http://fivethirtyeight.com/features/maybe-spotify-isnt-killing-the-music-industry-after-all/

For their analysis, Waldfogel and Aguiar took Spotify at its word, and used the median per-stream point ($0.007) to estimate any new revenue generated through streaming. They found that revenue roughly offsets the revenue lost from any drop in sales. In other words, they think Spotify has had a revenue-neutral impact on the music industry, though whether Spotify has cut into artists’ earnings is a different question not directly addressed in this paper.

There is one thing Page and Waldfogel do agree about: legal streaming’s effect on piracy. In the working paper, the economists compared the growth of Spotify streaming to the weekly volumes of torrents for 8,000 top artists, using data from Musicmetric, a music analytics company. Every additional 47 streams displaced one pirated download, they concluded. The economists even cited Page’s own work showing Spotify lowered unpaid downloads. But as Waldfogel said, “reducing piracy is not the same as increasing revenue.”