ASB is forecasting three rises to the official cash rate (OCR) this year, saying it's time for rates to start moving.
It comes as unemployment, forecast to drop from 4.7 percent to 4.4 percent, fell to 4 percent in the June 2021 quarter.
The OCR has remained on the emergency setting of 0.25 percent since March 2020, when the Reserve Bank made a 75 basis-point cut.
ASB chief economist Nick Tuffley said the bank had originally forecast the cash rate to reach 1 percent by February.
Following Wednesday's unemployment rate announcement, which shows the labour market is tightening up "even quicker than expected", he anticipates the Reserve Bank will increase the OCR "relatively swiftly".
The bank is forecasting three cash rate rises this year, each by 25 basis points - the first this month.
"We now expect the OCR will increase by 25 basis points in each of August, October and November, reaching its pre-COVID rate of 1 percent by the end of this year," Tuffley said in ASB's labour market statement.
Wage growth has picked up more than expected, he said. Future wage pressure is expected to be stronger than anticipated, feeding through to higher costs for businesses - higher inflation.
Although a cash rate increase could be delayed by a community outbreak of COVID-19, unless there were a prolonged lockdown, the Reserve Bank is unlikely to hold off.
Unemployment data and price inflation data show inflation pressures have returned more rapidly than expected.
The Reserve Bank aims to achieve price stability, keeping inflation between 1 and 3 percent, and maximum sustainable employment.
Latest figures show inflation reached 3.3 percent in the June quarter, and it's expected to peak around 4 percent later this year before dropping back to 2.5 percent, Tuffley said.
And June unemployment figures show the labour market is close to running out of people.
"It's time for rates to start moving back to something more 'normal'... higher than where we are now," Tuffley said.
Upon releasing Kiwibank's 'First view' unemployment report on Wednesday, Kiwibank chief economist Jarrod Kerr people should strap themselves in for four rate hikes in "reasonably quick succession".
"I think we'll see a cash rate of 1.5 percent by the end of next year," Kerr said.
He expects all lending rates - and savings rates - to continue to rise.
"Fixed mortgage rates with a 2 in front of it will go and we'll see mortgage rates getting closer to 4 percent into next year."
The Reserve Bank will make an OCR announcement at its scheduled Monetary Policy Statement on August 18.