Princeton undergrad, Eric Boorstin, solves the does-filesharing-affect-music-sales research question:

In this paper I examine the effect of Internet access on compact disc sales. I combine U.S. census data on population characteristics with Nielson SoundScan data on CD sales for 99 metropolitan areas in the years 1998, 2000, and 2001. Controlling for year, income, and the fixed effects within each area, I estimate the relationship between Internet access and CD sales for four age groups. Overall, Internet access has a positive and statistically significant effect on CD sales. For children aged 5 to 14, Internet access has a negative but statistically insignificant effect on CD sales. For youths aged 15 to 24, Internet access has a negative and statistically significant effect on CD sales. And for the adult groups aged 25 to 44 and aged 45 and older, Internet access has a significant positive effect. My findings suggest that file sharing is not the cause of the recent decline in record sales, and that file sharing decreases the record purchases of younger people while increasing the purchases of older people.

See also Edward Felten's Grand Unified Theory of Filesharing. (Both links via Boing Boing.)

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