The most recent review on this that I know of is File-Sharing and Copyright, a 2009 paper (pdf). The results are unclear:
Because the theoretical results are inconclusive, the effect of file
sharing on industry profitability is largely an empirical question. We
summarize the findings of some of the major studies in table 5. As the
list shows, the results are decidedly mixed. There are two studies
that document a positive effect of file-sharing on sales: Andersen and
Franz (2008) for a representative sample of Canadian consumers and,
more narrowly, Gopal et al. (2006) for the effect of sampling on CD
sales.17 The majority of studies finds that file sharing reduces
sales, with estimated displacement rates ranging 3.5% for movies (Rob
and Waldfogel, 2007) to rates as high as 30% for music (Zentner,
2006).18 A typical estimate is a displacement rate of about 20%. One
implication of these results is that developments other than file
sharing must have had a profound impact on sales. For music, the
popularity of new types of (internet-based) entertainment and the end
of the transition from LPs to CDs are leading explanations for the
overall decline in sales (Hong, 2004; Oberholzer-Gee and Strumpf,
2007). While many studies find some displacement, an important group
of papers reports that file-sharing does not hurt sales at all
(Tanaka, 2004; Bhattacharjee et al., 2007; Oberholzer-Gee and Strumpf,
2007; Smith and Telang, 2008). And even among the studies that show
some displacement, there tend to be important subsamples that were not
affected. For example, Rob and Waldfogel (2006) find an average
displacement effect of 20% but report that file sharing had no impact
on hit albums.
It also notes that many of the studies rely on questionable methodology. For instance, many rely on self-reporting (quite unreliable when surveying illegal activity), or use internet penetration as a proxy for piracy. It's worth noting that in the studies where researchers have actually collected data on file-sharing networks and measured file-sharing activity, the results have been "no effect":
We emphasize these issues because the results in table 5 seem to
suggest that measurement choices have a systematic impact on results.
While the majority of papers reports some sales displacement, the four
studies using actual measures of file sharing (Tanaka, 2004;
Bhattacharjee et al., 2007; Oberholzer-Gee and Strumpf, 2007; Smith
and Telang, 2008) find that file sharing is unrelated to changes in
sales.
For some fields, there may be complement effects. For instance, for music performers, a possible loss of sales may be offset by increased concert attendance:
As Table 6 shows, concerts and merchandising have become an important
source of income for major artists (Connolly and Krueger, 2006).
Concerts and new recordings are complements. A recording becomes more
enjoyable if one can reminisce about the time at the concert, and
knowing the songs in advance might make the concert more enjoyable. In
the presence of complementary goods, file sharing will have two
opposing effects (for a formal model, see Mortimer and Sorenson,
2005). As the effective price of music falls close to zero, a larger
number of consumers will be familiar with an album, driving up the
demand for concerts. At the same time, artists have weaker incentives
to tour because concerts are a less effective way to increase revenues
from a new recording if a large fraction of the audience shares files.
Which of these effects is more important? Figure 6 shows that concert
prices rose much more quickly than the CPI, and the difference appears
to have widened since the advent of file sharing (Krueger, 2005). More
detailed evidence on the link between file sharing and concerts comes
from Mortimer and Sorenson (2005). Studying 2,135 artists over a
ten-year period, they also conclude that the demand for concerts
increased due to file sharing. One way to see this is to ask how many
CDs an artist needs to sell to produce $20 of concert revenue. This
number fell from 8.47 in the pre-Napster era to 6.36 in the 1999 to
2002 period. Not surprisingly, artists responded to these incentives
by touring more frequently. Overall, the shift in relative prices and
activities led to a sharp increase in income for the typical artist
included in the authors’ dataset.
This tidbit from the paper might also be of interest, though it does not answer the question directly:
Overall production figures for the creative industries appear to be
consistent with this view that file sharing has not discouraged
artists and publishers. While album sales have generally fallen since
2000, the number of albums being created has exploded. In 2000, 35,516
albums were released. Seven years later, 79,695 albums (including
25,159 digital albums) were published (Nielsen SoundScan, 2008). Even
if file sharing were the reason that sales have fallen, the new
technology does not appear to have exacted a toll on the quantity of
music produced.25 Obviously, it would be nice to adjust output for
differences in quality, but we are not aware of any research that has
tackled this question.
Similar trends can be seen in other creative industries. For example,
the worldwide number of feature films produced each year has increased
from 3,807 in 2003 to 4,989 in 2007 (Screen Digest, 2004 and 2008).
Countries where film piracy is rampant have typically increased
production. This is true in South Korea (80 to 124), India (877 to
1164), and China (140 to 402). During this period, U.S. feature film
production has increased from 459 feature films in 2003 to 590 in 2007
(MPAA, 2007).
