Sharply lower crude oil prices are expected to translate into a decline in the consumers price index (CPI) for the June quarter.
Market expectations are for 0.5 per cent fall in the CPI over the quarter, which would make for a 1.5 per cent gain over the June year.
ASB said a quarterly outcome in line with its expectations of a 0.4 per cent decline would make it the lowest quarterly outcome in close to five years.
The Reserve Bank has forecast a 0.7 per cent quarterly fall, and a 1.3 per cent annual gain.
Whichever way it goes, Stats NZ's CPI release, due out on Thursday, is likely to show an annual outcome well short of the 2 per cent mid-point of the Reserve Bank's 1 to 3 per cent target range.
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ASB expects annual inflation to dip toward zero in early 2021 before gradually pushing higher.
"We do not expect 2 per cent annual CPI inflation anytime soon," the bank said in a commentary.
Low inflation means that monetary policy settings will likely remain highly expansionary for a long time, economists said.
"Sharply lower fuel prices will weigh on Q2 consumer prices and we will be looking for signs of moderating core and non-tradable CPI inflation," the bank said.
"Risks are broadly balanced, but we admit a greater degree of uncertainty than usual around our CPI pick and would not rule out a weaker set of inflation numbers emerging.
"Policymakers in NZ and abroad have pulled out all of the stops and will maintain highly stimulatory settings until they are confident economic activity and inflation has turned the corner."
ASB expects the Reserve Bank's OCR to not move above 0.25 per cent - where it stands at the moment - until 2024.
Kiwibank chief economist Jared Kerr said this week's data will reflect an extraordinary period for the economy.
"Large parts of our economy have been hit by the lockdown and there has been some significant discounting coming out of the lockdown," Kerr said.
"The good news is that that we have seen quite a lift in spending so the pain that we are feeling is not as bad as we had feared," he said.
Even so, persistently low inflation out-turns will take the economy close to deflation, which central banks want to avoid at all costs.
"We have been hurt by the lockdown and we are going through what will probably be the biggest recession that we have seen for 100 years. It's going to cause damage," says Kerr.
He said deflation was a risk on the horizon.
To that end, economists expect the Reserve Bank to pull out all stops to prevent a deflationary spiral.
Many expect the Reserve Bank to ramp up its bond-buying activities when it releases its monetary policy statement on August 12.
Kerr expects the Reserve Bank to extend the programme from May next year out to 2022 and to lift the size of the programme to $100 billion from $60b.
BNZ economist Doug Steel said unlike previous CPI releases, the market's focus is very much on growth rather than inflation.
"This particular quarter is going to be heavily weighed down by fuel prices due to the massive fall in international crude prices over the period," Steel said.
"But the broader aspect is that we have seen a massive opening up of spare capacity in the economy - unemployment - that is weighing on the outlook for prices," he said.
Given the risk of deflation and the likelihood of a deep recession, Kiwibank's Kerr expects the Reserve Bank to "keep its foot on the gas".