Are more expensive colleges better? 
Working at a community college, I’d have to say “not necessarily.” They could be, and sometimes they are, but it depends on how they use that money. That’s why this piece -- about a study of liberal arts colleges showing little relation between cost and value -- didn’t especially surprise me.
In the community college sector, we focus intently on teaching the first two years of the undergraduate curriculum, along with some pre-undergraduate (“developmental”) material. We also do a fair amount of non-credit workforce development and personal enrichment instruction. But we don’t do junior and senior level courses, graduate education, high-profile sports, or cutting-edge scientific research outside of the scholarship of teaching and learning.
Community colleges tend to spend the least of any sector, and to charge even less than that. (Public subsidies make up the difference.) That means there isn’t much to spend on non-essentials. Budgets tend to be modest, and focused pretty clearly on instruction. Even student services tend to be focused on helping students succeed academically, such as tutoring or providing accessibility technology. We don’t have a climbing wall, let alone a football team. (Though to be fair, that may be a Northeastern thing; I’ve heard of community colleges in other states with football teams.)
Colleges that do those other things are playing a different game, in some ways. In that sense, direct comparisons can be difficult.
Does having a football team help first-year students learn?
Directly, no. But indirectly, it’s possible: if a successful football team leads to alumni giving, and the alumni giving becomes far more than is spent on football, then it’s possible that the payoff from alumni giving will have salutary effects on students in the first year, whether through scholarships, general operating support, or various gifts for various programs. If the football program is high-profile enough -- I’m thinking here of the University of Michigan -- it can draw strong students who want the football Saturday experience; their presence enriches the experience of other students who could care less about football.
And that’s where I see the more expensive schools playing a different game. Community colleges (and most tuition-driven colleges) have to focus pretty intently on the core function. Grants are helpful in developing experiments and taking the longer view, but even there, the experiments and view in question are pretty close to the core function. For example, would shortening a developmental sequence improve student completion rates?
But the higher-cost places are doing what pool players call bank shots. Instead of focusing more resources on the core function, many of them make a choice to pour their greater money into ancillary functions, in hope of harvesting even greater incidental payoffs over time. Those payoffs could come from technology transfer, or alumni giving, or political favor, or nearly anything else. If we have the best rowing team, the the alums of our rowing team will give more! If we become a national power in basketball, then we’ll attract the upper-middle-class kids who love sports!
Bank shots are great when they work. But they don’t always work, and even they do, the payoff is often delayed. I endured the godawful Rutgers football teams of the 90’s when I was in grad school there, and it was hard to watch all that money be spent on a series of terrible teams while graduate students lived three to an apartment in New Brunswick. I can safely say that the money the typical community college spends on a tutoring center does far more for first-year student learning than the money that Rutgers spent trying to pretend it was Ann Arbor.
The paper elicited plenty of critiques in the comments on IHE, including some pretty good ones. Yes, it was based on self-reporting, which is notoriously sketchy. Yes, different colleges categorize spending differently. But I’m thinking that if you go cross-sectoral -- which, to be fair, the original paper didn’t -- you’d find that some of the gap comes from having different goals. If your goal is to help the student right in front of you right now, you’ll get a much better bang for your buck at many community colleges than you would at some much more expensive places. The more expensive places have something else in mind.