g(νSAT ) into a probability of failure as follows: π = 1 −λgrad g(νSAT ); where λgrad=0.9. We specify g(·) such that the top percentile of SAT scores will fail with probability (1-λgrad), while the first percentile will fail with probability λgrad.
Thus, in this crude linear model in the 2013 study with no direct empirical support, someone with a perfect SAT score fails 10% of the time, while someone with a zero SAT score fails to graduate 90% of the time. 

The only actual data relied upon by the model shows that college enrollment is very high for students with 1600 point scale SAT scores of 1100 or more, slacks a little in the SAT score range of 900-1100, and is significantly lower for students with an SAT score of below 900. But, this is based upon an ability to be admitted to college and uniformed perceptions about probabilities of success that marginal students have, rather than the actual probability of success of marginal students.

This outcome does relate to another conclusion of the model that may be valid, however. The returns to an investment in higher education in their model when the probability of failure is 50% (whenever that may be) are dramatically greater than if the probability of failure is 66% which in turn is dramatically greater than if the probability of failure is 82%. In contrast, returns in their model improve only modestly between a 50% chance of success and a 34% chance of success, and improve even more modestly for higher chances of success. The extent to which trying to graduate from college is a good idea drops out dramatically and non-linearly between a 50% chance of failure and an 82% chance of failure at which the return is almost nil.  So, if one can identify the level of academic ability that corresponds to a 70%-80% chance of failure, one need not worry too much that denying a student in that rank admission to college will tend to be a good decision for the student making the decision ex ante and for the public deciding if the investment in this student is worth it.

A more direct measurement of the benefits of college admission to academically marginal students based upon a "natural experiment" in Florida in a 2014 study, however, finds the economic benefits of college admission for such students are very substantial. The author of that study sums up the implications of the empirical question as follows:
Why has supply not kept pace with demand? 
One possible explanation is that the returns for students on the margin of college attendance are much lower than the average returns to college. This is consistent with the large body of evidence suggesting that many US primary and secondary schools do a poor job of preparing their students for college, as well as with evidence from structural models of schooling choice suggesting that relaxing financial constraints on postsecondary attendance would have little effect on educational attainment. 
Alternatively, it may be the case that the returns to college for students on the margin of attendance are high but that these students are constrained in some way. Possible constraints include short-term credit constraints, constraints based on limited access to or costly acquisition of information on the costs and benefits of college and the admissions process, and constraints on the supply of places in appropriate postsecondary institutions. 
Distinguishing between these lines of reasoning is of critical importance for higher education policy. If many students are capable of making high return human capital investments but cannot because they are constrained in some way, then policies aimed at relaxing these constraints will be enough to increase the supply of college graduates. If low marginal returns are the dominant story, then policies aimed at improving primary and secondary education so that students emerge better prepared for college are more appropriate. The key question is whether students who are only marginally prepared for college are able to realize economic returns large enough to justify the investment of time and money, and, if so, which constraints need to be relaxed so that more such students actually do make these investments.
This study then ultimately concludes that:
Students with grades just above a threshold for admissions eligibility at a large public university in Florida are much more likely to attend any university than below-threshold students. The marginal admission yields earnings gains of 22% between 8 and 14 years after high school completion. These gains outstrip the costs of college attendance, and they are largest for male students and free lunch recipients.
The study involved:
a large sample of Florida high school students with a regression discontinuity design around a state-level GPA (grade point average) cutoff for admission to the Florida State University System (SUS) to estimate the returns to 4-year college admission for students at the margin of admission to any SUS campus. I focus my analysis on Florida International University (FIU), a SUS campus that was especially generous in the way it computed the GPAs used for admissions during the period in question and that thus functioned as the SUS campus of last resort for many students. I find that students just above the admissions threshold at FIU are 23.4 percentage points more likely to be admitted to FIU and 11.9 percentage points more likely to attend any SUS campus than students just below the admissions threshold. On average, students induced to attend college by “threshold-crossing” attend a SUS campus for an additional 3.8 years, and they graduate at rates similar to those in the broader student population. Threshold-crossing produces a $372 gain in quarterly earnings between 8 and 14 years after high school completion, corresponding to a $1,593 increase in quarterly earnings per marginal admission. This is equal to 22% of expected earnings just below the threshold. Driving earnings gains are large effects for male students ($4,191 per marginal admission) and free-lunch recipients ($2,695 per marginal admission). Gains for female students and students who do not receive free lunch are close to zero. . . .
The closest precedent in the literature on the earnings effects of education is Hoekstra (2009). Hoekstra uses a test score admissions cutoff to estimate the returns to attending a flagship state university. His analysis differs from what is presented here in that students who are not admitted to the flagship university most likely attend other colleges, although Hoekstra cannot verify such attendance directly with the available data, and students near the admissions cutoff in his analysis have stronger academic backgrounds than students near the admissions cutoff in the present article. The average combined SAT score for students near the cutoff in the Hoekstra study was roughly 1000 on the pre-1995 SAT, which corresponds to a score of 1100 on the current test. The average score for students near the cutoff in the present analysis is 839, a score that would place a student in the 21st percentile of college-bound seniors in 2011. 
While 22% gains are lower than the gains experienced by the average college graduate relative to the average person who does not graduate from college (who experience 97% earning gains), they are still significant enough to be worth it to the marginal college applicant.

The gender gap is also particularly notable because one of the economic reasons that many women identify for attending college is to find a college educated spouse, yet women who are on the margin of being admitted to college or not do not appear to receive any economic benefit from doing so (although this may be an artifact of the fact that the study used post-admissions "earnings" rather than household income is used to evaluate the returns to college admission in the study).

There is even a calculator to estimate a student's chance of graduating, although how it was validated is unclear.

In the same vein, a study of college expansion in Russia finds, in a nutshell, that the greatest benefit arises where it provides access to the smartest groups of people who didn't have access to higher education before, such as cities that previously had no colleges or universities nearby, while providing much less benefit in places that already had multiple higher educational options.

Still, if you wanted to set a cutoff as a matter of policy in an intelligent manner, you would like to have this kind of data so that you could compare how many people among those denied admission would be statistically likely to graduate and how many people granted admission will be statistically likely to not graduate in six years. Better yet, you'd like to study what factors distinguish people admitted with marginal admissions criteria who do graduate from those who do not, to better refine the model. Even beyond that, one would like to study how those marginal admitted students who did graduate compared to other graduates after graduation on measures of economic success.

How Much Should We Care About These Caveats?

If a policy maker was a dictator who could impose the cutoff on every single four year college program in the country, the risk of being too strict and denying any path to higher education to the rare exceptional individual who could have graduated and thrived despite seemingly weak admissions criteria would be a great concern. But, given the fact that no one policy maker has a monopoly of admissions criteria at institutions that might admit a marginal student, and that an alternate route to a four year degree via two years of success at a community college followed by a transfer to a four year college exists, this concern shouldn't be grounds for policy making paralysis.

But, IQ and any measure related to it, predicts academic ability better than just about anything else that IQ predicts. So, it wouldn't be surprising if below a certain IQ (to the extent the measurement is accurate), a student is just not going to be able to handle college level work. It doesn't do anyone any good for a student with a 100 IQ who is in the bottom half of a representative graduating class with a B- or C+ GPA and test scores to match to embark upon trying to earn a four year college degree and failing. Yet, every year, hundreds of thousands of students with strong encouragement from their parents and teachers and guidance counselors try to do just that.


Generally, graduation rates are closely tied to selectivity in admissions. But, even the very most selective institution (e.g. Yale University with a 96% graduation rate) fail to graduate some of their incoming freshmen.

I was surprised to learn that Johnson and Wales University and College America, both of which have the "feel" of for profit institutions are non-profits. Meanwhile, one for profit institution which has the "feel" of a non-profit institution, the Rocky Mountain College of Art + Design, is an outlier with a respectable for a "for profit" 48% graduation rate.

Seven out of ten of the institutions with the lowest graduates rates are for profit. New federal regulations for federal financial aid, however, are likely to put most of these institutions out of business or dramatically restrict their scale in the next few years. Given their predominantly very poor performance (and the poor performing institutions often have very high numbers of students with very high percentages receiving government grants and government guaranteed loans), this is good policy for both students and the taxpayer alike.

Two basically open admissions four year state institutions, Metropolitan State University in Denver, and Adams State University, as well as one basically open admissions non-profit institution, Colorado Heights University (formerly Tokyo-Loretto Heights) in Denver (which had very lenient admissions requirements - basically a GED or a high school diploma and a 2.0 GPA), share the distinction of having graduation rates below 30%.

Note that full-time first bachelor's degree students are not typical at some of these institutions.  For example, they make up only 8% of students at Nazarene Bible College. Graduation rate is not necessary a good tool for evaluating how well bachelor's degree programs serve part-time and otherwise non-traditional students.  

One reason that I refrained from evaluating two year programs here is that such a large share of students in those programs are part-time, are non-traditional students, and/or are primarily seeking certificates short of a degree or vocational programs rather than relatively comparable to each other bachelor's degrees. But, the problems are arguably even more acute there. Only about 25% of community college students in Colorado receive a degree (typically a two year program) or certificate (often a less than two year program) in three years, despite the lower achievement threshold involved than a bachelor's degree, and at the Community College of Denver the graduation rate is half that. Most community college students need remedial work before advancing to college level work, and their ultimate prospects of getting a degree are particularly low. Also, the community college as a stepping stone to a four year degree approach has real problems in practice.

Graduation rates are a matter of policy when it comes to government operated institutions of higher education which receive significant per student funding subsidies. Is our money well spent on students who don't graduate? Are students better off if they don't graduate (when they often have student loans that can't be discharged in bankruptcy but not degree to improve their earning power)?

Is it relevant that a large share of all non-graduating freshmen drop out within the first year, limiting the wasted time and money for all involved?

Yet, a disproportionate share of poor, working class and middle middle class students who do earn degrees attend schools with low graduation rates (and often lower tuition than other options and room and board at home instead of on campus).

The Apparent Academic Ability Graduation Cutoff 

Graduation rates seem to imply that the rigor of studies at less selective institutions isn't that much lower than at more selective institutions, because otherwise degree inflation would allow more students at less selective institutions to graduate.  There may still be some differences in rigor, of course, but they don't seem overwhelming.

Would it be feasible to set minimum academic standard statewide, designed to exclude students with little chance of graduating, in order to be eligible for state subsidized tuition?

At a school where X% of students graduate, the typical test scores of students who are in the top X% of the entering class in test scores is at roughly the 65th to the 70th percentile.  Put another way, the percentage of non-graduates at an institution is pretty similar to the percentage of admitted students who score below the 65th to 70th percentiles on standardized tests (an ACT composite ca. 22-24, a New SAT composite of about 1073-1113, or an old SAT composite of about 1610-1670). This should correspond to a class rank in the top 30%-35% of the class.  In terms of grades, that is roughly a B+ in GPA. 

This cutoff, for example, is comparable predictive at Metropolitan State University of Denver (with a 25% graduation rate), at Colorado Mesa University (with a 32% graduation rate), at University of Colorado at Colorado Springs (with a 47% graduation rate), and at the University of Denver (with a 76% graduation rate). It also isn't grossly inconsistent with the 86% graduation rate of Colorado College where the 25th percentile ACT score of the admitted students is 27, the mean is 29, and the 75th percentile is 32, although some interpolation is required to estimate the 14th percentile test scores of incoming students there. 

The threshold was much higher at the Colorado School of Mines, however, probably because of its more rigorous STEM curriculum. Also, it is pretty clear that at least 3%-5% of students will fail to graduate in six years no matter how will academically prepared and screened they are for reasons that are generally completely unrelated to any lack of academic ability or study skills or interpersonal skills, such as a serious illness or injury, death, family financial woes, elder care demands, deciding to have children, or pursuing a promising non-academic opportunity (e.g. founding a national company with some partners). But, the remainder of the non-graduation rate seems to be strongly correlated with academic ability.

This tends to contradict a recent study exploiting a "natural experiment" that suggested that individual student graduation rates are significantly improved at higher quality colleges. Specifically, it can reduce a student's odds of graduating on time by 40%. But, it is consistent with the findings of a 1970 study of Wisconsin college students who graduated or did not graduate by 1964, which found that:
A stepwise multiple regression analysis shows that type of college attended explains a small but significant proportion of variance in college graduation beyond what can be accounted for by measured intelligence, rank in high school class, socioeconomic background, and level of occupational aspiration in high school. Other findings are that different types of colleges have different effects for students of different socioeconomic status and intelligence levels and that the selection process into different types of schools has some effect on the overall educational selection process.
Student characteristics in that study explained 25% of the variance in dropout rates, while institution type explained just under 10% of the variance. Of the student characteristics, high school class rank was the best predictor, followed by socioeconomic status, followed by intelligence, although obviously, these variables are not entirely independent of each other.

One of the better sets of data with marginal graduation probabilities involves a comparison of likelihood of graduating from Northern Iowa Area Community College between students with some college level work exposures in high school and those without this exposure. It compared the performance of students at the lowest quartile (with an average high school GPA of 2.29, the middle quartile with an average high school GPA of 2.74 and the highest quartile with an average high school GPA of 3.21). For those without exposure to college level work, graduation rates were as follows, while those exposed (about a fifth of the sample) had the rates in parenthesis: 

Lowest Quartile:  Male 4.18% (6.57%); Female 17.17% (25.04%)
Middle Quartile:  Male 19.04% (27.49%); Female 44.51%  (56.38%)
Highest Quartile: Male 41.25% (53.08%); Female 68.58% (77.86%)

Nothing in the other literature had suggested that the gender disparity in graduation rates was so stark, although this might be a product of the Northern Iowa economy in which the economic prospects for less educated men in the farming economy might be greater than the economic prospects for less educated women.

Another study focused on the benefits of remedial courses, if any, finds that there are benefits (a bit less than a 10% reduction in the odds of dropping out relative to other students with the same academic qualifications who don't take remedial classes) but also sets forth some useful baseline information:
[S]tudents placed into remediation had lower ACT scores and high school GPAs. For example, students placed in math remediation scored a mean of 17.4 on the math section of the ACT while students who did not take the classes scored 23.3 (a similar gap, 15.8 versus 22.8, is found for English remediation). A simple comparison of the outcomes of students placed into remediation and those who are not suggests that remedial students had worse educational outcomes. After five years, a larger proportion of them dropped out of college without a degree (65.2 for those in math remediation versus 30.8 percent) and fewer of them completed a baccalaureate degree (18.1 for those in math remediation versus 53.3 percent). 
In any case, about 60% of high school graduates go to college, even though 25%-30% of high school graduates are basically on track to go to college and drop out (many in the first year), while 30%-35% of high school graduates are actually on track to go to college and graduate.

Footnotes and Additional Sources

Excludes 100% distance learning programs, Argosy University which has only 2 full time undergraduate students, an extension campus of Columbia C. - Missouri in Centennial which is Non-Profit, and Jones International University - Centennial which is For Profit.

Partially related, a recent Congressional report on for profit higher education in the United States can be found here.

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