The number of people out of work is expected to have dipped slightly in the September quarter, partly because of the Rugby World Cup.
Statistics New Zealand's Household Labour Force Survey out on Thursday is picked to show unemployment in the September quarter nudged down by 0.1% from the previous quarter to 6.4%.
Deutsche Bank's chief economist Darren Gibbs says there are signs of a small improvement in employment.
He says demand for workers has risen across the board, with a more significant pickup in the construction sector and a rise in temporary employment in the services sector relating to the Rugby World Cup.
Meanwhile, the Labour Cost Index out on Tuesday is expected to show a 0.5% rise in wages for the September quarter, taking the annual rate to a 2% increase.
Mr Gibbs says unemployment is still relatively high and so it is likely there will only be a very gradual pickup in wage growth.
He says strong growth in wages would be detrimental to getting people back into work at this stage.