Economists expect to see evidence that unemployment has fallen further when fresh data is released on Wednesday.
ANZ senior economist Philip Borkin said he was expecting to see a slight drop in unemployment from 4.9 per cent in the first quarter to 4.8 per cent in the second.
"We think the numbers are going to look good," he said. "The labour demand is certainly strong and firms are telling us right now that there biggest problem right now is finding skilled staff."
But despite touching an eight and a half year low, expectations are not high that labour demand will push wages higher.
Wage inflation, and inflation more broadly, had been "missing in action" in this economic cycle, Borkin said.
He was hopeful that pressure from the stronger labour figures would start to have an effect.
"I think we are at the cusp of seeing it lift off low levels," he said.
But there were big structural forces, like technological change, which were pushing against the positive cyclical story and meant job security is not what it was, he said.
"Which means peoples ability to push for wages increases is not what it was."
ASB economist Kim Mundy is also picking the jobless rate will have dipped to 4.8 per cent on the back of a solid 0.7 per cent lift in employment (quarter on quarter). "We also expect the labour force participation rate to hit a new record high of 70.7 per cent as net migration continues to run at elevated levels," she said.
"However, with strong growth in the supply of workers, wage pressures have so far been lagging behind an otherwise robust labour market. We expect this to have continued in Q2 and for the Labour Cost Index and Quarterly Employment Survey (QES) to show subdued wage growth over the quarter."
However, she also noted that expect wage pressures should pick up "as the robust growth outlook continues to boost the labour market."
Westpac economists are picking the unemployment rate to stay steady at 4.9 per cent but also see labour force particpiation hitting a record high of 70.7 per cent.
On wages "things are still looking pretty muted," sais Westpac senior economist Satish Ranchhod. "There are some sectors, like construction, where growing
demand has given wages a bit of a lift over the past year.
But even with the economy now into its seventh year of continued expansion, we're yet to see a broad-based lift in wage growth."
Westpac was expecting to see the June quarter Labour Cost Index to show that base wage rates rose by only 1.6 per cent over the past year. The broader QES measure of average hourly earnings is expected to have risen by only 1.3 per cent in the year
Ranchhood notes that on top of the firming in economic conditions more generally, the overall level of wage inflation in the economy will receive a sizeable boost in August as a result of the recent equal pay settlement for caregivers in the health
This historic agreement will boost the wages of around 55,000 workers by a sizeable amount.