This question is addressed in (Gilbin 2013). At p. 41, she specifically mentions the claim in this question:
The New Zealand Federation Against Copyright Theft (NZFACT) claimed that the number of major US films shared by New Zealand users each month effectively halved when the law came into operation, before increasing slightly and then plateauing.
Gilbin says that "the underlying studies and methodologies on which these claims are based are not publicly available".
Gilbin also talks about "[a] much more transparent study was conducted by researchers at Waikato University". "The study suggested that P2P traffic and the number of users engaged in P2P file sharing decreased by at least half after the law came into force." (Citing Alcock and Nelson 2012)
Gilbin adds though:
However, as discussed in more detail below, it [Alcock 2012] also found a massive increase in the amount of HTTPS traffic. HTTPS if a form of encryption which prevents traffic from being easily analyzed. The researchers theorized that this increase was caused by a shift towards non-P2P sources of infringement, which fell outside the scheme.
There is no public data supporting the claim that internet piracy has halved. The group claiming the halving of internet privacy has not released their studies. Another group that witnessed a drop in P2P traffic also noticed an increase in HTTPS traffic, and could not rule out a shifting of piracy behaviours.
Alcock, S. and Nelson, R., Measuring the Impact of the Copyright Amendment Act on New Zealand Residential DSL Users, WAND NETWORK RESEARCH GROUP (2012)
Giblin, Rebecca, Evaluating Graduated Response (September 6, 2013). Available at SSRN: http://ssrn.com/abstract=2322516