Income distributions, college choices, and such

Topics/tags: Academia, data junkie, long, rambly

A few years ago, the New York Times published an interactive data set entitled Some Colleges Have More Students From the Top 1 Percent Than the Bottom 60. I keep getting sent back to that data set, whether it be in a talk at the Tapia Celebration, a reading group on The Privileged Poor [1], or a crappy article from Medium [2]. Today I decided to a slightly deeper dive into the data.

It’s depressing to see how many of our peers appear at the top of the list. Colorado College is second, with 24.2% of their students in the studied group from the top 1% and 10.5% of their students from the bottom 60%. Washington and Lee is third, with 19.1% from the top 1% and 8.4 from the bottom 60% [3]. Kenyon is eighth, with 19.8% from the top 1% and 12.2 from the bottom 65%.

How about Grinnell? Let’s see. We are 182nd, with 5.5% of our students from the top 1% [4] and 24.6% from the bottom 60%. I wonder where we rank relative to the comparison group we use for various studies [9]. Let’s see.

Rank	Institution	Top 1%	Bottom 60%	Ratio
002	Colorado	24.2	10.5	2.30
003	Washington and Lee	19.1	8.4	2.27
008	Kenyon	19.8	12.2	1.62
025	Bowdoin	20.4	17.5	1.17
033	Davidson	17.4	16.4	1.06
042	Carleton	14.4	15.5	0.93
044	Williams	18.1	19.6	0.92
047	Amherst	21.1	24.4	0.86
066	Oberlin	9.3	13.3	0.70
071	Pomona	14.2	21.8	0.65
082	St. Olaf	8.3	15.3	0.54
096	Swarthmore	9.0	18.2	0.49
109	Reed	7.8	18.0	0.43
126	Vassar	9.3	26.1	0.36
140	Macalester	6.8	22.0	0.31
182	Grinnell	5.5	24.6	0.22
230	Smith	4.4	27.2	0.16

We’re almost at the bottom [10]. In some sense, that’s good; we’re serving an implicit part of our mission to provide a top-quality undergraduate education to students who could not otherwise afford such an education. The comparatively small percentage of those from the top 1% may also be a good thing in other ways; it means that students are less comfortable with open displays of wealth, something that can make other students feel like outsiders [11].

There are, of course, also some significant disadvantages associated with having limited numbers of students from the top 1%. Not surprisingly, as you look to grow the endowment [14] you’re much more likely to get large donations from that group than even those in the rest of the top 10%; after all, the 1% usually have more much available to give. As we look toward opportunities for our students, there are also advantages to having a reasonable set of wealthy students. In part, it means that when students network [16], they have connections to a broader group. I don’t know if there has been a formal study of this third issue, but I would expect that there’s a hidden benefit to enrolling high-income students: It increases the odds those who hire for that high-end jobs will have heard of the institution: Oh, yeah, I’ve heard of Grinnell. It’s a good school. My nephew (or colleague’s daughter, or whatever) went there. [17]

So, although I’m proud of our ratio, and firmly believe that a central part of our mission is to support talented students who could not otherwise afford an elite liberal arts education, I can understand some of the reasons the Trustees want more full-pay students.

I guess that covers the first part of the [18] Times article: I’m proud, I wonder about the effects of international students on the data, and I think it’s worth considering other implications.

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I’d forgotten, but I see that the article also has a table of elite colleges that enroll the highest percentage of low- and middle-income students. As far as I can tell, these data come from Pell recipients. Let’s see how we stand relative to our peers.

Rank	Institution	Pct. from bottom 40%
04	Grinnell	14.3
04	Smith	14.2
05	Vassar	13.8
12	Amherst	12.0
17	Williams	11.2
19	Macalester	10.8
20	Pomona	10.7
21	Swarthmore	10.6
28	Reed	9.5
34	Bowdoin	9.2
40	Davidson	8.2
44	Carleton	7.9
63	St. Olaf	6.2
64	Oberlin	6.2 [19]
71	Colorado	4.9
72	Kenyon	4.8
74	Washington and Lee	4.5

Hmmm … two tables. I think that means that I can combine the data to see the ratio of 1%-ers to those in the bottom two quintiles.

Institution	Top 1%	Bottom 40%	Ratio
Colorado	24.2	4.9	4.9
Kenyon	19.8	4.2	4.7/td>
Washington and Lee	19.1	4.5	4.2
Bowdoin	20.4	9.2	2.2
Davidson	17.4	8.2	2.1
Carleton	14.4	7.9	1.8
Amherst	21.1	12.0	1.8
Williams	18.1	11.2	1.6
Oberlin	9.3	6.2	1.5
St. Olaf	8.3	6.2	1.3
Pomona	14.2	10.7	1.3
Swarthmore	9.0	10.6	0.8
Reed	7.8	9.5	0.8
Vassar	9.3	13.8	0.7
Macalester	6.8	10.8	0.6
Grinnell	5.5	14.3	0.4
Smith	4.4	14.2	0.3

I didn’t learn much from that exercise; the schools stayed mostly in the same order. The one thing I did learn is that most schools, except Grinnell, seem to have about the same number of students from the middle quintile and the bottom two quintiles. Grinnell, in contrast, has about one-and-a-half times as many from the bottom two quintiles as from the middle quintile. At a recent discussion, some of us had noted that we seem to have fewer middle-income students than in the past; I wonder if this is evidence thereof.

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That second table I grabbed from the Times article says that it’s for elite colleges. What makes a college elite? The Times says roughly 80 of the most selective colleges in the United States, as measured by a 2009 index created by Barron’s. My first search for those data yielded the 2015 list, as reported by the Jack Kent Cooke Foundation. The Cooke foundation refers to selectivity; it looks like elite is either most competitive (1) or highly competitive (2)

Institution	Selectivity	US News Rating
Amherst	1	2
Bowdoin	1	5
Carleton	1	6
Colorado	1	27
Davidson	1	10
Grinnell	2	11
Kenyon	1	30
Macalester	1	27
Oberlin	1	30
Pomona	1	5
Reed	1	90 [20]
Smith	1	11
St. Olaf	2	61
Swarthmore	1	3
Vassar	1	11
Washington and Lee	11	1
Williams	1	1

Fascinating. In spite of being less selective than most of these institutions, we rank better than five of the higher-selectivity institutions. I wonder if we are the highest-ranked selectivity 2 institution. Let’s see. What are the other top schools on the US News top-twenty list?

Wellesley	1	3
Middlebury	1	5
Claremont McKenna	1	9
Haverford	1	11
Colgate	1	16
Hamilton	1	16
Colby	1	18
Harvey Mudd	1	18
United States Military Academy	18	1
Wesleyan (CT)	1	18

Okay, we’re the highest-ranked selectivity 2 institution in the top twenty. How far down do we have to go to reach the next one? Mount Holyoke, at 30 [21]. After that, it’s Lafayette at 36. Hmmm … does US News use selectivity? Their description of their methodology doesn’t suggest that they look at yield, which I assume is a core aspect of the Barron’s study. Strange. Ah! U.S. News indicates that they’ve removed it. But they do write A school’s academic atmosphere is influenced by the selectivity of its admissions, and they do take both grades and standardized scores into account.

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Eventually, I found what seems to be The Barrons’ 2009 list which also appears in The New York Times. In the 2009 list, we’re a 3. I see that the 2015 list has collapsed highly competitive (e.g., Grinnell) with highly competitive plus (e.g., Colorado, in the 2009 list). I don’t think it’s worth following up on that; I wonder why The Times used the 2009 list rather than the 2015 list; perhaps it’s that they had the 2009 data more readily at hand.

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Am I done? Well, there’s one more table in the Times article. It’s about a statistic that they call mobility rate, computed as the product of the percent of students from the bottom two quintiles times the success rate at moving them to the upper-part of the distribution. Or, in simpler words, it’s the proportion of students at the school who start in the bottom two quintiles and end up in some undefined upper part [22]. Is that a useful statistic? I’m not sure.

But I do see that it uses very different data. In that study, only 9.5% of Grinnell students come from the bottom two quintiles. Didn’t that earlier study suggest that 14.3% of Grinnell students come from the bottom two quintiles? I’m surprised at how much the percents vary from year to year. Or maybe the data are wrong. Who knows?

I am puzzled at how, for example, the John Jay College of Criminal Justice can have a success rate of 61.1% yet their six-year graduation rate is only about 45% [23].

In any case, the table suggests that most of these elite schools are having much less success, at least according to this metric. But I’m not sure what we would do about that. I don’t think we should change our mode of instruction, which remains costly. But I don’t know how we would make significant changes to our percent of high-need students without also significantly changing the institution. Ah, well. I guess that’s a task for better minds than mine to consider.

Perhaps I’ll come back to the original study at some point and see how they ended up with the data they did. And perhaps I’ll find another useful metric for assessing the comparative benefit schools like Grinnell provide. But that’s a task for another day.

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Hmmm. The Times article ends with this note.

Selectivity tiers used here are based on a 2009 index created by Barron’s. Ivy plus colleges include the eight colleges of the Ivy League in addition to Stanford, the University of Chicago, Duke and M.I.T. Other elite colleges represent colleges with a selectivity index of 1 excluding the Ivy plus colleges. Highly selective colleges represent those with a selectivity index of 2; selective colleges represent those with a selectivity index from 3 to 5; nonselective colleges represent those with a selectivity index greater than 5 or unlisted in Barron’s.

So why does Grinnell appear in the table of elite colleges? And why would someone choose criteria that should not classify all of the U.S. News top twenty as elite? I have no idea.

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What did I learn from this whole exercise? Not as much as I had hoped. I remain proud of my institution. I seem to have found that we are doing better than peers in some metrics, but I’m not sure how useful those metrics are.

In the end, I was reminded that you should not take data at face value. There’s also a lot of variation in these data from year to year.

At least I had fun looking for data.

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[1] Musing coming soon.

[2] I might also muse about this article. From my perspective, it falls into the clueless academic at elite institution category. But what do I know?

[3] When last I visited, they seemed to have a very active cadre of QuestBridge scholars. But I guess that doesn’t have as much of an impact as I would have imagined.

[4] I wonder if that counts our international students [5]. While Grinnell has a share of full-pay international students, I also think of us as making an important difference to international students who are unlikely to be full pay, some of whom are here on full-ride scholarships.

[5] The Times [6] says that The researchers tracked about 30 million students born between 1980 and 1991, linking anonymized tax returns to attendance records from nearly every college in the country. So it sounds like it’s only US students [7].

[6] Should that be The Times or The Times? I’ve seen both used.

[7] Let’s do some WAG [8] estimates. About 20% of our students can be classified as international students. Let’s assume that half of those are 1%’ers (probably an excessive estimate) and the rest are bottom 60% (possibly also an excessive estimate). That would give us about 14.4% in the top 1% and about 29.7% in the bottom 60%, moving our ratio from 0.22 to 0.48, fairly close to Swarthmore’s. If we assume that 1/4 were 1%’ers and 1/4 were bottom 60%, we’d get 9.4% vs. 24.7%, we get a ratio of 0.38, somewhere between Mac and Vassar. Of course, we’d also need to do the analysis for all of those institutions.

[8] Wild-Ass Guess

[9] Peer institution list taken from https://www.grinnell.edu/about/offices-services/institutional-research/resources.

[10] Well, the bottom of our peer group. I’m pretty sure that there are a few thousand schools in the list.

[11] At least that’s my take from reading The Privileged Poor. Of course, that book looks at the kind of wealth that you see at places like Amherst and Harvard [12].

[12] I was surprised to see that Harvard has both a smaller percentage from the top 1% (15.1%) and from the bottom 60% (20.4%) than Amherst.

[14] And yes, it’s important to grow the endowment. Ours may be huge, but it’s that huge endowment that allows us to simultaneously provide a high-end undergraduate education while remaining need-blind in admissions and meeting full demonstrated financial need [15].

[15] Yes, I realize that full demonstrated financial need is a complicated proposition and that most students do not feel like we do enough.

[16] I realize that networking is easier for those with higher social capital. I also learned in The Privileged Poor that low-SES students are often raised to do it on your own rather than to take advantage of networking. Nonetheless, students benefit from the opportunity to network with those who have family who might offer you internships and connections.

[17] I’m not saying that it’s fair. I’m just acknowledging that it happens.

[18] The Times article seems correct, and better than The The Times article.

[19] No, I don’t understand why Grinnell and Smith have the same ranking but different percentages, while St. Olaf and Oberlin have the same percentage but different rankings.

[20] A recent study suggests that Reed belongs at #36 and that US News is punishing them for not participating in the study.

[21] Soka is ranked 22 but is not on the list of Barron’s selectivity ratings that I found.

[22] Upon further inspection, I see that the table legend says Success rate measures the percent of lower-income students who ended up in the top 40 percent.

[23] College factual: CUNY John Jay College of Criminal Justice Graduation Rate & Retention Rates. https://www.collegefactual.com/colleges/cuny-john-jay-college-of-criminal-justice/academic-life/graduation-and-retention/.

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Version 1.0 of 2019-07-26.