If you read all the things pundits and researchers write about cities these days, you’d be pretty confused: Cities are either growing or shrinking. People either want to live in them or they don’t. Businesses are either gravitating to them or moving away. Maybe young people like cities now, but they won’t like them when they have kids. Or maybe middle-aged people don’t like cities yet, but will later on.

Now into the mix comes Yonah Freemark, a Ph.D. student in urban planning at the Massachusetts Institute of Technology, who makes a provocative argument: Central cities are losing population relative to their suburbs, and close-in neighborhoods are losing population relative to newer neighborhoods.

It’s a little jarring to see a guy with such a distinctly pro-urban orientation sound so much like Joel Kotkin, an unabashed proponent of sprawl. But in the process of laying out his argument, Freemark shows that the situation is a little more complicated than the typical pundit would admit. His basic point is that urban neighborhoods that were already developed in 1960 generally have fewer residents now than they had back then, especially in younger Sun Belt cities.

At first glance, this might seem counterintuitive, given all the publicity in the media -- including this column -- about how millennials like urban living and therefore downtown populations are growing. But if you dig a little deeper, Freemark’s research shows two other important trends.

First, the urban revitalization patterns of the last decade aren’t really about the number of people but about changing demographics and the changing distribution of wealth. Yes, fewer people live in neighborhoods close to downtown, but more people live in downtowns. That’s because household sizes are smaller -- there are more one- and two-person households now -- and few people actually lived downtown 50 years ago. And even though fewer people live close in today, the people that do have more money.

Second, although this trend is true in some parts of the Sun Belt, it’s not true in others. In particular, it’s not true in Southwestern and Western cities. Sure, Houston has a large stock of vacant land in older neighborhoods near downtown. But, as Freemark notes, the list of six cities with the highest population increase in close-in neighborhoods includes Las Vegas, Los Angeles, Miami and San Jose, Calif. What all these cities have in common -- and this is in contrast to Houston -- has nothing to do with downtown or close-in neighborhoods. All five are land-constrained on the periphery and therefore growth has nowhere else to go.

It’s tempting to make the debate about urban revitalization a one-size-fits-all argument. But as Freemark’s numbers show, it’s not. Even where the population has gone down, economic activity has gone up. And there is a relationship between what goes on at the center and what happens on the fringe.