A new report from public policy think tank, the New Zealand Initiative, suggests it is New Zealanders - not foreigners - who are pushing up house prices in Auckland and other fast-growing areas.

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The New New Zealanders report said high levels of migration and high house prices occurred when the economy was doing well - but one did not necessarily cause the other.

People on temporary visas, like students, opted to rent rather than buy, it said. While that meant they were competing with those who are New Zealand born, the rental market wasn't showing the same signs of stress as the house buying market.

Economists said New Zealanders who were feeling confident about their economic prospects were choosing to stay in the country and invest in housing, which was pushing up prices.

The report warned that changing immigration policy to influence house prices may not have the desired effect.

But a growing population, whether through natural increases or migration, increased demand for infrastructure, such as roads, footpaths, water pipes, libraries, highways and public transport.

The cost of infrastructure falls on local ratepayers and taxpayers, and the report suggested this could be an area where the government could recover costs from migrants - potentially through an upfront levy.

But the New Zealand Initiative said while there was "undoubtedly" a cost to high levels of migration, it was outweighed by the benefits that foreigners bring to the country.

It said current policy settings were "broadly fit for purpose", but policymakers needed to be vigilant to ensure that remained the case.

It also said the government should consider reducing some of the red tape in the immigration system.

"Measures such as letting high salaries count towards a migrant's point tally and letting private businesses sponsor migrants could ease some of the red tape that keeps high quality migrants from moving here."

About 125,000 people moved to New Zealand on a permanent and long-term basis in the June 2016 year.