So if we were doing this seriously, the first thing we would need to do is actually determine the markets in question. And that turns out to be extremely complicated. There certainly is not just one big market in which students are all able to shop. Indeed, serious analysis of these institutions ends up usually identifying them a operating in multisided network markets. Like, their functions include connecting students and teachers, students and other students, grantors and researchers, researchers and other researchers, recent graduates and established alums, donors and . . . well that’s VERY complicated, and so on.
OK, so unsurprisingly, different prospective students apply to different colleges, and you can see that as at least in part explainable by different students being interested in different mixes of networking opportunities. And then colleges also compete for some of those students with other colleges, because their various other stakeholders all want to network with those students, and the students can only attend one college each.
OK, so if you wanted to seriously to analyze “market power” when it comes yielding admitted students, this would involve looking at what applicants they are admitting, and then who else is actually operating in those markets, and how that goes.
Unfortunately, since these markets are not neatly divided up, but instead overlap, this becomes a problem of enormous complexity to sort out, and in some sense it isn’t even clear what you might be trying to determine with colleges that don’t have that much market overlap.
Speaking of which, Parchment has its head to head revealed preference page, and it will report percentages with error bars. But when it doesn’t have enough data, it indicates that with grey numbers as opposed to red and green.
I just checked, and for Penn and WashU they have it at 50-50 exactly, but they are are grey. Not enough data.
And I think that is about right. Realistically, there isn’t going to be enough market overlap between Penn and WashU to make for a serious relative to market power analysis. Of course I know in certain circles, it sounds like everyone applies to all the US News T25 or whatever, but out in the real world, that’s very rare. Most college bound kids are not applying to any of those, but even among those who do, they are not typically applying to all of them, and then the ones they choose tend to cluster in certain ways.
By the way, even if we could meaningfully determine the relative market power of two of these institutions in a market with sufficient overlap, I’d still resist calling that a measure of which is “better”. I can think of plenty examples of markets in which I shop where a certain brand or whatever obviously has more market power, but I don’t actually think they are better, or at least not better for me.
The basic problem here is this sort of market structure is sometimes known as a differentiated product market. Not every producer offers the exact same thing, the only difference being price. Each is offering its own complicated bundle of stuff. And so even if, say, 75% in some definable market end up choosing A and 25% B, that doesn’t mean the 25% who chose B are somehow missing something the 75% who chose A figured out. It just means that for them, while they were willing to consider both A and B, in the end they ended up preferring the mix offered to them by B.
This is all very sketchy still, but at least it helps define some of the basic issues here. The bottom line is any market analysis would be enormously complex, and not really provide many satisfying “A is better than B” answers anyway. Which is fine, it just means college bound kids need to figure out for themselves what they really want in a college.