Slate columnist Tim Harford writes an article on the issue of the illicit antiquities trade, and a possible solution to eliminating the market.  

 As the article mentions, the black market in antiquities is created when countries place a ban on the trading of national antiquities. However, these policies unfortunately create the side effect of pushing the activities underground

They replace the logic of the market with the logic of the black market, which means that smugglers would try to conceal the locations of new archaeological sites, to erase or forge the historical record surrounding objects, and to excavate and ship objects without the care that could be lavished on an operation that was legal. Beyond these purely archaeological considerations, illegal objects are less likely to end up in the top museums and may be relegated to purely private collections, which is in itself a shame.

Havocscope is currently listing the market value for Art and Antique Smuggling to be worth $10 billion.  

Be sure to also read Slate’s Tomb Raider 101 for information on the trade.