This is the same problem that has plagued the gigantic performing arts centers that many cities erected in the late 20th century. Unable to draw large crowds with the classical music and dance programs they were meant to showcase, many have booked touring Broadway shows, comedians, ice shows, and circuses to generate revenue. Could that devolution happen to second-tier museums that have overexpanded?

Absolutely not, directors respond. They believe that their new buildings will improve their ability to show great art. Shapiro says the High's three-year partnership with the Louvre was stimulated by the expansion. David Gordon, Bowman's successor in Milwaukee, says the new wing put the city on the art-world map and enabled him to lure a top chief curator, Joseph Ketner, to MAM's staff. Museums in Seattle, Dallas, and elsewhere have landed billions of dollars' worth of art from private collectors that never would have been given to their older, smaller selves. Denver claims its Hamilton wing was a magnet for all three: loans, collections, and a hotshot contemporary curator, Christoph Heinrich, from the Hamburger Kunsthalle, in Germany.

That's the official line anyway. But nonart activities are already increasing, especially space rentals for weddings, bar mitzvahs, and corporate parties that add to earned income—as well as risk. Milwaukee is still living down the 2006 "Martinifest" incident, when drunken partygoers at a private event were caught climbing on sculptures, vomiting, and passing out in the Calatrava wing.

It will be years before it's clear which institutions overreached and which didn't. Sooner or later, though, all museums will have to contend with underlying trends. For the past few decades, NEA research shows, attendance has been rising a bit, but that's largely because the overall population is growing. Interest in art is fairly stable. Confronted with this picture, the museum world offers a ready answer: Its investments are about the long term. With a sense of optimism as lavish as their financial gifts, the current generation of donors has decided to take a chance and build for the future—even if it means taking a leap of faith now.

“If You Build It, Will They Come?” was originally published in the July 2007 issue of Art & Auction magazine.