I have to say that I have been quite skeptical of the anticipated impacts of movie production on tourist arrivals. Like the Tourism New Zealand site, most of what has been written seems to be based on anecdote, and seasoned with a generous dose of excessive optimism. For example, this report from NZIER shows some evidence of a rise in tourist arrivals following the release of The Hobbit, although the analysis is fairly weak and it doesn't demonstrate causality.
I just read a paper (ungated version here) that has been sitting in my 'to-be-read' pile since 2012, by Heather Mitchell and Mark Fergusson Stewart (both from RMIT). In the paper, they look at time series data on tourist arrivals in New Zealand around the time of the release of the Lord of the Rings films, as well as in Australia around the time of the release of the Mad Max films and the Crocodile Dundee films. For good measure, they look at data on employment in hotels and restaurants in Kazakhstan around the time of the release of Borat.
Focusing on the New Zealand-specific results, they find no significant impact of the first Lord of the Rings film on tourist arrivals, but significant impacts following the release of the second and third films. Specifically, after the third film they find that monthly tourist arrivals were six percent higher. However, this was offset by a decrease in the upward trend in tourist arrivals. This slower trend increase was enough to offset the short-term boost in tourist arrivals in less than two years.
In the epidemiology literature (specifically the literature on mortality) there is a term called 'harvesting', which refers to events that are brought forward in time by the effect of exposure to some stimulus. For instance, a spell of extremely hot weather might temporarily increase mortality, but much of that mortality would be among the frail, who are at high risk of death already. Short-term mortality may be higher as a result, but overall mortality might barely change.
I suspect that we probably observe a harvesting effect on tourist arrivals. Potential tourists who have an interest in New Zealand might be induced to come to New Zealand earlier than they otherwise might have as a result of the Lord of the Rings or The Hobbit. That would lead to a short term increase in tourist arrivals, but since those tourists won't visit in the future, the longer-term effect might be close to zero.
Unsurprisingly, the NZIER report doesn't even mention the possibility of harvesting. I'm not convinced that the Mitchell and Stewart paper does the best job of evaluating this either, since they look at only a relatively short time series after the release of the films - it would be interesting to know whether the decrease in trend arrivals growth is persistent, or whether it eventually tapers out and there is a return to the long-run trend growth. Perhaps there's an opportunity here for an honours project - the required data are easily obtainable from Statistics New Zealand.
The question of whether there is sustained growth in tourist arrivals is important. It is often trumpeted as a reason to subsidise movie production (in addition to direct job creation in movie production and related industries). However, if there is only a short-term tourism impact and the long-term tourism impact is negligible, then that changes the cost-benefit evaluation of movie subsidies. Although that assumes that the government even carefully considered the costs and benefits of the deal they did with Warner Bros, and other movie subsidies they provide.