The fortunes of downtown areas in the US have diverged since the onset of the coronavirus pandemic, new research shows, with one class of cities largely restored to vibrancy and another emptier and more forlorn.

The differences are tied to a city’s size, according to a paper by economists at Georgetown University and the University of Chicago. Using mobility data from smartphones, housing prices and other factors from 274 US cities, they found that central business districts in smaller cities were more likely than larger ones to have returned to pre-pandemic activity.

The implications — for commercial real estate values, local tax receipts and street life, among others — are serious. Larger cities’ business districts seem “stuck” in this new world, said Ferdinando Monte, an economist at Georgetown and co-author of the study.