Tyler Cowen points to a paper by Harvard economics professor Michael Kremer that makes the following argument:
"Most countries prohibit the export of certain antiquities. This practice often leads to illegal excavation and looting for the black market, which damages the items and destroys important aspects of the archaeological record. We argue that long-term leases of antiquities would raise revenue for the country of origin while preserving its long-term ownership rights. By putting the object into the hands of the highest value consumer in each period, allowing leases would generate incentives for protection of objects."
Tyler thinks it's worth a shot, but doesn't think it would make much of a difference:
"Collectors, being irrational creatures and 'completists,' wish to own rather than lease, even if the lease extends past their expected lifetimes. Museum donors wish to fund museum acquisitions more than museum borrowings. Similarly, it is much easier for a non-profit to raise money for buying a building than leasing one long-term. So the demand for leased antiquities won't be all that huge."