But critics of the practice also question whether museums curry favor with possible donors by accepting loans, and they complain that works are sometimes exhibited without the context or curatorial judgment that museums traditionally provide. A recent visit to the Portland museum found some lent works exhibited haphazardly: a Cubist work from the 1950s, for example, placed amid American art from the 1980s.

“It is an amazing opportunity for these smaller cities to show these works,” said Mack McFarland, a curator at the Pacific Northwest College of Art, in Portland. “But one does have to wonder, doing a cost-benefit analysis on a more global scale, whether or not the tax break for these wealthy collectors is worth it.”

States employ use taxes to compensate for residents who avoid sales taxes by shopping in another state. The tax rate is generally the same as the sales tax, and people are supposed to calculate what they owe on items bought out of state, then pay that amount as part of their tax filings.

Art collectors who seek to avoid the tax typically offer a recently purchased work to a museum in one of five states — New Hampshire, Oregon, Alaska, Montana and Delaware — that do not have a use tax so that the loan does not incur a tax.

As long as the painting stays at the museum for an extended period, typically more than three months, before being shipped home, the practice in several states where collectors live, like California, is to regard the exhibition as a first “use” of the item and waive any tax. The result is a tax-free transaction.

The Hallie Ford Museum of Art at Willamette University in Salem, Ore.; the Delaware Art Museum in Wilmington; and the Hood Museum of Art at Dartmouth College in Hanover, N.H., are among other institutions where collectors have lent art because of tax considerations.