From the abstract

A longstanding economic question is the appropriate level of protection for intellectual property. The Internet has drastically lowered the cost of copying information goods and provides a natural crucible to assess the implications of reduced protection. We consider the specific case of file sharing and its effect on the legal sales of music. A dataset containing 0.01% of the world's downloads is matched to U.S. sales data for a large number of albums. ... Downloads have an effect on sales which is statistically indistinguishable from zero, despite rather precise estimates. Moreover, these estimates are of moderate economic significance and are inconsistent with claims that file sharing is the primary reason for the recent decline in music sales.

The key to their analysis is the use of instrumental variables such as network congestion, song length, and such things as school holidays that should drive downloads but change album sales only indirectly through the effect on downloads. This enables them to separate the impact of downloads from variables that might changes both downloads and album sales.

Also of interest is the issue of album popularity. Downloads have little effect on less popular albums - but a positive effect (one extra sale per 150 downloads) on more popular albums. So apparently if you have something good to sell, giving away free samples isn't a bad idea.