Publishers of computer software and music claimed losses of over $17.6 billion to piracy in 2002. Theoretically, however, piracy may raise legitimate demand through positive demand-side externalities, sampling, and sharing. Accordingly, the actual impact of piracy on the legitimate demand is an empirical issue. Addressing this issue in the context of recorded music, we develop and test hypotheses from theoretical models of piracy on international data for music CDs over the period 1994-98. Empirically, we find that the demand for music CDs decreased with piracy, suggesting that "theft" outweighed the "positive" effects of piracy. However, the impact of piracy on CD sales was considerably less than estimated by industry. We estimated that, in 1998, actual losses amounted to about 6.6% of sales, or 42% of industry estimates. But, we found evidence that publishers would have raised prices in the absence of piracy, suggesting that the actual revenue loss would have been higher.