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……

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.

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.

Correct link:

http://www.williams.edu/admin/president/letters/080229_SenateFinCom.pdf

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.

The response from President Morton Owen Schapiro (pdf)

> 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