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Stop The Presses

It’s Monday night and the Record comes out on Wednesday, but this needs to be the lead story.

Williams College has responded to the U.S. Senate Finance Committee with information it asked for on the college’s endowment, fees, and financial aid.

The committee requested the information from the 136 colleges and universities in the country with endowments of $500 million or more. Williams’ endowment as of last June 30 was $1.89 billion.

The response from President Morton Owen Schapiro (pdf) stressed the college’s focus on providing “the finest possible liberal arts education that is accessible to students of all economic backgrounds” and pointed out that Williams admits students without regard to their ability to pay and promises all admitted students the financial aid needed for them to attend for four years.

This is one of the most important stories of the year. The report provides a rare look at the underlying data and — Surprise! — validates several of the points that I have been making for the last 5 years. See below for more details. And, if you are a Record reporter, drop me a line. I give good quote. (And don’t forget these questions.)

1) I don’t have time to do a thorough analysis of the pdf but there are a lot of details here worth pondering.

2) We can see that there has been a dramatic transfer of wealth from Williams to its students. See page 11. Total spending on financial aid has gone from $12.9 million to $31.1 million. Part of that is caused by inflation and by the rise in tuition. But the overwhelming cause is that the College is handing more money to more students, independent of family income. (There is no evidence that Williams students have become poorer over the last 10 years.) Why this sudden jump on aid? Is Morty just a nicer guy than Hank Payne? No! Competition among elite colleges has driven this wealth transfer. In just a decade, Williams has foregone around $15 million dollars, money that it used to demand that students/families beg, borrow or steal. If Williams had not done so, then hundreds of Ephs would be going elsewhere. Start here for previous commentary.

What’s important about this report is that it is the first time we have seen the raw dollar figures. Also, there is enough supplementary data, that we (read: Record reporters) can disentangle the effects of inflation, fee/tuition hikes, and changing family income/wealth. But the basic points seems obvious. Williams is significantly cheaper now then it was ten years ago from almost all non-millionaires.

3) We can see that there is no evidence that the socio-economic diversity of Williams has increased in the last decade and some circumstantial evidence that it has stayed the same. Note that the (true!) fact that Williams is giving more money to all sorts of students tells us little about whether or not the socioeconomic diversity of the student body has increased. For example, if all students were millionaires, and the College handed everyone a $100 on the first day of classes, then, Presto!, everyone would be receiving financial aid from the College.

The circumstantial evidence comes on page 12 in the table of the “Parental Income of Aided Students.” The College likes to trumpet the fact that it is giving more money to wealthier families. So, the 95th percentile of family income among aided families has risen. Fine. That is interesting. But that tells us little about the change in the distribution of family income among all families at Williams. (Actually, we should be able to combine this data with information on the number of aided students, but ignore that complexity for now.) More importantly, we can see that the 5th percentile has stayed largely constant for the last 10 years. Williams is letting in about the same number of very poor students today as it did 10 years ago. So, on that measure, there has been no meaningful increase in socioeconomic diversity, despite the endless praise of Questbridge.

Recall from Lindsey Taylor’s ’05 thesis that this data probably overstates the number of poor students at Williams. Because of divorce, retirements and other special situations, many of these families with very low income this year are actually not poor at all.

The key question for a Record reporter becomes: What is the 10th, 25th and 50th percentile for family income among aided students over the last 10 years? (Since students not on financial aid do not submit income statements, the College does not have data on them.) The problem with the 95th percentile is that it is changing as the College becomes more generous. But everyone in the 50th percentile was getting aid 10 years ago as well. And, with about half the students on financial aid, the 50th percentile of aided students represents the 25th percentile for all students.

I bet that the 50th percentile of family income for aided students has stayed mostly constant for the last decade and that, therefore, Williams is no more socioeconomically diverse today than it was in the late 1990s. In fact, you could easily take that same analysis back into the 1980s and, I bet, find the same thing. Now, I have no problem with that result. I just don’t like to see Williams imply something that is not true.

More commentary later. What interesting points do readers see in the report?

UPDATE: I just noticed that that table includes the median, i.e., the 50th percentile for aided families. So, in 1998 the median aided family was number 426 in the 2000 or so Williams families ranked by income from lowest to highest — 50th percentile of 853 and assuming that all poor families apply for aid. That family made $63,791. In 2007, we know that family number 495 (50th percentile of 990) made $72,293. The next step is to account for inflation and make some assumptions about the income distribution of families at Williams. But just consider the data we have.

  426 495
1998 64k  
2008   72k

It sure seems plausible that family number 495 might have had an income of around 72k in 1998 and, conversely, family 426 might have had an income in the neighborhood of 64k in 2008. (And, obviously, these are different families each year.) In anything, I would not be surprised if family 426 had a higher income than 64k in 2008, i.e., that the 20th percentile in family income at Williams has risen in the last decade. It is an empirical question.

Yet despite the endless bragging by Williams that socioeconomic diversity has increased, there is no evidence for that claim. If anything, we have good reason for not believing it.

But maybe there are more billionaires at Williams. Socioeconomic diversity has increased, just at the high end. Not that there is anything wrong with that!

UPDATE II: In fact, with information about the mean and the number of students (along with data on the 5th, 50th and 95th percentiles), we should be able to figure this out exactly. Surely there is a smart reader who can provide the solution in the comments.

To be precise: Assume that all non-rich students seek aid. What is the family income of the 400th poorest family (about the 20th percentile) at Williams over the last 10 years? (For extra credit, provide confidence intervals for your answers.) My intuition is that this number is largely constant. Williams is just as much a rich kid’s school today as it was a decade ago.

UPDATE III: Here is the assignment for students in STAT 201. For each year, fit a lognormal distribution to the data. Or perhaps there is an analytic solution we can use that just relies on the mean and median? Then, estimate where the 400th ranked family falls in that distribution by looking for the 400/number-of-families percentile in that year. Using random draws to create confidence intervals for the estimate for each year. Plot the year-to-year number and associated confidence intervals.

UPDATE IV: I am having so much fun, I can’t stop! Because the lognormal distribution is hard and there is not much skew in the data, I just went with a normal distribution and played around with some plausible values for the start and end years. Here are two lines of R code:

> qnorm(c(0.05, 400/853, 0.5, 0.95), mean = 65, sd = 36)
[1] 5.8 62.2 65.0 124.2
> qnorm(c(0.05, 400/990, 0.5, 0.95), mean = 79, sd = 43)
[1] 8.3 68.6 79.0 149.7
>

It is obvious that the normal distribution does not fit that well in the tails. But it doesn’t fit too poorly either. Moreover, since we are interested in data that is close to the median anyway, it is not that important what happens in the tails.

The key conclusion is that, while the number of families getting aid has risen (853 to 990 or up 16%), the median income of those families has risen faster (65k to 79k or up 22%) so the wealth of the family at the 20th percentile of all Williams families has risen (about 10%) as well. If anything, Williams is less socioeconomically diverse than it was a decade ago.

UPDATE V: Whoops! I should have used the median numbers from that table, not the means. Sorry! Basic conclusion doesn’t change. Perhaps a kind reader could redo the R analysis.

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#1 Comment By Benny On March 4, 2008 @ 12:15 am

Why would you use the median instead of the mean?

> qnorm(c(0.05, 400/853, 0.5, 0.95), mean = 63.8, sd = 36)
[1] 4.585269 60.993733 63.800000 123.014731
> qnorm(c(0.05, 400/990, 0.5, 0.95), mean = 72, sd = 43)
[1] 1.271294 61.555186 72.000000 142.728706

#2 Comment By Neil On March 4, 2008 @ 12:27 am

dkane, is this link working for you? i’m getting Error 404.

The response from President Morton Owen Schapiro (pdf)

#3 Comment By hwc On March 4, 2008 @ 1:01 am

dkane:

1) IMO, it’s a mistake to talk about “financial aid spending”. Financial aid is a price discount, plain and simple. That’s how colleges view it in their financial reports.

2) What is going on in elite college pricing is also quite simple, although seldom explicitly stated: a steady march towards a progressive pricing structure. Raise the sticker price (what the wealthy customers gladly pay) in order to discount the price for middle and low income families.

The figures cited in the report regarding net average price charged have been widely available for years. In fact, these figures are the basis of a college’s annual financial reports.

#4 Comment By wslack On March 4, 2008 @ 1:16 am

#5 Comment By dkane On March 4, 2008 @ 8:30 am

1) Thanks. Linked now fixed.

2) hwc is correct that, nowadays, financial aid is really just a price discount and that the constant raising of tuition does mean that Williams charges its millionaire students more. Still, I would be hard pressed to call the system, and where it is going, “progressive.” Very soon, Williams will be free everyone from a family making less than $200,000 per year. This is progressive in a relative sense (Herb Allen pays full freight!) but not in an absolute sense.

If you make $200,000 per year, you are rich. If Williams is free for (some) rich people, then you can’t meaningfully describe its pricing as “progressive.”

3) I should use the median because we have three percentiles from each distribution (the 5th, 50th (median) and 95th). Those are the numbers that I am trying to match using qnorm. Now, as you show, it is hard to match the outlying percentiles well given that there is a skew to the right, but this is still the right way to think about it.

What parametric distribution should we use and how do we estimate that using three percentiles and the mean? Suggestions welcome.

#6 Comment By hwc On March 4, 2008 @ 11:43 am

<blockquote.Very soon, Williams will be free everyone from a family making less than $200,000 per year. This is progressive in a relative sense (Herb Allen pays full freight!) but not in an absolute sense.

Fair enough. “Progressive” might be a stretch.

Of course, Morty has written that the big-dog colleges and universities might very well end up with free tuition for all or even (as at top grad schools today) paying the best students to attend.

All of this recent no-loan stuff has very little to do with low-income customers. It’s a form of merit aid to middle income families — the kind of customer that might get a $15,000 discount, but is still capable of paying $30,000 a year. The intense pricing pressure in the marketplace is really on the tiers of schools just below the big dogs…the schools that have been using merit price discounting to compete.

#7 Comment By aparent On March 4, 2008 @ 12:40 pm

As a parent, I was drawn to Pres. Schapiro’s statements that “We anticipate … expand(ing) our financial aid still further” (p. 2) and that “additional changes in … financial aid policies” (p. 4) may be forthcoming — just hope it’s soon enough to mean we’ll have to borrow less over the next couple years.

#8 Trackback By Statistical Modeling, Causal Inference, and Social Science On March 11, 2008 @ 7:19 pm

Specifying a distribution from the mean and quantiles, or, just in case you thought this blog was nothing but square footage and Starbucks…

David Kane writes, What is the best way to simulate from a distribution for which you know only the 5th, 50th and 95th percentile along with the mean? In particular, I want to estimate the value for a different percentile……

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