Alexander believes that the Government and Reserve Bank are likely to impose additional measures to cool the runaway housing market in the coming year.
The forecaster predicted any new rules would likely be focused on investors buying existing properties.
Reserve Bank governor Adrian Orr and Finance Minister Grant Robertson are reviewing the potential introduction of debt to income ratios as house prices soar.
There is mounting speculation about interest-only lending limits. Robertson has asked the RBNZ to consider whether curbs would lower risks in the NZ financial system.
Alexander said new restrictions are likely to mark a "structural downward shift coming in the average pace of house price growth in New Zealand over the next 5-30 years".
"My expectation is that having risen on average 6.8% per annum since 1992, the average pace of house price inflation will now slow down toward 5%," he said. "We are unlikely to fall to that pace this year, but over 2022-2023 such a slowing is possible assisted by slowly rising house supply."
It comes after the Government instructed the Reserve Bank to consider house price inflation as it sets monetary policy.
The new RBNZ remit could prompt the central bank to lift existing LVR restrictions, Alexander added.
It does increase the chances, quite strongly, that the 40% minimum deposit for investors buying a house with debt will be taken to 50% before the end of this year. Sixty per cent cannot be ruled out but it is unlikely."