The minutes acknowledged that May's move upward was unexpected after April's pause, but said that inflation remains the primary concern.
"Members noted that the forecasts presented at the meeting were predicated on a technical assumption for the path of the cash rate that involved one further increase," the minutes read.
"Members also agreed that further increases in interest rates may still be required, but that this would depend on how the economy and inflation evolve."
RBA could push to 4.35%: NAB
NAB economists pencilled in one more rate rise in July, taking it to 4.10%, however said if inflation shows little sign of tempering, the RBA could go one more.
“At least one additional rate rise is likely to be necessary to limit the risk this timeline slips any further," said Alan Oster, NAB's chief economist.
“We wouldn’t rule out the prospect of an additional rise to 4.35% if the data stays stronger for longer.”
The next quarterly inflation data is due to be released after the RBA's July monetary policy meeting, however the monthly indicator for May will be released in late June.
One more hike in August: ANZ
ANZ economists anticipate one more hike but that it wouldn't happen until August.
"The minutes of the RBA Board's May meeting strike us in tone as on the hawkish side," said Adam Boyton, ANZ head of Australian economics.
That would bring the terminal rate to 4.10%, and by August some important economic data would have had time to digest: one release on GDP, one inflation print, one wages growth data set, and multiple labour force releases.
"The arguments in favour of an increase in interest rates were inflation staying above the top of the target band until mid-2025, the 'persistence in services price inflation in many other countries'," Mr Boyton said.
CBA sticking solid with forecasts
CBA economists have maintained that they expect 50 basis points of cuts in the final three months of 2023, bringing the cash rate down to 3.35%.
It also anticipates a further 75 basis points' worth of cuts in 2024, taking it to 2.60%, which they call a neutral rate - one that favours neither economic growth nor contraction.
"Markets have struggled more recently with interpreting the RBA’s communication. The decision to raise the cash rate in May was not anticipated by financial markets or the majority of the forecasting community," said Gareth Aird, CBA head of Australian economics.
"For context, money markets had priced a negligible 12% chance of a 25 basis point rate increase in May. The ‘surprise’ decision to increase the cash rate has left many market participants unsure of the Board’s next policy move."
Too much flip flopping of forecasts: AMP
AMP chief economist Dr Shane Oliver has consistently maintained that there'll be no more rate rises, but that he could have gotten that view wrong.
Speaking to the Savings Tip Jar podcast, he said that AMP wasn't in the game of constantly changing forecasts.
"I don't think much has happened economically [to warrant changing forecasts]," Dr Oliver said.
"The RBA is obviously concerned that inflation is still too high even though it's starting to fall. And they're also concerned that there are signs out there that the property market is turning up again, starting in Sydney, but it's spread to other cities as well.
"If that continues, then obviously it reverses the negative wealth effect from falling property prices. It makes the Reserve Bank's job harder.
"I do worry that the RBA is not paying enough attention to the lagged impact of past rate hikes, which are going to lead to a sharp slowing in growth this year, which runs the risk of a harder landing and higher unemployment."
Productivity, wages growth in-focus
While the RBA forecasts a peak in wages growth of 4% later this year, it also anticipates slowing economic growth.
Minutes highlighted that labour productivity had been weak over the past few years.
"Various factors might explain the weak productivity outcomes, including COVID-19-related disruptions and strong growth in employment in government-funded services, where achieving productivity increases is often difficult," minutes read.
Mr Aird said that this is a growing area of concern for the RBA.
"The first-quarter GDP figures, which print the day after the June Board meeting, will be particularly important for assessing the changes in both unit labour costs and measured productivity," he said.
NAB economist Tapas Strickland said Wednesday's wage growth data could have influence on the RBA's meeting in June.
"An earlier hike in June cannot be ruled out if the first-quarter wage price index were to print above the RBA’s expectations of around 0.9% quarter-on-quarter - NAB has also pencilled in 0.9%," Mr Strickland said.